Development of an orthotropic hole element

NASA Technical Reports Server (NTRS)

Smith, C. V.; Markham, J. W.; Kelley, J. W.; Kathiresan, K.

1981-01-01

A finite element was developed which adequately represents the state of stress in the region around a circular hole in orthotropic material experiencing reasonably general loading. This was achieved with a complementary virtual work formulation of the stiffness and stress matrices for a square element with center circular hole. The assumed stress state provides zero shearing stress on the hole boundary, so the element is suitable for problems involving load transfer without friction. The element has been implemented in the NASTRAN computer program, and sample problem results are presented.

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

NASA Technical Reports Server (NTRS)

Tsiveriotis, K.; Brown, R. A.

1993-01-01

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

A computer program for anisotropic shallow-shell finite elements using symbolic integration

NASA Technical Reports Server (NTRS)

Andersen, C. M.; Bowen, J. T.

1976-01-01

A FORTRAN computer program for anisotropic shallow-shell finite elements with variable curvature is described. A listing of the program is presented together with printed output for a sample case. Computation times and central memory requirements are given for several different elements. The program is based on a stiffness (displacement) finite-element model in which the fundamental unknowns consist of both the displacement and the rotation components of the reference surface of the shell. Two triangular and four quadrilateral elements are implemented in the program. The triangular elements have 6 or 10 nodes, and the quadrilateral elements have 4 or 8 nodes. Two of the quadrilateral elements have internal degrees of freedom associated with displacement modes which vanish along the edges of the elements (bubble modes). The triangular elements and the remaining two quadrilateral elements do not have bubble modes. The output from the program consists of arrays corresponding to the stiffness, the geometric stiffness, the consistent mass, and the consistent load matrices for individual elements. The integrals required for the generation of these arrays are evaluated by using symbolic (or analytic) integration in conjunction with certain group-theoretic techniques. The analytic expressions for the integrals are exact and were developed using the symbolic and algebraic manipulation language.

Probabilistic Structures Analysis Methods (PSAM) for select space propulsion system components

NASA Technical Reports Server (NTRS)

1991-01-01

The basic formulation for probabilistic finite element analysis is described and demonstrated on a few sample problems. This formulation is based on iterative perturbation that uses the factorized stiffness on the unperturbed system as the iteration preconditioner for obtaining the solution to the perturbed problem. This approach eliminates the need to compute, store and manipulate explicit partial derivatives of the element matrices and force vector, which not only reduces memory usage considerably, but also greatly simplifies the coding and validation tasks. All aspects for the proposed formulation were combined in a demonstration problem using a simplified model of a curved turbine blade discretized with 48 shell elements, and having random pressure and temperature fields with partial correlation, random uniform thickness, and random stiffness at the root.

Basic research on design analysis methods for rotorcraft vibrations

NASA Technical Reports Server (NTRS)

Hanagud, S.

1991-01-01

The objective of the present work was to develop a method for identifying physically plausible finite element system models of airframe structures from test data. The assumed models were based on linear elastic behavior with general (nonproportional) damping. Physical plausibility of the identified system matrices was insured by restricting the identification process to designated physical parameters only and not simply to the elements of the system matrices themselves. For example, in a large finite element model the identified parameters might be restricted to the moduli for each of the different materials used in the structure. In the case of damping, a restricted set of damping values might be assigned to finite elements based on the material type and on the fabrication processes used. In this case, different damping values might be associated with riveted, bolted and bonded elements. The method itself is developed first, and several approaches are outlined for computing the identified parameter values. The method is applied first to a simple structure for which the 'measured' response is actually synthesized from an assumed model. Both stiffness and damping parameter values are accurately identified. The true test, however, is the application to a full-scale airframe structure. In this case, a NASTRAN model and actual measured modal parameters formed the basis for the identification of a restricted set of physically plausible stiffness and damping parameters.

A locally refined rectangular grid finite element method - Application to computational fluid dynamics and computational physics

NASA Technical Reports Server (NTRS)

Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.

1991-01-01

The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.

On Hybrid and mixed finite element methods

NASA Technical Reports Server (NTRS)

Pian, T. H. H.

1981-01-01

Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.

On Dynamics of Spinning Structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.; Ibrahim, A.

2012-01-01

This paper provides details of developments pertaining to vibration analysis of gyroscopic systems, that involves a finite element structural discretization followed by the solution of the resulting matrix eigenvalue problem by a progressive, accelerated simultaneous iteration technique. Thus Coriolis, centrifugal and geometrical stiffness matrices are derived for shell and line elements, followed by the eigensolution details as well as solution of representative problems that demonstrates the efficacy of the currently developed numerical procedures and tools.

Symmetric tridiagonal structure preserving finite element model updating problem for the quadratic model

NASA Astrophysics Data System (ADS)

Rakshit, Suman; Khare, Swanand R.; Datta, Biswa Nath

2018-07-01

One of the most important yet difficult aspect of the Finite Element Model Updating Problem is to preserve the finite element inherited structures in the updated model. Finite element matrices are in general symmetric, positive definite (or semi-definite) and banded (tridiagonal, diagonal, penta-diagonal, etc.). Though a large number of papers have been published in recent years on various aspects of solutions of this problem, papers dealing with structure preservation almost do not exist. A novel optimization based approach that preserves the symmetric tridiagonal structures of the stiffness and damping matrices is proposed in this paper. An analytical expression for the global minimum solution of the associated optimization problem along with the results of numerical experiments obtained by both the analytical expressions and by an appropriate numerical optimization algorithm are presented. The results of numerical experiments support the validity of the proposed method.

An efficient approach for the assembly of mass and stiffness matrices of structures with modifications

NASA Astrophysics Data System (ADS)

Wagner, Andreas; Spelsberg-Korspeter, Gottfried

2013-09-01

The finite element method is one of the most common tools for the comprehensive analysis of structures with applications reaching from static, often nonlinear stress-strain, to transient dynamic analyses. For single calculations the expense to generate an appropriate mesh is often insignificant compared to the analysis time even for complex geometries and therefore negligible. However, this is not the case for certain other applications, most notably structural optimization procedures, where the (re-)meshing effort is very important with respect to the total runtime of the procedure. Thus it is desirable to find methods to efficiently generate mass and stiffness matrices allowing to reduce this effort, especially for structures with modifications of minor complexity, e.g. panels with cutouts. Therefore, a modeling approach referred to as Energy Modification Method is proposed in this paper. The underlying idea is to model and discretize the basis structure, e.g. a plate, and the modifications, e.g. holes, separately. The discretized energy expressions of the modifications are then subtracted from (or added to) the energy expressions of the basis structure and the coordinates are related to each other by kinematical constraints leading to the mass and stiffness matrices of the complete structure. This approach will be demonstrated by two simple examples, a rod with varying material properties and a rectangular plate with a rectangular or circular hole, using a finite element discretization as basis. Convergence studies of the method based on the latter example follow demonstrating the rapid convergence and efficiency of the method. Finally, the Energy Modification Method is successfully used in the structural optimization of a circular plate with holes, with the objective to split all its double eigenfrequencies.

Laminin active peptide/agarose matrices as multifunctional biomaterials for tissue engineering.

PubMed

Yamada, Yuji; Hozumi, Kentaro; Aso, Akihiro; Hotta, Atsushi; Toma, Kazunori; Katagiri, Fumihiko; Kikkawa, Yamato; Nomizu, Motoyoshi

2012-06-01

Cell adhesive peptides derived from extracellular matrix components are potential candidates to afford bio-adhesiveness to cell culture scaffolds for tissue engineering. Previously, we covalently conjugated bioactive laminin peptides to polysaccharides, such as chitosan and alginate, and demonstrated their advantages as biomaterials. Here, we prepared functional polysaccharide matrices by mixing laminin active peptides and agarose gel. Several laminin peptide/agarose matrices showed cell attachment activity. In particular, peptide AG73 (RKRLQVQLSIRT)/agarose matrices promoted strong cell attachment and the cell behavior depended on the stiffness of agarose matrices. Fibroblasts formed spheroid structures on the soft AG73/agarose matrices while the cells formed a monolayer with elongated morphologies on the stiff matrices. On the stiff AG73/agarose matrices, neuronal cells extended neuritic processes and endothelial cells formed capillary-like networks. In addition, salivary gland cells formed acini-like structures on the soft matrices. These results suggest that the peptide/agarose matrices are useful for both two- and three-dimensional cell culture systems as a multifunctional biomaterial for tissue engineering. Copyright © 2012 Elsevier Ltd. All rights reserved.

Vibration analyses of an inclined flat plate subjected to moving loads

NASA Astrophysics Data System (ADS)

Wu, Jia-Jang

2007-01-01

The object of this paper is to present a moving mass element so that one may easily perform the dynamic analysis of an inclined plate subjected to moving loads with the effects of inertia force, Coriolis force and centrifugal force considered. To this end, the mass, damping and stiffness matrices of the moving mass element, with respect to the local coordinate system, are derived first by using the principle of superposition and the definition of shape functions. Next, the last property matrices of the moving mass element are transformed into the global coordinate system and combined with the property matrices of the inclined plate itself to determine the effective overall property matrices and the instantaneous equations of motion of the entire vibrating system. Because the property matrices of the moving mass element have something to do with the instantaneous position of the moving load, both the property matrices of the moving mass element and the effective overall ones of the entire vibrating system are time-dependent. At any instant of time, solving the instantaneous equations of motion yields the instantaneous dynamic responses of the inclined plate. For validation, the presented technique is used to determine the dynamic responses of a horizontal pinned-pinned plate subjected to a moving load and a satisfactory agreement with the existing literature is achieved. Furthermore, extensive studies on the inclined plate subjected to moving loads reveal that the influences of moving-load speed, inclined angle of the plate and total number of the moving loads on the dynamic responses of the inclined plate are significant in most cases, and the effects of Coriolis force and centrifugal force are perceptible only in the case of higher moving-load speed.

The free and forced vibrations of structures using the finite dynamic element method. Ph.D. Thesis, Aug. 1991 Final Report

NASA Technical Reports Server (NTRS)

Fergusson, Neil J.

1992-01-01

In addition to an extensive review of the literature on exact and corrective displacement based methods of vibration analysis, a few theorems are proven concerning the various structural matrices involved in such analyses. In particular, the consistent mass matrix and the quasi-static mass matrix are shown to be equivalent, in the sense that the terms in their respective Taylor expansions are proportional to one another, and that they both lead to the same dynamic stiffness matrix when used with the appropriate stiffness matrix.

Finite elements based on consistently assumed stresses and displacements

NASA Technical Reports Server (NTRS)

Pian, T. H. H.

1985-01-01

Finite element stiffness matrices are derived using an extended Hellinger-Reissner principle in which internal displacements are added to serve as Lagrange multipliers to introduce the equilibrium constraint in each element. In a consistent formulation the assumed stresses are initially unconstrained and complete polynomials and the total displacements are also complete such that the corresponding strains are complete in the same order as the stresses. Several examples indicate that resulting properties for elements constructed by this consistent formulation are ideal and are less sensitive to distortions of element geometries. The method has been used to find the optimal stress terms for plane elements, 3-D solids, axisymmetric solids, and plate bending elements.

Substructure Versus Property-Level Dispersed Modes Calculation

NASA Technical Reports Server (NTRS)

Stewart, Eric C.; Peck, Jeff A.; Bush, T. Jason; Fulcher, Clay W.

2016-01-01

This paper calculates the effect of perturbed finite element mass and stiffness values on the eigenvectors and eigenvalues of the finite element model. The structure is perturbed in two ways: at the "subelement" level and at the material property level. In the subelement eigenvalue uncertainty analysis the mass and stiffness of each subelement is perturbed by a factor before being assembled into the global matrices. In the property-level eigenvalue uncertainty analysis all material density and stiffness parameters of the structure are perturbed modified prior to the eigenvalue analysis. The eigenvalue and eigenvector dispersions of each analysis (subelement and property-level) are also calculated using an analytical sensitivity approximation. Two structural models are used to compare these methods: a cantilevered beam model, and a model of the Space Launch System. For each structural model it is shown how well the analytical sensitivity modes approximate the exact modes when the uncertainties are applied at the subelement level and at the property level.

Equivalent model construction for a non-linear dynamic system based on an element-wise stiffness evaluation procedure and reduced analysis of the equivalent system

NASA Astrophysics Data System (ADS)

Kim, Euiyoung; Cho, Maenghyo

2017-11-01

In most non-linear analyses, the construction of a system matrix uses a large amount of computation time, comparable to the computation time required by the solving process. If the process for computing non-linear internal force matrices is substituted with an effective equivalent model that enables the bypass of numerical integrations and assembly processes used in matrix construction, efficiency can be greatly enhanced. A stiffness evaluation procedure (STEP) establishes non-linear internal force models using polynomial formulations of displacements. To efficiently identify an equivalent model, the method has evolved such that it is based on a reduced-order system. The reduction process, however, makes the equivalent model difficult to parameterize, which significantly affects the efficiency of the optimization process. In this paper, therefore, a new STEP, E-STEP, is proposed. Based on the element-wise nature of the finite element model, the stiffness evaluation is carried out element-by-element in the full domain. Since the unit of computation for the stiffness evaluation is restricted by element size, and since the computation is independent, the equivalent model can be constructed efficiently in parallel, even in the full domain. Due to the element-wise nature of the construction procedure, the equivalent E-STEP model is easily characterized by design parameters. Various reduced-order modeling techniques can be applied to the equivalent system in a manner similar to how they are applied in the original system. The reduced-order model based on E-STEP is successfully demonstrated for the dynamic analyses of non-linear structural finite element systems under varying design parameters.

Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

NASA Astrophysics Data System (ADS)

Chiang, C. K.; Xue, David Y.; Mei, Chuh

1993-04-01

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

NASA Technical Reports Server (NTRS)

Chiang, C. K.; Xue, David Y.; Mei, Chuh

1993-01-01

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

Development of computer program NAS3D using Vector processing for geometric nonlinear analysis of structures

NASA Technical Reports Server (NTRS)

Mangalgiri, P. D.; Prabhakaran, R.

1986-01-01

An algorithm for vectorized computation of stiffness matrices of an 8 noded isoparametric hexahedron element for geometric nonlinear analysis was developed. This was used in conjunction with the earlier 2-D program GAMNAS to develop the new program NAS3D for geometric nonlinear analysis. A conventional, modified Newton-Raphson process is used for the nonlinear analysis. New schemes for the computation of stiffness and strain energy release rates is presented. The organization the program is explained and some results on four sample problems are given. The study of CPU times showed that savings by a factor of 11 to 13 were achieved when vectorized computation was used for the stiffness instead of the conventional scalar one. Finally, the scheme of inputting data is explained.

Cell-mediated fibre recruitment drives extracellular matrix mechanosensing in engineered fibrillar microenvironments

NASA Astrophysics Data System (ADS)

Baker, Brendon M.; Trappmann, Britta; Wang, William Y.; Sakar, Mahmut S.; Kim, Iris L.; Shenoy, Vivek B.; Burdick, Jason A.; Chen, Christopher S.

2015-12-01

To investigate how cells sense stiffness in settings structurally similar to native extracellular matrices, we designed a synthetic fibrous material with tunable mechanics and user-defined architecture. In contrast to flat hydrogel surfaces, these fibrous materials recapitulated cell-matrix interactions observed with collagen matrices including stellate cell morphologies, cell-mediated realignment of fibres, and bulk contraction of the material. Increasing the stiffness of flat hydrogel surfaces induced mesenchymal stem cell spreading and proliferation; however, increasing fibre stiffness instead suppressed spreading and proliferation for certain network architectures. Lower fibre stiffness permitted active cellular forces to recruit nearby fibres, dynamically increasing ligand density at the cell surface and promoting the formation of focal adhesions and related signalling. These studies demonstrate a departure from the well-described relationship between material stiffness and spreading established with hydrogel surfaces, and introduce fibre recruitment as a previously undescribed mechanism by which cells probe and respond to mechanics in fibrillar matrices.

Matrix stiffness reverses the effect of actomyosin tension on cell proliferation.

PubMed

Mih, Justin D; Marinkovic, Aleksandar; Liu, Fei; Sharif, Asma S; Tschumperlin, Daniel J

2012-12-15

The stiffness of the extracellular matrix exerts powerful effects on cell proliferation and differentiation, but the mechanisms transducing matrix stiffness into cellular fate decisions remain poorly understood. Two widely reported responses to matrix stiffening are increases in actomyosin contractility and cell proliferation. To delineate their relationship, we modulated cytoskeletal tension in cells grown across a physiological range of matrix stiffnesses. On both synthetic and naturally derived soft matrices, and across a panel of cell types, we observed a striking reversal of the effect of inhibiting actomyosin contractility, switching from the attenuation of proliferation on rigid substrates to the robust promotion of proliferation on soft matrices. Inhibiting contractility on soft matrices decoupled proliferation from cytoskeletal tension and focal adhesion organization, but not from cell spread area. Our results demonstrate that matrix stiffness and actomyosin contractility converge on cell spreading in an unexpected fashion to control a key aspect of cell fate.

Matrix stiffness reverses the effect of actomyosin tension on cell proliferation

PubMed Central

Mih, Justin D.; Marinkovic, Aleksandar; Liu, Fei; Sharif, Asma S.; Tschumperlin, Daniel J.

2012-01-01

Summary The stiffness of the extracellular matrix exerts powerful effects on cell proliferation and differentiation, but the mechanisms transducing matrix stiffness into cellular fate decisions remain poorly understood. Two widely reported responses to matrix stiffening are increases in actomyosin contractility and cell proliferation. To delineate their relationship, we modulated cytoskeletal tension in cells grown across a physiological range of matrix stiffnesses. On both synthetic and naturally derived soft matrices, and across a panel of cell types, we observed a striking reversal of the effect of inhibiting actomyosin contractility, switching from the attenuation of proliferation on rigid substrates to the robust promotion of proliferation on soft matrices. Inhibiting contractility on soft matrices decoupled proliferation from cytoskeletal tension and focal adhesion organization, but not from cell spread area. Our results demonstrate that matrix stiffness and actomyosin contractility converge on cell spreading in an unexpected fashion to control a key aspect of cell fate. PMID:23097048

HFEM3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weiss, Chester J

Software solves the three-dimensional Poisson equation div(k(grad(u)) = f, by the finite element method for the case when material properties, k, are distributed over hierarchy of edges, facets and tetrahedra in the finite element mesh. Method is described in Weiss, CJ, Finite element analysis for model parameters distributed on a hierarchy of geometric simplices, Geophysics, v82, E155-167, doi:10.1190/GEO2017-0058.1 (2017). A standard finite element method for solving Poisson’s equation is augmented by including in the 3D stiffness matrix additional 2D and 1D stiffness matrices representing the contributions from material properties associated with mesh faces and edges, respectively. The resulting linear systemmore » is solved iteratively using the conjugate gradient method with Jacobi preconditioning. To minimize computer storage for program execution, the linear solver computes matrix-vector contractions element-by-element over the mesh, without explicit storage of the global stiffness matrix. Program output vtk compliant for visualization and rendering by 3rd party software. Program uses dynamic memory allocation and as such there are no hard limits on problem size outside of those imposed by the operating system and configuration on which the software is run. Dimension, N, of the finite element solution vector is constrained by the the addressable space in 32-vs-64 bit operating systems. Total storage requirements for the problem. Total working space required for the program is approximately 13*N double precision words.« less

A NASTRAN model of a large flexible swing-wing bomber. Volume 5: NASTRAN model development-fairing structure

NASA Technical Reports Server (NTRS)

Mock, W. D.; Latham, R. A.

1982-01-01

The NASTRAN model plan for the fairing structure was expanded in detail to generate the NASTRAN model of this substructure. The grid point coordinates, element definitions, material properties, and sizing data for each element were specified. The fairing model was thoroughly checked out for continuity, connectivity, and constraints. The substructure was processed for structural influence coefficients (SIC) point loadings to determine the deflection characteristics of the fairing model. Finally, a demonstration and validation processing of this substructure was accomplished using the NASTRAN finite element program. The bulk data deck, stiffness matrices, and SIC output data were delivered.

Mechanical Four-Pole Parameters: Transmission Matrices

DTIC Science & Technology

1976-04-19

moment of inertia, it is pcssible to state that 1, = i2 ’jV 2 (127) ~ =v 2 ,(128) B, = B2 ,(129) el e2 (130) 28 1 -JA 0 0 P2 0 1 0 0 VM 0 1 j :(. 131 ...Eq. 129 now becomes + JCI ,2(1.32) so that F1 1 -JaM 0 0 F2 V, 0 1 0 0 V2 ~ :~ (133) B. 0 0o 1 Jcn B 2 1 2 3. Spring of Stiffness K in Cascade [Fig...transmission matrix is that of Eq. 131 in which the element - JaM has been replaced py - Za. 9. VALUES OF TRANSMISSION MATRICES (BERNOULLI-EUER BEANS

The vibration characteristics of a coupled helicopter rotor-fuselage by a finite element analysis

NASA Technical Reports Server (NTRS)

Rutkowski, M. J.

1983-01-01

The dynamic coupling between the rotor system and the fuselage of a simplified helicopter model in hover was analytically investigated. Mass, aerodynamic damping, and elastic and centrifugal stiffness matrices are presented for the analytical model; the model is based on a beam finite element, with polynomial mass and stiffness distributions for both the rotor and fuselage representations. For this analytical model, only symmetric fuselage and collective blade degrees of freedom are treated. Real and complex eigen-analyses are carried out to obtain coupled rotor-fuselage natural modes and frequencies as a function of rotor speed. Vibration response results are obtained for the coupled system subjected to a radially uniform, harmonic blade loading. The coupled response results are compared with response results from an uncoupled analysis in which hub loads for an isolated rotor system subjected to the same sinusoidal blade loading as the coupled system are applied to a free-free fuselage.

Study of propellant dynamics in a shuttle type launch vehicle

NASA Technical Reports Server (NTRS)

Jones, C. E.; Feng, G. C.

1972-01-01

A method and an associated digital computer program for evaluating the vibrational characteristics of large liquid-filled rigid wall tanks of general shape are presented. A solution procedure was developed in which slosh modes and frequencies are computed for systems mathematically modeled as assemblages of liquid finite elements. To retain sparsity in the assembled system mass and stiffness matrices, a compressible liquid element formulation was incorporated in the program. The approach taken in the liquid finite element formulation is compatible with triangular and quadrilateral structural finite elements so that the analysis of liquid motion can be coupled with flexible tank wall motion at some future time. The liquid element repertoire developed during the course of this study consists of a two-dimensional triangular element and a three-dimensional tetrahedral element.

Storage strategies of eddy-current FE-BI model for GPU implementation

NASA Astrophysics Data System (ADS)

Bardel, Charles; Lei, Naiguang; Udpa, Lalita

2013-01-01

In the past few years graphical processing units (GPUs) have shown tremendous improvements in computational throughput over standard CPU architecture. However, this comes at the cost of restructuring the algorithms to meet the strengths and drawbacks of this GPU architecture. A major drawback is the state of limited memory, and hence storage of FE stiffness matrices on the GPU is important. In contrast to storage on CPU the GPU storage format has significant influence on the overall performance. This paper presents an investigation of a storage strategy in the implementation of a two-dimensional finite element-boundary integral (FE-BI) model for Eddy current NDE applications, on GPU architecture. Specifically, the high dimensional matrices are manipulated by examining the matrix structure and optimally splitting into structurally independent component matrices for efficient storage and retrieval of each component. Results obtained using the proposed approach are compared to those of conventional CPU implementation for validating the method.

A NASTRAN model of a large flexible swing-wing bomber. Volume 3: NASTRAN model development-wing structure

NASA Technical Reports Server (NTRS)

Mock, W. D.; Latham, R. A.

1982-01-01

The NASTRAN model plan for the wing structure was expanded in detail to generate the NASTRAN model for this substructure. The grid point coordinates were coded for each element. The material properties and sizing data for each element were specified. The wing substructure model was thoroughly checked out for continuity, connectivity, and constraints. This substructure was processed for structural influence coefficients (SIC) point loadings and the deflections were compared to those computed for the aircraft detail model. Finally, a demonstration and validation processing of this substructure was accomplished using the NASTRAN finite element program. The bulk data deck, stiffness matrices, and SIC output data were delivered.

A NASTRAN model of a large flexible swing-wing bomber. Volume 4: NASTRAN model development-fuselage structure

NASA Technical Reports Server (NTRS)

Mock, W. D.; Latham, R. A.

1982-01-01

The NASTRAN model plan for the fuselage structure was expanded in detail to generate the NASTRAN model for this substructure. The grid point coordinates were coded for each element. The material properties and sizing data for each element were specified. The fuselage substructure model was thoroughly checked out for continuity, connectivity, and constraints. This substructure was processed for structural influence coefficients (SIC) point loadings and the deflections were compared to those computed for the aircraft detail model. Finally, a demonstration and validation processing of this substructure was accomplished using the NASTRAN finite element program. The bulk data deck, stiffness matrices, and SIC output data were delivered.

Direct structural parameter identification by modal test results

NASA Technical Reports Server (NTRS)

Chen, J.-C.; Kuo, C.-P.; Garba, J. A.

1983-01-01

A direct identification procedure is proposed to obtain the mass and stiffness matrices based on the test measured eigenvalues and eigenvectors. The method is based on the theory of matrix perturbation in which the correct mass and stiffness matrices are expanded in terms of analytical values plus a modification matrix. The simplicity of the procedure enables real time operation during the structural testing.

NASTRAN implementation of an isoparametric doubly-curved quadrilateral shell element

NASA Technical Reports Server (NTRS)

Potvin, A. B.; Leick, R. D.

1978-01-01

A quadrilateral shell element, CQUAD4, was added to level 15.5 and subsequently to level 16.0 of NASTRAN. The element exhibited doubly curved surfaces and used biquadratic interpolation functions. Reduced integration techniques were used to improve the performance of the element in thin shell problems. The creation of several new bulk data items is discussed, along with a special module, GPNORM, to process SHLNORM bulk data cards. In addition to the theoretical basis for the element stiffness matrix, consistent mass and load matrices are presented. Several potential sources of degenerate behavior of the element were investigated. Guidelines for proper use of the element were suggested. Performance of the element on several widely published classical examples was demonstrated. The results showed a significant improvement over presently available NASTRAN shell elements for even the coarsest meshes. Potential applications to two classes of practical problems are discussed.

Rapid iterative reanalysis for automated design

NASA Technical Reports Server (NTRS)

Bhatia, K. G.

1973-01-01

A method for iterative reanalysis in automated structural design is presented for a finite-element analysis using the direct stiffness approach. A basic feature of the method is that the generalized stiffness and inertia matrices are expressed as functions of structural design parameters, and these generalized matrices are expanded in Taylor series about the initial design. Only the linear terms are retained in the expansions. The method is approximate because it uses static condensation, modal reduction, and the linear Taylor series expansions. The exact linear representation of the expansions of the generalized matrices is also described and a basis for the present method is established. Results of applications of the present method to the recalculation of the natural frequencies of two simple platelike structural models are presented and compared with results obtained by using a commonly applied analysis procedure used as a reference. In general, the results are in good agreement. A comparison of the computer times required for the use of the present method and the reference method indicated that the present method required substantially less time for reanalysis. Although the results presented are for relatively small-order problems, the present method will become more efficient relative to the reference method as the problem size increases. An extension of the present method to static reanalysis is described, ana a basis for unifying the static and dynamic reanalysis procedures is presented.

The Fractional Step Method Applied to Simulations of Natural Convective Flows

NASA Technical Reports Server (NTRS)

Westra, Douglas G.; Heinrich, Juan C.; Saxon, Jeff (Technical Monitor)

2002-01-01

This paper describes research done to apply the Fractional Step Method to finite-element simulations of natural convective flows in pure liquids, permeable media, and in a directionally solidified metal alloy casting. The Fractional Step Method has been applied commonly to high Reynold's number flow simulations, but is less common for low Reynold's number flows, such as natural convection in liquids and in permeable media. The Fractional Step Method offers increased speed and reduced memory requirements by allowing non-coupled solution of the pressure and the velocity components. The Fractional Step Method has particular benefits for predicting flows in a directionally solidified alloy, since other methods presently employed are not very efficient. Previously, the most suitable method for predicting flows in a directionally solidified binary alloy was the penalty method. The penalty method requires direct matrix solvers, due to the penalty term. The Fractional Step Method allows iterative solution of the finite element stiffness matrices, thereby allowing more efficient solution of the matrices. The Fractional Step Method also lends itself to parallel processing, since the velocity component stiffness matrices can be built and solved independently of each other. The finite-element simulations of a directionally solidified casting are used to predict macrosegregation in directionally solidified castings. In particular, the finite-element simulations predict the existence of 'channels' within the processing mushy zone and subsequently 'freckles' within the fully processed solid, which are known to result from macrosegregation, or what is often referred to as thermo-solutal convection. These freckles cause material property non-uniformities in directionally solidified castings; therefore many of these castings are scrapped. The phenomenon of natural convection in an alloy under-going directional solidification, or thermo-solutal convection, will be explained. The development of the momentum and continuity equations for natural convection in a fluid, a permeable medium, and in a binary alloy undergoing directional solidification will be presented. Finally, results for natural convection in a pure liquid, natural convection in a medium with a constant permeability, and for directional solidification will be presented.

Free and forced vibrations of a tyre using a wave/finite element approach

NASA Astrophysics Data System (ADS)

Waki, Y.; Mace, B. R.; Brennan, M. J.

2009-06-01

Free and forced vibrations of a tyre are predicted using a wave/finite element (WFE) approach. A short circumferential segment of the tyre is modelled using conventional finite element (FE) methods, a periodicity condition applied and the mass and stiffness matrices post-processed to yield wave properties. Since conventional FE methods are used, commercial FE packages and existing element libraries can be utilised. An eigenvalue problem is formulated in terms of the transfer matrix of the segment. Zhong's method is used to improve numerical conditioning. The eigenvalues and eigenvectors give the wavenumbers and wave mode shapes, which in turn define transformations between the physical and wave domains. A method is described by which the frequency dependent material properties of the rubber components of the tyre can be included without the need to remesh the structure. Expressions for the forced response are developed which are numerically well-conditioned. Numerical results for a smooth tyre are presented. Dispersion curves for real, imaginary and complex wavenumbers are shown. The propagating waves are associated with various forms of motion of the tread supported by the stiffness of the side wall. Various dispersion phenomena are observed, including curve veering, non-zero cut-off and waves for which the phase velocity and the group velocity have opposite signs. Results for the forced response are compared with experimental measurements and good agreement is seen. The forced response is numerically determined for both finite area and point excitations. It is seen that the size of area of the excitation is particularly important at high frequencies. When the size of the excitation area is small enough compared to the tread thickness, the response at high frequencies becomes stiffness-like (reactive) and the effect of shear stiffness becomes important.

A new pre-loaded beam geometric stiffness matrix with full rigid body capabilities

NASA Astrophysics Data System (ADS)

Bosela, P. A.; Fertis, D. G.; Shaker, F. J.

1992-09-01

Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the 'blanket' of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as 'grounding', or false stiffening, of the stiffness matrix occurs during rigid body rotation. The authors have previously shown that the grounding phenomenon is caused by a lack of rigid body rotational capability, and is typical in beam geometric stiffness matrices formulated by others, including those which contain higher order effects. The cause of the problem was identified as the force imbalance inherent in the formulations. In this paper, the authors develop a beam geometric stiffness matrix for a directed force problem, and show that the resultant global stiffness matrix contains complete rigid body mode capabilities, and performs very well in the diagonalization methodology customarily used in dynamic analysis.

Modulation of hematopoietic progenitor cell fate in vitro by varying collagen oligomer matrix stiffness in the presence or absence of osteoblasts.

PubMed

Chitteti, Brahmananda Reddy; Kacena, Melissa A; Voytik-Harbin, Sherry L; Srour, Edward F

2015-10-01

To recreate the in vivo hematopoietic cell microenvironment or niche and to study the impact of extracellular matrix (ECM) biophysical properties on hematopoietic progenitor cell (HPC) proliferation and function, mouse bone-marrow derived HPC (Lin-Sca1+cKit+/(LSK) were cultured within three-dimensional (3D) type I collagen oligomer matrices. To generate a more physiologic milieu, 3D cultures were established in both the presence and absence of calvariae-derived osteoblasts (OB). Collagen oligomers were polymerized at varying concentration to give rise to matrices of different fibril densities and therefore matrix stiffness (shear storage modulus, 50-800 Pa). Decreased proliferation and increased clonogenicity of LSK cells was associated with increase of matrix stiffness regardless of whether OB were present or absent from the 3D culture system. Also, regardless of whether OB were or were not added to the 3D co-culture system, LSK within 800 Pa collagen oligomer matrices maintained the highest percentage of Lin-Sca1+ cells as well as higher percentage of cells in quiescent state (G0/G1) compared to 50 Pa or 200Pa matrices. Collectively, these data illustrate that biophysical features of collagen oligomer matrices, specifically fibril density-induced modulation of matrix stiffness, provide important guidance cues in terms of LSK expansion and differentiation and therefore maintenance of progenitor cell function. Copyright © 2015. Published by Elsevier B.V.

A user's guide to the SUDAN computer program for determining the vibration modes of structural systems. Ph.D. Thesis - Case Western Reserve Univ., Jun. 1963

NASA Technical Reports Server (NTRS)

Kvaternik, R. G.; Durling, B. J.

1978-01-01

The use of the SUDAN computer program for analyzing structural systems for their natural modes and frequencies of vibration is described. SUDAN is intended for structures which can be represented as an equivalent system of beam, spring, and rigid-body substructures. User-written constraint equations are used to analytically join the mass and stiffness matrices of the substructures to form the mass and stiffness matrices of the complete structure from which all the frequencies and modes of the system are determined. The SUDAN program can treat the case in which both the mass and stiffness matrices of the coupled system may be singular simultaneously. A general description of the FORTRAN IV program is given, the computer hardware and software specifications are indicated, and the input required by the program is described.

Joining of Components of Complex Structures for Improved Dynamic Response

DTIC Science & Technology

2011-10-28

system- level mass and stiffness matrices and force vector (at each frequency in the range of interest). To address this issue a series of complex...displacements of all candidate joint locations by using the system- level mass and stiffness matrices and force vector (at each frequency in the range of...joints. In contrast, Li et al. [10] proposed a fastener layout/topology that achieves an almost uniform stress level in each joint, and adopted

Integrated smart panel and support structure response

NASA Astrophysics Data System (ADS)

DeGiorgi, Virginia G.

1998-06-01

The performance of smart structures is a complex interaction between active and passive components. Active components, even when non-activated, can have an impact on structural performance and, conversely, structural characteristics of passive components can have a measurable impact on active component performance. The present work is an evaluation of the structural characteristics of an active panel designed for acoustic quieting. The support structure is included in the panel design as evaluated. Finite element methods are used to determine the active panel-support structure response. Two conditions are considered; a hollow unfilled support structure and the same structure filled with a polymer compound. Finite element models were defined so that stiffness values corresponding to the center of individual pistons could be determined. Superelement techniques were used to define mass and stiffness values representative of the combined active and support structure at the center of each piston. Results of interest obtained from the analysis include mode shapes, natural frequencies, and equivalent spring stuffiness for use in structural response models to represent the support structure. The effects on plate motion on piston performance cannot be obtained from this analysis, however mass and stiffness matrices for use in an integrated system model to determine piston head velocities can be obtained from this work.

A new parallel-vector finite element analysis software on distributed-memory computers

NASA Technical Reports Server (NTRS)

Qin, Jiangning; Nguyen, Duc T.

1993-01-01

A new parallel-vector finite element analysis software package MPFEA (Massively Parallel-vector Finite Element Analysis) is developed for large-scale structural analysis on massively parallel computers with distributed-memory. MPFEA is designed for parallel generation and assembly of the global finite element stiffness matrices as well as parallel solution of the simultaneous linear equations, since these are often the major time-consuming parts of a finite element analysis. Block-skyline storage scheme along with vector-unrolling techniques are used to enhance the vector performance. Communications among processors are carried out concurrently with arithmetic operations to reduce the total execution time. Numerical results on the Intel iPSC/860 computers (such as the Intel Gamma with 128 processors and the Intel Touchstone Delta with 512 processors) are presented, including an aircraft structure and some very large truss structures, to demonstrate the efficiency and accuracy of MPFEA.

A modified moment-fitted integration scheme for X-FEM applications with history-dependent material data

NASA Astrophysics Data System (ADS)

Zhang, Ziyu; Jiang, Wen; Dolbow, John E.; Spencer, Benjamin W.

2018-01-01

We present a strategy for the numerical integration of partial elements with the eXtended finite element method (X-FEM). The new strategy is specifically designed for problems with propagating cracks through a bulk material that exhibits inelasticity. Following a standard approach with the X-FEM, as the crack propagates new partial elements are created. We examine quadrature rules that have sufficient accuracy to calculate stiffness matrices regardless of the orientation of the crack with respect to the element. This permits the number of integration points within elements to remain constant as a crack propagates, and for state data to be easily transferred between successive discretizations. In order to maintain weights that are strictly positive, we propose an approach that blends moment-fitted weights with volume-fraction based weights. To demonstrate the efficacy of this simple approach, we present results from numerical tests and examples with both elastic and plastic material response.

User's Guide for ENSAERO_FE Parallel Finite Element Solver

NASA Technical Reports Server (NTRS)

Eldred, Lloyd B.; Guruswamy, Guru P.

1999-01-01

A high fidelity parallel static structural analysis capability is created and interfaced to the multidisciplinary analysis package ENSAERO-MPI of Ames Research Center. This new module replaces ENSAERO's lower fidelity simple finite element and modal modules. Full aircraft structures may be more accurately modeled using the new finite element capability. Parallel computation is performed by breaking the full structure into multiple substructures. This approach is conceptually similar to ENSAERO's multizonal fluid analysis capability. The new substructure code is used to solve the structural finite element equations for each substructure in parallel. NASTRANKOSMIC is utilized as a front end for this code. Its full library of elements can be used to create an accurate and realistic aircraft model. It is used to create the stiffness matrices for each substructure. The new parallel code then uses an iterative preconditioned conjugate gradient method to solve the global structural equations for the substructure boundary nodes.

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

NASA Astrophysics Data System (ADS)

Liu, X.; Banerjee, J. R.

2017-03-01

A highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J0) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.

Grounding of space structures

NASA Astrophysics Data System (ADS)

Bosela, P. A.; Fertis, D. G.; Shaker, F. J.

1992-09-01

Space structures, such as the Space Station solar arrays, must be extremely light-weight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a controls system. The tension pre-load in the 'blanket' of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomenon known as 'grounding', or false stiffening, of the stiffness matrix occurs during rigid body rotation. This paper examines the grounding phenomenon in detail. Numerous stiffness matrices developed by others are examined for rigid body rotation capability, and found lacking. A force imbalance inherent in the formulations examined is the likely cause of the grounding problem, suggesting the need for a directed force formulation.

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

Improved throughput traction microscopy reveals pivotal role for matrix stiffness in fibroblast contractility and TGF-β responsiveness

PubMed Central

Marinković, Aleksandar; Mih, Justin D.; Park, Jin-Ah; Liu, Fei

2012-01-01

Lung fibroblast functions such as matrix remodeling and activation of latent transforming growth factor-β1 (TGF-β1) are associated with expression of the myofibroblast phenotype and are directly linked to fibroblast capacity to generate force and deform the extracellular matrix. However, the study of fibroblast force-generating capacities through methods such as traction force microscopy is hindered by low throughput and time-consuming procedures. In this study, we improved at the detail level methods for higher-throughput traction measurements on polyacrylamide hydrogels using gel-surface-bound fluorescent beads to permit autofocusing and automated displacement mapping, and transduction of fibroblasts with a fluorescent label to streamline cell boundary identification. Together these advances substantially improve the throughput of traction microscopy and allow us to efficiently compute the forces exerted by lung fibroblasts on substrates spanning the stiffness range present in normal and fibrotic lung tissue. Our results reveal that lung fibroblasts dramatically alter the forces they transmit to the extracellular matrix as its stiffness changes, with very low forces generated on matrices as compliant as normal lung tissue. Moreover, exogenous TGF-β1 selectively accentuates tractions on stiff matrices, mimicking fibrotic lung, but not on physiological stiffness matrices, despite equivalent changes in Smad2/3 activation. Taken together, these results demonstrate a pivotal role for matrix mechanical properties in regulating baseline and TGF-β1-stimulated contraction of lung fibroblasts and suggest that stiff fibrotic lung tissue may promote myofibroblast activation through contractility-driven events, whereas normal lung tissue compliance may protect against such feedback amplification of fibroblast activation. PMID:22659883

Automating FEA programming

NASA Technical Reports Server (NTRS)

Sharma, Naveen

1992-01-01

In this paper we briefly describe a combined symbolic and numeric approach for solving mathematical models on parallel computers. An experimental software system, PIER, is being developed in Common Lisp to synthesize computationally intensive and domain formulation dependent phases of finite element analysis (FEA) solution methods. Quantities for domain formulation like shape functions, element stiffness matrices, etc., are automatically derived using symbolic mathematical computations. The problem specific information and derived formulae are then used to generate (parallel) numerical code for FEA solution steps. A constructive approach to specify a numerical program design is taken. The code generator compiles application oriented input specifications into (parallel) FORTRAN77 routines with the help of built-in knowledge of the particular problem, numerical solution methods and the target computer.

Exact finite element method analysis of viscoelastic tapered structures to transient loads

NASA Technical Reports Server (NTRS)

Spyrakos, Constantine Chris

1987-01-01

A general method is presented for determining the dynamic torsional/axial response of linear structures composed of either tapered bars or shafts to transient excitations. The method consists of formulating and solving the dynamic problem in the Laplace transform domain by the finite element method and obtaining the response by a numerical inversion of the transformed solution. The derivation of the torsional and axial stiffness matrices is based on the exact solution of the transformed governing equation of motion, and it consequently leads to the exact solution of the problem. The solution permits treatment of the most practical cases of linear tapered bars and shafts, and employs modeling of structures with only one element per member which reduces the number of degrees of freedom involved. The effects of external viscous or internal viscoelastic damping are also taken into account.

Lecture Notes on Multigrid Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vassilevski, P S

The Lecture Notes are primarily based on a sequence of lectures given by the author while been a Fulbright scholar at 'St. Kliment Ohridski' University of Sofia, Sofia, Bulgaria during the winter semester of 2009-2010 academic year. The notes are somewhat expanded version of the actual one semester class he taught there. The material covered is slightly modified and adapted version of similar topics covered in the author's monograph 'Multilevel Block-Factorization Preconditioners' published in 2008 by Springer. The author tried to keep the notes as self-contained as possible. That is why the lecture notes begin with some basic introductory matrix-vectormore » linear algebra, numerical PDEs (finite element) facts emphasizing the relations between functions in finite dimensional spaces and their coefficient vectors and respective norms. Then, some additional facts on the implementation of finite elements based on relation tables using the popular compressed sparse row (CSR) format are given. Also, typical condition number estimates of stiffness and mass matrices, the global matrix assembly from local element matrices are given as well. Finally, some basic introductory facts about stationary iterative methods, such as Gauss-Seidel and its symmetrized version are presented. The introductory material ends up with the smoothing property of the classical iterative methods and the main definition of two-grid iterative methods. From here on, the second part of the notes begins which deals with the various aspects of the principal TG and the numerous versions of the MG cycles. At the end, in part III, we briefly introduce algebraic versions of MG referred to as AMG, focusing on classes of AMG specialized for finite element matrices.« less

GPU-accelerated element-free reverse-time migration with Gauss points partition

NASA Astrophysics Data System (ADS)

Zhou, Zhen; Jia, Xiaofeng; Qiang, Xiaodong

2018-06-01

An element-free method (EFM) has been demonstrated successfully in elasticity, heat conduction and fatigue crack growth problems. We present the theory of EFM and its numerical applications in seismic modelling and reverse time migration (RTM). Compared with the finite difference method and the finite element method, the EFM has unique advantages: (1) independence of grids in computation and (2) lower expense and more flexibility (because only the information of the nodes and the boundary of the concerned area is required). However, in EFM, due to improper computation and storage of some large sparse matrices, such as the mass matrix and the stiffness matrix, the method is difficult to apply to seismic modelling and RTM for a large velocity model. To solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition and utilise the graphics processing unit to improve the computational efficiency. We employ the compressed sparse row format to compress the intermediate large sparse matrices and attempt to simplify the operations by solving the linear equations with CULA solver. To improve the computation efficiency further, we introduce the concept of the lumped mass matrix. Numerical experiments indicate that the proposed method is accurate and more efficient than the regular EFM.

Matrix Stiffness Corresponding to Strictured Bowel Induces a Fibrogenic Response in Human Colonic Fibroblasts

PubMed Central

Johnson, Laura A.; Rodansky, Eva S.; Sauder, Kay L.; Horowitz, Jeffrey C.; Mih, Justin D.; Tschumperlin, Daniel J.; Higgins, Peter D.

2013-01-01

Background Crohn’s disease is characterized by repeated cycles of inflammation and mucosal healing which ultimately progress to intestinal fibrosis. This inexorable progression towards fibrosis suggests that fibrosis becomes inflammation-independent and auto-propagative. We hypothesized that matrix stiffness regulates this auto-propagation of intestinal fibrosis. Methods The stiffness of fresh ex vivo samples from normal human small intestine, Crohn’s disease strictures, and the unaffected margin were measured with a microelastometer. Normal human colonic fibroblasts were cultured on physiologically normal or pathologically stiff matrices corresponding to the physiological stiffness of normal or fibrotic bowel. Cellular response was assayed for changes in cell morphology, α-smooth muscle actin (αSMA) staining, and gene expression. Results Microelastometer measurements revealed a significant increase in colonic tissue stiffness between normal human colon and Crohn’s strictures as well as between the stricture and adjacent tissue margin. In Ccd-18co cells grown on stiff matrices corresponding to Crohn’s strictures, cellular proliferation increased. Pathologic stiffness induced a marked change in cell morphology and increased αSMA protein expression. Growth on a stiff matrix induced fibrogenic gene expression, decreased matrix metalloproteinase and pro-inflammatory gene expression, and was associated with nuclear localization of the transcriptional cofactor MRTF-A. Conclusions Matrix stiffness, representative of the pathological stiffness of Crohn’s strictures, activates human colonic fibroblasts to a fibrogenic phenotype. Matrix stiffness affects multiple pathways suggesting the mechanical properties of the cellular environment are critical to fibroblast function and may contribute to autopropagation of intestinal fibrosis in the absence of inflammation, thereby contributing to the intractable intestinal fibrosis characteristic of Crohn’s disease. PMID:23502354

Numerical solution of quadratic matrix equations for free vibration analysis of structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1975-01-01

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

A computer package for the design and eigenproblem solution of damped linear multidegree of freedom systems

NASA Technical Reports Server (NTRS)

Ahmadian, M.; Inman, D. J.

1982-01-01

Systems described by the matrix differental equation are considered. An interactive design routine is presented for positive definite mass, damping, and stiffness matrices. Designing is accomplished by adjusting the mass, damping, and stiffness matrices to obtain a desired oscillation behavior. The algorithm also features interactively modifying the physical structure of the system, obtaining the matrix structure and a number of other system properties. In case of a general system, where the M, C, and K matrices lack any special properties, a routine for the eigenproblem solution of the system is developed. The latent roots are obtained by computing the characteristic polynomial of the system and solving for its roots. The above routines are prepared in FORTRAN IV and prove to be usable for the machines with low core memory.

Considerations for the application of finite element beam modeling to vibration analysis of flight vehicle structures. Ph.D. Thesis - Case Western Reserve Univ.

NASA Technical Reports Server (NTRS)

Kvaternik, R. G.

1976-01-01

The manner of representing a flight vehicle structure as an assembly of beam, spring, and rigid-body components for vibration analysis is described. The development is couched in terms of a substructures methodology which is based on the finite-element stiffness method. The particular manner of employing beam, spring, and rigid-body components to model such items as wing structures, external stores, pylons supporting engines or external stores, and sprung masses associated with launch vehicle fuel slosh is described by means of several simple qualitative examples. A detailed numerical example consisting of a tilt-rotor VTOL aircraft is included to provide a unified illustration of the procedure for representing a structure as an equivalent system of beams, springs, and rigid bodies, the manner of forming the substructure mass and stiffness matrices, and the mechanics of writing the equations of constraint which enforce deflection compatibility at the junctions of the substructures. Since many structures, or selected components of structures, can be represented in this manner for vibration analysis, the modeling concepts described and their application in the numerical example shown should prove generally useful to the dynamicist.

Performance of Infinitely Wide Parabolic and Inclined Slider Bearings Lubricated with Couple Stress or Magnetic Fluids

NASA Astrophysics Data System (ADS)

Oladeinde, Mobolaji Humphrey; Akpobi, John Ajokpaoghene

2011-10-01

The hydrodynamic and magnetohydrodynamic (MHD) lubrication problem of infinitely wide inclined and parabolic slider bearings is solved numerically using the finite element method. The bearing configurations are discretized into three-node isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations are solved using Gauss quadrature to obtain a finite number of stiffness matrices. The global system of equations obtained from enforcing nodal continuity of pressure for the bearings are solved using the Gauss-Seidel iterative scheme with a convergence criterion of 10-10. Numerical computations reveal that, when compared for similar profile and couple stress parameters, greater pressure builds up in a parabolic slider compared to an inclined slider, indicating a greater wedge effect in the parabolic slider. The parabolic slider bearing is also shown to develop a greater load capacity when lubricated with magnetic fluids. The superior performance of parabolic slider bearing is more pronounced at greater Hartmann numbers for identical bearing structural parameters. It is also shown that when load carrying capacity is the yardstick for comparison, the parabolic slider bearings are superior to the inclined bearings when lubricated with couple stress or magnetic lubricants.

Acoustic intensity calculations for axisymmetrically modeled fluid regions

NASA Technical Reports Server (NTRS)

Hambric, Stephen A.; Everstine, Gordon C.

1992-01-01

An algorithm for calculating acoustic intensities from a time harmonic pressure field in an axisymmetric fluid region is presented. Acoustic pressures are computed in a mesh of NASTRAN triangular finite elements of revolution (TRIAAX) using an analogy between the scalar wave equation and elasticity equations. Acoustic intensities are then calculated from pressures and pressure derivatives taken over the mesh of TRIAAX elements. Intensities are displayed as vectors indicating the directions and magnitudes of energy flow at all mesh points in the acoustic field. A prolate spheroidal shell is modeled with axisymmetric shell elements (CONEAX) and submerged in a fluid region of TRIAAX elements. The model is analyzed to illustrate the acoustic intensity method and the usefulness of energy flow paths in the understanding of the response of fluid-structure interaction problems. The structural-acoustic analogy used is summarized for completeness. This study uncovered a NASTRAN limitation involving numerical precision issues in the CONEAX stiffness calculation causing large errors in the system matrices for nearly cylindrical cones.

Effect of length to thickness ratio on free vibration analysis of thick fiber reinforced plastic skew cross-ply laminate with circular cutout

NASA Astrophysics Data System (ADS)

Srividya, K.; Reddy, Ch. Kishore; Sumanth, Ch. Mohan; Krishnaiah, P. Gopala; Kishan, V. Mallikharjuna

2018-04-01

The present investigation deals with the free vibration analysis of a thick four-layered symmetric cross-ply skew laminated composite plate with a circular cutout. Three dimensional finite element models (FEM) which use the elasticity theory for the determination of stiffness matrices are modeled in ANSYS software to evaluate first five natural frequencies of the laminate. The variations of the first five natural frequencies with respect to length to thickness ratio (S) for different diameter to length ratios (d/l) are presented. It is observed that, the natural frequencies decreases with increase of thickness ratio(S).

Design of multiple-ply laminated composite tapered beams

NASA Technical Reports Server (NTRS)

Rodriguez, P.

1993-01-01

A study of a special case of symmetric laminated composite cantilever beams is presented. The approach models beams that are tapered both in depth and width and investigates the effect of the ply layup angle and the ply taper on bending and interlaminar shearing stresses. For the determination of stresses and deflections, the beam stiffness matrices are expressed as linear functions of the beam length. Using classical lamination theory (CLT) the stiffness matrices are determined and assembled at strategic locations along the length of the beam. They are then inverted and necessary stiffness parameters are obtained numerically and extracted for determination of design information at each location chosen. Several ply layup configurations are investigated, and design considerations are presented based on the findings. Finally, recommendations for the design of these beams are presented, and a means for anticipating the location of highest stresses is offered.

Design of multiple-ply laminated composite tapered beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rodriguez, P.

1993-06-01

A study of a special case of symmetric laminated composite cantilever beams is presented. The approach models beams that are tapered both in depth and width and investigates the effect of the ply layup angle and the ply taper on bending and interlaminar shearing stresses. For the determination of stresses and deflections, the beam stiffness matrices are expressed as linear functions of the beam length. Using classical lamination theory (CLT) the stiffness matrices are determined and assembled at strategic locations along the length of the beam. They are then inverted and necessary stiffness parameters are obtained numerically and extracted formore » determination of design information at each location chosen. Several ply layup configurations are investigated, and design considerations are preSDsented based on the findings. Finally, recommendations for the design of these beams are presented, and a means for anticipating the location of highest stresses is offered.« less

Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu Benzhuo; Holst, Michael J.; Center for Theoretical Biological Physics, University of California San Diego, La Jolla, CA 92093

2010-09-20

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for simulating electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised formore » time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.« less

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions

PubMed Central

Lu, Benzhuo; Holst, Michael J.; McCammon, J. Andrew; Zhou, Y. C.

2010-01-01

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems. PMID:21709855

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions.

PubMed

Lu, Benzhuo; Holst, Michael J; McCammon, J Andrew; Zhou, Y C

2010-09-20

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.

Distributed parameter modeling of repeated truss structures

NASA Technical Reports Server (NTRS)

Wang, Han-Ching

1994-01-01

A new approach to find homogeneous models for beam-like repeated flexible structures is proposed which conceptually involves two steps. The first step involves the approximation of 3-D non-homogeneous model by a 1-D periodic beam model. The structure is modeled as a 3-D non-homogeneous continuum. The displacement field is approximated by Taylor series expansion. Then, the cross sectional mass and stiffness matrices are obtained by energy equivalence using their additive properties. Due to the repeated nature of the flexible bodies, the mass, and stiffness matrices are also periodic. This procedure is systematic and requires less dynamics detail. The first step involves the homogenization from a 1-D periodic beam model to a 1-D homogeneous beam model. The periodic beam model is homogenized into an equivalent homogeneous beam model using the additive property of compliance along the generic axis. The major departure from previous approaches in literature is using compliance instead of stiffness in homogenization. An obvious justification is that the stiffness is additive at each cross section but not along the generic axis. The homogenized model preserves many properties of the original periodic model.

Time dependent response of low velocity impact induced composite conical shells under multiple delamination

NASA Astrophysics Data System (ADS)

Dey, Sudip; Karmakar, Amit

2014-02-01

This paper presents the time dependent response of multiple delaminated angle-ply composite pretwisted conical shells subjected to low velocity normal impact. The finite element formulation is based on Mindlin's theory incorporating rotary inertia and effects of transverse shear deformation. An eight-noded isoparametric plate bending element is employed to satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. A multipoint constraint algorithm is incorporated which leads to asymmetric stiffness matrices. The modified Hertzian contact law which accounts for permanent indentation is utilized to compute the contact force, and the time dependent equations are solved by Newmark's time integration algorithm. Parametric studies are conducted with respect to triggering parameters like laminate configuration, location of delamination, angle of twist, velocity of impactor, and impactor's displacement for centrally impacted shells.

Modeling of heterogeneous elastic materials by the multiscale hp-adaptive finite element method

NASA Astrophysics Data System (ADS)

Klimczak, Marek; Cecot, Witold

2018-01-01

We present an enhancement of the multiscale finite element method (MsFEM) by combining it with the hp-adaptive FEM. Such a discretization-based homogenization technique is a versatile tool for modeling heterogeneous materials with fast oscillating elasticity coefficients. No assumption on periodicity of the domain is required. In order to avoid direct, so-called overkill mesh computations, a coarse mesh with effective stiffness matrices is used and special shape functions are constructed to account for the local heterogeneities at the micro resolution. The automatic adaptivity (hp-type at the macro resolution and h-type at the micro resolution) increases efficiency of computation. In this paper details of the modified MsFEM are presented and a numerical test performed on a Fichera corner domain is presented in order to validate the proposed approach.

Mechanosignaling through YAP and TAZ drives fibroblast activation and fibrosis

PubMed Central

Liu, Fei; Lagares, David; Choi, Kyoung Moo; Stopfer, Lauren; Marinković, Aleksandar; Vrbanac, Vladimir; Probst, Clemens K.; Hiemer, Samantha E.; Sisson, Thomas H.; Horowitz, Jeffrey C.; Rosas, Ivan O.; Fredenburgh, Laura E.; Feghali-Bostwick, Carol; Varelas, Xaralabos; Tager, Andrew M.

2014-01-01

Pathological fibrosis is driven by a feedback loop in which the fibrotic extracellular matrix is both a cause and consequence of fibroblast activation. However, the molecular mechanisms underlying this process remain poorly understood. Here we identify yes-associated protein (YAP) (homolog of drosophila Yki) and transcriptional coactivator with PDZ-binding motif (TAZ) (also known as Wwtr1), transcriptional effectors of the Hippo pathway, as key matrix stiffness-regulated coordinators of fibroblast activation and matrix synthesis. YAP and TAZ are prominently expressed in fibrotic but not healthy lung tissue, with particularly pronounced nuclear expression of TAZ in spindle-shaped fibroblastic cells. In culture, both YAP and TAZ accumulate in the nuclei of fibroblasts grown on pathologically stiff matrices but not physiologically compliant matrices. Knockdown of YAP and TAZ together in vitro attenuates key fibroblast functions, including matrix synthesis, contraction, and proliferation, and does so exclusively on pathologically stiff matrices. Profibrotic effects of YAP and TAZ operate, in part, through their transcriptional target plasminogen activator inhibitor-1, which is regulated by matrix stiffness independent of transforming growth factor-β signaling. Immortalized fibroblasts conditionally expressing active YAP or TAZ mutant proteins overcome soft matrix limitations on growth and promote fibrosis when adoptively transferred to the murine lung, demonstrating the ability of fibroblast YAP/TAZ activation to drive a profibrotic response in vivo. Together, these results identify YAP and TAZ as mechanoactivated coordinators of the matrix-driven feedback loop that amplifies and sustains fibrosis. PMID:25502501

Non-Muscle Myosin II Isoforms Have Different Functions in Matrix Rearrangement by MDA-MB-231 Cells

PubMed Central

Hindman, Bridget; Goeckeler, Zoe; Sierros, Kostas; Wysolmerski, Robert

2015-01-01

The role of a stiffening extra-cellular matrix (ECM) in cancer progression is documented but poorly understood. Here we use a conditioning protocol to test the role of nonmuscle myosin II isoforms in cell mediated ECM arrangement using collagen constructs seeded with breast cancer cells expressing shRNA targeted to either the IIA or IIB heavy chain isoform. While there are several methods available to measure changes in the biophysical characteristics of the ECM, we wanted to use a method which allows for the measurement of global stiffness changes as well as a dynamic response from the sample over time. The conditioning protocol used allows the direct measurement of ECM stiffness. Using various treatments, it is possible to determine the contribution of various construct and cellular components to the overall construct stiffness. Using this assay, we show that both the IIA and IIB isoforms are necessary for efficient matrix remodeling by MDA-MB-231 breast cancer cells, as loss of either isoform changes the stiffness of the collagen constructs as measured using our conditioning protocol. Constructs containing only collagen had an elastic modulus of 0.40 Pascals (Pa), parental MDA-MB-231 constructs had an elastic modulus of 9.22 Pa, while IIA and IIB KD constructs had moduli of 3.42 and 7.20 Pa, respectively. We also calculated the cell and matrix contributions to the overall sample elastic modulus. Loss of either myosin isoform resulted in decreased cell stiffness, as well as a decrease in the stiffness of the cell-altered collagen matrices. While the total construct modulus for the IIB KD cells was lower than that of the parental cells, the IIB KD cell-altered matrices actually had a higher elastic modulus than the parental cell-altered matrices (4.73 versus 4.38 Pa). These results indicate that the IIA and IIB heavy chains play distinct and non-redundant roles in matrix remodeling. PMID:26136073

Optimal trace inequality constants for interior penalty discontinuous Galerkin discretisations of elliptic operators using arbitrary elements with non-constant Jacobians

NASA Astrophysics Data System (ADS)

Owens, A. R.; Kópházi, J.; Eaton, M. D.

2017-12-01

In this paper, a new method to numerically calculate the trace inequality constants, which arise in the calculation of penalty parameters for interior penalty discretisations of elliptic operators, is presented. These constants are provably optimal for the inequality of interest. As their calculation is based on the solution of a generalised eigenvalue problem involving the volumetric and face stiffness matrices, the method is applicable to any element type for which these matrices can be calculated, including standard finite elements and the non-uniform rational B-splines of isogeometric analysis. In particular, the presented method does not require the Jacobian of the element to be constant, and so can be applied to a much wider variety of element shapes than are currently available in the literature. Numerical results are presented for a variety of finite element and isogeometric cases. When the Jacobian is constant, it is demonstrated that the new method produces lower penalty parameters than existing methods in the literature in all cases, which translates directly into savings in the solution time of the resulting linear system. When the Jacobian is not constant, it is shown that the naive application of existing approaches can result in penalty parameters that do not guarantee coercivity of the bilinear form, and by extension, the stability of the solution. The method of manufactured solutions is applied to a model reaction-diffusion equation with a range of parameters, and it is found that using penalty parameters based on the new trace inequality constants result in better conditioned linear systems, which can be solved approximately 11% faster than those produced by the methods from the literature.

System identification of analytical models of damped structures

NASA Technical Reports Server (NTRS)

Fuh, J.-S.; Chen, S.-Y.; Berman, A.

1984-01-01

A procedure is presented for identifying linear nonproportionally damped system. The system damping is assumed to be representable by a real symmetric matrix. Analytical mass, stiffness and damping matrices which constitute an approximate representation of the system are assumed to be available. Given also are an incomplete set of measured natural frequencies, damping ratios and complex mode shapes of the structure, normally obtained from test data. A method is developed to find the smallest changes in the analytical model so that the improved model can exactly predict the measured modal parameters. The present method uses the orthogonality relationship to improve mass and damping matrices and the dynamic equation to find the improved stiffness matrix.

Superelement Analysis of Tile-Reinforced Composite Armor

NASA Technical Reports Server (NTRS)

Davila, Carlos G.

1998-01-01

Super-elements can greatly improve the computational efficiency of analyses of tile-reinforced structures such as the hull of the Composite Armored Vehicle. By taking advantage of the periodicity in this type of construction, super-elements can be used to simplify the task of modeling, to virtually eliminate the time required to assemble the stiffness matrices, and to reduce significantly the analysis solution time. Furthermore, super-elements are fully transferable between analyses and analysts, so that they provide a consistent method to share information and reduce duplication. This paper describes a methodology that was developed to model and analyze large upper hull components of the Composite Armored Vehicle. The analyses are based on two types of superelement models. The first type is based on element-layering, which consists of modeling a laminate by using several layers of shell elements constrained together with compatibility equations. Element layering is used to ensure the proper transverse shear deformation in the laminate rubber layer. The second type of model uses three-dimensional elements. Since no graphical pre-processor currently supports super-elements, a special technique based on master-elements was developed. Master-elements are representations of super-elements that are used in conjunction with a custom translator to write the superelement connectivities as input decks for ABAQUS.

Submerged Shock Response of a Linearly Elastic Shell of Revolution Containing Internal Structure. User’s Manual for the ELSHOK Code.

DTIC Science & Technology

1982-05-01

execution of PICRUST, influence coefficients corresponding to the base or support motions of a substructure (the gji of Eq. (10) or the constraint...stiffness matrices (M and K, respectively) are also determined. These matrices are required for the calculation of the constraint modes gji of Eq.(lO) and

Theoretical and experimental investigation of architected core materials incorporating negative stiffness elements

NASA Astrophysics Data System (ADS)

Chang, Chia-Ming; Keefe, Andrew; Carter, William B.; Henry, Christopher P.; McKnight, Geoff P.

2014-04-01

Structural assemblies incorporating negative stiffness elements have been shown to provide both tunable damping properties and simultaneous high stiffness and damping over prescribed displacement regions. In this paper we explore the design space for negative stiffness based assemblies using analytical modeling combined with finite element analysis. A simplified spring model demonstrates the effects of element stiffness, geometry, and preloads on the damping and stiffness performance. Simplified analytical models were validated for realistic structural implementations through finite element analysis. A series of complementary experiments was conducted to compare with modeling and determine the effects of each element on the system response. The measured damping performance follows the theoretical predictions obtained by analytical modeling. We applied these concepts to a novel sandwich core structure that exhibited combined stiffness and damping properties 8 times greater than existing foam core technologies.

Damage location and quantification of a pretensioned concrete beam using stochastic subspace identification

NASA Astrophysics Data System (ADS)

Cancelli, Alessandro; Micheli, Laura; Laflamme, Simon; Alipour, Alice; Sritharan, Sri; Ubertini, Filippo

2017-04-01

Stochastic subspace identification (SSID) is a first-order linear system identification technique enabling modal analysis through the time domain. Research in the field of structural health monitoring has demonstrated that SSID can be used to successfully retrieve modal properties, including modal damping ratios, using output-only measurements. In this paper, the utilization of SSID for indirectly retrieving structures' stiffness matrix was investigated, through the study of a simply supported reinforced concrete beam subjected to dynamic loads. Hence, by introducing a physical model of the structure, a second-order identification method is achieved. The reconstruction is based on system condensation methods, which enables calculation of reduced order stiffness, damping, and mass matrices for the structural system. The methods compute the reduced order matrices directly from the modal properties, obtained through the use of SSID. Lastly, the reduced properties of the system are used to reconstruct the stiffness matrix of the beam. The proposed approach is first verified through numerical simulations and then validated using experimental data obtained from a full-scale reinforced concrete beam that experienced progressive damage. Results show that the SSID technique can be used to diagnose, locate, and quantify damage through the reconstruction of the stiffness matrix.

How deep cells feel: Mean-field Computations and Experiments

NASA Astrophysics Data System (ADS)

Buxboim, Amnon; Sen, Shamik; Discher, Dennis E.

2009-03-01

Most cells in solid tissues exert contractile forces that mechanically couple them to elastic surroundings and that significantly influence cell adhesion, cytoskeletal organization and differentiation. However, strains within the depths of matrices are often unclear and are likely relevant to thin matrices, such as basement membranes, relative to cell size as well as to defining how far cells can ``feel.'' We present experimental results for cell spreading on thin, ligand- coated gels and for prestress in stem cells in relation to gel stiffness. Matrix thickness affects cell spread area, focal adhesions and cytoskeleton organization in stem cells, which we will compare to differentiated cells. We introduce a finite element computation to estimate the elastostatic deformations within the matrix on which a cell is placed. Interfacial strains between cell and matrix show large deviations only when soft matrices are a fraction of cell dimensions, proving consistent with experiments. 3-D cell morphologies that model stem cell-derived neurons, myoblasts, and osteoblasts show that a cylinder-shaped myoblast induces the highest strains, consistent with the prominent contractility of muscle. Groups of such cells show a weak crosstalk via matrix strains only when cells are much closer than a cell-width. Cells thus feel on length scales closer to that of adhesions than on cellular scales.

Inclusion of transverse shear deformation in the exact buckling and vibration analysis of composite plate assemblies

NASA Technical Reports Server (NTRS)

Anderson, Melvin S.; Kennedy, David

1993-01-01

The problem considered is the development of the necessary plate stiffnesses for use in the general purpose program VICONOPT for buckling and vibration of composite plate assemblies. The required stiffnesses include the effects of transverse shear deformation and are for sinusoidal response along the plate length as required in VICONOPT. The method is based on the exact solution of the plate differential equations for a composite laminate having fully populated A, B, and D stiffness matrices which leads to an ordinary differential equation of tenth order.

Emerin modulates spatial organization of chromosome territories in cells on softer matrices

PubMed Central

Pradhan, Roopali; Ranade, Devika

2018-01-01

Abstract Cells perceive and relay external mechanical forces into the nucleus through the nuclear envelope. Here we examined the effect of lowering substrate stiffness as a paradigm to address the impact of altered mechanical forces on nuclear structure-function relationships. RNA sequencing of cells on softer matrices revealed significant transcriptional imbalances, predominantly in chromatin associated processes and transcriptional deregulation of human Chromosome 1. Furthermore, 3-Dimensional fluorescence in situ hybridization (3D-FISH) analyses showed a significant mislocalization of Chromosome 1 and 19 Territories (CT) into the nuclear interior, consistent with their transcriptional deregulation. However, CT18 with relatively lower transcriptional dysregulation, also mislocalized into the nuclear interior. Furthermore, nuclear Lamins that regulate chromosome positioning, were mislocalized into the nuclear interior in response to lowered matrix stiffness. Notably, Lamin B2 overexpression retained CT18 near the nuclear periphery in cells on softer matrices. While, cells on softer matrices also activated emerin phosphorylation at a novel Tyr99 residue, the inhibition of which in a phospho-deficient mutant (emerinY99F), selectively retained chromosome 18 and 19 but not chromosome 1 territories at their conserved nuclear locations. Taken together, emerin functions as a key mechanosensor, that modulates the spatial organization of chromosome territories in the interphase nucleus. PMID:29684168

Nonlinear Analysis of Bonded Composite Single-LAP Joints

NASA Technical Reports Server (NTRS)

Oterkus, E.; Barut, A.; Madenci, E.; Smeltzer, S. S.; Ambur, D. R.

2004-01-01

This study presents a semi-analytical solution method to analyze the geometrically nonlinear response of bonded composite single-lap joints with tapered adherend edges under uniaxial tension. The solution method provides the transverse shear and normal stresses in the adhesive and in-plane stress resultants and bending moments in the adherends. The method utilizes the principle of virtual work in conjunction with von Karman s nonlinear plate theory to model the adherends and the shear lag model to represent the kinematics of the thin adhesive layer between the adherends. Furthermore, the method accounts for the bilinear elastic material behavior of the adhesive while maintaining a linear stress-strain relationship in the adherends. In order to account for the stiffness changes due to thickness variation of the adherends along the tapered edges, their in-plane and bending stiffness matrices are varied as a function of thickness along the tapered region. The combination of these complexities results in a system of nonlinear governing equilibrium equations. This approach represents a computationally efficient alternative to finite element method. Comparisons are made with corresponding results obtained from finite-element analysis. The results confirm the validity of the solution method. The numerical results present the effects of taper angle, adherend overlap length, and the bilinear adhesive material on the stress fields in the adherends, as well as the adhesive, of a single-lap joint

A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations

NASA Astrophysics Data System (ADS)

Lin, Zeng; Wang, Dongdong

2017-10-01

Due to the nonlocal property of the fractional derivative, the finite element analysis of fractional diffusion equation often leads to a dense and non-symmetric stiffness matrix, in contrast to the conventional finite element formulation with a particularly desirable symmetric and banded stiffness matrix structure for the typical diffusion equation. This work first proposes a finite element formulation that preserves the symmetry and banded stiffness matrix characteristics for the fractional diffusion equation. The key point of the proposed formulation is the symmetric weak form construction through introducing a fractional weight function. It turns out that the stiffness part of the present formulation is identical to its counterpart of the finite element method for the conventional diffusion equation and thus the stiffness matrix formulation becomes trivial. Meanwhile, the fractional derivative effect in the discrete formulation is completely transferred to the force vector, which is obviously much easier and efficient to compute than the dense fractional derivative stiffness matrix. Subsequently, it is further shown that for the general fractional advection-diffusion-reaction equation, the symmetric and banded structure can also be maintained for the diffusion stiffness matrix, although the total stiffness matrix is not symmetric in this case. More importantly, it is demonstrated that under certain conditions this symmetric diffusion stiffness matrix formulation is capable of producing very favorable numerical solutions in comparison with the conventional non-symmetric diffusion stiffness matrix finite element formulation. The effectiveness of the proposed methodology is illustrated through a series of numerical examples.

Direct system parameter identification of mechanical structures with application to modal analysis

NASA Technical Reports Server (NTRS)

Leuridan, J. M.; Brown, D. L.; Allemang, R. J.

1982-01-01

In this paper a method is described to estimate mechanical structure characteristics in terms of mass, stiffness and damping matrices using measured force input and response data. The estimated matrices can be used to calculate a consistent set of damped natural frequencies and damping values, mode shapes and modal scale factors for the structure. The proposed technique is attractive as an experimental modal analysis method since the estimation of the matrices does not require previous estimation of frequency responses and since the method can be used, without any additional complications, for multiple force input structure testing.

Structure, Stiffness and Substates of the Dickerson-Drew Dodecamer

PubMed Central

Dršata, Tomáš; Pérez, Alberto; Orozco, Modesto; Morozov, Alexandre V.; Šponer, Jiřĺ; Lankaš, Filip

2013-01-01

The Dickerson–Drew dodecamer (DD) d-[CGCGAATTCGCG]2 is a prototypic B-DNA molecule whose sequence-specific structure and dynamics have been investigated by many experimental and computational studies. Here, we present an analysis of DD properties based on extensive atomistic molecular dynamics (MD) simulations using different ionic conditions and water models. The 0.6–2.4-µs-long MD trajectories are compared to modern crystallographic and NMR data. In the simulations, the duplex ends can adopt an alternative base-pairing, which influences the oligomer structure. A clear relationship between the BI/BII backbone substates and the basepair step conformation has been identified, extending previous findings and exposing an interesting structural polymorphism in the helix. For a given end pairing, distributions of the basepair step coordinates can be decomposed into Gaussian-like components associated with the BI/BII backbone states. The nonlocal stiffness matrices for a rigid-base mechanical model of DD are reported for the first time, suggesting salient stiffness features of the central A-tract. The Riemann distance and Kullback–Leibler divergence are used for stiffness matrix comparison. The basic structural parameters converge very well within 300 ns, convergence of the BI/BII populations and stiffness matrices is less sharp. Our work presents new findings about the DD structural dynamics, mechanical properties, and the coupling between basepair and backbone configurations, including their statistical reliability. The results may also be useful for optimizing future force fields for DNA. PMID:23976886

Atomistic modeling of thermomechanical properties of SWNT/Epoxy nanocomposites

NASA Astrophysics Data System (ADS)

Fasanella, Nicholas; Sundararaghavan, Veera

2015-09-01

Molecular dynamics simulations are performed to compute thermomechanical properties of cured epoxy resins reinforced with pristine and covalently functionalized carbon nanotubes. A DGEBA-DDS epoxy network was built using the ‘dendrimer’ growth approach where 75% of available epoxy sites were cross-linked. The epoxy model is verified through comparisons to experiments, and simulations are performed on nanotube reinforced cross-linked epoxy matrix using the CVFF force field in LAMMPS. Full stiffness matrices and linear coefficient of thermal expansion vectors are obtained for the nanocomposite. Large increases in stiffness and large decreases in thermal expansion were seen along the direction of the nanotube for both nanocomposite systems when compared to neat epoxy. The direction transverse to nanotube saw a 40% increase in stiffness due to covalent functionalization over neat epoxy at 1 K whereas the pristine nanotube system only saw a 7% increase due to van der Waals effects. The functionalized SWNT/epoxy nanocomposite showed an additional 42% decrease in thermal expansion along the nanotube direction when compared to the pristine SWNT/epoxy nanocomposite. The stiffness matrices are rotated over every possible orientation to simulate the effects of an isotropic system of randomly oriented nanotubes in the epoxy. The randomly oriented covalently functionalized SWNT/Epoxy nanocomposites showed substantial improvements over the plain epoxy in terms of higher stiffness (200% increase) and lower thermal expansion (32% reduction). Through MD simulations, we develop means to build simulation cells, perform annealing to reach correct densities, compute thermomechanical properties and compare with experiments.

Rolling Element Bearing Stiffness Matrix Determination (Presentation)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Y.; Parker, R.

2014-01-01

Current theoretical bearing models differ in their stiffness estimates because of different model assumptions. In this study, a finite element/contact mechanics model is developed for rolling element bearings with the focus of obtaining accurate bearing stiffness for a wide range of bearing types and parameters. A combined surface integral and finite element method is used to solve for the contact mechanics between the rolling elements and races. This model captures the time-dependent characteristics of the bearing contact due to the orbital motion of the rolling elements. A numerical method is developed to determine the full bearing stiffness matrix corresponding tomore » two radial, one axial, and two angular coordinates; the rotation about the shaft axis is free by design. This proposed stiffness determination method is validated against experiments in the literature and compared to existing analytical models and widely used advanced computational methods. The fully-populated stiffness matrix demonstrates the coupling between bearing radial, axial, and tilting bearing deflections.« less

Q3DG: A computer program for strain-energy-release rates for delamination growth in composite laminates

NASA Technical Reports Server (NTRS)

Raju, I. S.

1986-01-01

The Q3DG is a computer program developed to perform a quasi-three-dimensional stress analysis for composite laminates which may contain delaminations. The laminates may be subjected to mechanical, thermal, and hygroscopic loads. The program uses the finite element method and models the laminates with eight-noded parabolic isoparametric elements. The program computes the strain-energy-release components and the total strain-energy release in all three modes for delamination growth. A rectangular mesh and data file generator, DATGEN, is included. The DATGEN program can be executed interactively and is user friendly. The documentation includes sections dealing with the Q3D analysis theory, derivation of element stiffness matrices and consistent load vectors for the parabolic element. Several sample problems with the input for Q3DG and output from the program are included. The capabilities of the DATGEN program are illustrated with examples of interactive sessions. A microfiche of all the examples is included. The Q3DG and DATGEN programs have been implemented on CYBER 170 class computers. Q3DG and DATGEN were developed at the Langley Research Center during the early eighties and documented in 1984 to 1985.

On the symbolic manipulation and code generation for elasto-plastic material matrices

NASA Technical Reports Server (NTRS)

Chang, T. Y.; Saleeb, A. F.; Wang, P. S.; Tan, H. Q.

1991-01-01

A computerized procedure for symbolic manipulations and FORTRAN code generation of an elasto-plastic material matrix for finite element applications is presented. Special emphasis is placed on expression simplifications during intermediate derivations, optimal code generation, and interface with the main program. A systematic procedure is outlined to avoid redundant algebraic manipulations. Symbolic expressions of the derived material stiffness matrix are automatically converted to RATFOR code which is then translated into FORTRAN statements through a preprocessor. To minimize the interface problem with the main program, a template file is prepared so that the translated FORTRAN statements can be merged into the file to form a subroutine (or a submodule). Three constitutive models; namely, von Mises plasticity, Drucker-Prager model, and a concrete plasticity model, are used as illustrative examples.

An automated procedure for calculating system matrices from perturbation data generated by an EAI Pacer and 100 hybrid computer system

NASA Technical Reports Server (NTRS)

Milner, E. J.; Krosel, S. M.

1977-01-01

Techniques are presented for determining the elements of the A, B, C, and D state variable matrices for systems simulated on an EAI Pacer 100 hybrid computer. An automated procedure systematically generates disturbance data necessary to linearize the simulation model and stores these data on a floppy disk. A separate digital program verifies this data, calculates the elements of the system matrices, and prints these matrices appropriately labeled. The partial derivatives forming the elements of the state variable matrices are approximated by finite difference calculations.

Experimental measurements of hydrodynamic stiffness matrices for a centrifugal pump impeller

NASA Technical Reports Server (NTRS)

Chamieh, D. S.; Acosta, A. J.; Brennen, C. E.; Caughey, T. K.; Franz, R.

1982-01-01

The objective of the Rotor Force Test Facility at the California Institute of Technology is to artificially orbit the center of rotation of an impeller enclosed within a volute over a range of frequencies from zero to synchronous and to measure the resulting forces on the impeller. Preliminary data from the first stage experiments in which the shaft is orbited at low frequency is reported. Steady volute forces along with stiffness matrices due to the change in position of the rotor center are measured. Static pressure taps around the volute are used to obtain volute pressure distributions for various fixed positions of the impeller center and for various flow rates. Static pressure forces are calculated from these pressure distributions allowing a more complete analysis of the components of the impeller forces. Comparison is made with various existing theoretical and experimental results.

Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Youshan, E-mail: ysliu@mail.iggcas.ac.cn; Teng, Jiwen, E-mail: jwteng@mail.iggcas.ac.cn; Xu, Tao, E-mail: xutao@mail.iggcas.ac.cn

2017-05-01

The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate newmore » cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational efficiency, the OTSEM is more efficient than the Fekete-based TSEM, although it is slightly costlier than the QSEM when a comparable numerical accuracy is required. - Highlights: • Higher-order cubature points for degrees 7 to 9 are developed. • The effects of quadrature rule on the mass and stiffness matrices has been conducted. • The cubature points have always positive integration weights. • Freeing from the inversion of a wide bandwidth mass matrix. • The accuracy of the TSEM has been improved in about one order of magnitude.« less

A new method for computation of eigenvector derivatives with distinct and repeated eigenvalues in structural dynamic analysis

NASA Astrophysics Data System (ADS)

Li, Zhengguang; Lai, Siu-Kai; Wu, Baisheng

2018-07-01

Determining eigenvector derivatives is a challenging task due to the singularity of the coefficient matrices of the governing equations, especially for those structural dynamic systems with repeated eigenvalues. An effective strategy is proposed to construct a non-singular coefficient matrix, which can be directly used to obtain the eigenvector derivatives with distinct and repeated eigenvalues. This approach also has an advantage that only requires eigenvalues and eigenvectors of interest, without solving the particular solutions of eigenvector derivatives. The Symmetric Quasi-Minimal Residual (SQMR) method is then adopted to solve the governing equations, only the existing factored (shifted) stiffness matrix from an iterative eigensolution such as the subspace iteration method or the Lanczos algorithm is utilized. The present method can deal with both cases of simple and repeated eigenvalues in a unified manner. Three numerical examples are given to illustrate the accuracy and validity of the proposed algorithm. Highly accurate approximations to the eigenvector derivatives are obtained within a few iteration steps, making a significant reduction of the computational effort. This method can be incorporated into a coupled eigensolver/derivative software module. In particular, it is applicable for finite element models with large sparse matrices.

Time simulation of flutter with large stiffness changes

NASA Technical Reports Server (NTRS)

Karpel, M.; Wieseman, C. D.

1992-01-01

Time simulation of flutter, involving large local structural changes, is formulated with a state-space model that is based on a relatively small number of generalized coordinates. Free-free vibration modes are first calculated for a nominal finite-element model with relatively large fictitious masses located at the area of structural changes. A low-frequency subset of these modes is then transformed into a set of structural modal coordinates with which the entire simulation is performed. These generalized coordinates and the associated oscillatory aerodynamic force coefficient matrices are used to construct an efficient time-domain, state-space model for basic aeroelastic case. The time simulation can then be performed by simply changing the mass, stiffness and damping coupling terms when structural changes occur. It is shown that the size of the aeroelastic model required for time simulation with large structural changes at a few a priori known locations is similar to that required for direct analysis of a single structural case. The method is applied to the simulation of an aeroelastic wind-tunnel model. The diverging oscillations are followed by the activation of a tip-ballast decoupling mechanism that stabilizes the system but may cause significant transient overshoots.

Time simulation of flutter with large stiffness changes

NASA Technical Reports Server (NTRS)

Karpel, Mordechay; Wieseman, Carol D.

1992-01-01

Time simulation of flutter, involving large local structural changes, is formulated with a state-space model that is based on a relatively small number of generalized coordinates. Free-free vibration modes are first calculated for a nominal finite-element model with relatively large fictitious masses located at the area of structural changes. A low-frequency subset of these modes is then transformed into a set of structural modal coordinates with which the entire simulation is performed. These generalized coordinates and the associated oscillatory aerodynamic force coefficient matrices are used to construct an efficient time-domain, state-space model for a basic aeroelastic case. The time simulation can then be performed by simply changing the mass, stiffness, and damping coupling terms when structural changes occur. It is shown that the size of the aeroelastic model required for time simulation with large structural changes at a few apriori known locations is similar to that required for direct analysis of a single structural case. The method is applied to the simulation of an aeroelastic wind-tunnel model. The diverging oscillations are followed by the activation of a tip-ballast decoupling mechanism that stabilizes the system but may cause significant transient overshoots.

In vitro model to study the effects of matrix stiffening on Ca2+ handling and myofilament function in isolated adult rat cardiomyocytes.

PubMed

van Deel, Elza D; Najafi, Aref; Fontoura, Dulce; Valent, Erik; Goebel, Max; Kardux, Kim; Falcão-Pires, Inês; van der Velden, Jolanda

2017-07-15

This paper describes a novel model that allows exploration of matrix-induced cardiomyocyte adaptations independent of the passive effect of matrix rigidity on cardiomyocyte function. Detachment of adult cardiomyocytes from the matrix enables the study of matrix effects on cell shortening, Ca 2+ handling and myofilament function. Cell shortening and Ca 2+ handling are altered in cardiomyocytes cultured for 24 h on a stiff matrix. Matrix stiffness-impaired cardiomyocyte contractility is reversed upon normalization of extracellular stiffness. Matrix stiffness-induced reduction in unloaded shortening is more pronounced in cardiomyocytes isolated from obese ZSF1 rats with heart failure with preserved ejection fraction compared to lean ZSF1 rats. Extracellular matrix (ECM) stiffening is a key element of cardiac disease. Increased rigidity of the ECM passively inhibits cardiac contraction, but if and how matrix stiffening also actively alters cardiomyocyte contractility is incompletely understood. In vitro models designed to study cardiomyocyte-matrix interaction lack the possibility to separate passive inhibition by a stiff matrix from active matrix-induced alterations of cardiomyocyte properties. Here we introduce a novel experimental model that allows exploration of cardiomyocyte functional alterations in response to matrix stiffening. Adult rat cardiomyocytes were cultured for 24 h on matrices of tuneable stiffness representing the healthy and the diseased heart and detached from their matrix before functional measurements. We demonstrate that matrix stiffening, independent of passive inhibition, reduces cell shortening and Ca 2+ handling but does not alter myofilament-generated force. Additionally, detachment of adult cultured cardiomyocytes allowed the transfer of cells from one matrix to another. This revealed that stiffness-induced cardiomyocyte changes are reversed when matrix stiffness is normalized. These matrix stiffness-induced changes in cardiomyocyte function could not be explained by adaptation in the microtubules. Additionally, cardiomyocytes isolated from stiff hearts of the obese ZSF1 rat model of heart failure with preserved ejection fraction show more pronounced reduction in unloaded shortening in response to matrix stiffening. Taken together, we introduce a method that allows evaluation of the influence of ECM properties on cardiomyocyte function separate from the passive inhibitory component of a stiff matrix. As such, it adds an important and physiologically relevant tool to investigate the functional consequences of cardiomyocyte-matrix interactions. © 2017 The Authors. The Journal of Physiology published by John Wiley & Sons Ltd on behalf of The Physiological Society.

Modeling the two-way feedback between contractility and matrix realignment reveals a nonlinear mode of cancer cell invasion

PubMed Central

Ahmadzadeh, Hossein; Webster, Marie R.; Behera, Reeti; Jimenez Valencia, Angela M.; Wirtz, Denis; Weeraratna, Ashani T.; Shenoy, Vivek B.

2017-01-01

Cancer cell invasion from primary tumors is mediated by a complex interplay between cellular adhesions, actomyosin-driven contractility, and the physical characteristics of the extracellular matrix (ECM). Here, we incorporate a mechanochemical free-energy–based approach to elucidate how the two-way feedback loop between cell contractility (induced by the activity of chemomechanical interactions such as Ca2+ and Rho signaling pathways) and matrix fiber realignment and strain stiffening enables the cells to polarize and develop contractile forces to break free from the tumor spheroids and invade into the ECM. Interestingly, through this computational model, we are able to identify a critical stiffness that is required by the matrix to break intercellular adhesions and initiate cell invasion. Also, by considering the kinetics of the cell movement, our model predicts a biphasic invasiveness with respect to the stiffness of the matrix. These predictions are validated by analyzing the invasion of melanoma cells in collagen matrices of varying concentration. Our model also predicts a positive correlation between the elongated morphology of the invading cells and the alignment of fibers in the matrix, suggesting that cell polarization is directly proportional to the stiffness and alignment of the matrix. In contrast, cells in nonfibrous matrices are found to be rounded and not polarized, underscoring the key role played by the nonlinear mechanics of fibrous matrices. Importantly, our model shows that mechanical principles mediated by the contractility of the cells and the nonlinearity of the ECM behavior play a crucial role in determining the phenotype of the cell invasion. PMID:28196892

Inclusion of transverse shear deformation in exact buckling and vibration analysis of composite plate assemblies

NASA Technical Reports Server (NTRS)

Anderson, Melvin S.; Kennedy, David

1992-01-01

The problem considered is the development of the necessary plate stiffnesses for use in a general purpose program for buckling and vibration of composite plate assemblies. The required stiffnesses are for the assumption of sinusoidal response along the plate length with transverse shear included. The method is based on the exact solution of the plate differential equations for a composite laminate having fully populated A, B, and D matrices which leads to a differential equation of tenth order.

The effect of material heterogeneities in long term multiscale seismic cycle simulations

NASA Astrophysics Data System (ADS)

Kyriakopoulos, C.; Richards-Dinger, K. B.; Dieterich, J. H.

2016-12-01

A fundamental part of the simulation of the earthquake cycles in large-scale multicycle earthquake simulators is the pre-computation of elastostatic Greens functions collected into the stiffness matrix (K). The stiffness matrices are typically based on the elastostatic solutions of Okada (1992), Gimbutas et al. (2012), or similar. While these analytic solutions are computationally very fast, they are limited to modeling a homogeneous isotropic half-space. It is thus unknown how such simulations may be affected by material heterogeneity characterizing the earth medium. We are currently working on the estimation of the effects of heterogeneous material properties in the earthquake simulator RSQSim (Richards-Dinger and Dieterich, 2012). In order to do that we are calculating elastostatic solutions in a heterogeneous medium using the Finite Element (FE) method instead of any of the analytical solutions. The investigated region is a 400 x 400 km area centered on the Anza zone in southern California. The fault system geometry is based on that of the UCERF3 deformation models in the area of interest, which we then implement in a finite element mesh using Trelis 15. The heterogeneous elastic structure is based on available tomographic data (seismic wavespeeds and density) for the region (SCEC CVM and Allam et al., 2014). For computation of the Greens functions we are using the open source FE code Defmod (https://bitbucket.org/stali/defmod/wiki/Home) to calculate the elastostatic solutions due to unit slip on each patch. Earthquake slip on the fault plane is implemented through linear constraint equations (Ali et al., 2014, Kyriakopoulos et al., 2013, Aagard et al, 2015) and more specifically with the use of Lagrange multipliers adjunction. The elementary responses are collected into the "heterogeneous" stiffness matrix Khet and used in RSQSim instead of the ones generated with Okada. Finally, we compare the RSQSim results based on the "heterogeneous" Khet with results from Khom (stiffness matrix generated from the same mesh as Khet but using homogeneous material properties). The estimation of the effect of heterogeneous material properties in the seismic cycles simulated by RSQSim is a needed experiment that will allow us to evaluate the impact of heterogeneities in earthquake simulators.

The inverted pendulum model of bipedal standing cannot be stabilized through direct feedback of force and contractile element length and velocity at realistic series elastic element stiffness.

PubMed

van Soest, A J Knoek; Rozendaal, Leonard A

2008-07-01

Control of bipedal standing is typically analyzed in the context of a single-segment inverted pendulum model. The stiffness K (SE) of the series elastic element that transmits the force generated by the contractile elements of the ankle plantarflexors to the skeletal system has been reported to be smaller in magnitude than the destabilizing gravitational stiffness K ( g ). In this study, we assess, in case K (SE) + K ( g ) < 0, if bipedal standing can be locally stable under direct feedback of contractile element length, contractile element velocity (both sensed by muscle spindles) and muscle force (sensed by Golgi tendon organs) to alpha-motoneuron activity. A theoretical analysis reveals that even though positive feedback of force may increase the stiffness of the muscle-tendon complex to values well over the destabilizing gravitational stiffness, dynamic instability makes it impossible to obtain locally stable standing under the conditions assumed.

A theoretical analysis and finite element simulation of fixator-bone system stiffness on healing progression.

PubMed

Li, Jianfeng; Zhao, Xia; Hu, Xiaojie; Tao, Chunjing; Ji, Run

2018-03-01

The unilateral external fixator has become a quick and easy application for fracture stabilization of the extremities; the main value for evaluation of mechanical stability of the external fixator is stiffness. The stiffness property of the external fixator affects the local biomechanical environment of fractured bone. In this study, a theoretical model with changing Young's modulus of the callus is established by using the Castigliano's theory, investigating compression stiffness, torsional stiffness and bending stiffness of the fixator-bone system during the healing process. The effects of pin deviation angle on three stiffness methods are also investigated. In addition, finite element simulation is discussed regarding the stress distribution between the fixator and bone. The results reveal the three stiffness evaluation methods are similar for the fixator-bone system. Finite element simulation shows that with increased healing time, the transmission of the load between the fixator and bone are different. In addition, the finite element analyses verify the conclusions obtained from the theoretical model. This work helps orthopedic doctors to monitor the progression of fracture healing and determine the appropriate time for removal of a fixation device and provide important theoretical methodology.

Stiffness modeling of compliant parallel mechanisms and applications in the performance analysis of a decoupled parallel compliant stage

NASA Astrophysics Data System (ADS)

Jiang, Yao; Li, Tie-Min; Wang, Li-Ping

2015-09-01

This paper investigates the stiffness modeling of compliant parallel mechanism (CPM) based on the matrix method. First, the general compliance matrix of a serial flexure chain is derived. The stiffness modeling of CPMs is next discussed in detail, considering the relative positions of the applied load and the selected displacement output point. The derived stiffness models have simple and explicit forms, and the input, output, and coupling stiffness matrices of the CPM can easily be obtained. The proposed analytical model is applied to the stiffness modeling and performance analysis of an XY parallel compliant stage with input and output decoupling characteristics. Then, the key geometrical parameters of the stage are optimized to obtain the minimum input decoupling degree. Finally, a prototype of the compliant stage is developed and its input axial stiffness, coupling characteristics, positioning resolution, and circular contouring performance are tested. The results demonstrate the excellent performance of the compliant stage and verify the effectiveness of the proposed theoretical model. The general stiffness models provided in this paper will be helpful for performance analysis, especially in determining coupling characteristics, and the structure optimization of the CPM.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fukuoka, T.

Many studies have been devoted to investigate how the maximum stress occurring in the bolted joint could be reduced. Patterson and Kenny suggest that a modified nut with a straight bevel at the bearing surface is effective. However, they only dealt with M30, and estimations on the nut geometry had not been necessarily sufficient. In this study, an extensive finite element approach for solving general multi-body contact problem is proposed by incorporating a regularization method into stiffness matrices with singularity involved; thus, numerical analyses are executed to accurately determine the optimal shape of the modified nut for various design factors.more » A modified nut with a curved bevel is also treated, and it is concluded that the modified nuts are significantly effective for bolts with larger nominal diameter and fine pitch, and are practically useful compared to pitch modification and tapered thread methods.« less

Rotordynamic analysis using the Complex Transfer Matrix: An application to elastomer supports using the viscoelastic correspondence principle

NASA Astrophysics Data System (ADS)

Varney, Philip; Green, Itzhak

2014-11-01

Numerous methods are available to calculate rotordynamic whirl frequencies, including analytic methods, finite element analysis, and the transfer matrix method. The typical real-valued transfer matrix (RTM) suffers from several deficiencies, including lengthy computation times and the inability to distinguish forward and backward whirl. Though application of complex coordinates in rotordynamic analysis is not novel per se, specific advantages gained from using such coordinates in a transfer matrix analysis have yet to be elucidated. The present work employs a complex coordinate redefinition of the transfer matrix to obtain reduced forms of the elemental transfer matrices in inertial and rotating reference frames, including external stiffness and damping. Application of the complex-valued state variable redefinition results in a reduction of the 8×8 RTM to the 4×4 Complex Transfer Matrix (CTM). The CTM is advantageous in that it intrinsically separates forward and backward whirl, eases symbolic manipulation by halving the transfer matrices’ dimension, and provides significant improvement in computation time. A symbolic analysis is performed on a simple overhung rotor to demonstrate the mathematical motivation for whirl frequency separation. The CTM's utility is further shown by analyzing a rotordynamic system supported by viscoelastic elastomer rings. Viscoelastic elastomer ring supports can provide significant damping while reducing the cost and complexity associated with conventional components such as squeeze film dampers. The stiffness and damping of a viscoelastic damper ring are determined herein as a function of whirl frequency using the viscoelastic correspondence principle and a constitutive fractional calculus viscoelasticity model. The CTM is then employed to obtain the characteristic equation, where the whirl frequency dependent stiffness and damping of the elastomer supports are included. The Campbell diagram is shown, demonstrating the CTM's ability to intrinsically separate synchronous whirl direction for a non-trivial rotordynamic system. Good agreement is found between the CTM results and previously obtained analytic and experimental results for the elastomer ring supported rotordynamic system.

Improved accuracy for finite element structural analysis via an integrated force method

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Hopkins, D. A.; Aiello, R. A.; Berke, L.

1992-01-01

A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.

High frequency, multi-axis dynamic stiffness analysis of a fractionally damped elastomeric isolator using continuous system theory

NASA Astrophysics Data System (ADS)

Fredette, Luke; Singh, Rajendra

2017-02-01

A spectral element approach is proposed to determine the multi-axis dynamic stiffness terms of elastomeric isolators with fractional damping over a broad range of frequencies. The dynamic properties of a class of cylindrical isolators are modeled by using the continuous system theory in terms of homogeneous rods or Timoshenko beams. The transfer matrix type dynamic stiffness expressions are developed from exact harmonic solutions given translational or rotational displacement excitations. Broadband dynamic stiffness magnitudes (say up to 5 kHz) are computationally verified for axial, torsional, shear, flexural, and coupled stiffness terms using a finite element model. Some discrepancies are found between finite element and spectral element models for the axial and flexural motions, illustrating certain limitations of each method. Experimental validation is provided for an isolator with two cylindrical elements (that work primarily in the shear mode) using dynamic measurements, as reported in the prior literature, up to 600 Hz. Superiority of the fractional damping formulation over structural or viscous damping models is illustrated via experimental validation. Finally, the strengths and limitations of the spectral element approach are briefly discussed.

Prediction of local proximal tibial subchondral bone structural stiffness using subject-specific finite element modeling: Effect of selected density-modulus relationship.

PubMed

Nazemi, S Majid; Amini, Morteza; Kontulainen, Saija A; Milner, Jaques S; Holdsworth, David W; Masri, Bassam A; Wilson, David R; Johnston, James D

2015-08-01

Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain initiation. Calculation of bone elastic moduli from image data is a basic step when constructing finite element models. However, different relationships between elastic moduli and imaged density (known as density-modulus relationships) have been reported in the literature. The objective of this study was to apply seven different trabecular-specific and two cortical-specific density-modulus relationships from the literature to finite element models of proximal tibia subchondral bone, and identify the relationship(s) that best predicted experimentally measured local subchondral structural stiffness with highest explained variance and least error. Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using published density-modulus relationships and mapped to corresponding finite element models. Proximal tibial structural stiffness values were compared to experimentally measured stiffness values from in-situ macro-indentation testing directly on the subchondral bone surface (47 indentation points). Regression lines between experimentally measured and finite element calculated stiffness had R(2) values ranging from 0.56 to 0.77. Normalized root mean squared error varied from 16.6% to 337.6%. Of the 21 evaluated density-modulus relationships in this study, Goulet combined with Snyder and Schneider or Rho appeared most appropriate for finite element modeling of local subchondral bone structural stiffness. Though, further studies are needed to optimize density-modulus relationships and improve finite element estimates of local subchondral bone structural stiffness. Copyright © 2015 Elsevier Ltd. All rights reserved.

Mechanical phenotype of cancer cells: cell softening and loss of stiffness sensing.

PubMed

Lin, Hsi-Hui; Lin, Hsiu-Kuan; Lin, I-Hsuan; Chiou, Yu-Wei; Chen, Horn-Wei; Liu, Ching-Yi; Harn, Hans I-Chen; Chiu, Wen-Tai; Wang, Yang-Kao; Shen, Meng-Ru; Tang, Ming-Jer

2015-08-28

The stiffness sensing ability is required to respond to the stiffness of the matrix. Here we determined whether normal cells and cancer cells display distinct mechanical phenotypes. Cancer cells were softer than their normal counterparts, regardless of the type of cancer (breast, bladder, cervix, pancreas, or Ha-RasV12-transformed cells). When cultured on matrices of varying stiffness, low stiffness decreased proliferation in normal cells, while cancer cells and transformed cells lost this response. Thus, cancer cells undergo a change in their mechanical phenotype that includes cell softening and loss of stiffness sensing. Caveolin-1, which is suppressed in many tumor cells and in oncogene-transformed cells, regulates the mechanical phenotype. Caveolin-1-upregulated RhoA activity and Y397FAK phosphorylation directed actin cap formation, which was positively correlated with cell elasticity and stiffness sensing in fibroblasts. Ha-RasV12-induced transformation and changes in the mechanical phenotypes were reversed by re-expression of caveolin-1 and mimicked by the suppression of caveolin-1 in normal fibroblasts. This is the first study to describe this novel role for caveolin-1, linking mechanical phenotype to cell transformation. Furthermore, mechanical characteristics may serve as biomarkers for cell transformation.

Local 3D matrix microenvironment regulates cell migration through spatiotemporal dynamics of contractility-dependent adhesions

NASA Astrophysics Data System (ADS)

Doyle, Andrew D.; Carvajal, Nicole; Jin, Albert; Matsumoto, Kazue; Yamada, Kenneth M.

2015-11-01

The physical properties of two-dimensional (2D) extracellular matrices (ECMs) modulate cell adhesion dynamics and motility, but little is known about the roles of local microenvironmental differences in three-dimensional (3D) ECMs. Here we generate 3D collagen gels of varying matrix microarchitectures to characterize their regulation of 3D adhesion dynamics and cell migration. ECMs containing bundled fibrils demonstrate enhanced local adhesion-scale stiffness and increased adhesion stability through balanced ECM/adhesion coupling, whereas highly pliable reticular matrices promote adhesion retraction. 3D adhesion dynamics are locally regulated by ECM rigidity together with integrin/ECM association and myosin II contractility. Unlike 2D migration, abrogating contractility stalls 3D migration regardless of ECM pore size. We find force is not required for clustering of activated integrins on 3D native collagen fibrils. We propose that efficient 3D migration requires local balancing of contractility with ECM stiffness to stabilize adhesions, which facilitates the detachment of activated integrins from ECM fibrils.

Towards a large-scale scalable adaptive heart model using shallow tree meshes

NASA Astrophysics Data System (ADS)

Krause, Dorian; Dickopf, Thomas; Potse, Mark; Krause, Rolf

2015-10-01

Electrophysiological heart models are sophisticated computational tools that place high demands on the computing hardware due to the high spatial resolution required to capture the steep depolarization front. To address this challenge, we present a novel adaptive scheme for resolving the deporalization front accurately using adaptivity in space. Our adaptive scheme is based on locally structured meshes. These tensor meshes in space are organized in a parallel forest of trees, which allows us to resolve complicated geometries and to realize high variations in the local mesh sizes with a minimal memory footprint in the adaptive scheme. We discuss both a non-conforming mortar element approximation and a conforming finite element space and present an efficient technique for the assembly of the respective stiffness matrices using matrix representations of the inclusion operators into the product space on the so-called shallow tree meshes. We analyzed the parallel performance and scalability for a two-dimensional ventricle slice as well as for a full large-scale heart model. Our results demonstrate that the method has good performance and high accuracy.

A Feasibility Study on a Parallel Mechanism for Examining the Space Shuttle Orbiter Payload Bay Radiators

NASA Technical Reports Server (NTRS)

Roberts, Rodney G.; LopezdelCastillo, Eduardo

1996-01-01

The goal of the project was to develop the necessary analysis tools for a feasibility study of a cable suspended robot system for examining the space shuttle orbiter payload bay radiators These tools were developed to address design issues such as workspace size, tension requirements on the cable, the necessary accuracy and resolution requirements and the stiffness and movement requirements of the system. This report describes the mathematical models for studying the inverse kinematics, statics, and stiffness of the robot. Each model is described by a matrix. The manipulator Jacobian was also related to the stiffness matrix, which characterized the stiffness of the system. Analysis tools were then developed based on the singular value decomposition (SVD) of the corresponding matrices. It was demonstrated how the SVD can be used to quantify the robot's performance and to provide insight into different design issues.

An experimental nonlinear low dynamic stiffness device for shock isolation

NASA Astrophysics Data System (ADS)

Francisco Ledezma-Ramirez, Diego; Ferguson, Neil S.; Brennan, Michael J.; Tang, Bin

2015-07-01

The problem of shock generated vibration is very common in practice and difficult to isolate due to the high levels of excitation involved and its transient nature. If not properly isolated it could lead to large transmitted forces and displacements. Typically, classical shock isolation relies on the use of passive stiffness elements to absorb energy by deformation and some damping mechanism to dissipate residual vibration. The approach of using nonlinear stiffness elements is explored in this paper, focusing in providing an isolation system with low dynamic stiffness. The possibilities of using such a configuration for a shock mount are studied experimentally following previous theoretical models. The model studied considers electromagnets and permanent magnets in order to obtain nonlinear stiffness forces using different voltage configurations. It is found that the stiffness nonlinearities could be advantageous in improving shock isolation in terms of absolute displacement and acceleration response when compared with linear elastic elements.

A Comparison between Element Salience versus Context as Item Difficulty Factors in Raven's Matrices

ERIC Educational Resources Information Center

Perez-Salas, Claudia P.; Streiner, David L.; Roberts, Maxwell J.

2012-01-01

The nature of contextual facilitation effects for items derived from Raven's Progressive Matrices was investigated in two experiments. For these, the original matrices were modified, creating either abstract versions with high element salience, or versions which comprised realistic entities set in familiar contexts. In order to replicate and…

In vitro model to study the effects of matrix stiffening on Ca2+ handling and myofilament function in isolated adult rat cardiomyocytes

PubMed Central

Najafi, Aref; Fontoura, Dulce; Valent, Erik; Goebel, Max; Kardux, Kim; Falcão‐Pires, Inês; van der Velden, Jolanda

2017-01-01

Key points This paper describes a novel model that allows exploration of matrix‐induced cardiomyocyte adaptations independent of the passive effect of matrix rigidity on cardiomyocyte function.Detachment of adult cardiomyocytes from the matrix enables the study of matrix effects on cell shortening, Ca2+ handling and myofilament function.Cell shortening and Ca2+ handling are altered in cardiomyocytes cultured for 24 h on a stiff matrix.Matrix stiffness‐impaired cardiomyocyte contractility is reversed upon normalization of extracellular stiffness.Matrix stiffness‐induced reduction in unloaded shortening is more pronounced in cardiomyocytes isolated from obese ZSF1 rats with heart failure with preserved ejection fraction compared to lean ZSF1 rats. Abstract Extracellular matrix (ECM) stiffening is a key element of cardiac disease. Increased rigidity of the ECM passively inhibits cardiac contraction, but if and how matrix stiffening also actively alters cardiomyocyte contractility is incompletely understood. In vitro models designed to study cardiomyocyte–matrix interaction lack the possibility to separate passive inhibition by a stiff matrix from active matrix‐induced alterations of cardiomyocyte properties. Here we introduce a novel experimental model that allows exploration of cardiomyocyte functional alterations in response to matrix stiffening. Adult rat cardiomyocytes were cultured for 24 h on matrices of tuneable stiffness representing the healthy and the diseased heart and detached from their matrix before functional measurements. We demonstrate that matrix stiffening, independent of passive inhibition, reduces cell shortening and Ca2+ handling but does not alter myofilament‐generated force. Additionally, detachment of adult cultured cardiomyocytes allowed the transfer of cells from one matrix to another. This revealed that stiffness‐induced cardiomyocyte changes are reversed when matrix stiffness is normalized. These matrix stiffness‐induced changes in cardiomyocyte function could not be explained by adaptation in the microtubules. Additionally, cardiomyocytes isolated from stiff hearts of the obese ZSF1 rat model of heart failure with preserved ejection fraction show more pronounced reduction in unloaded shortening in response to matrix stiffening. Taken together, we introduce a method that allows evaluation of the influence of ECM properties on cardiomyocyte function separate from the passive inhibitory component of a stiff matrix. As such, it adds an important and physiologically relevant tool to investigate the functional consequences of cardiomyocyte–matrix interactions. PMID:28485491

Optimizing finite element predictions of local subchondral bone structural stiffness using neural network-derived density-modulus relationships for proximal tibial subchondral cortical and trabecular bone.

PubMed

Nazemi, S Majid; Amini, Morteza; Kontulainen, Saija A; Milner, Jaques S; Holdsworth, David W; Masri, Bassam A; Wilson, David R; Johnston, James D

2017-01-01

Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain. However, it is unclear what density-modulus equation(s) should be applied with subchondral cortical and subchondral trabecular bone when constructing finite element models of the tibia. Using a novel approach applying neural networks, optimization, and back-calculation against in situ experimental testing results, the objective of this study was to identify subchondral-specific equations that optimized finite element predictions of local structural stiffness at the proximal tibial subchondral surface. Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using multiple density-modulus equations (93 total variations) then mapped to corresponding finite element models. For each variation, root mean squared error was calculated between finite element prediction and in situ measured stiffness at 47 indentation sites. Resulting errors were used to train an artificial neural network, which provided an unlimited number of model variations, with corresponding error, for predicting stiffness at the subchondral bone surface. Nelder-Mead optimization was used to identify optimum density-modulus equations for predicting stiffness. Finite element modeling predicted 81% of experimental stiffness variance (with 10.5% error) using optimized equations for subchondral cortical and trabecular bone differentiated with a 0.5g/cm 3 density. In comparison with published density-modulus relationships, optimized equations offered improved predictions of local subchondral structural stiffness. Further research is needed with anisotropy inclusion, a smaller voxel size and de-blurring algorithms to improve predictions. Copyright © 2016 Elsevier Ltd. All rights reserved.

Improved accuracy for finite element structural analysis via a new integrated force method

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.; Aiello, Robert A.; Berke, Laszlo

1992-01-01

A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.

A comparative study on dynamic stiffness in typical finite element model and multi-body model of C6-C7 cervical spine segment.

PubMed

Wang, Yawei; Wang, Lizhen; Du, Chengfei; Mo, Zhongjun; Fan, Yubo

2016-06-01

In contrast to numerous researches on static or quasi-static stiffness of cervical spine segments, very few investigations on their dynamic stiffness were published. Currently, scale factors and estimated coefficients were usually used in multi-body models for including viscoelastic properties and damping effects, meanwhile viscoelastic properties of some tissues were unavailable for establishing finite element models. Because dynamic stiffness of cervical spine segments in these models were difficult to validate because of lacking in experimental data, we tried to gain some insights on current modeling methods through studying dynamic stiffness differences between these models. A finite element model and a multi-body model of C6-C7 segment were developed through using available material data and typical modeling technologies. These two models were validated with quasi-static response data of the C6-C7 cervical spine segment. Dynamic stiffness differences were investigated through controlling motions of C6 vertebrae at different rates and then comparing their reaction forces or moments. Validation results showed that both the finite element model and the multi-body model could generate reasonable responses under quasi-static loads, but the finite element segment model exhibited more nonlinear characters. Dynamic response investigations indicated that dynamic stiffness of this finite element model might be underestimated because of the absence of dynamic stiffen effect and damping effects of annulus fibrous, while representation of these effects also need to be improved in current multi-body model. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

A 2D Daubechies finite wavelet domain method for transient wave response analysis in shear deformable laminated composite plates

NASA Astrophysics Data System (ADS)

Nastos, C. V.; Theodosiou, T. C.; Rekatsinas, C. S.; Saravanos, D. A.

2018-03-01

An efficient numerical method is developed for the simulation of dynamic response and the prediction of the wave propagation in composite plate structures. The method is termed finite wavelet domain method and takes advantage of the outstanding properties of compactly supported 2D Daubechies wavelet scaling functions for the spatial interpolation of displacements in a finite domain of a plate structure. The development of the 2D wavelet element, based on the first order shear deformation laminated plate theory is described and equivalent stiffness, mass matrices and force vectors are calculated and synthesized in the wavelet domain. The transient response is predicted using the explicit central difference time integration scheme. Numerical results for the simulation of wave propagation in isotropic, quasi-isotropic and cross-ply laminated plates are presented and demonstrate the high spatial convergence and problem size reduction obtained by the present method.

Finite Element Modeling of the NASA Langley Aluminum Testbed Cylinder

NASA Technical Reports Server (NTRS)

Grosveld, Ferdinand W.; Pritchard, Joselyn I.; Buehrle, Ralph D.; Pappa, Richard S.

2002-01-01

The NASA Langley Aluminum Testbed Cylinder (ATC) was designed to serve as a universal structure for evaluating structural acoustic codes, modeling techniques and optimization methods used in the prediction of aircraft interior noise. Finite element models were developed for the components of the ATC based on the geometric, structural and material properties of the physical test structure. Numerically predicted modal frequencies for the longitudinal stringer, ring frame and dome component models, and six assembled ATC configurations were compared with experimental modal survey data. The finite element models were updated and refined, using physical parameters, to increase correlation with the measured modal data. Excellent agreement, within an average 1.5% to 2.9%, was obtained between the predicted and measured modal frequencies of the stringer, frame and dome components. The predictions for the modal frequencies of the assembled component Configurations I through V were within an average 2.9% and 9.1%. Finite element modal analyses were performed for comparison with 3 psi and 6 psi internal pressurization conditions in Configuration VI. The modal frequencies were predicted by applying differential stiffness to the elements with pressure loading and creating reduced matrices for beam elements with offsets inside external superelements. The average disagreement between the measured and predicted differences for the 0 psi and 6 psi internal pressure conditions was less than 0.5%. Comparably good agreement was obtained for the differences between the 0 psi and 3 psi measured and predicted internal pressure conditions.

Element-topology-independent preconditioners for parallel finite element computations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

New class of thermosetting plastics has improved strength, thermal and chemical stability

NASA Technical Reports Server (NTRS)

Burns, E. A.; Dubrow, B.; Lubowitz, H. R.

1967-01-01

New class of thermosetting plastics has high hydrocarbon content, high stiffness, thermal stability, humidity resistance, and workability in the precured state. It is designated cyclized polydiene urethane, and is applicable as matrices to prepare chemically stable ablative materials for rocket nose cones of nozzles.

Calculation of reaction forces in the boiler supports using the method of equivalent stiffness of membrane wall.

PubMed

Sertić, Josip; Kozak, Dražan; Samardžić, Ivan

2014-01-01

The values of reaction forces in the boiler supports are the basis for the dimensioning of bearing steel structure of steam boiler. In this paper, the application of the method of equivalent stiffness of membrane wall is proposed for the calculation of reaction forces. The method of equalizing displacement, as the method of homogenization of membrane wall stiffness, was applied. On the example of "Milano" boiler, using the finite element method, the calculation of reactions in the supports for the real geometry discretized by the shell finite element was made. The second calculation was performed with the assumption of ideal stiffness of membrane walls and the third using the method of equivalent stiffness of membrane wall. In the third case, the membrane walls are approximated by the equivalent orthotropic plate. The approximation of membrane wall stiffness is achieved using the elasticity matrix of equivalent orthotropic plate at the level of finite element. The obtained results were compared, and the advantages of using the method of equivalent stiffness of membrane wall for the calculation of reactions in the boiler supports were emphasized.

Acoustic and elastic properties of Sn(2)P(2)S(6) crystals.

PubMed

Mys, O; Martynyuk-Lototska, I; Grabar, A; Vlokh, R

2009-07-01

We present the results concerned with acoustic and elastic properties of Sn(2)P(2)S(6) crystals. The complete matrices of elastic stiffness and compliance coefficients are determined in both the crystallographic coordinate system and the system associated with eigenvectors of the elastic stiffness tensor. The acoustic slowness surfaces are constructed and the propagation and polarization directions of the slowest acoustic waves promising for acousto-optic interactions are determined on this basis. The acoustic obliquity angle and the deviation of polarization of the acoustic waves from purely transverse or longitudinal states are quantitatively analysed.

Asymptotic (h tending to infinity) absolute stability for BDFs applied to stiff differential equations. [Backward Differentiation Formulas

NASA Technical Reports Server (NTRS)

Krogh, F. T.; Stewart, K.

1984-01-01

Methods based on backward differentiation formulas (BDFs) for solving stiff differential equations require iterating to approximate the solution of the corrector equation on each step. One hope for reducing the cost of this is to make do with iteration matrices that are known to have errors and to do no more iterations than are necessary to maintain the stability of the method. This paper, following work by Klopfenstein, examines the effect of errors in the iteration matrix on the stability of the method. Application of the results to an algorithm is discussed briefly.

Tuning three-dimensional collagen matrix stiffness independently of collagen concentration modulates endothelial cell behavior.

PubMed

Mason, Brooke N; Starchenko, Alina; Williams, Rebecca M; Bonassar, Lawrence J; Reinhart-King, Cynthia A

2013-01-01

Numerous studies have described the effects of matrix stiffening on cell behavior using two-dimensional synthetic surfaces; however, less is known about the effects of matrix stiffening on cells embedded in three-dimensional in vivo-like matrices. A primary limitation in investigating the effects of matrix stiffness in three dimensions is the lack of materials that can be tuned to control stiffness independently of matrix density. Here, we use collagen-based scaffolds where the mechanical properties are tuned using non-enzymatic glycation of the collagen in solution, prior to polymerization. Collagen solutions glycated prior to polymerization result in collagen gels with a threefold increase in compressive modulus without significant changes to the collagen architecture. Using these scaffolds, we show that endothelial cell spreading increases with matrix stiffness, as does the number and length of angiogenic sprouts and the overall spheroid outgrowth. Differences in sprout length are maintained even when the receptor for advanced glycation end products is inhibited. Our results demonstrate the ability to de-couple matrix stiffness from matrix density and structure in collagen gels, and that increased matrix stiffness results in increased sprouting and outgrowth. Copyright © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A highly precise frequency-based method for estimating the tension of an inclined cable with unknown boundary conditions

NASA Astrophysics Data System (ADS)

Ma, Lin

2017-11-01

This paper develops a method for precisely determining the tension of an inclined cable with unknown boundary conditions. First, the nonlinear motion equation of an inclined cable is derived, and a numerical model of the motion of the cable is proposed using the finite difference method. The proposed numerical model includes the sag-extensibility, flexural stiffness, inclination angle and rotational stiffness at two ends of the cable. Second, the influence of the dynamic parameters of the cable on its frequencies is discussed in detail, and a method for precisely determining the tension of an inclined cable is proposed based on the derivatives of the eigenvalues of the matrices. Finally, a multiparameter identification method is developed that can simultaneously identify multiple parameters, including the rotational stiffness at two ends. This scheme is applicable to inclined cables with varying sag, varying flexural stiffness and unknown boundary conditions. Numerical examples indicate that the method provides good precision. Because the parameters of cables other than tension (e.g., the flexural stiffness and rotational stiffness at the ends) are not accurately known in practical engineering, the multiparameter identification method could further improve the accuracy of cable tension measurements.

Use of Mueller and non-Mueller matrices to describe polarization properties of telescope-based polarimeters

NASA Astrophysics Data System (ADS)

Seagraves, P. H.; Elmore, David F.

1994-09-01

Systems using optical elements such as linear polarizers, retarders, and mirrors can be represented by Mueller matrices. Some polarimeters include elements with time-varying polarization properties, multiple light beams, light detectors, and signal processing equipment. Standard Mueller matrix forms describing time-varying retarders, and beam splitters are presented, as well as non-Mueller matrices which describe detection and signal processing. These matrices provide a compact and intuitive mathematical description of polarimeter response which can aid in the refining of instrument designs.

Static, free vibration and thermal analysis of composite plates and shells using a flat triangular shell element

NASA Astrophysics Data System (ADS)

Kapania, R. K.; Mohan, P.

1996-09-01

Finite element static, free vibration and thermal analysis of thin laminated plates and shells using a three noded triangular flat shell element is presented. The flat shell element is a combination of the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element derived from the Linear Strain Triangular (LST) element with a total of 18 degrees of freedom (3 translations and 3 rotations per node). Explicit formulations are used for the membrane, bending and membrane-bending coupling stiffness matrices and the thermal load vector. Due to a strong analogy between the induced strain caused by the thermal field and the strain induced in a structure due to an electric field the present formulation is readily applicable for the analysis of structures excited by surface bonded or embedded piezoelectric actuators. The results are presented for (i) static analysis of (a) simply supported square plates under doubly sinusoidal load and uniformly distributed load (b) simply supported spherical shells under a uniformly distributed load, (ii) free vibration analysis of (a) square cantilever plates, (b) skew cantilever plates and (c) simply supported spherical shells; (iii) Thermal deformation analysis of (a) simply supported square plates, (b) simply supported-clamped square plate and (c) simply supported spherical shells. A numerical example is also presented demonstrating the application of the present formulation to analyse a symmetrically laminated graphite/epoxy laminate excited by a layer of piezoelectric polyvinylidene flouride (PVDF). The results presented are in good agreement with those available in the literature.

Pressure deformation of tires using differential stiffness for triangular solid-of-revolution elements

NASA Technical Reports Server (NTRS)

Chen, C. H. S.

1975-01-01

The derivation is presented of the differential stiffness for triangular solid of revolution elements. The derivation takes into account the element rigid body rotation only, the rotation being about the circumferential axis. Internal pressurization of a pneumatic tire is used to illustrate the application of this feature.

Effect of Bending Stiffness of the Electroactive Polymer Element on the Performance of a Hybrid Actuator System (HYBAS)

NASA Technical Reports Server (NTRS)

Xu, Tian-Bing; Su, Ji; Jiang, Xiaoning; Rehrig, Paul W.; Zhang, Shujun; Shrout, Thomas R.; Zhang, Qiming

2006-01-01

An electroactive polymer (EAP)-ceramic hybrid actuation system (HYBAS) was developed recently at NASA Langley Research Center. This paper focuses on the effect of the bending stiffness of the EAP component on the performance of a HYBAS, in which the actuation of the EAP element can match the theoretical prediction at various length/thickness ratios for a constant elastic modulus of the EAP component. The effects on the bending stiffness of the elastic modulus and length/thickness ratio of the EAP component were studied. A critical bending stiffness to keep the actuation of the EAP element suitable for a rigid beam theory-based modeling was found for electron irradiated P(VDF-TrFE) copolymer. For example, the agreement of experimental data and theoretical modeling for a HYBAS with the length/thickness ratio of EAP element at 375 times is demonstrated. However, the beam based theoretical modeling becomes invalid (i.e., the profile of the HYBAS movement does not follow the prediction of theoretical modeling) when the bending stiffness is lower than a critical value.

Calculation of Reaction Forces in the Boiler Supports Using the Method of Equivalent Stiffness of Membrane Wall

PubMed Central

Sertić, Josip; Kozak, Dražan; Samardžić, Ivan

2014-01-01

The values of reaction forces in the boiler supports are the basis for the dimensioning of bearing steel structure of steam boiler. In this paper, the application of the method of equivalent stiffness of membrane wall is proposed for the calculation of reaction forces. The method of equalizing displacement, as the method of homogenization of membrane wall stiffness, was applied. On the example of “Milano” boiler, using the finite element method, the calculation of reactions in the supports for the real geometry discretized by the shell finite element was made. The second calculation was performed with the assumption of ideal stiffness of membrane walls and the third using the method of equivalent stiffness of membrane wall. In the third case, the membrane walls are approximated by the equivalent orthotropic plate. The approximation of membrane wall stiffness is achieved using the elasticity matrix of equivalent orthotropic plate at the level of finite element. The obtained results were compared, and the advantages of using the method of equivalent stiffness of membrane wall for the calculation of reactions in the boiler supports were emphasized. PMID:24959612

The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

NASA Astrophysics Data System (ADS)

Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.

2018-04-01

The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

Multiscale Modeling of Carbon Nanotube-Epoxy Nanocomposites

NASA Astrophysics Data System (ADS)

Fasanella, Nicholas A.

Epoxy-composites are widely used in the aerospace industry. In order to improve upon stiffness and thermal conductivity; carbon nanotube additives to epoxies are being explored. This dissertation presents multiscale modeling techniques to study the engineering properties of single walled carbon nanotube (SWNT)-epoxy nanocomposites, consisting of pristine and covalently functionalized systems. Using Molecular Dynamics (MD), thermomechanical properties were calculated for a representative polymer unit cell. Finite Element (FE) and orientation distribution function (ODF) based methods were used in a multiscale framework to obtain macroscale properties. An epoxy network was built using the dendrimer growth approach. The epoxy model was verified by matching the experimental glass transition temperature, density, and dilatation. MD, via the constant valence force field (CVFF), was used to explore the mechanical and dilatometric effects of adding pristine and functionalized SWNTs to epoxy. Full stiffness matrices and linear coefficient of thermal expansion vectors were obtained. The Green-Kubo method was used to investigate the thermal conductivity as a function of temperature for the various nanocomposites. Inefficient phonon transport at the ends of nanotubes is an important factor in the thermal conductivity of the nanocomposites, and for this reason discontinuous nanotubes were modeled in addition to long nanotubes. To obtain continuum-scale elastic properties from the MD data, multiscale modeling was considered to give better control over the volume fraction of nanotubes, and investigate the effects of nanotube alignment. Two methods were considered; an FE based method, and an ODF based method. The FE method probabilistically assigned elastic properties of elements from the MD lattice results based on the desired volume fraction and alignment of the nanotubes. For the ODF method, a distribution function was generated based on the desired amount of nanotube alignment; and the stiffness matrix was calculated. A rule of mixture approach was implemented in the ODF model to vary the SWNT volume fraction. Both the ODF and FE models are compared and contrasted. ODF analysis is significantly faster for nanocomposites and is a novel contribution in this thesis. Multiscale modeling allows for the effects of nanofillers in epoxy systems to be characterized without having to run costly experiments.

Direct influence of culture dimensionality on human mesenchymal stem cell differentiation at various matrix stiffnesses using a fibrous self-assembling peptide hydrogel.

PubMed

Hogrebe, Nathaniel J; Gooch, Keith J

2016-09-01

Much is unknown about the effects of culture dimensionality on cell behavior due to the lack of biomimetic substrates that are suitable for directly comparing cells grown on two-dimensional (2D) and encapsulated within three-dimensional (3D) matrices of the same stiffness and biochemistry. To overcome this limitation, we used a self-assembling peptide hydrogel system that has tunable stiffness and cell-binding site density as well as a fibrous microarchitecture resembling the structure of collagen. We investigated the effect of culture dimensionality on human mesenchymal stem cell differentiation at different values of matrix stiffness (G' = 0.25, 1.25, 5, and 10 kPa) and a constant RGD (Arg-Gly-Asp) binding site concentration. In the presence of the same soluble induction factors, culture on top of stiff gels facilitated the most efficient osteogenesis, while encapsulation within the same stiff gels resulted in a switch to predominantly terminal chondrogenesis. Adipogenesis dominated at soft conditions, and 3D culture induced better adipogenic differentiation than 2D culture at a given stiffness. Interestingly, initial matrix-induced cell morphology was predictive of these end phenotypes. Furthermore, optimal culture conditions corresponded to each cell type's natural niche within the body, highlighting the importance of incorporating native matrix dimensionality and stiffness into tissue engineering strategies. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 104A: 2356-2368, 2016. © 2016 Wiley Periodicals, Inc.

Dissecting the Impact of Matrix Anchorage and Elasticity in Cell Adhesion

PubMed Central

Pompe, Tilo; Glorius, Stefan; Bischoff, Thomas; Uhlmann, Ina; Kaufmann, Martin; Brenner, Sebastian; Werner, Carsten

2009-01-01

Abstract Extracellular matrices determine cellular fate decisions through the regulation of intracellular force and stress. Previous studies suggest that matrix stiffness and ligand anchorage cause distinct signaling effects. We show herein how defined noncovalent anchorage of adhesion ligands to elastic substrates allows for dissection of intracellular adhesion signaling pathways related to matrix stiffness and receptor forces. Quantitative analysis of the mechanical balance in cell adhesion using traction force microscopy revealed distinct scalings of the strain energy imparted by the cells on the substrates dependent either on matrix stiffness or on receptor force. Those scalings suggested the applicability of a linear elastic theoretical framework for the description of cell adhesion in a certain parameter range, which is cell-type-dependent. Besides the deconvolution of biophysical adhesion signaling, site-specific phosphorylation of focal adhesion kinase, dependent either on matrix stiffness or on receptor force, also demonstrated the dissection of biochemical signaling events in our approach. Moreover, the net contractile moment of the adherent cells and their strain energy exerted on the elastic substrate was found to be a robust measure of cell adhesion with a unifying power-law scaling exponent of 1.5 independent of matrix stiffness. PMID:19843448

Stress-stiffening-mediated stem-cell commitment switch in soft responsive hydrogels

NASA Astrophysics Data System (ADS)

Das, Rajat K.; Gocheva, Veronika; Hammink, Roel; Zouani, Omar F.; Rowan, Alan E.

2016-03-01

Bulk matrix stiffness has emerged as a key mechanical cue in stem cell differentiation. Here, we show that the commitment and differentiation of human mesenchymal stem cells encapsulated in physiologically soft (~0.2-0.4 kPa), fully synthetic polyisocyanopeptide-based three-dimensional (3D) matrices that mimic the stiffness of adult stem cell niches and show biopolymer-like stress stiffening, can be readily switched from adipogenesis to osteogenesis by changing only the onset of stress stiffening. This mechanical behaviour can be tuned by simply altering the material’s polymer length whilst maintaining stiffness and ligand density. Our findings introduce stress stiffening as an important parameter that governs stem cell fate in a 3D microenvironment, and reveal a correlation between the onset of stiffening and the expression of the microtubule-associated protein DCAMKL1, thus implicating DCAMKL1 in a stress-stiffening-mediated, mechanotransduction pathway that involves microtubule dynamics in stem cell osteogenesis.

Adaptive tuned vibration absorber based on magnetorheological elastomer-shape memory alloy composite

NASA Astrophysics Data System (ADS)

Kumbhar, Samir B.; Chavan, S. P.; Gawade, S. S.

2018-02-01

Shape memory alloy (SMA) is an attractive smart material which could be used as stiffness tuning element in adaptive tuned vibration absorber (ATVA). The sharp modulus change in SMA material during phase transformation creates difficulties for smooth tuning to track forcing frequency to minimize vibrations of primary system. However, high hysteresis damping at low temperature martensitic phase degrades performance of vibration absorber. This paper deals with the study of dynamic response of system in which SMA and magnetorheological elastomer (MRE) are combined together to act as a smart spring- mass-damper system in a tuned vibration absorber. This composite is used as two way stiffness tuning element in ATVA for smooth and continuous tuning and to minimize the adverse effect at low temperature by increasing equivalent stiffness. The stiffnesses of SMA element and MRE are varied respectively by changing temperature and strength of external magnetic field. The two way stiffness tuning ability and adaptivity have been demonstrated analytically and experimentally. The experimental results show good agreement with analytical results. The proposed composite is able to shift the stiffness consequently the natural frequency of primary system as well as reduce the vibration level of primary system by substantial mount.

Investigation of the torsional stiffness of flexible disc coupling

NASA Astrophysics Data System (ADS)

Buryy, A.; Simonovsky, V.; Obolonik, V.

2017-08-01

Calculation of flexible coupling torsional stiffness is required when analyzing the torsional vibrations of the reciprocating machinery train. While having the lowest torsional stiffness of all the elements of the train, flexible coupling has a significant influence on the natural frequencies of torsional vibration. However, considering structural complexity of coupling, precise definition of its torsional stiffness is quite a difficult task. The paper presents a method for calculating the torsional stiffness of flexible disc coupling based on the study of its finite element model response under the action of torque. The analysis of the basic parameters that quantitatively and qualitatively affect the coupling torsional stiffness has been also provided. The results of the calculation as well as model adequacy, sufficient for practical application, have been confirmed at the experimental measurement of flexible disc coupling torsional stiffness. The obtained elastic characteristics (dependences of applied torque and torsional stiffness versus twist angle) are nonlinear in the initial stage of loading. This feature should be taken into account when creating reliable mathematical models of torsional vibrations of reciprocating machinery trains containing flexible disc couplings.

Accounting for spatial variation of trabecular anisotropy with subject-specific finite element modeling moderately improves predictions of local subchondral bone stiffness at the proximal tibia.

PubMed

Nazemi, S Majid; Kalajahi, S Mehrdad Hosseini; Cooper, David M L; Kontulainen, Saija A; Holdsworth, David W; Masri, Bassam A; Wilson, David R; Johnston, James D

2017-07-05

Previously, a finite element (FE) model of the proximal tibia was developed and validated against experimentally measured local subchondral stiffness. This model indicated modest predictions of stiffness (R 2 =0.77, normalized root mean squared error (RMSE%)=16.6%). Trabecular bone though was modeled with isotropic material properties despite its orthotropic anisotropy. The objective of this study was to identify the anisotropic FE modeling approach which best predicted (with largest explained variance and least amount of error) local subchondral bone stiffness at the proximal tibia. Local stiffness was measured at the subchondral surface of 13 medial/lateral tibial compartments using in situ macro indentation testing. An FE model of each specimen was generated assuming uniform anisotropy with 14 different combinations of cortical- and tibial-specific density-modulus relationships taken from the literature. Two FE models of each specimen were also generated which accounted for the spatial variation of trabecular bone anisotropy directly from clinical CT images using grey-level structure tensor and Cowin's fabric-elasticity equations. Stiffness was calculated using FE and compared to measured stiffness in terms of R 2 and RMSE%. The uniform anisotropic FE model explained 53-74% of the measured stiffness variance, with RMSE% ranging from 12.4 to 245.3%. The models which accounted for spatial variation of trabecular bone anisotropy predicted 76-79% of the variance in stiffness with RMSE% being 11.2-11.5%. Of the 16 evaluated finite element models in this study, the combination of Synder and Schneider (for cortical bone) and Cowin's fabric-elasticity equations (for trabecular bone) best predicted local subchondral bone stiffness. Copyright © 2017 Elsevier Ltd. All rights reserved.

Dynamic Stability of Uncertain Laminated Beams Under Subtangential Loads

NASA Technical Reports Server (NTRS)

Goyal, Vijay K.; Kapania, Rakesh K.; Adelman, Howard (Technical Monitor); Horta, Lucas (Technical Monitor)

2002-01-01

Because of the inherent complexity of fiber-reinforced laminated composites, it can be challenging to manufacture composite structures according to their exact design specifications, resulting in unwanted material and geometric uncertainties. In this research, we focus on the deterministic and probabilistic stability analysis of laminated structures subject to subtangential loading, a combination of conservative and nonconservative tangential loads, using the dynamic criterion. Thus a shear-deformable laminated beam element, including warping effects, is derived to study the deterministic and probabilistic response of laminated beams. This twenty-one degrees of freedom element can be used for solving both static and dynamic problems. In the first-order shear deformable model used here we have employed a more accurate method to obtain the transverse shear correction factor. The dynamic version of the principle of virtual work for laminated composites is expressed in its nondimensional form and the element tangent stiffness and mass matrices are obtained using analytical integration The stability is studied by giving the structure a small disturbance about an equilibrium configuration, and observing if the resulting response remains small. In order to study the dynamic behavior by including uncertainties into the problem, three models were developed: Exact Monte Carlo Simulation, Sensitivity Based Monte Carlo Simulation, and Probabilistic FEA. These methods were integrated into the developed finite element analysis. Also, perturbation and sensitivity analysis have been used to study nonconservative problems, as well as to study the stability analysis, using the dynamic criterion.

On the stiffness matrix of the intervertebral joint: application to total disk replacement.

PubMed

O'Reilly, Oliver M; Metzger, Melodie F; Buckley, Jenni M; Moody, David A; Lotz, Jeffrey C

2009-08-01

The traditional method of establishing the stiffness matrix associated with an intervertebral joint is valid only for infinitesimal rotations, whereas the rotations featured in spinal motion are often finite. In the present paper, a new formulation of this stiffness matrix is presented, which is valid for finite rotations. This formulation uses Euler angles to parametrize the rotation, an associated basis, which is known as the dual Euler basis, to describe the moments, and it enables a characterization of the nonconservative nature of the joint caused by energy loss in the poroviscoelastic disk and ligamentous support structure. As an application of the formulation, the stiffness matrix of a motion segment is experimentally determined for the case of an intact intervertebral disk and compared with the matrices associated with the same segment after the insertion of a total disk replacement system. In this manner, the matrix is used to quantify the changes in the intervertebral kinetics associated with total disk replacements. As a result, this paper presents the first such characterization of the kinetics of a total disk replacement.

PEG-chitosan hydrogel with tunable stiffness for study of drug response of breast cancer cells

PubMed Central

Chang, Fei-Chien; Tsao, Ching-Ting; Lin, Anqi; Zhang, Mengying; Levengood, Sheeny Lan; Zhang, Miqin

2016-01-01

Mechanical properties of the extracellular matrix have a profound effect on the behavior of anchorage-dependent cells. However, the mechanisms that define the effects of matrix stiffness on cell behavior remains unclear. Therefore, the development and fabrication of synthetic matrices with well-defined stiffness is invaluable for studying the interactions of cells with their biophysical microenvironment in vitro. We demonstrate a methoxypolyethylene glycol (mPEG)-modified chitosan hydrogel network where hydrogel stiffness can be easily modulated under physiological conditions by adjusting the degree of mPEG grafting onto chitosan (PEGylation). We show that the storage modulus of the hydrogel increases as PEGylation decreases and the gels exhibit instant self-recovery after deformation. Breast cancer cells cultured on the stiffest hydrogels adopt a more malignant phenotype with increased resistance to doxorubicin as compared with cells cultured on tissue culture polystyrene or Matrigel. This work demonstrates the utility of mPEG-modified chitosan hydrogel, with tunable mechanical properties, as an improved replacement of conventional culture system for in vitro characterization of breast cancer cell phenotype and evaluation of cancer therapies. PMID:27595012

Detection of stiff nanoparticles within cellular structures by contact resonance atomic force microscopy subsurface nanomechanical imaging.

PubMed

Reggente, Melania; Passeri, Daniele; Angeloni, Livia; Scaramuzzo, Francesca Anna; Barteri, Mario; De Angelis, Francesca; Persiconi, Irene; De Stefano, Maria Egle; Rossi, Marco

2017-05-04

Detecting stiff nanoparticles buried in soft biological matrices by atomic force microscopy (AFM) based techniques represents a new frontier in the field of scanning probe microscopies, originally developed as surface characterization methods. Here we report the detection of stiff (magnetic) nanoparticles (NPs) internalized in cells by using contact resonance AFM (CR-AFM) employed as a potentially non-destructive subsurface characterization tool. Magnetite (Fe 3 O 4 ) NPs were internalized in microglial cells from cerebral cortices of mouse embryos of 18 days by phagocytosis. Nanomechanical imaging of cells was performed by detecting the contact resonance frequencies (CRFs) of an AFM cantilever held in contact with the sample. Agglomerates of NPs internalized in cells were visualized on the basis of the local increase in the contact stiffness with respect to the surrounding biological matrix. A second AFM-based technique for nanomechanical imaging, i.e., HarmoniX™, as well as magnetic force microscopy and light microscopy were used to confirm the CR-AFM results. Thus, CR-AFM was demonstrated as a promising technique for subsurface imaging of nanomaterials in biological samples.

A Global Overview of Exposure Levels and Biological Effects of Trace Elements in Penguins.

PubMed

Espejo, Winfred; Celis, José E; GonzÃlez-Acuña, Daniel; Banegas, Andiranel; Barra, Ricardo; Chiang, Gustavo

2018-01-01

Trace elements are chemical contaminants that can be present almost anywhere on the planet. The study of trace elements in biotic matrices is a topic of great relevance for the implications that it can have on wildlife and human health. Penguins are very useful, since they live exclusively in the Southern Hemisphere and represent about 90% of the biomass of birds of the Southern Ocean. The levels of trace elements (dry weight) in different biotic matrices of penguins were reviewed here. Maps of trace element records in penguins were included. Data on exposure and effects of trace elements in penguins were collected from the literature. The most reported trace elements in penguins are aluminum, arsenic, cadmium, lead, mercury, copper, zinc, and manganese. Trace elements have been measured in 11 of the 18 species of penguins. The most studied biotic matrices are feathers and excreta. Most of the studies have been performed in Antarctica and subantarctic Islands. Little is known about the interaction among metals, which could provide better knowledge about certain mechanisms of detoxification in penguins. Future studies of trace elements in penguins must incorporate other metals such as vanadium, cobalt, nickel, and chromium. Data of metals in the species such as Eudyptes pachyrhynchus, Eudyptes moseleyi, Eudyptes sclateri, Eudyptes robustus, Eudyptes schlegeli, Spheniscus demersus, Spheniscus mendiculus, and Megadyptes antipodes are urged. It is important to correlate levels of metals in different biotic matrices with the effects on different species and in different geographic locations.

A general algorithm using finite element method for aerodynamic configurations at low speeds

NASA Technical Reports Server (NTRS)

Balasubramanian, R.

1975-01-01

A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.

Discrete Kalman filtering equations of second-order form for control-structure interaction simulations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alvin, K. F.; Belvin, W. Keith

1991-01-01

A second-order form of discrete Kalman filtering equations is proposed as a candidate state estimator for efficient simulations of control-structure interactions in coupled physical coordinate configurations as opposed to decoupled modal coordinates. The resulting matrix equation of the present state estimator consists of the same symmetric, sparse N x N coupled matrices of the governing structural dynamics equations as opposed to unsymmetric 2N x 2N state space-based estimators. Thus, in addition to substantial computational efficiency improvement, the present estimator can be applied to control-structure design optimization for which the physical coordinates associated with the mass, damping and stiffness matrices of the structure are needed instead of modal coordinates.

Design of helicopter rotor blades for optimum dynamic characteristics

NASA Technical Reports Server (NTRS)

Peters, D. A.; Ko, T.; Korn, A.; Rossow, M. P.

1984-01-01

The optimal design of helicopter rotor blades is addressed. The forced response of an initial (i.e., non-optimized) blade to those of a final (optimized) blade are compared. Response of starting design and optimal designs for varying forcing frequencies, blade response to harmonics of rotor speed, and derivation of mass and stiffness matrices or functions of natural frequencies are discussed.

The nonlinear aeroelastic characteristics of a folding wing with cubic stiffness

NASA Astrophysics Data System (ADS)

Hu, Wei; Yang, Zhichun; Gu, Yingsong; Wang, Xiaochen

2017-07-01

This paper focuses on the nonlinear aeroelastic characteristics of a folding wing in the quasi-steady condition (namely at fixed folding angles) and during the morphing process. The structure model of the folding wing is formulated by the Lagrange equations, and the constraint equation is used to describe the morphing strategy. The aerodynamic influence coefficient matrices at several folding angles are calculated by the Doublet Lattice method, and described as rational functions in the Laplace domain by the rational function approximation, and then the Kriging agent model technique is adopted to interpolate the coefficient matrices of the rational functions, and the aerodynamics model of the folding wing during the morphing process is built. The aeroelastic responses of the folding wing with cubic stiffness are simulated, and the results show that the motion types of aeroelastic responses in the quasi-steady condition and during the morphing process are all sensitive to the initial condition and folding angle. During the morphing process, the transition of the motion types is observed. And apart from the period of transition, the aeroelastic response at some folding angles may exhibit different motion types, which can be found from the results in the quasi-steady condition.

Vibration transmission through rolling element bearings in geared rotor system, part 1. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Lim, Teik Chin

1989-01-01

A mathematical model is proposed to examine the vibration transmission through rolling element bearings in geared rotor systems. Current bearing models, based on either ideal boundary conditions for the shaft or purely translational stiffness element description, cannot explain how the vibratory motion may be transmitted from the rotating shaft to the casing. This study clarifies this issue qualitatively and quantitatively by developing a comprehensive bearing stiffness matrix of dimension 6 model for the precision rolling element bearings from basic principles. The proposed bearing formulation is extended to analyze the overall geared rotor system dynamics including casing and mounts. The bearing stiffness matrix is included in discrete system models using lumped parameter and/or dynamic finite element techniques. Eigensolution and forced harmonic response due to rotating mass unbalance or kinematic transmission error excitation for a number of examples are computed.

Acceleration of boundary element method for linear elasticity

NASA Astrophysics Data System (ADS)

Zapletal, Jan; Merta, Michal; Čermák, Martin

2017-07-01

In this work we describe the accelerated assembly of system matrices for the boundary element method using the Intel Xeon Phi coprocessors. We present a model problem, provide a brief overview of its discretization and acceleration of the system matrices assembly using the coprocessors, and test the accelerated version using a numerical benchmark.

Development of procedures for calculating stiffness and damping properties of elastomers. Part 3: The effects of temperature, dissipation level and geometry

NASA Technical Reports Server (NTRS)

Smalley, A. J.; Tessarzik, J. M.

1975-01-01

Effects of temperature, dissipation level and geometry on the dynamic behavior of elastomer elements were investigated. Force displacement relationships in elastomer elements and the effects of frequency, geometry and temperature upon these relationships are reviewed. Based on this review, methods of reducing stiffness and damping data for shear and compression test elements to material properties (storage and loss moduli) and empirical geometric factors are developed and tested using previously generated experimental data. A prediction method which accounts for large amplitudes of deformation is developed on the assumption that their effect is to increase temperature through the elastomers, thereby modifying the local material properties. Various simple methods of predicting the radial stiffness of ring cartridge elements are developed and compared. Material properties were determined from the shear specimen tests as a function of frequency and temperature. Using these material properties, numerical predictions of stiffness and damping for cartridge and compression specimens were made and compared with corresponding measurements at different temperatures, with encouraging results.

The Value Range of Contact Stiffness Factor between Pile and Soil Based on Penalty Function

NASA Astrophysics Data System (ADS)

Chen, Sandy H. L.; Wu, Xinliu

2018-03-01

The value range of contact stiffness factor based on penalty function is studied when we use finite element software ANSYS to analyze contact problems, take single pile and soil of a certain project for example, the normal contact between pile and soil is analyzed with 2D simplified model in horizontal load. The study shows that when adopting linear elastic model to simulate soil, the maximum contact pressure and penetration approach steady value as the contact stiffness factor increases. The reasonable value range of contact stiffness factor reduces as the underlying element thickness decreases, but the rule reverses when refers to the soil stiffness. If choose DP model to simulate soil, the stiffness factor should be magnified 100 times compares to the elastic model regardless of the soil bears small force and still in elastic deformation stage or into the plastic deformation stage. When the soil bears big force and into plastic deformation stage, the value range of stiffness factor relates to the plastic strain range of the soil, and reduces as the horizontal load increases.

Finite element analysis and cadaveric cinematic analysis of fixation options for anteriorly implanted trabecular metal interbody cages.

PubMed

Berjano, Pedro; Blanco, Juan Francisco; Rendon, Diego; Villafañe, Jorge Hugo; Pescador, David; Atienza, Carlos Manuel

2015-11-01

To assess, with finite element analysis and an in vitro biomechanical study in cadaver, whether the implementation of an anterior interbody cage made of hedrocel with nitinol shape memory staples in compression increases the stiffness of the stand-alone interbody cage and to compare these constructs' stiffness to other constructs common in clinical practice. A biomechanical study with a finite element analysis and cadaveric testing assessed the stiffness of different fixation modes for the L4-L5 functional spinal unit: intact spine, destabilized spine with discectomy, posterior pedicle-screw fixation, anterior stand-alone interbody cage, anterior interbody cage with bilateral pedicle screws and anterior interbody cage with two shape memory staples in compression. These modalities of vertebral fixation were compared in four loading modes (flexion, extension, lateral bending, and axial rotation). The L4-L5 spinal unit with an anterior interbody cage and two staples was stiffer than the stand-alone cage. The construct stiffness was similar to that of a model of posterior pedicular stabilization. The stiffness was lower than that of the anterior cage plus bilateral pedicle-screw fixation. The use of an anterior interbody implant with shape memory staples in compression may be an alternative to isolated posterior fixation and to anterior isolated implants, with increased stiffness.

Indentation stiffness does not discriminate between normal and degraded articular cartilage.

PubMed

Brown, Cameron P; Crawford, Ross W; Oloyede, Adekunle

2007-08-01

Relative indentation characteristics are commonly used for distinguishing between normal healthy and degraded cartilage. The application of this parameter in surgical decision making and an appreciation of articular cartilage biomechanics has prompted us to hypothesise that it is difficult to define a reference stiffness to characterise normal articular cartilage. This hypothesis is tested for validity by carrying out biomechanical indentation of articular cartilage samples that are characterised as visually normal and degraded relative to proteoglycan depletion and collagen disruption. Compressive loading was applied at known strain rates to visually normal, artificially degraded and naturally osteoarthritic articular cartilage and observing the trends of their stress-strain and stiffness characteristics. While our results demonstrated a 25% depreciation in the stiffness of individual samples after proteoglycan depletion, they also showed that when compared to the stiffness of normal samples only 17% lie outside the range of the stress-strain behaviour of normal samples. We conclude that the extent of the variability in the properties of normal samples, and the degree of overlap (81%) of the biomechanical properties of normal and degraded matrices demonstrate that indentation data cannot form an accurate basis for distinguishing normal from abnormal articular cartilage samples with consequences for the application of this mechanical process in the clinical environment.

Improved Equivalent Linearization Implementations Using Nonlinear Stiffness Evaluation

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Muravyov, Alexander A.

2001-01-01

This report documents two new implementations of equivalent linearization for solving geometrically nonlinear random vibration problems of complicated structures. The implementations are given the acronym ELSTEP, for "Equivalent Linearization using a STiffness Evaluation Procedure." Both implementations of ELSTEP are fundamentally the same in that they use a novel nonlinear stiffness evaluation procedure to numerically compute otherwise inaccessible nonlinear stiffness terms from commercial finite element programs. The commercial finite element program MSC/NASTRAN (NASTRAN) was chosen as the core of ELSTEP. The FORTRAN implementation calculates the nonlinear stiffness terms and performs the equivalent linearization analysis outside of NASTRAN. The Direct Matrix Abstraction Program (DMAP) implementation performs these operations within NASTRAN. Both provide nearly identical results. Within each implementation, two error minimization approaches for the equivalent linearization procedure are available - force and strain energy error minimization. Sample results for a simply supported rectangular plate are included to illustrate the analysis procedure.

Influence of Tension Stiffening on the Flexural Stiffness of Reinforced Concrete Circular Sections

PubMed Central

Morelli, Francesco; Amico, Cosimo; Salvatore, Walter; Squeglia, Nunziante; Stacul, Stefano

2017-01-01

Within this paper, the assessment of tension stiffening effects on a reinforced concrete element with circular section subjected to axial and bending loads is presented. To this purpose, an enhancement of an analytical model already present within the actual technical literature is proposed. The accuracy of the enhanced method is assessed by comparing the experimental results carried out in past research and the numerical ones obtained by the model. Finally, a parametric study is executed in order to study the influence of axial compressive force on the flexural stiffness of reinforced concrete elements that are characterized by a circular section, comparing the secant stiffness evaluated at yielding and at maximum resistance, considering and not considering the effects of tension stiffness. PMID:28773028

Influence of Tension Stiffening on the Flexural Stiffness of Reinforced Concrete Circular Sections.

PubMed

Morelli, Francesco; Amico, Cosimo; Salvatore, Walter; Squeglia, Nunziante; Stacul, Stefano

2017-06-18

Within this paper, the assessment of tension stiffening effects on a reinforced concrete element with the circular sections subjected to axial and bending loads is presented. To this purpose, an enhancement of an analytical model already present within the actual technical literature is proposed. The accuracy of the enhanced method is assessed by comparing the experimental results carried out in past research and the numerical ones obtained by the model. Finally, a parametric study is executed in order to study the influence of axial compressive force on the flexural stiffness of reinforced concrete elements that are characterized by a circular section, comparing the secant stiffness evaluated at yielding and at maximum resistance, considering and not considering the effects of tension stiffness.

Aeroelastic passive control optimization of supersonic composite wing with external stores

NASA Astrophysics Data System (ADS)

Sulaeman, E.; Abdullah, N. A.; Kashif, S. M.

2017-03-01

This paper provides a study on passive aeroelastic control optimization, by means of aeroelastic tailoring, of a composite supersonic wing equipped with external stores. The objective of the optimization is to minimize wing weight by considering the aeroelastic flutter and divergence instability speeds as constraints at several flight altitudes. The optimization variables are the composite ply angle and skin thickness of the wing box, wing rib and its control surfaces. The aeroelastic instability speed is set as constraint such that it should be higher than the flutter speed of a metallic base line model of supersonic wing having previously published. A finite element analysis is applied to determine the stiffness and mass matric of the wing and its multi stores. The boundary element method in the form of doublet lattice method is used to model the unsteady aerodynamic load. The results indicate that, for the present wing configuration, the high modulus Graphite/Epoxy composite provides a desired higher flutter speed and lower wing weight compare to that of Kevlar/Epoxy composite as well as the base line metallic wing materials. The aeroelastic boundary thus can be enlarged to higher speed zone and in the same time reduce the structural weight which is important for a further optimization process.

An infinitely-stiff elastic system via a tuned negative-stiffness component stabilized by rotation-produced gyroscopic forces

NASA Astrophysics Data System (ADS)

Kochmann, D. M.; Drugan, W. J.

2016-06-01

An elastic system containing a negative-stiffness element tuned to produce positive-infinite system stiffness, although statically unstable as is any such elastic system if unconstrained, is proved to be stabilized by rotation-produced gyroscopic forces at sufficiently high rotation rates. This is accomplished in possibly the simplest model of a composite structure (or solid) containing a negative-stiffness component that exhibits all these features, facilitating a conceptually and mathematically transparent, completely closed-form analysis.

Placing three-dimensional isoparametric elements into NASTRAN. [alterations in matrix assembly to simplify generation of higher order elements

NASA Technical Reports Server (NTRS)

Newman, M. B.; Filstrup, A. W.

1973-01-01

Linear (8 node), parabolic (20 node), cubic (32 node) and mixed (some edges linear, some parabolic and some cubic) have been inserted into NASTRAN, level 15.1. First the dummy element feature was used to check out the stiffness matrix generation routines for the linear element in NASTRAN. Then, the necessary modules of NASTRAN were modified to include the new family of elements. The matrix assembly was changed so that the stiffness matrix of each isoparametric element is only generated once as the time to generate these higher order elements tends to be much longer than the other elements in NASTRAN. This paper presents some of the experiences and difficulties of inserting a new element or family of elements into NASTRAN.

Extraction and Analysis of Sulfur Mustard (HD) from Various Food Matrices by Gas ChromatographyMass Spectrometry

DTIC Science & Technology

2016-01-01

EXTRACTION AND ANALYSIS OF SULFUR MUSTARD (HD) FROM VARIOUS FOOD MATRICES BY GAS CHROMATOGRAPHY–MASS...Sulfur Mustard (HD) from Various Food Matrices by Gas Chromatography–Mass Spectrometry 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT...spectrometry was used to analyze sulfur mustard (HD) in various food matrices. The development of a solid-phase extraction method using a normal

Ritz method for transient response in systems having unsymmetric stiffness

NASA Technical Reports Server (NTRS)

Butler, Thomas G.

1989-01-01

The DMAP coding was automated to such an extent by using the device of bubble vectors, that it is useable for analyses in its present form. This feasibility study demonstrates that the Ritz Method is so compelling as to warrant coding its modules in FORTRAN and organizing the resulting coding into a new Rigid Format. Even though this Ritz technique was developed for unsymmetric stiffness matrices, it offers advantages to problems with symmetric stiffnesses. If used for the symmetric case the solution would be simplified to one set of modes, because the adjoint would be the same as the primary. Its advantage in either type of symmetry over a classical eigenvalue modal expansion is that information density per Ritz mode is far richer than per eigenvalue mode; thus far fewer modes would be needed for the same accuracy and every mode would actively participate in the response. Considerable economy can be realized in adapting Ritz vectors for modal solutions. This new Ritz capability now makes NASTRAN even more powerful than before.

Error estimation and adaptive mesh refinement for parallel analysis of shell structures

NASA Technical Reports Server (NTRS)

Keating, Scott C.; Felippa, Carlos A.; Park, K. C.

1994-01-01

The formulation and application of element-level, element-independent error indicators is investigated. This research culminates in the development of an error indicator formulation which is derived based on the projection of element deformation onto the intrinsic element displacement modes. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited for obtaining error values and driving adaptive mesh refinements on parallel computers where access to neighboring elements residing on different processors may incur significant overhead. In addition such estimators are insensitive to the presence of physical interfaces and junctures. An error indicator qualifies as 'element-independent' when only visible quantities such as element stiffness and nodal displacements are used to quantify error. Error evaluation at the element level and element independence for the error indicator are highly desired properties for computing error in production-level finite element codes. Four element-level error indicators have been constructed. Two of the indicators are based on variational formulation of the element stiffness and are element-dependent. Their derivations are retained for developmental purposes. The second two indicators mimic and exceed the first two in performance but require no special formulation of the element stiffness mesh refinement which we demonstrate for two dimensional plane stress problems. The parallelizing of substructures and adaptive mesh refinement is discussed and the final error indicator using two-dimensional plane-stress and three-dimensional shell problems is demonstrated.

Exchange Stiffness in Thin-Film Cobalt Alloys

NASA Astrophysics Data System (ADS)

Eyrich, Charles

The exchange stiffness, Aex, is one of the key parameters controlling magnetization reversal in magnetic materials but is very difficult to measure, especially in thin films. We developed a new technique for measuring the exchange stiffness of a magnetic material based on the formation of a spin spiral within two antiferromagnetically coupled ferromagnetic films [1]. Using this method, I was able to measure the exchange stiffness of thin film Co alloyed with Cr, Fe, Ni, Pd, Pt and Ru. The results of this work showed that the rate at which a substituent element reduces the exchange stiffness is not directly related to its effect on the magnetization of the alloy. These measured trends have been understood by combining measurements of element specific magnetic moments obtained using X-ray magnetic circular dichroism (XMCD) and material specific modeling based on density functional theory (DFT) within the local density approximation (LDA). The experimental results also hint at significant reduction of the exchange stiffness at the interface that can account for the difference between our results and those obtained on bulk materials.

Development of elements of the condition monitoring system of turbo generators of thermal power stations and nuclear power plants

NASA Astrophysics Data System (ADS)

Kumenko, A. I.; Kostyukov, V. N.; Kuz'minykh, N. Yu.; Boichenko, S. N.; Timin, A. V.

2017-08-01

The rationale is given for the improvement of the regulatory framework for the use of shaft sensors for the in-service condition monitoring of turbo generators and the development of control systems of shaft surfacing and misalignments of supports. A modern concept and a set of methods are proposed for the condition monitoring of the "shaft line-thrust bearing oil film-turbo generator supports" system elements based on the domestic COMPACS® technology. The system raw data are design, technology, installation, and operating parameters of the turbo generator as well as measured parameters of the absolute vibration of supports and mechanical quantities, relative displacements and relative vibration of the rotor teeth in accordance with GOST R 55263-2012. The precalculated shaft line assembly line in the cold state, the nominal parameters of rotor teeth positions on the dynamic equilibrium curve, the static and dynamic characteristics of the oil film of thrust bearings, and the shaft line stiffness matrix of unit support displacements have been introduced into the system. Using the COMPACS-T system, it is planned to measure positions and oscillations of rotor teeth, to count corresponding static and dynamic characteristics of the oil film, and the static and dynamic loads in the supports in real time. Using the obtained data, the system must determine the misalignments of supports and corrective alignments of rotors of coupling halves, voltages in rotor teeth, welds, and bolts of the coupling halves, and provide automatic conclusion if condition monitoring parameters correspond to standard values. A part of the methodological support for the proposed system is presented, including methods for determining static reactions of supports under load, the method for determining shaft line stiffness matrices, and the method for solving the inverse problem, i.e., the determination of the misalignments of the supports by measurements of rotor teeth relative positions in bearing housings. The procedure for calculating misalignments of turbo generator shaft line supports is set out.

Bend-Twist Coupled Carbon-Fiber Laminate Beams: Fundamental Behavior and Applications

NASA Astrophysics Data System (ADS)

Babuska, Pavel

Material-induced bend-twist coupling in laminated composite beams has seen applications in engineered structures for decades, ranging from airplane wings to turbine blades. Symmetric, unbalanced, carbon fiber laminates which exhibit bend-twist coupling can be difficult to characterize and exhibit unintuitive deformation states which may pose challenges to the engineer. In this thesis, bend-twist coupled beams are investigated comprehensively, by experimentation, numerical modeling, and analytical methods. Beams of varying fiber angle and amount of coupling were manufactured and physically tested in both linear and nonlinear static and dynamic settings. Analytical mass and stiffness matrices were derived for the development of a beam element to use in the stiffness matrix analysis method. Additionally, an ABAQUS finite element model was used in conjunction with the analytical methods to predict and further characterize the behavior of the beams. The three regimes, experimental, analytical, and numerical, represent a full-field characterization of bend-twist coupling in composite beams. A notable application of bend-twist coupled composites is for passively adaptive turbine blades whereby the deformation coupling can be built into the blade structure to simultaneously bend and twist, thus pitching the blade into or away from the fluid flow, changing the blade angle of attack. Passive pitch adaptation has been implemented successfully in wind turbine blades, however, for marine turbine blades, the technology is still in the development phase. Bend-twist coupling has been shown numerically to be beneficial to the tidal turbine performance, however little validation has been conducted in the experimental regime. In this thesis, passively adaptive experiment scale tidal turbine blades were designed, analyzed, manufactured, and physically tested, validating the foundational numerical work. It was shown that blade forces and root moments as well as turbine thrust and power coefficients can be manipulated by inclusion of passive pitch adaption by bend-twist coupling.

Novel Framework for Reduced Order Modeling of Aero-engine Components

NASA Astrophysics Data System (ADS)

Safi, Ali

The present study focuses on the popular dynamic reduction methods used in design of complex assemblies (millions of Degrees of Freedom) where numerous iterations are involved to achieve the final design. Aerospace manufacturers such as Rolls Royce and Pratt & Whitney are actively seeking techniques that reduce computational time while maintaining accuracy of the models. This involves modal analysis of components with complex geometries to determine the dynamic behavior due to non-linearity and complicated loading conditions. In such a case the sub-structuring and dynamic reduction techniques prove to be an efficient tool to reduce design cycle time. The components whose designs are finalized can be dynamically reduced to mass and stiffness matrices at the boundary nodes in the assembly. These matrices conserve the dynamics of the component in the assembly, and thus avoid repeated calculations during the analysis runs for design modification of other components. This thesis presents a novel framework in terms of modeling and meshing of any complex structure, in this case an aero-engine casing. In this study the affect of meshing techniques on the run time are highlighted. The modal analysis is carried out using an extremely fine mesh to ensure all minor details in the structure are captured correctly in the Finite Element (FE) model. This is used as the reference model, to compare against the results of the reduced model. The study also shows the conditions/criteria under which dynamic reduction can be implemented effectively, proving the accuracy of Criag-Bampton (C.B.) method and limitations of Static Condensation. The study highlights the longer runtime needed to produce the reduced matrices of components compared to the overall runtime of the complete unreduced model. Although once the components are reduced, the assembly run is significantly. Hence the decision to use Component Mode Synthesis (CMS) is to be taken judiciously considering the number of iterations that may be required during the design cycle.

Determination of impurities in uranium matrices by time-of-flight ICP-MS using matrix-matched method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buerger, Stefan; Riciputi, Lee R; Bostick, Debra A

2007-01-01

The analysis of impurities in uranium matrices is performed in a variety of fields, e.g. for quality control in the production stream converting uranium ores to fuels, as element signatures in nuclear forensics and safeguards, and for non-proliferation control. We have investigated the capabilities of time-of-flight ICP-MS for the analysis of impurities in uranium matrices using a matrix-matched method. The method was applied to the New Brunswick Laboratory CRM 124(1-7) series. For the seven certified reference materials, an overall precision and accuracy of approximately 5% and 14%, respectively, were obtained for 18 analyzed elements.

Further insights into normal aortic valve function: role of a compliant aortic root on leaflet opening and valve orifice area.

PubMed

Sripathi, Vangipuram Canchi; Kumar, Ramarathnam Krishna; Balakrishnan, Komarakshi R

2004-03-01

This study aims to find the fundamental differences in the mechanism of opening and closing of a normal aortic valve and a valve with a stiff root, using a dynamic finite element model. A dynamic, finite element model with time varying pressure was used in this study. Shell elements with linear elastic properties for the leaflet and root were used. Two different cases were analyzed: (1) normal leaflets inside a compliant root, and (2) normal leaflets inside a stiff root. A compliant aortic root contributes substantially to the smooth and symmetrical leaflet opening with minimal gradients. In contrast, the leaflet opening inside a stiff root is delayed, asymmetric, and wrinkled. However, this wrinkling is not associated with increased leaflet stresses. In compliant roots, the effective valve orifice area can substantially increase because of increased root pressure and transvalvular gradients. In stiff roots this effect is strikingly absent. A compliant aortic root contributes substantially to smooth and symmetrical leaflet opening with minimal gradients. The compliance also contributes much to the ability of the normal aortic valve to increase its effective valve orifice in response to physiologic demands of exercise. This effect is strikingly absent in stiff roots.

Redistribution of Sr and rare earth elements in the matrices of CV3 carbonaceous chondrites during aqueous alteration in their parent body

NASA Astrophysics Data System (ADS)

Jogo, Kaori; Ito, Motoo; Nakamura, Tomoki; Kobayashi, Sachio; Lee, Jong Ik

2018-03-01

We measured the abundances of Sr and rare earth elements (REEs) in the matrices of five CV3 carbonaceous chondrites: Meteorite Hills (MET) 00430, MET 01070, La Paz ice field (LAP) 02206, Asuka (A) 881317 and Roberts Massif (RBT) 04143. In the MET 00430 and MET 01074 matrices, the Sr/CI and light REE (LREE, La-Nd)/CI ratios positively correlate with the amounts of Ca-rich secondary minerals, which formed during aqueous alteration in the CV3 chondrite parent body. In contrast, in the LAP 02206 and RBT 04143 matrices, although the Sr/CI ratios correlate with the amounts of Ca-rich secondary minerals, the LREE/CI ratios vary independently from the amounts of any secondary minerals. This suggests that the LREE/CI ratios in these matrices were produced prior to the parent body alteration, probably in the solar nebula. The LREE/CI ratios of the LAP 02206 and RBT 04143 matrices reveal the mixing process of matrix minerals prior to the accretion of the CV3 chondrite parent body. The mixing degrees of matrix minerals might be different between these two matrices. Because solid materials would be mixed over time according to the radial diffusion model of a turbulent disk, the matrix minerals consisting of LAP 02206 and RBT 04143 matrices might be incorporated into their parent body with different timing.

Complete pulpodentin complex regeneration by modulating the stiffness of biomimetic matrix.

PubMed

Qu, Tiejun; Jing, Junjun; Ren, Yinshi; Ma, Chi; Feng, Jian Q; Yu, Qing; Liu, Xiaohua

2015-04-01

Dental caries is one of the most prevalent chronic diseases in all populations. The regeneration of dentin-pulp tissues (pulpodentin) using a scaffold-based tissue engineering strategy is a promising approach to replacing damaged dental structures and restoring their biological functions. However, the current scaffolding design for pulpodentin regeneration does not take into account the distinct difference between pulp and dentin, therefore, is incapable of regenerating a complete tooth-like pulpodentin complex. In this study, we determined that scaffolding stiffness is a crucial biophysical cue to modulate dental pulp stem cell (DPSC) differentiation. The DPSCs on a high-stiffness three-dimensional (3D) nanofibrous gelatin (NF-gelatin) scaffold had more organized cytoskeletons and a larger spreading area than on a low-stiffness NF-gelatin scaffold. In the same differentiation medium, a high-stiffness NF-gelatin facilitated DPSC differentiation to form a mineralized tissue, while a low-stiffness NF-gelatin promoted a soft pulp-like tissue formation from the DPSCs. A facile method was then developed to integrate the low- and high-stiffness gelatin matrices into a single scaffold (S-scaffold) for pulpodentin complex regeneration. A 4-week in vitro experiment showed that biomineralization took place only in the high-stiffness peripheral area and formed a ring-like structure surrounding the non-mineralized central area of the DPSC/S-scaffold construct. A complete pulpodentin complex similar to natural pulpodentin was successfully regenerated after subcutaneous implantation of the DPSC/S-scaffold in nude mice for 4weeks. Histological staining showed a significant amount of extracellular matrix (ECM) formation in the newly formed pulpodentin complex, and a number of blood vessels were observed in the pulp tissue. Taken together, this work shows that modulating the stiffness of the NF-gelatin scaffold is a successful approach to regenerating a complete tooth-like pulpodentin complex. Published by Elsevier Ltd.

Using molecular dynamics simulations and finite element method to study the mechanical properties of nanotube reinforced polyethylene and polyketone

NASA Astrophysics Data System (ADS)

Rouhi, S.; Alizadeh, Y.; Ansari, R.; Aryayi, M.

2015-09-01

Molecular dynamics simulations are used to study the mechanical behavior of single-walled carbon nanotube reinforced composites. Polyethylene and polyketone are selected as the polymer matrices. The effects of nanotube atomic structure and diameter on the mechanical properties of polymer matrix nanocomposites are investigated. It is shown that although adding nanotube to the polymer matrix raises the longitudinal elastic modulus significantly, the transverse tensile and shear moduli do not experience important change. As the previous finite element models could not be used for polymer matrices with the atom types other than carbon, molecular dynamics simulations are used to propose a finite element model which can be used for any polymer matrices. It is shown that this model can predict Young’s modulus with an acceptable accuracy.

Graph theory approach to the eigenvalue problem of large space structures

NASA Technical Reports Server (NTRS)

Reddy, A. S. S. R.; Bainum, P. M.

1981-01-01

Graph theory is used to obtain numerical solutions to eigenvalue problems of large space structures (LSS) characterized by a state vector of large dimensions. The LSS are considered as large, flexible systems requiring both orientation and surface shape control. Graphic interpretation of the determinant of a matrix is employed to reduce a higher dimensional matrix into combinations of smaller dimensional sub-matrices. The reduction is implemented by means of a Boolean equivalent of the original matrices formulated to obtain smaller dimensional equivalents of the original numerical matrix. Computation time becomes less and more accurate solutions are possible. An example is provided in the form of a free-free square plate. Linearized system equations and numerical values of a stiffness matrix are presented, featuring a state vector with 16 components.

Hydrodynamic impeller stiffness, damping, and inertia in the rotordynamics of centrifugal flow pumps

NASA Technical Reports Server (NTRS)

Jery, S.; Acosta, A. J.; Brennen, C. E.; Caughey, T. K.

1984-01-01

The lateral hydrodynamic forces experienced by a centrifugal pump impeller performing circular whirl motions within several volute geometries were measured. The lateral forces were decomposed into: (1) time averaged lateral forces and (2) hydrodynamic force matrices representing the variation of the lateral forces with position of the impeller center. It is found that these force matrices essentially consist of equal diagonal terms and skew symmetric off diagonal terms. One consequence of this is that during its whirl motion the impeller experiences forces acting normal and tangential to the locus of whirl. Data on these normal and tangential forces are presented; it is shown that there exists a region of positive reduced whirl frequencies, within which the hydrodynamic forces can be destablizing with respect to whirl.

Macro Scale Independently Homogenized Subcells for Modeling Braided Composites

NASA Technical Reports Server (NTRS)

Blinzler, Brina J.; Goldberg, Robert K.; Binienda, Wieslaw K.

2012-01-01

An analytical method has been developed to analyze the impact response of triaxially braided carbon fiber composites, including the penetration velocity and impact damage patterns. In the analytical model, the triaxial braid architecture is simulated by using four parallel shell elements, each of which is modeled as a laminated composite. Currently, each shell element is considered to be a smeared homogeneous material. The commercial transient dynamic finite element code LS-DYNA is used to conduct the simulations, and a continuum damage mechanics model internal to LS-DYNA is used as the material constitutive model. To determine the stiffness and strength properties required for the constitutive model, a top-down approach for determining the strength properties is merged with a bottom-up approach for determining the stiffness properties. The top-down portion uses global strengths obtained from macro-scale coupon level testing to characterize the material strengths for each subcell. The bottom-up portion uses micro-scale fiber and matrix stiffness properties to characterize the material stiffness for each subcell. Simulations of quasi-static coupon level tests for several representative composites are conducted along with impact simulations.

Boundary Layer Effect on Behavior of Discrete Models.

PubMed

Eliáš, Jan

2017-02-10

The paper studies systems of rigid bodies with randomly generated geometry interconnected by normal and tangential bonds. The stiffness of these bonds determines the macroscopic elastic modulus while the macroscopic Poisson's ratio of the system is determined solely by the normal/tangential stiffness ratio. Discrete models with no directional bias have the same probability of element orientation for any direction and therefore the same mechanical properties in a statistical sense at any point and direction. However, the layers of elements in the vicinity of the boundary exhibit biased orientation, preferring elements parallel with the boundary. As a consequence, when strain occurs in this direction, the boundary layer becomes stiffer than the interior for the normal/tangential stiffness ratio larger than one, and vice versa. Nonlinear constitutive laws are typically such that the straining of an element in shear results in higher strength and ductility than straining in tension. Since the boundary layer tends, due to the bias in the elemental orientation, to involve more tension than shear at the contacts, it also becomes weaker and less ductile. The paper documents these observations and compares them to the results of theoretical analysis.

A simplified computer solution for the flexibility matrix of contacting teeth for spiral bevel gears

NASA Technical Reports Server (NTRS)

Hsu, C. Y.; Cheng, H. S.

1987-01-01

A computer code, FLEXM, was developed to calculate the flexibility matrices of contacting teeth for spiral bevel gears using a simplified analysis based on the elementary beam theory for the deformation of gear and shaft. The simplified theory requires a computer time at least one order of magnitude less than that needed for the complete finite element method analysis reported earlier by H. Chao, and it is much easier to apply for different gear and shaft geometries. Results were obtained for a set of spiral bevel gears. The teeth deflections due to torsion, bending moment, shearing strain and axial force were found to be in the order 10(-5), 10(-6), 10(-7), and 10(-8) respectively. Thus, the torsional deformation was the most predominant factor. In the analysis of dynamic load, response frequencies were found to be larger when the mass or moment of inertia was smaller or the stiffness was larger. The change in damping coefficient had little influence on the resonance frequency, but has a marked influence on the dynamic load at the resonant frequencies.

Multimodal vibration damping of a plate by piezoelectric coupling to its analogous electrical network

NASA Astrophysics Data System (ADS)

Lossouarn, B.; Deü, J.-F.; Aucejo, M.; Cunefare, K. A.

2016-11-01

Multimodal damping can be achieved by coupling a mechanical structure to an electrical network exhibiting similar modal properties. Focusing on a plate, a new topology for such an electrical analogue is found from a finite difference approximation of the Kirchhoff-Love theory and the use of the direct electromechanical analogy. Discrete models based on element dynamic stiffness matrices are proposed to simulate square plate unit cells coupled to their electrical analogues through two-dimensional piezoelectric transducers. A setup made of a clamped plate covered with an array of piezoelectric patches is built in order to validate the control strategy and the numerical models. The analogous electrical network is implemented with passive components as inductors, transformers and the inherent capacitance of the piezoelectric patches. The effect of the piezoelectric coupling on the dynamics of the clamped plate is significant as it creates the equivalent of a multimodal tuned mass damping. An adequate tuning of the network then yields a broadband vibration reduction. In the end, the use of an analogous electrical network appears as an efficient solution for the multimodal control of a plate.

A geometrically exact formulation for three-dimensional numerical simulation of the umbilical cable in a deep-sea ROV system

NASA Astrophysics Data System (ADS)

Quan, Wei-cai; Zhang, Zhu-ying; Zhang, Ai-qun; Zhang, Qi-feng; Tian, Yu

2015-04-01

This paper proposes a geometrically exact formulation for three-dimensional static and dynamic analyses of the umbilical cable in a deep-sea remotely operated vehicle (ROV) system. The presented formulation takes account of the geometric nonlinearities of large displacement, effects of axial load and bending stiffness for modeling of slack cables. The resulting nonlinear second-order governing equations are discretized spatially by the finite element method and solved temporally by the generalized- α implicit time integration algorithm, which is adapted to the case of varying coefficient matrices. The ability to consider three-dimensional union action of ocean current and ship heave motion upon the umbilical cable is the key feature of this analysis. The presented formulation is firstly validated, and then three numerical examples for the umbilical cable in a deep-sea ROV system are demonstrated and discussed, including the steady configurations only under the action of depth-dependent ocean current, the dynamic responses in the case of the only ship heave motion, and in the case of the combined action of the ship heave motion and ocean current.

Optimization of custom cementless stem using finite element analysis and elastic modulus distribution for reducing stress-shielding effect.

PubMed

Saravana Kumar, Gurunathan; George, Subin Philip

2017-02-01

This work proposes a methodology involving stiffness optimization for subject-specific cementless hip implant design based on finite element analysis for reducing stress-shielding effect. To assess the change in the stress-strain state of the femur and the resulting stress-shielding effect due to insertion of the implant, a finite element analysis of the resected femur with implant assembly is carried out for a clinically relevant loading condition. Selecting the von Mises stress as the criterion for discriminating regions for elastic modulus difference, a stiffness minimization method was employed by varying the elastic modulus distribution in custom implant stem. The stiffness minimization problem is formulated as material distribution problem without explicitly penalizing partial volume elements. This formulation enables designs that could be fabricated using additive manufacturing to make porous implant with varying levels of porosity. Stress-shielding effect, measured as difference between the von Mises stress in the intact and implanted femur, decreased as the elastic modulus distribution is optimized.

Potential function of element measurement for form-finding of wide sense tensegrity

NASA Astrophysics Data System (ADS)

Soe, C. K.; Obiya, H.; Koga, D.; Nizam, Z. M.; Ijima, K.

2018-04-01

Tensegrity is a unique morphological structure in which disconnected compression members and connected tension members make the whole structure in self-equilibrium. Many researches have been done on tensegrity structure because of its mysteriousness in form-finding analysis. This study is proposed to investigate the trends and to group into some patterns of the shape that a tensegrity structure can have under the same connectivity and support condition. In this study, tangent stiffness method adopts two different functions, namely power function and logarithm function to element measurement. Numerical examples are based on a simplex initial shape with statically determinate support condition to examine the pure effectiveness of two proposed methods. The tangent stiffness method that can evaluate strict rigid body displacement of elements has a superiority to define various measure potentials and to allow the use of virtual element stiffness freely. From the results of numerical examples, the finding of the dominant trends and patterns of the equilibrium solutions is achieved although it has many related solutions under the same circumstances.

Stiffness Parameter Design of Suspension Element of Under-Chassis-Equipment for A Rail Vehicle

NASA Astrophysics Data System (ADS)

Ma, Menglin; Wang, Chengqiang; Deng, Hai

2017-06-01

According to the frequency configuration requirements of the vibration of railway under-chassis-equipment, the three- dimension stiffness of the suspension elements of under-chassis-equipment is designed based on the static principle and dynamics principle. The design results of the concrete engineering case show that, compared with the design method based on the static principle, the three- dimension stiffness of the suspension elements designed by the dynamic principle design method is more uniform. The frequency and decoupling degree analysis show that the calculation frequency of under-chassis-equipment under the two design methods is basically the same as the predetermined frequency. Compared with the design method based on the static principle, the design method based on the dynamic principle is adopted. The decoupling degree can be kept high, and the coupling vibration of the corresponding vibration mode can be reduced effectively, which can effectively reduce the fatigue damage of the key parts of the hanging element.

Effect of Augmentation Material Stiffness on Adjacent Vertebrae after Osteoporotic Vertebroplasty Using Finite Element Analysis with Different Loading Methods.

PubMed

Cho, Ah-Reum; Cho, Sang-Bong; Lee, Jae-Ho; Kim, Kyung-Hoon

2015-11-01

Vertebroplasty is an effective treatment for osteoporotic vertebral fractures, which are one of the most common fractures associated with osteoporosis. However, clinical observation has shown that the risk of adjacent vertebral body fractures may increase after vertebroplasty. The mechanism underlying adjacent vertebral body fracture after vertebroplasty is not clear; excessive stiffness resulting from polymethyl methacrylate has been suspected as an important mechanism. The aim of our study was to compare the effects of bone cement stiffness on adjacent vertebrae after osteoporotic vertebroplasty under load-controlled versus displacement-controlled conditions. An experimental computer study using a finite element analysis. Medical research institute, university hospital, Korean. A three-dimensional digital anatomic model of L1/2 bone structure was reconstructed from human computed tomographic images. The reconstructed three-dimensional geometry was processed for finite element analysis such as meshing elements and applying material properties. Two boundary conditions, load-controlled and displacement-controlled methods, were applied to each of 5 deformation modes: compression, flexion, extension, lateral bending, and torsion. The adjacent L1 vertebra, irrespective of augmentation, revealed nearly similar maximum von Mises stresses under the load-controlled condition. However, for the displacement-controlled condition, the maximum von Mises stresses in the cortical bone and inferior endplate of the adjacent L1 vertebra increased significantly after cement augmentation. This increase was more significant than that with stiffer bone cement under all modes, except the torsion mode. The finite element model was simplified, excluding muscular forces and incorporating a large volume of bone cement, to more clearly demonstrate effects of bone cement stiffness on adjacent vertebrae after vertebroplasty. Excessive stiffness of augmented bone cement increases the risk of adjacent vertebral fractures after vertebroplasty in an osteoporotic finite element model. This result was most prominently observed using the displacement-controlled method.

Extraction Methodological Contributions Toward Ultra-Performance Liquid ChromatographyTime-of-Flight Mass Spectrometry: Quantification of Free GB from Various Food Matrices

DTIC Science & Technology

2016-02-01

SPECTROMETRY: QUANTIFICATION OF FREE GB FROM VARIOUS FOOD MATRICES ECBC-TR-1351 Sue Y. Bae Mark D. Winemiller RESEARCH AND TECHNOLOGY DIRECTORATE...Flight Mass Spectrometry: Quantification of Free GB from Various Food Matrices 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER...methylphosphonofluoridate (sarin, GB) in various food matrices. The development of a solid-phase extraction method using a normal-phase silica gel column for

Micro-finite element analysis applied to high-resolution MRI reveals improved bone mechanical competence in the distal femur of female pre-professional dancers

PubMed Central

Rajapakse, C. S.; Diamond, M.; Honig, S.; Recht, M. P.; Weiss, D. S.; Regatte, R. R.

2013-01-01

Summary Micro-finite element analysis applied to high-resolution (0.234-mm length scale) MRI reveals greater whole and cancellous bone stiffness, but not greater cortical bone stiffness, in the distal femur of female dancers compared to controls. Greater whole bone stiffness appears to be mediated by cancellous, rather than cortical bone adaptation. Introduction The purpose of this study was to compare bone mechanical competence (stiffness) in the distal femur of female dancers compared to healthy, relatively inactive female controls. Methods This study had institutional review board approval. We recruited nine female modern dancers (25.7± 5.8 years, 1.63±0.06 m, 57.1±4.6 kg) and ten relatively inactive, healthy female controls matched for age, height, and weight (32.1±4.8 years, 1.6±0.04 m, 55.8±5.9 kg). We scanned the distal femur using a 7-T MRI scanner and a three-dimensional fast low-angle shot sequence (TR/TE= 31 ms/5.1 ms, 0.234 mm×0.234 mm×1 mm, 80 slices). We applied micro-finite element analysis to 10-mm-thick volumes of interest at the distal femoral diaphysis, metaphysis, and epiphysis to compute stiffness and cross-sectional area of whole, cortical, and cancellous bone, as well as cortical thickness. We applied two-tailed t-tests and ANCOVA to compare groups. Results Dancers demonstrated greater whole and cancellous bone stiffness and cross-sectional area at all locations (p< 0.05). Cortical bone stiffness, cross-sectional area, and thickness did not differ between groups (>0.08). At all locations, the percent of intact whole bone stiffness for cortical bone alone was lower in dancers (p<0.05). Adjustment for cancellous bone cross-sectional area eliminated significant differences in whole bone stiffness between groups (p>0.07), but adjustment for cortical bone cross-sectional area did not (p<0.03). Conclusions Modern dancers have greater whole and cancellous bone stiffness in the distal femur compared to controls. Elevated whole bone stiffness in dancers may be mediated via cancellous, rather than cortical bone adaptation. PMID:22893356

A Crossover from High Stiffness to High Hardness: The Case of Osmium and Its Borides

NASA Astrophysics Data System (ADS)

Bian, Yongming; Liu, Xiaomei; Li, Anhu; Liang, Yongcheng

2016-09-01

Transition-metal light-element compounds are currently raising great expectations for hard and superhard materials. Using the widely attracting osmium (Os) and its borides (OsB, Os2B3 and OsB2) as prototypes, we demonstrate by first-principles calculations that heavy transition metals, which possess high stiffness but low hardness, can be converted into highly hard materials by incorporating of light elements to form compounds. Such a crossover is a manifestation that the underlying sources of high stiffness and high hardness are fundamentally different. The stiffness is related to elastic deformation that is closely associated with valence electron density, whereas the hardness depends strongly on plastic deformation that is determined by bonding nature. Therefore, the incorporation of light atoms into transition metal should be a valid pathway of designing hard and superhard materials. This strategy is in principle also applicable to other transition-metal borides, carbides, and nitrides.

A split band-Cholesky equation solving strategy for finite element analysis of transient field problems. [in fluid mechanics

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1978-01-01

The paper describes the split-Cholesky strategy for banded matrices arising from the large systems of equations in certain fluid mechanics problems. The basic idea is that for a banded matrix the computation can be carried out in pieces, with only a small portion of the matrix residing in core. Mesh considerations are discussed by demonstrating the manner in which the assembly of finite element equations proceeds for linear trial functions on a triangular mesh. The FORTRAN code which implements the out-of-core decomposition strategy for banded symmetric positive definite matrices (mass matrices) of a coupled initial value problem is given.

Constrained hierarchical least square nonlinear equation solvers. [for indefinite stiffness and large structural deformations

NASA Technical Reports Server (NTRS)

Padovan, J.; Lackney, J.

1986-01-01

The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.

Improving Stiffness-to-weight Ratio of Spot-welded Structures based upon Nonlinear Finite Element Modelling

NASA Astrophysics Data System (ADS)

Zhang, Shengyong

2017-07-01

Spot welding has been widely used for vehicle body construction due to its advantages of high speed and adaptability for automation. An effort to increase the stiffness-to-weight ratio of spot-welded structures is investigated based upon nonlinear finite element analysis. Topology optimization is conducted for reducing weight in the overlapping regions by choosing an appropriate topology. Three spot-welded models (lap, doubt-hat and T-shape) that approximate “typical” vehicle body components are studied for validating and illustrating the proposed method. It is concluded that removing underutilized material from overlapping regions can result in a significant increase in structural stiffness-to-weight ratio.

Stability and Convergence of Underintegrated Finite Element Approximations

NASA Technical Reports Server (NTRS)

Oden, J. T.

1984-01-01

The effects of underintegration on the numerical stability and convergence characteristics of certain classes of finite element approximations were analyzed. Particular attention is given to hourglassing instabilities that arise from underintegrating the stiffness matrix entries and checkerboard instabilities that arise from underintegrating constrain terms such as those arising from incompressibility conditions. A fundamental result reported here is the proof that the fully integrated stiffness is restored in some cases through a post-processing operation.

Influence of Joint Flexibility on Vibration Analysis of Free-Free Beams

NASA Astrophysics Data System (ADS)

Gunda, Jagadish Babu; Krishna, Y.

2014-12-01

In present work, joint flexibility (or looseness) of the free-free beam is investigated by using a two noded beam finite element formulation with transverse displacement and joint rotations as the degrees of freedom per node at joint location. Flexibility of the joint is primarily represented by means of a rotational spring analogy, where the stiffness of the rotational spring characterizes the looseness of the flexible joint for an applied bending moment. Influence of joint location as well as joint stiffness on modal behavior of first five modes of slender, uniform free-free beams are discussed for various values of non-dimensional rotational spring stiffness parameter. Numerical accuracy of the results obtained from the present finite element formulation are validated by using the commercially available finite element software which shows the confidence gained on the numerical results discussed in the present study.

Experimental Validation of Normalized Uniform Load Surface Curvature Method for Damage Localization

PubMed Central

Jung, Ho-Yeon; Sung, Seung-Hoon; Jung, Hyung-Jo

2015-01-01

In this study, we experimentally validated the normalized uniform load surface (NULS) curvature method, which has been developed recently to assess damage localization in beam-type structures. The normalization technique allows for the accurate assessment of damage localization with greater sensitivity irrespective of the damage location. In this study, damage to a simply supported beam was numerically and experimentally investigated on the basis of the changes in the NULS curvatures, which were estimated from the modal flexibility matrices obtained from the acceleration responses under an ambient excitation. Two damage scenarios were considered for the single damage case as well as the multiple damages case by reducing the bending stiffness (EI) of the affected element(s). Numerical simulations were performed using MATLAB as a preliminary step. During the validation experiments, a series of tests were performed. It was found that the damage locations could be identified successfully without any false-positive or false-negative detections using the proposed method. For comparison, the damage detection performances were compared with those of two other well-known methods based on the modal flexibility matrix, namely, the uniform load surface (ULS) method and the ULS curvature method. It was confirmed that the proposed method is more effective for investigating the damage locations of simply supported beams than the two conventional methods in terms of sensitivity to damage under measurement noise. PMID:26501286

2D-DIGE proteomic analysis of mesenchymal stem cell cultured on the elasticity-tunable hydrogels.

PubMed

Kuboki, Thasaneeya; Kantawong, Fahsai; Burchmore, Richard; Dalby, Matthew J; Kidoaki, Satoru

2012-01-01

The present study focuses on mechanotransduction in mesenchymal stem cells (MSCs) in response to matrix elasticity. By using photocurable gelatinous gels with tunable stiffness, proteomic profiles of MSCs cultured on tissue culture plastic, soft (3 kPa) and stiff (52 kPa) matrices were deciphered using 2-dimensional differential in-gel analysis (2D-DIGE). The DIGE data, tied to immunofluorescence, indicated abundance and organization changes in the cytoskeletonal proteins as well as differential regulation of important signaling-related proteins, stress-responsing proteins and also proteins involved in collagen synthesis. The major CSK proteins including actin, tubulin and vimentin of the cells cultured on the gels were remarkably changed their expressions. Significant down-regulation of α-tubulin and β-actin can be observed on gel samples in comparison to the rigid tissue culture plates. The expression abundance of vimentin appeared to be highest in the MSCs cultured on hard gels. These results suggested that the substrate stiffness significantly affects expression balances in cytoskeletal proteins of MSCs with some implications to cellular tensegrity.

Unbalance Response Prediction for Rotors on Ball Bearings Using Speed and Load Dependent Nonlinear Bearing Stiffness

NASA Technical Reports Server (NTRS)

Fleming, David P.; Poplawski, J. V.

2003-01-01

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic analysis requires that bearing forces corresponding to the actual bearing deflection be utilized. For this work bearing forces were calculated by COBRA-AHS, a recently developed rolling-element bearing analysis code. Bearing stiffness was found to be a strong function of bearing deflection, with higher deflection producing markedly higher stiffness. Curves fitted to the bearing data for a range of speeds and loads were supplied to a flexible rotor unbalance response analysis. The rotordynamic analysis showed that vibration response varied nonlinearly with the amount of rotor imbalance. Moreover, the increase in stiffness as critical speeds were approached caused a large increase in rotor and bearing vibration amplitude over part of the speed range compared to the case of constant bearing stiffness. Regions of bistable operation were possible, in which the amplitude at a given speed was much larger during rotor acceleration than during deceleration. A moderate amount of damping will eliminate the bistable region, but this damping is not inherent in ball bearings.

Parameter identification and optimization of slide guide joint of CNC machine tools

NASA Astrophysics Data System (ADS)

Zhou, S.; Sun, B. B.

2017-11-01

The joint surface has an important influence on the performance of CNC machine tools. In order to identify the dynamic parameters of slide guide joint, the parametric finite element model of the joint is established and optimum design method is used based on the finite element simulation and modal test. Then the mode that has the most influence on the dynamics of slip joint is found through harmonic response analysis. Take the frequency of this mode as objective, the sensitivity analysis of the stiffness of each joint surface is carried out using Latin Hypercube Sampling and Monte Carlo Simulation. The result shows that the vertical stiffness of slip joint surface constituted by the bed and the slide plate has the most obvious influence on the structure. Therefore, this stiffness is taken as the optimization variable and the optimal value is obtained through studying the relationship between structural dynamic performance and stiffness. Take the stiffness values before and after optimization into the FEM of machine tool, and it is found that the dynamic performance of the machine tool is improved.

A Subspace Approach to the Structural Decomposition and Identification of Ankle Joint Dynamic Stiffness.

PubMed

Jalaleddini, Kian; Tehrani, Ehsan Sobhani; Kearney, Robert E

2017-06-01

The purpose of this paper is to present a structural decomposition subspace (SDSS) method for decomposition of the joint torque to intrinsic, reflexive, and voluntary torques and identification of joint dynamic stiffness. First, it formulates a novel state-space representation for the joint dynamic stiffness modeled by a parallel-cascade structure with a concise parameter set that provides a direct link between the state-space representation matrices and the parallel-cascade parameters. Second, it presents a subspace method for the identification of the new state-space model that involves two steps: 1) the decomposition of the intrinsic and reflex pathways and 2) the identification of an impulse response model of the intrinsic pathway and a Hammerstein model of the reflex pathway. Extensive simulation studies demonstrate that SDSS has significant performance advantages over some other methods. Thus, SDSS was more robust under high noise conditions, converging where others failed; it was more accurate, giving estimates with lower bias and random errors. The method also worked well in practice and yielded high-quality estimates of intrinsic and reflex stiffnesses when applied to experimental data at three muscle activation levels. The simulation and experimental results demonstrate that SDSS accurately decomposes the intrinsic and reflex torques and provides accurate estimates of physiologically meaningful parameters. SDSS will be a valuable tool for studying joint stiffness under functionally important conditions. It has important clinical implications for the diagnosis, assessment, objective quantification, and monitoring of neuromuscular diseases that change the muscle tone.

From deep TLS validation to ensembles of atomic models built from elemental motions

DOE PAGES

Urzhumtsev, Alexandre; Afonine, Pavel V.; Van Benschoten, Andrew H.; ...

2015-07-28

The translation–libration–screw model first introduced by Cruickshank, Schomaker and Trueblood describes the concerted motions of atomic groups. Using TLS models can improve the agreement between calculated and experimental diffraction data. Because the T, L and S matrices describe a combination of atomic vibrations and librations, TLS models can also potentially shed light on molecular mechanisms involving correlated motions. However, this use of TLS models in mechanistic studies is hampered by the difficulties in translating the results of refinement into molecular movement or a structural ensemble. To convert the matrices into a constituent molecular movement, the matrix elements must satisfy severalmore » conditions. Refining the T, L and S matrix elements as independent parameters without taking these conditions into account may result in matrices that do not represent concerted molecular movements. Here, a mathematical framework and the computational tools to analyze TLS matrices, resulting in either explicit decomposition into descriptions of the underlying motions or a report of broken conditions, are described. The description of valid underlying motions can then be output as a structural ensemble. All methods are implemented as part of the PHENIX project.« less

The pearl oyster Pinctada fucata martensii genome and multi-omic analyses provide insights into biomineralization

PubMed Central

Fan, Guangyi; Jiao, Yu; Zhang, He; Huang, Ronglian; Zheng, Zhe; Bian, Chao; Deng, Yuewen; Wang, Qingheng; Wang, Zhongduo; Liang, Xinming; Liang, Haiying; Shi, Chengcheng; Zhao, Xiaoxia; Sun, Fengming; Hao, Ruijuan; Bai, Jie; Liu, Jialiang; Chen, Wenbin; Liang, Jinlian; Liu, Weiqing; Xu, Zhe; Shi, Qiong; Xu, Xun

2017-01-01

Abstract Nacre, the iridescent material found in pearls and shells of molluscs, is formed through an extraordinary process of matrix-assisted biomineralization. Despite recent advances, many aspects of the biomineralization process and its evolutionary origin remain unknown. The pearl oyster Pinctada fucata martensii is a well-known master of biomineralization, but the molecular mechanisms that underlie its production of shells and pearls are not fully understood. We sequenced the highly polymorphic genome of the pearl oyster and conducted multi-omic and biochemical studies to probe nacre formation. We identified a large set of novel proteins participating in matrix-framework formation, many in expanded families, including components similar to that found in vertebrate bones such as collagen-related VWA-containing proteins, chondroitin sulfotransferases, and regulatory elements. Considering that there are only collagen-based matrices in vertebrate bones and chitin-based matrices in most invertebrate skeletons, the presence of both chitin and elements of collagen-based matrices in nacre suggests that elements of chitin- and collagen-based matrices have deep roots and might be part of an ancient biomineralizing matrix. Our results expand the current shell matrix-framework model and provide new insights into the evolution of diverse biomineralization systems. PMID:28873964

Boundary Layer Effect on Behavior of Discrete Models

PubMed Central

Eliáš, Jan

2017-01-01

The paper studies systems of rigid bodies with randomly generated geometry interconnected by normal and tangential bonds. The stiffness of these bonds determines the macroscopic elastic modulus while the macroscopic Poisson’s ratio of the system is determined solely by the normal/tangential stiffness ratio. Discrete models with no directional bias have the same probability of element orientation for any direction and therefore the same mechanical properties in a statistical sense at any point and direction. However, the layers of elements in the vicinity of the boundary exhibit biased orientation, preferring elements parallel with the boundary. As a consequence, when strain occurs in this direction, the boundary layer becomes stiffer than the interior for the normal/tangential stiffness ratio larger than one, and vice versa. Nonlinear constitutive laws are typically such that the straining of an element in shear results in higher strength and ductility than straining in tension. Since the boundary layer tends, due to the bias in the elemental orientation, to involve more tension than shear at the contacts, it also becomes weaker and less ductile. The paper documents these observations and compares them to the results of theoretical analysis. PMID:28772517

Finite-element grid improvement by minimization of stiffness matrix trace

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.

1989-01-01

A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.

Finite-element grid improvement by minimization of stiffness matrix trace

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.

1987-01-01

A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.

Applications of synchrotron μ-XRF to study the distribution of biologically important elements in different environmental matrices: a review.

PubMed

Majumdar, Sanghamitra; Peralta-Videa, Jose R; Castillo-Michel, Hiram; Hong, Jie; Rico, Cyren M; Gardea-Torresdey, Jorge L

2012-11-28

Environmental matrices including soils, sediments, and living organisms are reservoirs of several essential as well as non-essential elements. Accurate qualitative and quantitative information on the distribution and interaction of biologically significant elements is vital to understand the role of these elements in environmental and biological samples. Synchrotron micro-X-ray fluorescence (μ-SXRF) allows in situ mapping of biologically important elements at nanometer to sub-micrometer scale with high sensitivity, negligible sample damage and enable tuning of the incident energy as desired. Beamlines in the synchrotron facilities are rapidly increasing their analytical versatility in terms of focusing optics, detector technologies, incident energy, and sample environment. Although extremely competitive, it is now feasible to find stations offering complimentary techniques like micro-X-ray diffraction (μ-XRD) and micro-X-ray absorption spectroscopy (μ-XAS) that will allow a more complete characterization of complex matrices. This review includes the most recent literature on the emerging applications and challenges of μ-SXRF in studying the distribution of biologically important elements and manufactured nanoparticles in soils, sediments, plants, and microbes. The advantages of using μ-SXRF and complimentary techniques in contrast to conventional techniques used for the respective studies are discussed. Copyright © 2012 Elsevier B.V. All rights reserved.

Reduced order modeling, statistical analysis and system identification for a bladed rotor with geometric mistuning

NASA Astrophysics Data System (ADS)

Vishwakarma, Vinod

Modified Modal Domain Analysis (MMDA) is a novel method for the development of a reduced-order model (ROM) of a bladed rotor. This method utilizes proper orthogonal decomposition (POD) of Coordinate Measurement Machine (CMM) data of blades' geometries and sector analyses using ANSYS. For the first time ROM of a geometrically mistuned industrial scale rotor (Transonic rotor) with large size of Finite Element (FE) model is generated using MMDA. Two methods for estimating mass and stiffness mistuning matrices are used a) exact computation from sector FE analysis, b) estimates based on POD mistuning parameters. Modal characteristics such as mistuned natural frequencies, mode shapes and forced harmonic response are obtained from ROM for various cases, and results are compared with full rotor ANSYS analysis and other ROM methods such as Subset of Nominal Modes (SNM) and Fundamental Model of Mistuning (FMM). Accuracy of MMDA ROM is demonstrated with variations in number of POD features and geometric mistuning parameters. It is shown for the aforementioned case b) that the high accuracy of ROM studied in previous work with Academic rotor does not directly translate to the Transonic rotor. Reasons for such mismatch in results are investigated and attributed to higher mistuning in Transonic rotor. Alternate solutions such as estimation of sensitivities via least squares, and interpolation of mass and stiffness matrices on manifolds are developed, and their results are discussed. Statistics such as mean and standard deviations of forced harmonic response peak amplitude are obtained from random permutations, and are shown to have similar results as those of Monte Carlo simulations. These statistics are obtained and compared for 3 degree of freedom (DOF) lumped parameter model (LPM) of rotor, Academic rotor and Transonic rotor. A state -- estimator based on MMDA ROM and Kalman filter is also developed for offline or online estimation of harmonic forcing function from measurements of forced response. Forcing function is estimated for synchronous excitation of 3DOF rotor model, Academic rotor and Transonic rotor from measurement of response at few nodes. For asynchronous excitation forcing function is estimated only for 3DOF rotor model and Academic rotor from measurement of response. The impact of number of measurement locations and accuracy of ROM on the estimation of forcing function is discussed. iv.

Fully Coupled Nonlinear Fluid Flow and Poroelasticity in Arbitrarily Fractured Porous Media: A Hybrid-Dimensional Computational Model

NASA Astrophysics Data System (ADS)

Jin, L.; Zoback, M. D.

2017-10-01

We formulate the problem of fully coupled transient fluid flow and quasi-static poroelasticity in arbitrarily fractured, deformable porous media saturated with a single-phase compressible fluid. The fractures we consider are hydraulically highly conductive, allowing discontinuous fluid flux across them; mechanically, they act as finite-thickness shear deformation zones prior to failure (i.e., nonslipping and nonpropagating), leading to "apparent discontinuity" in strain and stress across them. Local nonlinearity arising from pressure-dependent permeability of fractures is also included. Taking advantage of typically high aspect ratio of a fracture, we do not resolve transversal variations and instead assume uniform flow velocity and simple shear strain within each fracture, rendering the coupled problem numerically more tractable. Fractures are discretized as lower dimensional zero-thickness elements tangentially conforming to unstructured matrix elements. A hybrid-dimensional, equal-low-order, two-field mixed finite element method is developed, which is free from stability issues for a drained coupled system. The fully implicit backward Euler scheme is employed for advancing the fully coupled solution in time, and the Newton-Raphson scheme is implemented for linearization. We show that the fully discretized system retains a canonical form of a fracture-free poromechanical problem; the effect of fractures is translated to the modification of some existing terms as well as the addition of several terms to the capacity, conductivity, and stiffness matrices therefore allowing the development of independent subroutines for treating fractures within a standard computational framework. Our computational model provides more realistic inputs for some fracture-dominated poromechanical problems like fluid-induced seismicity.

Use of system identification techniques for improving airframe finite element models using test data

NASA Technical Reports Server (NTRS)

Hanagud, Sathya V.; Zhou, Weiyu; Craig, James I.; Weston, Neil J.

1991-01-01

A method for using system identification techniques to improve airframe finite element models was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory.

Dynamic characteristics of a vibrating beam with periodic variation in bending stiffness

NASA Technical Reports Server (NTRS)

Townsend, John S.

1987-01-01

A detailed dynamic analysis is performed of a vibrating beam with bending stiffness periodic in the spatial coordinate. The effects of system parameters on beam response are explored with a perturbation expansion technique. It is found that periodic stiffness acts to modulate the modal displacements from the characteristic shape of a simple sine wave. The results are verified by a finite element solution and through experimental testing.

Stiffness degradation-based damage model for RC members and structures using fiber-beam elements

NASA Astrophysics Data System (ADS)

Guo, Zongming; Zhang, Yaoting; Lu, Jiezhi; Fan, Jian

2016-12-01

To meet the demand for an accurate and highly efficient damage model with a distinct physical meaning for performance-based earthquake engineering applications, a stiffness degradation-based damage model for reinforced concrete (RC) members and structures was developed using fiber beam-column elements. In this model, damage indices for concrete and steel fibers were defined by the degradation of the initial reloading modulus and the low-cycle fatigue law. Then, section, member, story and structure damage was evaluated by the degradation of the sectional bending stiffness, rod-end bending stiffness, story lateral stiffness and structure lateral stiffness, respectively. The damage model was realized in Matlab by reading in the outputs of OpenSees. The application of the damage model to RC columns and a RC frame indicates that the damage model is capable of accurately predicting the magnitude, position, and evolutionary process of damage, and estimating story damage more precisely than inter-story drift. Additionally, the damage model establishes a close connection between damage indices at various levels without introducing weighting coefficients or force-displacement relationships. The development of the model has perfected the damage assessment function of OpenSees, laying a solid foundation for damage estimation at various levels of a large-scale structure subjected to seismic loading.

Micromechanical models for textile structural composites

NASA Technical Reports Server (NTRS)

Marrey, Ramesh V.; Sankar, Bhavani V.

1995-01-01

The objective is to develop micromechanical models for predicting the stiffness and strength properties of textile composite materials. Two models are presented to predict the homogeneous elastic constants and coefficients of thermal expansion of a textile composite. The first model is based on rigorous finite element analysis of the textile composite unit-cell. Periodic boundary conditions are enforced between opposite faces of the unit-cell to simulate deformations accurately. The second model implements the selective averaging method (SAM), which is based on a judicious combination of stiffness and compliance averaging. For thin textile composites, both models can predict the plate stiffness coefficients and plate thermal coefficients. The finite element procedure is extended to compute the thermal residual microstresses, and to estimate the initial failure envelope for textile composites.

Experimental characterization and numerical simulation of riveted lap-shear joints using Rivet Element

NASA Astrophysics Data System (ADS)

Vivio, Francesco; Fanelli, Pierluigi; Ferracci, Michele

2018-03-01

In aeronautical and automotive industries the use of rivets for applications requiring several joining points is now very common. In spite of a very simple shape, a riveted junction has many contact surfaces and stress concentrations that make the local stiffness very difficult to be calculated. To overcome this difficulty, commonly finite element models with very dense meshes are performed for single joint analysis because the accuracy is crucial for a correct structural analysis. Anyhow, when several riveted joints are present, the simulation becomes computationally too heavy and usually significant restrictions to joint modelling are introduced, sacrificing the accuracy of local stiffness evaluation. In this paper, we tested the accuracy of a rivet finite element presented in previous works by the authors. The structural behaviour of a lap joint specimen with a rivet joining is simulated numerically and compared to experimental measurements. The Rivet Element, based on a closed-form solution of a reference theoretical model of the rivet joint, simulates local and overall stiffness of the junction combining high accuracy with low degrees of freedom contribution. In this paper the Rivet Element performances are compared to that of a FE non-linear model of the rivet, built with solid elements and dense mesh, and to experimental data. The promising results reported allow to consider the Rivet Element able to simulate, with a great accuracy, actual structures with several rivet connections.

Global and local approaches to population analysis: Bonding patterns in superheavy element compounds

NASA Astrophysics Data System (ADS)

Oleynichenko, Alexander; Zaitsevskii, Andréi; Romanov, Stepan; Skripnikov, Leonid V.; Titov, Anatoly V.

2018-03-01

Relativistic effective atomic configurations of superheavy elements Cn, Nh and Fl and their lighter homologues (Hg, Tl and Pb) in their simple compounds with fluorine and oxygen are determined using the analysis of local properties of molecular Kohn-Sham density matrices in the vicinity of heavy nuclei. The difference in populations of atomic spinors with the same orbital angular momentum and different total angular momenta is demonstrated to be essential for understanding the peculiarities of chemical bonding in superheavy element compounds. The results are fully compatible with those obtained by the relativistic iterative version of conventional projection analysis of global density matrices.

Damage identification of a reinforced concrete frame by finite element model updating using damage parameterization

NASA Astrophysics Data System (ADS)

Fang, Sheng-En; Perera, Ricardo; De Roeck, Guido

2008-06-01

This paper develops a sensitivity-based updating method to identify the damage in a tested reinforced concrete (RC) frame modeled with a two-dimensional planar finite element (FE) by minimizing the discrepancies of modal frequencies and mode shapes. In order to reduce the number of unknown variables, a bidimensional damage (element) function is proposed, resulting in a considerable improvement of the optimization performance. For damage identification, a reference FE model of the undamaged frame divided into a few damage functions is firstly obtained and then a rough identification is carried out to detect possible damage locations, which are subsequently refined with new damage functions to accurately identify the damage. From a design point of view, it would be useful to evaluate, in a simplified way, the remaining bending stiffness of cracked beam sections or segments. Hence, an RC damage model based on a static mechanism is proposed to estimate the remnant stiffness of a cracked RC beam segment. The damage model is based on the assumption that the damage effect spreads over a region and the stiffness in the segment changes linearly. Furthermore, the stiffness reduction evaluated using this damage model is compared with the FE updating result. It is shown that the proposed bidimensional damage function is useful in producing a well-conditioned optimization problem and the aforementioned damage model can be used for an approximate stiffness estimation of a cracked beam segment.

Active noise control using noise source having adaptive resonant frequency tuning through stiffness variation

NASA Technical Reports Server (NTRS)

Rajiyah, Harindra (Inventor); Hedeen, Robert A. (Inventor); Pla, Frederic G. (Inventor); Renshaw, Anthony A. (Inventor)

1995-01-01

A noise source for an aircraft engine active noise cancellation system in which the resonant frequency of a noise radiating element is tuned to permit noise cancellation over a wide range of frequencies. The resonant frequency of the noise radiating element is tuned by a plurality of force transmitting mechanisms which contact the noise radiating element. Each one of the force transmitting mechanisms includes an expandable element and a spring in contact with the noise radiating element so that excitation of the element varies the spring force applied to the noise radiating element. The elements are actuated by a controller which receives input of a signal proportional to displacement of the noise radiating element and a signal corresponding to the blade passage frequency of the engine's fan. In response, the controller determines a control signal which is sent to the elements and causes the spring force applied to the noise radiating element to be varied. The force transmitting mechanisms can be arranged to either produce bending or linear stiffness variations in the noise radiating element.

Spatial distributions of pericellular stiffness in natural extracellular matrices are dependent on cell-mediated proteolysis and contractility.

PubMed

Keating, M; Kurup, A; Alvarez-Elizondo, M; Levine, A J; Botvinick, E

2017-07-15

Bulk tissue stiffness has been correlated with regulation of cellular processes and conversely cells have been shown to remodel their pericellular tissue according to a complex feedback mechanism critical to development, homeostasis, and disease. However, bulk rheological methods mask the dynamics within a heterogeneous fibrous extracellular matrix (ECM) in the region proximal to a cell (pericellular region). Here, we use optical tweezers active microrheology (AMR) to probe the distribution of the complex material response function (α=α'+α″, in units of µm/nN) within a type I collagen ECM, a biomaterial commonly used in tissue engineering. We discovered cells both elastically and plastically deformed the pericellular material. α' is wildly heterogeneous, with 1/α' values spanning three orders of magnitude around a single cell. This was observed in gels having a cell-free 1/α' of approximately 0.5nN/µm. We also found that inhibition of cell contractility instantaneously softens the pericellular space and reduces stiffness heterogeneity, suggesting the system was strain hardened and not only plastically remodeled. The remaining regions of high stiffness suggest cellular remodeling of the surrounding matrix. To test this hypothesis, cells were incubated within the type I collagen gel for 24-h in a media containing a broad-spectrum matrix metalloproteinase (MMP) inhibitor. While pericellular material maintained stiffness asymmetry, stiffness magnitudes were reduced. Dual inhibition demonstrates that the combination of MMP activity and contractility is necessary to establish the pericellular stiffness landscape. This heterogeneity in stiffness suggests the distribution of pericellular stiffness, and not bulk stiffness alone, must be considered in the study of cell-ECM interactions and design of complex biomaterial scaffolds. Collagen is a fibrous extracellular matrix (ECM) protein widely used to study cell-ECM interactions. Stiffness of ECM has been shown to instruct cells, which can in turn modify their ECM, as has been shown in the study of cancer and regenerative medicine. Here we measure the stiffness of the collagen microenvironment surrounding cells and quantitatively measure the dependence of pericellular stiffness on MMP activity and cytoskeletal contractility. Competent cell-mediated stiffening results in a wildly heterogeneous micromechanical topography, with values spanning orders of magnitude around a single cell. We speculate studies must consider this notable heterogeneity generated by cells when testing theories regarding the role of ECM mechanics in health and disease. Copyright © 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Study on Finite Element Model Updating in Highway Bridge Static Loading Test Using Spatially-Distributed Optical Fiber Sensors

PubMed Central

Wu, Bitao; Lu, Huaxi; Chen, Bo; Gao, Zhicheng

2017-01-01

A finite model updating method that combines dynamic-static long-gauge strain responses is proposed for highway bridge static loading tests. For this method, the objective function consisting of static long-gauge stains and the first order modal macro-strain parameter (frequency) is established, wherein the local bending stiffness, density and boundary conditions of the structures are selected as the design variables. The relationship between the macro-strain and local element stiffness was studied first. It is revealed that the macro-strain is inversely proportional to the local stiffness covered by the long-gauge strain sensor. This corresponding relation is important for the modification of the local stiffness based on the macro-strain. The local and global parameters can be simultaneously updated. Then, a series of numerical simulation and experiments were conducted to verify the effectiveness of the proposed method. The results show that the static deformation, macro-strain and macro-strain modal can be predicted well by using the proposed updating model. PMID:28753912

Study on Finite Element Model Updating in Highway Bridge Static Loading Test Using Spatially-Distributed Optical Fiber Sensors.

PubMed

Wu, Bitao; Lu, Huaxi; Chen, Bo; Gao, Zhicheng

2017-07-19

A finite model updating method that combines dynamic-static long-gauge strain responses is proposed for highway bridge static loading tests. For this method, the objective function consisting of static long-gauge stains and the first order modal macro-strain parameter (frequency) is established, wherein the local bending stiffness, density and boundary conditions of the structures are selected as the design variables. The relationship between the macro-strain and local element stiffness was studied first. It is revealed that the macro-strain is inversely proportional to the local stiffness covered by the long-gauge strain sensor. This corresponding relation is important for the modification of the local stiffness based on the macro-strain. The local and global parameters can be simultaneously updated. Then, a series of numerical simulation and experiments were conducted to verify the effectiveness of the proposed method. The results show that the static deformation, macro-strain and macro-strain modal can be predicted well by using the proposed updating model.

Modelling the effect of round window stiffness on residual hearing after cochlear implantation.

PubMed

Elliott, Stephen J; Ni, Guangjian; Verschuur, Carl A

2016-11-01

Preservation of residual hearing after cochlear implantation is now considered an important goal of surgery. However, studies indicate an average post-operative hearing loss of around 20 dB at low frequencies. One factor which may contribute to post-operative hearing loss, but which has received little attention in the literature to date, is the increased stiffness of the round window, due to the physical presence of the cochlear implant, and to its subsequent thickening or to bone growth around it. A finite element model was used to estimate that there is approximately a 100-fold increase in the round window stiffness due to a cochlear implant passing through it. A lumped element model was then developed to study the effects of this change in stiffness on the acoustic response of the cochlea. As the round window stiffness increases, the effects of the cochlear and vestibular aqueducts become more important. An increase of round window stiffness by a factor of 10 is predicted to have little effect on residual hearing, but increasing this stiffness by a factor of 100 reduces the acoustic sensitivity of the cochlea by about 20 dB, below 1 kHz, in reasonable agreement with the observed loss in residual hearing after implantation. It is also shown that the effect of this stiffening could be reduced by incorporating a small gas bubble within the cochlear implant. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Optimal lay-up design of variable stiffness laminated composite plates by a layer-wise optimization technique

NASA Astrophysics Data System (ADS)

Houmat, A.

2018-02-01

The optimal lay-up design for the maximum fundamental frequency of variable stiffness laminated composite plates is investigated using a layer-wise optimization technique. The design variables are two fibre orientation angles per ply. Thin plate theory is used in conjunction with a p-element to calculate the fundamental frequencies of symmetrically and antisymmetrically laminated composite plates. Comparisons with existing optimal solutions for constant stiffness symmetrically laminated composite plates show excellent agreement. It is observed that the maximum fundamental frequency can be increased considerably using variable stiffness design as compared to constant stiffness design. In addition, optimal lay-ups for the maximum fundamental frequency of variable stiffness symmetrically and antisymmetrically laminated composite plates with different aspect ratios and various combinations of free, simply supported and clamped edge conditions are presented. These should prove a useful benchmark for optimal lay-ups of variable stiffness laminated composite plates.

Transient Vibration Prediction for Rotors on Ball Bearings Using Load-dependent Non-linear Bearing Stiffness

NASA Technical Reports Server (NTRS)

Fleming, David P.; Poplawski, J. V.

2002-01-01

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic transient analysis requires bearing forces to be determined at each step of the transient solution. Analyses have been carried out to show the effect of accurate bearing transient forces (accounting for non-linear speed and load dependent bearing stiffness) as compared to conventional use of average rolling-element bearing stiffness. Bearing forces were calculated by COBRA-AHS (Computer Optimized Ball and Roller Bearing Analysis - Advanced High Speed) and supplied to the rotordynamics code ARDS (Analysis of Rotor Dynamic Systems) for accurate simulation of rotor transient behavior. COBRA-AHS is a fast-running 5 degree-of-freedom computer code able to calculate high speed rolling-element bearing load-displacement data for radial and angular contact ball bearings and also for cylindrical and tapered roller beatings. Results show that use of nonlinear bearing characteristics is essential for accurate prediction of rotordynamic behavior.

Solution of large nonlinear quasistatic structural mechanics problems on distributed-memory multiprocessor computers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blanford, M.

1997-12-31

Most commercially-available quasistatic finite element programs assemble element stiffnesses into a global stiffness matrix, then use a direct linear equation solver to obtain nodal displacements. However, for large problems (greater than a few hundred thousand degrees of freedom), the memory size and computation time required for this approach becomes prohibitive. Moreover, direct solution does not lend itself to the parallel processing needed for today`s multiprocessor systems. This talk gives an overview of the iterative solution strategy of JAS3D, the nonlinear large-deformation quasistatic finite element program. Because its architecture is derived from an explicit transient-dynamics code, it does not ever assemblemore » a global stiffness matrix. The author describes the approach he used to implement the solver on multiprocessor computers, and shows examples of problems run on hundreds of processors and more than a million degrees of freedom. Finally, he describes some of the work he is presently doing to address the challenges of iterative convergence for ill-conditioned problems.« less

Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

NASA Astrophysics Data System (ADS)

Banerjee, J. R.; Ananthapuvirajah, A.

2018-05-01

The free vibration analysis of functionally graded beams (FGBs) and frameworks containing FGBs is carried out by applying the dynamic stiffness method and deriving the elements of the dynamic stiffness matrix in explicit algebraic form. The usually adopted rule that the material properties of the FGB vary continuously through the thickness according to a power law forms the fundamental basis of the governing differential equations of motion in free vibration. The differential equations are solved in closed analytical form when the free vibratory motion is harmonic. The dynamic stiffness matrix is then formulated by relating the amplitudes of forces to those of the displacements at the two ends of the beam. Next, the explicit algebraic expressions for the dynamic stiffness elements are derived with the help of symbolic computation. Finally the Wittrick-Williams algorithm is applied as solution technique to solve the free vibration problems of FGBs with uniform cross-section, stepped FGBs and frameworks consisting of FGBs. Some numerical results are validated against published results, but in the absence of published results for frameworks containing FGBs, consistency checks on the reliability of results are performed. The paper closes with discussion of results and conclusions.

Use of system identification techniques for improving airframe finite element models using test data

NASA Technical Reports Server (NTRS)

Hanagud, Sathya V.; Zhou, Weiyu; Craig, James I.; Weston, Neil J.

1993-01-01

A method for using system identification techniques to improve airframe finite element models using test data was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in the total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all of the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory.

Tubing-Electrospinning: A One-Step Process for Fabricating Fibrous Matrices with Spatial, Chemical, and Mechanical Gradients.

PubMed

Kim, Jung-Suk; Im, Byung Gee; Jin, Gyuhyung; Jang, Jae-Hyung

2016-08-31

Guiding newly generated tissues in a gradient pattern, thereby precisely mimicking inherent tissue morphology and subsequently arranging the intimate networks between adjacent tissues, is essential to raise the technical levels of tissue engineering and facilitate its transition into the clinic. In this study, a straightforward electrospinning method (the tubing-electrospinning technique) was developed to create fibrous matrices readily with diverse gradient patterns and to induce patterned cellular responses. Gradient fibrous matrices can be produced simply by installing a series of polymer-containing lengths of tubing into an electrospinning circuit and sequentially processing polymers without a time lag. The loading of polymer samples with different characteristics, including concentration, wettability, and mechanical properties, into the tubing system enabled unique features in fibrous matrices, such as longitudinal gradients in fiber density, surface properties, and mechanical stiffness. The resulting fibrous gradients were shown to arrange cellular migration and residence in a gradient manner, thereby offering efficient cues to mediate patterned tissue formation. The one-step process using tubing-electrospinning apparatus can be used without significant modifications regardless of the type of fibrous gradient. Hence, the tubing-electrospinning system can serve as a platform that can be readily used by a wide-range of users to induce patterned tissue formation in a gradient manner, which will ultimately improve the functionality of tissue engineering scaffolds.

Composites reinforced via mechanical interlocking of surface-roughened microplatelets within ductile and brittle matrices.

PubMed

Libanori, R; Carnelli, D; Rothfuchs, N; Binelli, M R; Zanini, M; Nicoleau, L; Feichtenschlager, B; Albrecht, G; Studart, A R

2016-04-12

Load-bearing reinforcing elements in a continuous matrix allow for improved mechanical properties and can reduce the weight of structural composites. As the mechanical performance of composite systems are heavily affected by the interfacial properties, tailoring the interactions between matrices and reinforcing elements is a crucial problem. Recently, several studies using bio-inspired model systems suggested that interfacial mechanical interlocking is an efficient mechanism for energy dissipation in platelet-reinforced composites. While cheap and effective solutions are available at the macroscale, the modification of surface topography in micron-sized reinforcing elements still represents a challenging task. Here, we report a simple method to create nanoasperities with tailored sizes and densities on the surface of alumina platelets and investigate their micromechanical effect on the energy dissipation mechanisms of nacre-like materials. Composites reinforced with roughened platelets exhibit improved mechanical properties for both organic ductile epoxy and inorganic brittle cement matrices. Mechanical interlocking increases the modulus of toughness (area under the stress-strain curve) by 110% and 56% in epoxy and cement matrices, respectively, as compared to those reinforced with flat platelets. This interlocking mechanism can potentially lead to a significant reduction in the weight of mechanical components while retaining the structural performance required in the application field.

Polymer, metal and ceramic matrix composites for advanced aircraft engine applications

NASA Technical Reports Server (NTRS)

Mcdanels, D. L.; Serafini, T. T.; Dicarlo, J. A.

1985-01-01

Advanced aircraft engine research within NASA Lewis is being focused on propulsion systems for subsonic, supersonic, and hypersonic aircraft. Each of these flight regimes requires different types of engines, but all require advanced materials to meet their goals of performance, thrust-to-weight ratio, and fuel efficiency. The high strength/weight and stiffness/weight properties of resin, metal, and ceramic matrix composites will play an increasingly key role in meeting these performance requirements. At NASA Lewis, research is ongoing to apply graphite/polyimide composites to engine components and to develop polymer matrices with higher operating temperature capabilities. Metal matrix composites, using magnesium, aluminum, titanium, and superalloy matrices, are being developed for application to static and rotating engine components, as well as for space applications, over a broad temperature range. Ceramic matrix composites are also being examined to increase the toughness and reliability of ceramics for application to high-temperature engine structures and components.

A generalized theory for eccentric and misalignment effects in high-pressure annular seals

NASA Technical Reports Server (NTRS)

Chen, W. C.; Jackson, E. D.

1986-01-01

High-pressure annular seal leakage and dynamic coefficients vary with eccentricity and misalignment. Recent seal leakage data with both concentric and fully eccentric alignments support the seal leakage model with surface roughness and eccentricity effects included. In this paper, the seal dynamic coefficient calculation has been generalized and allows direct calculation of the seal dynamic coefficients at any circumferential location. The generalized solution agrees with the results obtained by using the calculated values of an earlier paper and performing a coordinate transformation. The analysis results coincide with the measured data in showing that the stiffness and damping matrices of seal coefficients are not skew symmetric, and the main diagonal seal coefficients are not equal. The measured direct stiffnesses were found higher than predicted by the concentric seal theory, but this may be explained by the presence of eccentricity in the test operating mode.

Efficient Reformulation of the Thermoelastic Higher-order Theory for Fgms

NASA Technical Reports Server (NTRS)

Bansal, Yogesh; Pindera, Marek-Jerzy; Arnold, Steven M. (Technical Monitor)

2002-01-01

Functionally graded materials (FGMs) are characterized by spatially variable microstructures which are introduced to satisfy given performance requirements. The microstructural gradation gives rise to continuously or discretely changing material properties which complicate FGM analysis. Various techniques have been developed during the past several decades for analyzing traditional composites and many of these have been adapted for the analysis of FGMs. Most of the available techniques use the so-called uncoupled approach in order to analyze graded structures. These techniques ignore the effect of microstructural gradation by employing specific spatial material property variations that are either assumed or obtained by local homogenization. The higher-order theory for functionally graded materials (HOTFGM) is a coupled approach developed by Aboudi et al. (1999) which takes the effect of microstructural gradation into consideration and does not ignore the local-global interaction of the spatially variable inclusion phase(s). Despite its demonstrated utility, however, the original formulation of the higher-order theory is computationally intensive. Herein, an efficient reformulation of the original higher-order theory for two-dimensional elastic problems is developed and validated. The use of the local-global conductivity and local-global stiffness matrix approach is made in order to reduce the number of equations involved. In this approach, surface-averaged quantities are the primary variables which replace volume-averaged quantities employed in the original formulation. The reformulation decreases the size of the global conductivity and stiffness matrices by approximately sixty percent. Various thermal, mechanical, and combined thermomechanical problems are analyzed in order to validate the accuracy of the reformulated theory through comparison with analytical and finite-element solutions. The presented results illustrate the efficiency of the reformulation and its advantages in analyzing functionally graded materials.

Spindle pole body component 25 homolog expressed by ECM stiffening is required for lung cancer cell proliferation.

PubMed

Jeong, Jangho; Keum, Seula; Kim, Daehwan; You, Eunae; Ko, Panseon; Lee, Jieun; Kim, Jaegu; Kim, Jung-Woong; Rhee, Sangmyung

2018-06-12

Accumulating evidence has shown that matrix stiffening in cancer tissue by the deposition of extracellular matrix (ECM) is closely related with severe tumor progression. However, much less is known about the genes affected by matrix stiffness and its signaling for cancer progression. In the current research, we investigated the differential gene expression of a non-small lung adenocarcinoma cell line, H1299, cultured under the conditions of soft (∼0.5 kPa) and stiff (∼40 kPa) matrices, mimicking the mechanical environments of normal and cancerous tissues, respectively. For integrated transcriptome analysis, the genes identified by ECM stiffening were compared with 8248 genes retrieved from The Cancer Genome Atlas Lung Adenocarcinoma (TCGA). In stiff matrix, 29 genes were significantly upregulated, while 75 genes were downregulated. The screening of hazard ratios for these genes using the Kaplan-Meier Plotter identified 8 genes most closely associated with cancer progression under the condition of matrix stiffening. Among these genes, spindle pole body component 25 homolog (SPC25) was one of the most up-regulated genes in stiff matrix and tumor tissue. Knockdown of SPC25 in H1299 cells using shRNA significantly inhibited cell proliferation with downregulation of the expression of checkpoint protein, Cyclin B1, under the condition of stiff matrix whereas the proliferation rate in soft matrix was not affected by SPC25 silencing. Thus, our findings provide novel key molecules for studying the relationship of extracellular matrix stiffening and cancer progression. Copyright © 2018 Elsevier Inc. All rights reserved.

Model Of Bearing With Hydrostatic Damper

NASA Technical Reports Server (NTRS)

Goggin, David G.

1991-01-01

Improved mathematical model of rotational and vibrational dynamics of bearing package in turbopump incorporates effects of hydrostatic damper. Part of larger finite-element model representing rotational and vibrational dynamics of rotor and housing of pump. Includes representations of deadband and nonlinear stiffness and damping of ball bearings, nonlinear stiffness and damping of hydrostatic film, and stiffness of bearing support. Enables incorporation of effects of hydrostatic damper into overall rotor-dynamic mathematical model without addition of mathematical submodel of major substructure.

Prediction of fracture load and stiffness of the proximal femur by CT-based specimen specific finite element analysis: cadaveric validation study.

PubMed

Miura, Michiaki; Nakamura, Junichi; Matsuura, Yusuke; Wako, Yasushi; Suzuki, Takane; Hagiwara, Shigeo; Orita, Sumihisa; Inage, Kazuhide; Kawarai, Yuya; Sugano, Masahiko; Nawata, Kento; Ohtori, Seiji

2017-12-16

Finite element analysis (FEA) of the proximal femur has been previously validated with large mesh size, but these were insufficient to simulate the model with small implants in recent studies. This study aimed to validate the proximal femoral computed tomography (CT)-based specimen-specific FEA model with smaller mesh size using fresh frozen cadavers. Twenty proximal femora from 10 cadavers (mean age, 87.1 years) were examined. CT was performed on all specimens with a calibration phantom. Nonlinear FEA prediction with stance configuration was performed using Mechanical Finder (mesh,1.5 mm tetrahedral elements; shell thickness, 0.2 mm; Poisson's coefficient, 0.3), in comparison with mechanical testing. Force was applied at a fixed vertical displacement rate, and the magnitude of the applied load and displacement were continuously recorded. The fracture load and stiffness were calculated from force-displacement curve, and the correlation between mechanical testing and FEA prediction was examined. A pilot study with one femur revealed that the equations proposed by Keller for vertebra were the most reproducible for calculating Young's modulus and the yield stress of elements of the proximal femur. There was a good linear correlation between fracture loads of mechanical testing and FEA prediction (R 2 = 0.6187) and between the stiffness of mechanical testing and FEA prediction (R 2 = 0.5499). There was a good linear correlation between fracture load and stiffness (R 2 = 0.6345) in mechanical testing and an excellent correlation between these (R 2 = 0.9240) in FEA prediction. CT-based specimen-specific FEA model of the proximal femur with small element size was validated using fresh frozen cadavers. The equations proposed by Keller for vertebra were found to be the most reproducible for the proximal femur in elderly people.

On the buckling of hexagonal boron nitride nanoribbons via structural mechanics

NASA Astrophysics Data System (ADS)

Giannopoulos, Georgios I.

2018-03-01

Monolayer hexagonal boron nitride nanoribbons have similar crystal structure as graphene nanoribbons, have excellent mechanical, thermal insulating and dielectric properties and additionally present chemical stability. These allotropes of boron nitride can be used in novel applications, in which graphene is not compatible, to achieve remarkable performance. The purpose of the present work is to provide theoretical estimations regarding the buckling response of hexagonal boron nitride monolayer under compressive axial loadings. For this reason, a structural mechanics method is formulated which employs the exact equilibrium atomistic structure of the specific two-dimensional nanomaterial. In order to represent the interatomic interactions appearing between boron and nitrogen atoms, the Dreiding potential model is adopted which is realized by the use of three-dimensional, two-noded, spring-like finite elements of appropriate stiffness matrices. The critical compressive loads that cause the buckling of hexagonal boron nitride nanoribbons are computed with respect to their size and chirality while some indicative buckled shapes of them are illustrated. Important conclusions arise regarding the effect of the size and chirality on the structural stability of the hexagonal boron nitride monolayers. An analytical buckling formula, which provides good fitting of the numerical outcome, is proposed.

A NASTRAN-based computer program for structural dynamic analysis of Horizontal Axis Wind Turbines

NASA Technical Reports Server (NTRS)

Lobitz, Don W.

1995-01-01

This paper describes a computer program developed for structural dynamic analysis of horizontal axis wind turbines (HAWT's). It is based on the finite element method through its reliance on NASTRAN for the development of mass, stiffness, and damping matrices of the tower end rotor, which are treated in NASTRAN as separate structures. The tower is modeled in a stationary frame and the rotor in one rotating at a constant angular velocity. The two structures are subsequently joined together (external to NASTRAN) using a time-dependent transformation consistent with the hub configuration. Aerodynamic loads are computed with an established flow model based on strip theory. Aeroelastic effects are included by incorporating the local velocity and twisting deformation of the blade in the load computation. The turbulent nature of the wind, both in space and time, is modeled by adding in stochastic wind increments. The resulting equations of motion are solved in the time domain using the implicit Newmark-Beta integrator. Preliminary comparisons with data from the Boeing/NASA MOD2 HAWT indicate that the code is capable of accurately and efficiently predicting the response of HAWT's driven by turbulent winds.

Investigation into discretization methods of the six-parameter Iwan model

NASA Astrophysics Data System (ADS)

Li, Yikun; Hao, Zhiming; Feng, Jiaquan; Zhang, Dingguo

2017-02-01

Iwan model is widely applied for the purpose of describing nonlinear mechanisms of jointed structures. In this paper, parameter identification procedures of the six-parameter Iwan model based on joint experiments with different preload techniques are performed. Four kinds of discretization methods deduced from stiffness equation of the six-parameter Iwan model are provided, which can be used to discretize the integral-form Iwan model into a sum of finite Jenkins elements. In finite element simulation, the influences of discretization methods and numbers of Jenkins elements on computing accuracy are discussed. Simulation results indicate that a higher accuracy can be obtained with larger numbers of Jenkins elements. It is also shown that compared with other three kinds of discretization methods, the geometric series discretization based on stiffness provides the highest computing accuracy.

Independent control of matrix adhesiveness and stiffness within a 3D self-assembling peptide hydrogel.

PubMed

Hogrebe, Nathaniel J; Reinhardt, James W; Tram, Nguyen K; Debski, Anna C; Agarwal, Gunjan; Reilly, Matthew A; Gooch, Keith J

2018-04-01

A cell's insoluble microenvironment has increasingly been shown to exert influence on its function. In particular, matrix stiffness and adhesiveness strongly impact behaviors such as cell spreading and differentiation, but materials that allow for independent control of these parameters within a fibrous, stromal-like microenvironment are very limited. In the current work, we devise a self-assembling peptide (SAP) system that facilitates user-friendly control of matrix stiffness and RGD (Arg-Gly-Asp) concentration within a hydrogel possessing a microarchitecture similar to stromal extracellular matrix. In this system, the RGD-modified SAP sequence KFE-RGD and the scrambled sequence KFE-RDG can be directly swapped for one another to change RGD concentration at a given matrix stiffness and total peptide concentration. Stiffness is controlled by altering total peptide concentration, and the unmodified base peptide KFE-8 can be included to further increase this stiffness range due to its higher modulus. With this tunable system, we demonstrate that human mesenchymal stem cell morphology and differentiation are influenced by both gel stiffness and the presence of functional cell binding sites in 3D culture. Specifically, cells 24 hours after encapsulation were only able to spread out in stiffer matrices containing KFE-RGD. Upon addition of soluble adipogenic factors, soft gels facilitated the greatest adipogenesis as determined by the presence of lipid vacuoles and PPARγ-2 expression, while increasing KFE-RGD concentration at a given stiffness had a negative effect on adipogenesis. This three-component hydrogel system thus allows for systematic investigation of matrix stiffness and RGD concentration on cell behavior within a fibrous, three-dimensional matrix. Physical cues from a cell's surrounding environment-such as the density of cell binding sites and the stiffness of the surrounding material-are increasingly being recognized as key regulators of cell function. Currently, most synthetic biomaterials used to independently tune these parameters lack the fibrous structure characteristic of stromal extracellular matrix, which can be important to cells naturally residing within stromal tissues. In this manuscript, we describe a 3D hydrogel encapsulation system that provides user-friendly control over matrix stiffness and binding site concentration within the context of a stromal-like microarchitecture. Binding site concentration and gel stiffness both influenced cell spreading and differentiation, highlighting the utility of this system to study the independent effects of these material properties on cell function. Copyright © 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

ESP Toolbox: A Computational Framework for Precise, Scale-Independent Analysis of Bulk Elastic and Seismic Properties

NASA Astrophysics Data System (ADS)

Johnson, S. E.; Vel, S. S.; Cook, A. C.; Song, W. J.; Gerbi, C. C.; Okaya, D. A.

2014-12-01

Owing to the abundance of highly anisotropic minerals in the crust, the Voigt and Reuss bounds on the seismic velocities can be separated by more than 1 km/s. These bounds are determined by modal mineralogy and crystallographic preferred orientations (CPO) of the constituent minerals, but where the true velocities lie between these bounds is determined by other fabric parameters such as the shapes, shape-preferred orientations, and spatial arrangements of grains. Thus, the calculation of accurate bulk stiffness relies on explicitly treating the grain-scale heterogeneity, and the same principle applies at larger scales, for example calculating accurate bulk stiffness for a crustal volume with varying proportions and distributions of folds or shear zones. We have developed stand-alone GUI software - ESP Toolbox - for the calculation of 3D bulk elastic and seismic properties of heterogeneous and polycrystalline materials using image or EBSD data. The GUI includes a number of different homogenization techniques, including Voigt, Reuss, Hill, geometric mean, self-consistent and asymptotic expansion homogenization (AEH) methods. The AEH method, which uses a finite element mesh, is most accurate since it explicitly accounts for elastic interactions of constituent minerals/phases. The user need only specify the microstructure and material properties of the minerals/phases. We use the Toolbox to explore changes in bulk elasticity and related seismic anisotropy caused by specific variables, including: (a) the quartz alpha-beta phase change in rocks with varying proportions of quartz, (b) changes in modal mineralogy and CPO fabric that occur during progressive deformation and metamorphism, and (c) shear zones of varying thickness, abundance and geometry in continental crust. The Toolbox allows rapid sensitivity analysis around these and other variables, and the resulting bulk stiffness matrices can be used to populate volumes for synthetic wave propagation experiments that allow direct visualization of how variables of interest might affect propagation at a variety of scales. Sensitivity analyses also illustrate the value of the more precise AEH method. The ESP Toolbox can be downloaded here: http://umaine.edu/mecheng/faculty-and-staff/senthil-vel/software/

Stimuli-Responsive DNA-Based Hydrogels: From Basic Principles to Applications.

PubMed

Kahn, Jason S; Hu, Yuwei; Willner, Itamar

2017-04-18

The base sequence of nucleic acids encodes structural and functional information into the DNA biopolymer. External stimuli such as metal ions, pH, light, or added nucleic acid fuel strands provide triggers to reversibly switch nucleic acid structures such as metal-ion-bridged duplexes, i-motifs, triplex nucleic acids, G-quadruplexes, or programmed double-stranded hybrids of oligonucleotides (DNA). The signal-triggered oligonucleotide structures have been broadly applied to develop switchable DNA nanostructures and DNA machines, and these stimuli-responsive assemblies provide functional scaffolds for the rapidly developing area of DNA nanotechnology. Stimuli-responsive hydrogels undergoing signal-triggered hydrogel-to-solution transitions or signal-controlled stiffness changes attract substantial interest as functional matrices for controlled drug delivery, materials exhibiting switchable mechanical properties, acting as valves or actuators, and "smart" materials for sensing and information processing. The integration of stimuli-responsive oligonucleotides with hydrogel-forming polymers provides versatile means to exploit the functional information encoded in the nucleic acid sequences to yield stimuli-responsive hydrogels exhibiting switchable physical, structural, and chemical properties. Stimuli-responsive DNA-based nucleic acid structures are integrated in acrylamide polymer chains and reversible, switchable hydrogel-to-solution transitions of the systems are demonstrated by applying external triggers, such as metal ions, pH-responsive strands, G-quadruplex, and appropriate counter triggers that bridge and dissociate the polymer chains. By combining stimuli-responsive nucleic acid bridges with thermosensitive poly(N-isopropylacrylamide) (pNIPAM) chains, systems undergoing reversible solution ↔ hydrogel ↔ solid transitions are demonstrated. Specifically, by bridging acrylamide polymer chains by two nucleic acid functionalities, where one type of bridging unit provides a stimuli-responsive element and the second unit acts as internal "bridging memory", shape-memory hydrogels undergoing reversible and switchable transitions between shaped hydrogels and shapeless quasi-liquid states are demonstrated. By using stimuli-responsive hydrogel cross-linking units that can assemble the bridging units by two different input signals, the orthogonally-triggered functions of the shape-memory were shown. Furthermore, a versatile approach to assemble stimuli-responsive DNA-based acrylamide hydrogel films on surfaces is presented. The method involves the activation of the hybridization chain-reaction (HCR) by a surface-confined promoter strand, in the presence of acrylamide chains modified with two DNA hairpin structures and appropriate stimuli-responsive tethers. The resulting hydrogel-modified surfaces revealed switchable stiffness properties and signal-triggered catalytic functions. By applying the method to assemble the hydrogel microparticles, substrate-loaded, stimuli-responsive microcapsules are prepared. The signal-triggered DNA-based hydrogel microcapsules are applied as drug carriers for controlled release. The different potential applications and future perspectives of stimuli responsive hydrogels are discussed. Specifically, the use of these smart materials and assemblies as carriers for controlled drug release and as shape-memory matrices for information storage and inscription and the use of surface-confined stimuli-responsive hydrogels, exhibiting switchable stiffness properties, for catalysis and controlled growth of cells are discussed.

Analysis and Development of Finite Element Methods for the Study of Nonlinear Thermomechanical Behavior of Structural Components

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley

1995-01-01

Underintegrated methods are investigated with respect to their stability and convergence properties. The focus was on identifying regions where they work and regions where techniques such as hourglass viscosity and hourglass control can be used. Results obtained show that underintegrated methods typically lead to finite element stiffness with spurious modes in the solution. However, problems exist (scalar elliptic boundary value problems) where underintegrated with hourglass control yield convergent solutions. Also, stress averaging in underintegrated stiffness calculations does not necessarily lead to stable or convergent stress states.

pyJac: Analytical Jacobian generator for chemical kinetics

NASA Astrophysics Data System (ADS)

Niemeyer, Kyle E.; Curtis, Nicholas J.; Sung, Chih-Jen

2017-06-01

Accurate simulations of combustion phenomena require the use of detailed chemical kinetics in order to capture limit phenomena such as ignition and extinction as well as predict pollutant formation. However, the chemical kinetic models for hydrocarbon fuels of practical interest typically have large numbers of species and reactions and exhibit high levels of mathematical stiffness in the governing differential equations, particularly for larger fuel molecules. In order to integrate the stiff equations governing chemical kinetics, generally reactive-flow simulations rely on implicit algorithms that require frequent Jacobian matrix evaluations. Some in situ and a posteriori computational diagnostics methods also require accurate Jacobian matrices, including computational singular perturbation and chemical explosive mode analysis. Typically, finite differences numerically approximate these, but for larger chemical kinetic models this poses significant computational demands since the number of chemical source term evaluations scales with the square of species count. Furthermore, existing analytical Jacobian tools do not optimize evaluations or support emerging SIMD processors such as GPUs. Here we introduce pyJac, a Python-based open-source program that generates analytical Jacobian matrices for use in chemical kinetics modeling and analysis. In addition to producing the necessary customized source code for evaluating reaction rates (including all modern reaction rate formulations), the chemical source terms, and the Jacobian matrix, pyJac uses an optimized evaluation order to minimize computational and memory operations. As a demonstration, we first establish the correctness of the Jacobian matrices for kinetic models of hydrogen, methane, ethylene, and isopentanol oxidation (number of species ranging 13-360) by showing agreement within 0.001% of matrices obtained via automatic differentiation. We then demonstrate the performance achievable on CPUs and GPUs using pyJac via matrix evaluation timing comparisons; the routines produced by pyJac outperformed first-order finite differences by 3-7.5 times and the existing analytical Jacobian software TChem by 1.1-2.2 times on a single-threaded basis. It is noted that TChem is not thread-safe, while pyJac is easily parallelized, and hence can greatly outperform TChem on multicore CPUs. The Jacobian matrix generator we describe here will be useful for reducing the cost of integrating chemical source terms with implicit algorithms in particular and algorithms that require an accurate Jacobian matrix in general. Furthermore, the open-source release of the program and Python-based implementation will enable wide adoption.

Introduction of organic/hydro-organic matrices in inductively coupled plasma optical emission spectrometry and mass spectrometry: a tutorial review. Part II. Practical considerations.

PubMed

Leclercq, Amélie; Nonell, Anthony; Todolí Torró, José Luis; Bresson, Carole; Vio, Laurent; Vercouter, Thomas; Chartier, Frédéric

2015-07-23

Inductively coupled plasma optical emission spectrometry (ICP-OES) and mass spectrometry (ICP-MS) are increasingly used to carry out analyses in organic/hydro-organic matrices. The introduction of such matrices into ICP sources is particularly challenging and can be the cause of numerous drawbacks. This tutorial review, divided in two parts, explores the rich literature related to the introduction of organic/hydro-organic matrices in ICP sources. Part I provided theoretical considerations associated with the physico-chemical properties of such matrices, in an attempt to understand the induced phenomena. Part II of this tutorial review is dedicated to more practical considerations on instrumentation, instrumental and operating parameters, as well as analytical strategies for elemental quantification in such matrices. Two important issues are addressed in this part: the first concerns the instrumentation and optimization of instrumental and operating parameters, pointing out (i) the description, benefits and drawbacks of different kinds of nebulization and desolvation devices and the impact of more specific instrumental parameters such as the injector characteristics and the material used for the cone; and, (ii) the optimization of operating parameters, for both ICP-OES and ICP-MS. Even if it is at the margin of this tutorial review, Electrothermal Vaporization and Laser Ablation will also be shortly described. The second issue is devoted to the analytical strategies for elemental quantification in such matrices, with particular insight into the isotope dilution technique, particularly used in speciation analysis by ICP-coupled separation techniques. Copyright © 2015 Elsevier B.V. All rights reserved.

A progress report on estuary modeling by the finite-element method

USGS Publications Warehouse

Gray, William G.

1978-01-01

Various schemes are investigated for finite-element modeling of two-dimensional surface-water flows. The first schemes investigated combine finite-element spatial discretization with split-step time stepping schemes that have been found useful in finite-difference computations. Because of the large number of numerical integrations performed in space and the large sparse matrices solved, these finite-element schemes were found to be economically uncompetitive with finite-difference schemes. A very promising leapfrog scheme is proposed which, when combined with a novel very fast spatial integration procedure, eliminates the need to solve any matrices at all. Additional problems attacked included proper propagation of waves and proper specification of the normal flow-boundary condition. This report indicates work in progress and does not come to a definitive conclusion as to the best approach for finite-element modeling of surface-water problems. The results presented represent findings obtained between September 1973 and July 1976. (Woodard-USGS)

Parameter design and experimental study of a bifunctional isolator for optical payload protection and stabilization

NASA Astrophysics Data System (ADS)

Wang, Guang-yuan; Guan, Xin; Cao, Dong-jing; Tang, Shao-fan; Chen, Xiang; Liang, Lu; Zheng, Gang-tie

2017-11-01

With the raise of resolution, optical payloads are becoming increasingly sensitive to satellite jitter. An approach where the entire spacecraft is pointed with great accuracy requires sophisticated and expensive bus design. In an effort to lower the overall cost of space missions that require highly stable line-of-sight pointing, a method of separating the bus and the payload with low frequency isolators is proposed. This isolation system can block the transmission of disturbance and allow relatively large bus motion. However, if the isolator is linear then there is a trade-off between isolation and static deflection as the launch and the on-orbit stage have difference requirements on the isolation frequency. Otherwise, an extra locking system should be appended to protect the payload before getting into orbit, as the STABLE isolation system[1] and the MIM isolation system[2] did. To overcome this limitation, an alternative approach is to design a nonlinear isolator with high-static stiffness during launch and low dynamic stiffness on orbit. Several specially designed nonlinear isolators have achieved low dynamic stiffness with large static load capacity. Virgin[3] considered a structure made from a highly deformed elastic element to achieve a softening spring. Platus[4] exploited the buckling of beams under axial load in a specific configuration to achieve a negative stiffness in combination with a positive stiffness, and hence low-dynamic stiffness. Others have achieved the same by connecting linear springs with positive stiffness in parallel with elements of negative stiffness[5] [7]. In the present study, a bifunctional isolator has been developed for optical payloads. The isolator have good performance both during launch and on orbit because of its specially designed nonlinear stiffness and damping. The isolator works in a linear part with low stiffness and small damping ratio under the micro-vibration and microgravity on orbit. The transmissibility requirement and the displacement restriction during launch are satisfied by tuning the nonlinear stiffness and damping parameters. A group of sample isolators are designed tested both statically and dynamically.

The algebraic theory of latent projectors in lambda matrices

NASA Technical Reports Server (NTRS)

Denman, E. D.; Leyva-Ramos, J.; Jeon, G. J.

1981-01-01

Multivariable systems such as a finite-element model of vibrating structures, control systems, and large-scale systems are often formulated in terms of differential equations which give rise to lambda matrices. The present investigation is concerned with the formulation of the algebraic theory of lambda matrices and the relationship of latent roots, latent vectors, and latent projectors to the eigenvalues, eigenvectors, and eigenprojectors of the companion form. The chain rule for latent projectors and eigenprojectors for the repeated latent root or eigenvalues is given.

Dynamic characteristics of a vibrating beam with periodic variation in bending stiffness

NASA Technical Reports Server (NTRS)

Townsend, John S.

1987-01-01

A detailed dynamic analysis is performed of a vibrating beam with bending stiffness periodic in the spatial coordinate. Using a perturbation expansion technique the free vibration solution is obtained in a closed-form, and the effects of system parameters on beam response are explored. It is found that periodic stiffness acts to modulate the modal displacements from the characteristic shape of a simple sine wave. The results are verified by a finite element solution and through experimental testing.

Trace Element Analysis of Biological Samples.

ERIC Educational Resources Information Center

Veillon, Claude

1986-01-01

Reviews background of atomic absorption spectrometry techniques. Discusses problems encountered and precautions to be taken in determining trace elements in the parts-per-billion concentration range and below. Concentrates on determining chromium in biological samples by graphite furnace atomic absorption. Considers other elements, matrices, and…

QCT/FEA predictions of femoral stiffness are strongly affected by boundary condition modeling

PubMed Central

Rossman, Timothy; Kushvaha, Vinod; Dragomir-Daescu, Dan

2015-01-01

Quantitative computed tomography-based finite element models of proximal femora must be validated with cadaveric experiments before using them to assess fracture risk in osteoporotic patients. During validation it is essential to carefully assess whether the boundary condition modeling matches the experimental conditions. This study evaluated proximal femur stiffness results predicted by six different boundary condition methods on a sample of 30 cadaveric femora and compared the predictions with experimental data. The average stiffness varied by 280% among the six boundary conditions. Compared with experimental data the predictions ranged from overestimating the average stiffness by 65% to underestimating it by 41%. In addition we found that the boundary condition that distributed the load to the contact surfaces similar to the expected contact mechanics predictions had the best agreement with experimental stiffness. We concluded that boundary conditions modeling introduced large variations in proximal femora stiffness predictions. PMID:25804260

An experimental study on Sodalite and SAP matrices for immobilization of spent chloride salt waste

NASA Astrophysics Data System (ADS)

Giacobbo, Francesca; Da Ros, Mirko; Macerata, Elena; Mariani, Mario; Giola, Marco; De Angelis, Giorgio; Capone, Mauro; Fedeli, Carlo

2018-02-01

In the frame of Generation IV reactors a renewed interest in pyro-processing of spent nuclear fuel is underway. Molten chloride salt waste arising from the recovering of uranium and plutonium through pyro-processing is one of the problematic wastes for direct application of vitrification or ceramization. In this work, Sodalite and SAP have been evaluated and compared as potential matrices for confinement of spent chloride salt waste coming from pyro-processing. To this aim Sodalite and SAP were synthesized both in pure form and mixed with different glass matrices, i.e. commercially available glass frit and borosilicate glass. The confining matrices were loaded with mixed chloride salts to study their retention capacities with respect to the elements of interest. The matrices were characterized and leached for contact times up to 150 days at room temperature and at 90 °C. SEM analyses were also performed in order to compare the matrix surface before and after leaching. Leaching results are discussed and compared in terms of normalized releases with similar results reported in literature. According to this comparative study the SAP matrix with glass frit binder resulted in the best matrix among the ones studied, with respect to retention capacities for both matrix and spent fuel elements.

Retrieval of the non-depolarizing components of depolarizing Mueller matrices by using symmetry conditions and least squares minimization

NASA Astrophysics Data System (ADS)

Kuntman, Ertan; Canillas, Adolf; Arteaga, Oriol

2017-11-01

Experimental Mueller matrices contain certain amount of uncertainty in their elements and these uncertainties can create difficulties for decomposition methods based on analytic solutions. In an earlier paper [1], we proposed a decomposition method for depolarizing Mueller matrices by using certain symmetry conditions. However, because of the experimental error, that method creates over-determined systems with non-unique solutions. Here we propose to use least squares minimization approach in order to improve the accuracy of our results. In this method, we are taking into account the number of independent parameters of the corresponding symmetry and the rank constraints on the component matrices to decide on our fitting model. This approach is illustrated with experimental Mueller matrices that include material media with different Mueller symmetries.

Design and dynamic modeling of electrorheological fluid-based variable-stiffness fin for robotic fish

NASA Astrophysics Data System (ADS)

Bazaz Behbahani, Sanaz; Tan, Xiaobo

2017-08-01

Fish actively control their stiffness in different swimming conditions. Inspired by such an adaptive behavior, in this paper we study the design, prototyping, and dynamic modeling of compact, tunable-stiffness fins for robotic fish, where electrorheological (ER) fluid serves as the enabling element. A multi-layer composite fin with an ER fluid core is prototyped and utilized to investigate the influence of electrical field on its performance. Hamilton's principle is used to derive the dynamic equations of motion of the flexible fin, and Lighthill's large-amplitude elongated-body theory is adopted to estimate the hydrodynamic force when the fin undergoes base-actuated rotation. The dynamic equations are then discretized using the finite element method, to obtain an approximate numerical solution. Experiments are conducted on the prototyped flexible ER fluid-filled beam for parameter identification and validation of the proposed model, and for examining the effectiveness of electrically controlled stiffness tuning. In particular, it is found that the natural frequency is increased by almost 40% when the applied electric field changes from 0 to 1.5× {10}6 {{V}} {{{m}}}-1.

Dynamic blocked transfer stiffness method of characterizing the magnetic field and frequency dependent dynamic viscoelastic properties of MRE

NASA Astrophysics Data System (ADS)

Poojary, Umanath R.; Hegde, Sriharsha; Gangadharan, K. V.

2016-11-01

Magneto rheological elastomer (MRE) is a potential resilient element for the semi active vibration isolator. MRE based isolators adapt to different frequency of vibrations arising from the source to isolate the structure over wider frequency range. The performance of MRE isolator depends on the magnetic field and frequency dependent characteristics of MRE. Present study is focused on experimentally evaluating the dynamic stiffness and loss factor of MRE through dynamic blocked transfer stiffness method. The dynamic stiffness variations of MRE exhibit strong magnetic field and mild frequency dependency. Enhancements in dynamic stiffness saturate with the increase in magnetic field and the frequency. The inconsistent variations of loss factor with the magnetic field substantiate the inability of MRE to have independent control over its damping characteristics.

Cohesive Modeling of Transverse Cracking in Laminates with a Single Layer of Elements per Ply

NASA Technical Reports Server (NTRS)

VanDerMeer, Frans P.; Davila, Carlos G.

2013-01-01

This study aims to bridge the gap between classical understanding of transverse cracking in cross-ply laminates and recent computational methods for the modeling of progressive laminate failure. Specifically, the study investigates under what conditions a finite element model with cohesive X-FEM cracks can reproduce the in situ effect for the ply strength. It is shown that it is possible to do so with a single element across the thickness of the ply, provided that the interface stiffness is properly selected. The optimal value for this interface stiffness is derived with an analytical shear lag model. It is also shown that, when the appropriate statistical variation of properties has been applied, models with a single element through the thickness of a ply can predict the density of transverse matrix cracks

Extension of the tridiagonal reduction (FEER) method for complex eigenvalue problems in NASTRAN

NASA Technical Reports Server (NTRS)

Newman, M.; Mann, F. I.

1978-01-01

As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum were extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order was much lower than that of the full size problem. The reduction process was effected automatically, and thus avoided the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admitted mass, damping, and stiffness matrices which were unrestricted in character, i.e., they might be real, symmetric or nonsymmetric, singular or nonsingular.

Vibration control of large linear quadratic symmetric systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Jeon, G. J.

1983-01-01

Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.

Buckling Analysis of Angle-ply Composite and Sandwich Plates by Combination of Geometric Stiffness Matrix

NASA Astrophysics Data System (ADS)

Zhen, Wu; Wanji, Chen

2007-05-01

Buckling response of angle-ply laminated composite and sandwich plates are analyzed using the global-local higher order theory with combination of geometric stiffness matrix in this paper. This global-local theory completely fulfills the free surface conditions and the displacement and stress continuity conditions at interfaces. Moreover, the number of unknowns in this theory is independent of the number of layers in the laminate. Based on this global-local theory, a three-noded triangular element satisfying C1 continuity conditions has also been proposed. The bending part of this element is constructed from the concept of DKT element. In order to improve the accuracy of the analysis, a method of modified geometric stiffness matrix has been introduced. Numerical results show that the present theory not only computes accurately the buckling response of general laminated composite plates but also predicts the critical buckling loads of soft-core sandwiches. However, the global higher-order theories as well as first order theories might encounter some difficulties and overestimate the critical buckling loads for soft-core sandwich plates.

Finite element based nonlinear normalization of human lumbar intervertebral disc stiffness to account for its morphology.

PubMed

Maquer, Ghislain; Laurent, Marc; Brandejsky, Vaclav; Pretterklieber, Michael L; Zysset, Philippe K

2014-06-01

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

On the representation matrices of the spin permutation group. [for atomic and molecular electronic structures

NASA Technical Reports Server (NTRS)

Wilson, S.

1977-01-01

A method is presented for the determination of the representation matrices of the spin permutation group (symmetric group), a detailed knowledge of these matrices being required in the study of the electronic structure of atoms and molecules. The method is characterized by the use of two different coupling schemes. Unlike the Yamanouchi spin algebraic scheme, the method is not recursive. The matrices for the fundamental transpositions can be written down directly in one of the two bases. The method results in a computationally significant reduction in the number of matrix elements that have to be stored when compared with, say, the standard Young tableaux group theoretical approach.

Toxicological importance of human biomonitoring of metallic and metalloid elements in different biological samples.

PubMed

Gil, F; Hernández, A F

2015-06-01

Human biomonitoring has become an important tool for the assessment of internal doses of metallic and metalloid elements. These elements are of great significance because of their toxic properties and wide distribution in environmental compartments. Although blood and urine are the most used and accepted matrices for human biomonitoring, other non-conventional samples (saliva, placenta, meconium, hair, nails, teeth, breast milk) may have practical advantages and would provide additional information on health risk. Nevertheless, the analysis of these compounds in biological matrices other than blood and urine has not yet been accepted as a useful tool for biomonitoring. The validation of analytical procedures is absolutely necessary for a proper implementation of non-conventional samples in biomonitoring programs. However, the lack of reliable and useful analytical methodologies to assess exposure to metallic elements, and the potential interference of external contamination and variation in biological features of non-conventional samples are important limitations for setting health-based reference values. The influence of potential confounding factors on metallic concentration should always be considered. More research is needed to ascertain whether or not non-conventional matrices offer definitive advantages over the traditional samples and to broaden the available database for establishing worldwide accepted reference values in non-exposed populations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Nonlinear Pressurization and Modal Analysis Procedure for Dynamic Modeling of Inflatable Structures

NASA Technical Reports Server (NTRS)

Smalley, Kurt B.; Tinker, Michael L.; Saxon, Jeff (Technical Monitor)

2002-01-01

An introduction and set of guidelines for finite element dynamic modeling of nonrigidized inflatable structures is provided. A two-step approach is presented, involving 1) nonlinear static pressurization of the structure and updating of the stiffness matrix and 2) hear normal modes analysis using the updated stiffness. Advantages of this approach are that it provides physical realism in modeling of pressure stiffening, and it maintains the analytical convenience of a standard bear eigensolution once the stiffness has been modified. Demonstration of the approach is accomplished through the creation and test verification of an inflated cylinder model using a large commercial finite element code. Good frequency and mode shape comparisons are obtained with test data and previous modeling efforts, verifying the accuracy of the technique. Problems encountered in the application of the approach, as well as their solutions, are discussed in detail.

Real-time control of geometry and stiffness in adaptive structures

NASA Technical Reports Server (NTRS)

Ramesh, A. V.; Utku, S.; Wada, B. K.

1991-01-01

The basic theory is presented for the geometry, stiffness, and damping control of adaptive structures, with emphasis on adaptive truss structures. Necessary and sufficient conditions are given for stress-free geometry control in statically determinate and indeterminate adaptive discrete structures. Two criteria for selecting the controls are proposed, and their use in real-time control is illustrated by numerical simulation results. It is shown that the stiffness and damping control of adaptive truss structures for vibration suppression is possible by elongation and elongation rate dependent feedback forces from the active elements.

Introduction of organic/hydro-organic matrices in inductively coupled plasma optical emission spectrometry and mass spectrometry: a tutorial review. Part I. Theoretical considerations.

PubMed

Leclercq, Amélie; Nonell, Anthony; Todolí Torró, José Luis; Bresson, Carole; Vio, Laurent; Vercouter, Thomas; Chartier, Frédéric

2015-07-23

Due to their outstanding analytical performances, inductively coupled plasma optical emission spectrometry (ICP-OES) and mass spectrometry (ICP-MS) are widely used for multi-elemental measurements and also for isotopic characterization in the case of ICP-MS. While most studies are carried out in aqueous matrices, applications involving organic/hydro-organic matrices become increasingly widespread. This kind of matrices is introduced in ICP based instruments when classical "matrix removal" approaches such as acid digestion or extraction procedures cannot be implemented. Due to the physico-chemical properties of organic/hydro-organic matrices and their associated effects on instrumentation and analytical performances, their introduction into ICP sources is particularly challenging and has become a full topic. In this framework, numerous theoretical and phenomenological studies of these effects have been performed in the past, mainly by ICP-OES, while recent literature is more focused on applications and associated instrumental developments. This tutorial review, divided in two parts, explores the rich literature related to the introduction of organic/hydro-organic matrices in ICP-OES and ICP-MS. The present Part I, provides theoretical considerations in connection with the physico-chemical properties of organic/hydro-organic matrices, in order to better understand the induced phenomena. This focal point is divided in four chapters highlighting: (i) the impact of organic/hydro-organic matrices from aerosol generation to atomization/excitation/ionization processes; (ii) the production of carbon molecular constituents and their spatial distribution in the plasma with respect to analytes repartition; (iii) the subsequent modifications of plasma fundamental properties; and (iv) the resulting spectroscopic and non spectroscopic interferences. This first part of this tutorial review is addressed either to beginners or to more experienced scientists who are interested in the analysis of organic/hydro-organic matrices by ICP sources and would like to consider the theoretical background of effects induced by such matrices. The second part of this tutorial review will be dedicated to more practical consideration on instrumentation, such as adapted introductions devices, as well as instrumental and operating parameters optimization. The analytical strategies for elemental quantification in such matrices will also be addressed. Copyright © 2015 Elsevier B.V. All rights reserved.

Human pericytes adopt myofibroblast properties in the microenvironment of the IPF lung.

PubMed

Sava, Parid; Ramanathan, Anand; Dobronyi, Amelia; Peng, Xueyan; Sun, Huanxing; Ledesma-Mendoza, Adrian; Herzog, Erica L; Gonzalez, Anjelica L

2017-12-21

Idiopathic pulmonary fibrosis (IPF) is a fatal disease of unknown etiology characterized by a compositionally and mechanically altered extracellular matrix. Poor understanding of the origin of α-smooth muscle actin (α-SMA) expressing myofibroblasts has hindered curative therapies. Though proposed as a source of myofibroblasts in mammalian tissues, identification of microvascular pericytes (PC) as contributors to α-SMA-expressing populations in human IPF and the mechanisms driving this accumulation remain unexplored. Here, we demonstrate enhanced detection of α-SMA+ cells coexpressing the PC marker neural/glial antigen 2 in the human IPF lung. Isolated human PC cultured on decellularized IPF lung matrices adopt expression of α-SMA, demonstrating that these cells undergo phenotypic transition in response to direct contact with the extracellular matrix (ECM) of the fibrotic human lung. Using potentially novel human lung-conjugated hydrogels with tunable mechanical properties, we decoupled PC responses to matrix composition and stiffness to show that α-SMA+ PC accumulate in a mechanosensitive manner independent of matrix composition. PC activated with TGF-β1 remodel the normal lung matrix, increasing tissue stiffness to facilitate the emergence of α-SMA+ PC via MKL-1/MTRFA mechanotranduction. Nintedanib, a tyrosine-kinase inhibitor approved for IPF treatment, restores the elastic modulus of fibrotic lung matrices to reverse the α-SMA+ phenotype. This work furthers our understanding of the role that microvascular PC play in the evolution of IPF, describes the creation of an ex vivo platform that advances the study of fibrosis, and presents a potentially novel mode of action for a commonly used antifibrotic therapy that has great relevance for human disease.

Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

NASA Astrophysics Data System (ADS)

Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José

2017-05-01

The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant-Friedrichs-Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational efficiency, the OTSEM is more efficient than the Fekete-based TSEM, although it is slightly costlier than the QSEM when a comparable numerical accuracy is required.

Stability analysis and backward whirl investigation of cracked rotors with time-varying stiffness

NASA Astrophysics Data System (ADS)

AL-Shudeifat, Mohammad A.

2015-07-01

The dynamic stability of dynamical systems with time-periodic stiffness is addressed here. Cracked rotor systems with time-periodic stiffness are well-known examples of such systems. Time-varying area moments of inertia at the cracked element cross-section of a cracked rotor have been used to formulate the time-periodic finite element stiffness matrix. The semi-infinite coefficient matrix obtained by applying the harmonic balance (HB) solution to the finite element (FE) equations of motion is employed here to study the dynamic stability of the system. Consequently, the sign of the determinant of a scaled version of a sub-matrix of this semi-infinite coefficient matrix at a finite number of harmonics in the HB solution is found to be sufficient for identifying the major unstable zones of the system in the parameter plane. Specifically, it is found that the negative determinant always corresponds to unstable zones in all of the systems considered. This approach is applied to a parametrically excited Mathieu's equation, a two degree-of-freedom linear time-periodic dynamical system, a cracked Jeffcott rotor and a finite element model of the cracked rotor system. Compared to the corresponding results obtained by Floquet's theory, the sign of the determinant of the scaled sub-matrix is found to be an efficient tool for identifying the major unstable zones of the linear time-periodic parametrically excited systems, especially large-scale FE systems. Moreover, it is found that the unstable zones for a FE cracked rotor with an open transverse crack model only appear at the backward whirl. The theoretical and experimental results have been found to agree well for verifying that the open crack model excites the backward whirl amplitudes at the critical backward whirling rotational speeds.

Determination of ankle external fixation stiffness by expedited interactive finite element analysis.

PubMed

Nielsen, Jonathan K; Saltzman, Charles L; Brown, Thomas D

2005-11-01

Interactive finite element analysis holds the potential to quickly and accurately determine the mechanical stiffness of alternative external fixator frame configurations. Using as an example Ilizarov distraction of the ankle, a finite element model and graphical user interface were developed that provided rapid, construct-specific information on fixation rigidity. After input of specific construct variables, the finite element software determined the resulting tibial displacement for a given configuration in typically 15s. The formulation was employed to investigate constructs used to treat end-stage arthritis, both in a parametric series and for five specific clinical distraction cases. Parametric testing of 15 individual variables revealed that tibial half-pins were much more effective than transfixion wires in limiting axial tibial displacement. Factors most strongly contributing to stiffening the construct included placing the tibia closer to the fixator rings, and mounting the pins to the rings at the nearest circumferential location to the bone. Benchtop mechanical validation results differed inappreciably from the finite element computations.

Advanced grid-stiffened composite shells for applications in heavy-lift helicopter rotor blade spars

NASA Astrophysics Data System (ADS)

Narayanan Nampy, Sreenivas

Modern rotor blades are constructed using composite materials to exploit their superior structural performance compared to metals. Helicopter rotor blade spars are conventionally designed as monocoque structures. Blades of the proposed Heavy Lift Helicopter are envisioned to be as heavy as 800 lbs when designed using the monocoque spar design. A new and innovative design is proposed to replace the conventional spar designs with light weight grid-stiffened composite shell. Composite stiffened shells have been known to provide excellent strength to weight ratio and damage tolerance with an excellent potential to reduce weight. Conventional stringer--rib stiffened construction is not suitable for rotor blade spars since they are limited in generating high torsion stiffness that is required for aeroelastic stability of the rotor. As a result, off-axis (helical) stiffeners must be provided. This is a new design space where innovative modeling techniques are needed. The structural behavior of grid-stiffened structures under axial, bending, and torsion loads, typically experienced by rotor blades need to be accurately predicted. The overall objective of the present research is to develop and integrate the necessary design analysis tools to conduct a feasibility study in employing grid-stiffened shells for heavy-lift rotor blade spars. Upon evaluating the limitations in state-of-the-art analytical models in predicting the axial, bending, and torsion stiffness coefficients of grid and grid-stiffened structures, a new analytical model was developed. The new analytical model based on the smeared stiffness approach was developed employing the stiffness matrices of the constituent members of the grid structure such as an arch, helical, or straight beam representing circumferential, helical, and longitudinal stiffeners. This analysis has the capability to model various stiffening configurations such as angle-grid, ortho-grid, and general-grid. Analyses were performed using an existing state-of-the-art and newly developed model to predict the torsion, bending, and axial stiffness of grid and grid-stiffened structures with various stiffening configurations. These predictions were compared to results generated using finite element analysis (FEA) to observe excellent correlation (within 6%) for a range of parameters for grid and grid-stiffened structures such as grid density, stiffener angle, and aspect ratio of the stiffener cross-section. Experimental results from cylindrical grid specimen testing were compared with analytical prediction using the new analysis. The new analysis predicted stiffness coefficients with nearly 7% error compared to FEA results. From the parametric studies conducted, it was observed that the previous state-of-the-art analysis on the other hand exhibited errors of the order of 39% for certain designs. Stability evaluations were also conducted by integrating the new analysis with established stability formulations. A design study was conducted to evaluate the potential weight savings of a simple grid-stiffened rotor blade spar structure compared to a baseline monocoque design. Various design constraints such as stiffness, strength, and stability were imposed. A manual search was conducted for design parameters such as stiffener density, stiffener angle, shell laminate, and stiffener aspect ratio that provide lightweight grid-stiffened designs compared to the baseline. It was found that a weight saving of 9.1% compared to the baseline is possible without violating any of the design constraints.

Direct estimation of human trabecular bone stiffness using cone beam computed tomography.

PubMed

Klintström, Eva; Klintström, Benjamin; Pahr, Dieter; Brismar, Torkel B; Smedby, Örjan; Moreno, Rodrigo

2018-04-10

The aim of this study was to evaluate the possibility of estimating the biomechanical properties of trabecular bone through finite element simulations by using dental cone beam computed tomography data. Fourteen human radius specimens were scanned in 3 cone beam computed tomography devices: 3-D Accuitomo 80 (J. Morita MFG., Kyoto, Japan), NewTom 5 G (QR Verona, Verona, Italy), and Verity (Planmed, Helsinki, Finland). The imaging data were segmented by using 2 different methods. Stiffness (Young modulus), shear moduli, and the size and shape of the stiffness tensor were studied. Corresponding evaluations by using micro-CT were regarded as the reference standard. The 3-D Accuitomo 80 (J. Morita MFG., Kyoto, Japan) showed good performance in estimating stiffness and shear moduli but was sensitive to the choice of segmentation method. NewTom 5 G (QR Verona, Verona, Italy) and Verity (Planmed, Helsinki, Finland) yielded good correlations, but they were not as strong as Accuitomo 80 (J. Morita MFG., Kyoto, Japan). The cone beam computed tomography devices overestimated both stiffness and shear compared with the micro-CT estimations. Finite element-based calculations of biomechanics from cone beam computed tomography data are feasible, with strong correlations for the Accuitomo 80 scanner (J. Morita MFG., Kyoto, Japan) combined with an appropriate segmentation method. Such measurements might be useful for predicting implant survival by in vivo estimations of bone properties. Copyright © 2018 Elsevier Inc. All rights reserved.

Excitation of ground vibration due to the passage of trains over a track with trackbed irregularities and a varying support stiffness

NASA Astrophysics Data System (ADS)

Auersch, Lutz

2015-01-01

Train-induced ground vibration can be excited by wheel and track irregularities and by two kinds of irregularities of the soil, by geometric irregularities or by the spatially varying soil stiffness. For both types of irregularities, the effective track irregularity on top of the track is calculated in wavenumber domain and with wavenumber integrals. For a general multi-beam track model, the wavenumber integrals are solved numerically. The irregularities of the soil are filtered by the track when transferred from the bottom to the top of the track. The high-wavenumber irregularities are strongly reduced due to the bending stiffness of the track and the compliance of the support. In addition, soft track elements reduce directly the stiffness variation of the support. Therefore, the mitigation effect of elastic track elements for these excitation components seems to be important. For under-sleeper pads and slab tracks, calculation and measurements are presented including additional excitation components and the dynamic vehicle-track interaction, and the relevance of the excitation mechanisms is discussed based on the dynamic forces which are acting on the ground. Due to the restricted amplitudes, the parametric excitation by the stiffness variation seems to be less important than the geometric irregularities. The calculations yield the correct trends of the measurements and many details of the measured ballast, slab, and under-sleeper-pad tracks.

Comparative study of diastolic filling under varying left ventricular wall stiffness

NASA Astrophysics Data System (ADS)

Mekala, Pritam; Santhanakrishnan, Arvind

2014-11-01

Pathological remodeling of the human cardiac left ventricle (LV) is observed in hypertensive heart failure as a result of pressure overload. Myocardial stiffening occurs in these patients prior to chronic maladaptive changes, resulting in increased LV wall stiffness. The goal of this study was to investigate the change in intraventricular filling fluid dynamics inside a physical model of the LV as a function of wall stiffness. Three LV models of varying wall stiffness were incorporated into an in vitro flow circuit driven by a programmable piston pump. Windkessel elements were used to tune the inflow and systemic pressure in the model with least stiffness to match healthy conditions. Models with stiffer walls were comparatively tested maintaining circuit compliance, resistance and pump amplitude constant. 2D phase-locked PIV measurements along the central plane showed that with increase in wall stiffness, the peak velocity and cardiac output inside the LV decreased. Further, inflow vortex ring propagation toward the LV apex was reduced with increasing stiffness. The above findings indicate the importance of considering LV wall relaxation characteristics in pathological studies of filling fluid dynamics.

Ultrasonic delineation of aortic microstructure: The relative contribution of elastin and collagen to aortic elasticity

NASA Astrophysics Data System (ADS)

Marsh, Jon N.; Takiuchi, Shin; Lin, Shiow Jiuan; Lanza, Gregory M.; Wickline, Samuel A.

2004-05-01

Aortic elasticity is an important factor in hemodynamic health, and compromised aortic compliance affects not only arterial dynamics but also myocardial function. A variety of pathologic processes (e.g., diabetes, Marfan's syndrome, hypertension) can affect aortic elasticity by altering the microstructure and composition of the elastin and collagen fiber networks within the tunica media. Ultrasound tissue characterization techniques can be used to obtain direct measurements of the stiffness coefficients of aorta by measurement of the speed of sound in specific directions. In this study we sought to define the contributions of elastin and collagen to the mechanical properties of aortic media by measuring the magnitude and directional dependence of the speed of sound before and after selective isolation of either the collagen or elastin fiber matrix. Formalin-fixed porcine aortas were sectioned for insonification in the circumferential, longitudinal, or radial direction and examined using high-frequency (50 MHz) ultrasound microscopy. Isolation of the collagen or elastin fiber matrices was accomplished through treatment with NaOH or formic acid, respectively. The results suggest that elastin is the primary contributor to aortic medial stiffness in the unloaded state, and that there is relatively little anisotropy in the speed of sound or stiffness in the aortic wall.

Detection of multiple damages employing best achievable eigenvectors under Bayesian inference

NASA Astrophysics Data System (ADS)

Prajapat, Kanta; Ray-Chaudhuri, Samit

2018-05-01

A novel approach is presented in this work to localize simultaneously multiple damaged elements in a structure along with the estimation of damage severity for each of the damaged elements. For detection of damaged elements, a best achievable eigenvector based formulation has been derived. To deal with noisy data, Bayesian inference is employed in the formulation wherein the likelihood of the Bayesian algorithm is formed on the basis of errors between the best achievable eigenvectors and the measured modes. In this approach, the most probable damage locations are evaluated under Bayesian inference by generating combinations of various possible damaged elements. Once damage locations are identified, damage severities are estimated using a Bayesian inference Markov chain Monte Carlo simulation. The efficiency of the proposed approach has been demonstrated by carrying out a numerical study involving a 12-story shear building. It has been found from this study that damage scenarios involving as low as 10% loss of stiffness in multiple elements are accurately determined (localized and severities quantified) even when 2% noise contaminated modal data are utilized. Further, this study introduces a term parameter impact (evaluated based on sensitivity of modal parameters towards structural parameters) to decide the suitability of selecting a particular mode, if some idea about the damaged elements are available. It has been demonstrated here that the accuracy and efficiency of the Bayesian quantification algorithm increases if damage localization is carried out a-priori. An experimental study involving a laboratory scale shear building and different stiffness modification scenarios shows that the proposed approach is efficient enough to localize the stories with stiffness modification.

An Integrated Magnetic Circuit Model and Finite Element Model Approach to Magnetic Bearing Design

NASA Technical Reports Server (NTRS)

Provenza, Andrew J.; Kenny, Andrew; Palazzolo, Alan B.

2003-01-01

A code for designing magnetic bearings is described. The code generates curves from magnetic circuit equations relating important bearing performance parameters. Bearing parameters selected from the curves by a designer to meet the requirements of a particular application are input directly by the code into a three-dimensional finite element analysis preprocessor. This means that a three-dimensional computer model of the bearing being developed is immediately available for viewing. The finite element model solution can be used to show areas of magnetic saturation and make more accurate predictions of the bearing load capacity, current stiffness, position stiffness, and inductance than the magnetic circuit equations did at the start of the design process. In summary, the code combines one-dimensional and three-dimensional modeling methods for designing magnetic bearings.

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

NASA Technical Reports Server (NTRS)

Muravyov, Alexander A.

1999-01-01

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

Analysing of critical force effects of aircraft seat belt using truss elements

NASA Astrophysics Data System (ADS)

Klemenc, Marek; Markopoulos, Alexandros; Maršálek, Pavel

2017-07-01

This paper deals with the mathematical modelling of an aircraft seat belt crash test. The main goal is determination of a time course of the reactions in a lap belt anchoring points and their maximum values. This work was created on the basis of practical requirements from industry. Results are going to be reflected in developing a new type of aircraft seats. We mainly focus on the mathematical modelling of dynamic problems using the finite element method (FEM). Derived procedures are implemented in the Python programming language and are verified by several examples. A final calculation algorithm is applied on the analysis of the safety belt. We consider that a seat belt bending stiffness is very small compared to a tensile stiffness, therefore we used a 2D plane truss element.

Propulsive performance of pitching foils with variable chordwise flexibility

NASA Astrophysics Data System (ADS)

Zeyghami, Samane; Moored, Keith; Lehigh University Team

2017-11-01

Many swimming and flying animals propel themselves efficiently through water by oscillating flexible fins. These fins are not homogeneously flexible, but instead their flexural stiffness varies along their chord and span. Here we seek to evaluate the effect stiffness profile on the propulsive performance of pitching foils. Stiffness profile characterizes the variation in the local fin stiffness along the chord. To this aim, we developed a low order model of a functionally-graded material where the chordwise flexibility is modeled by two torsional springs along the chordline and the stiffness and location of the springs can be varied arbitrarily. The torsional spring structural model is then strongly coupled to a boundary element fluid model to simulate the fluid-structure interactions. Keeping the leading edge kinematics unchanged, we alter the stiffness profile of the foil and allow it to swim freely in response to the resulting hydrodynamic forces. We then detail the dependency of the hydrodynamic performance and the wake structure to the variations in the local structural properties of the foil.

Stiffness monitoring and damage assessment of bridges under moving vehicular loads using spatially-distributed optical fiber sensors

NASA Astrophysics Data System (ADS)

Wu, Bitao; Wu, Gang; Lu, Huaxi; Feng, De-chen

2017-03-01

Fiber optic sensing technology has been widely used in civil infrastructure health monitoring due to its various advantages, e.g., anti-electromagnetic interference, corrosion resistance, etc. This paper investigates a new method for stiffness monitoring and damage identification of bridges under moving vehicle loads using spatially-distributed optical fiber sensors. The relationship between the element stiffness of the bridge and the long-gauge strain history is firstly studied, and a formula which is expressed by the long-gauge strain history is derived for the calculation of the bridge stiffness. Meanwhile, the stiffness coefficient from the formula can be used to identify the damage extent of the bridge. In order to verify the proposed method, a model test of a 1:10 scale bridge-vehicle system is conducted and the long-gauge strain history is obtained through fiber Bragg grating sensors. The test results indicate that the proposed method is suitable for stiffness monitoring and damage assessment of bridges under moving vehicular loads.

Variable stiffness sandwich panels using electrostatic interlocking core

NASA Astrophysics Data System (ADS)

Heath, Callum J. C.; Bond, Ian P.; Potter, Kevin D.

2016-04-01

Structural topology has a large impact on the flexural stiffness of a beam structure. Reversible attachment between discrete substructures allows for control of shear stress transfer between structural elements, thus stiffness modulation. Electrostatic adhesion has shown promise for providing a reversible latching mechanism for controllable internal connectivity. Building on previous research, a thin film copper polyimide laminate has been used to incorporate high voltage electrodes to Fibre Reinforced Polymer (FRP) sandwich structures. The level of electrostatic holding force across the electrode interface is key to the achievable level of stiffness modulation. The use of non-flat interlocking core structures can allow for a significant increase in electrode contact area for a given core geometry, thus a greater electrostatic holding force. Interlocking core geometries based on cosine waves can be Computer Numerical Control (CNC) machined from Rohacell IGF 110 Foam core. These Interlocking Core structures could allow for enhanced variable stiffness functionality compared to basic planar electrodes. This novel concept could open up potential new applications for electrostatically induced variable stiffness structures.

Mechanical evaluation of the SLM fabricated, stiffness-matched, mandibular bone fixation plates

NASA Astrophysics Data System (ADS)

Jahadakbar, Ahmadreza; Shayesteh Moghaddam, Narges; Amerinatanzi, Amirhesam; Dean, David; Elahinia, Mohammad

2018-03-01

The standard of the care for the treatment of mandibular segmental defects is the use of Ti-6Al-4V bone fixation plates and screws to immobilize the grafted bone and the host mandible. While Ti-6Al-4V bone fixation plates provide strong immobilization during the healing period, they may disturb the stress distribution in the repaired mandible. The highly stiff Ti-6Al-4V fixation carries a great portion of the load which was previously borne by the mandible, and stress shielding may occur on the surrounding cortical bone. Based on the bone remodeling theory, stress shielding causes bone resorption in the effected region and may eventually lead to the failure of the surgical reconstruction. To address this issue, we have developed a new generation of the patient-specific, porous NiTi bone fixation plates which benefit from stiffness-matching of the adjacent bone. Using the CT scan data of the patient's defective mandible, the geometry for the required bone fixation plates is designed and the stiffness of the surrounding regions is measured. By introducing specific level and type of porosity to the bone fixation plate, its stiffness can be tuned. Finite Element simulations has verified the reduced level of stress shielding on the reconstructed mandible, in case of using the proposed bone fixation plates. Selective Lase Sintering has been used for fabrication of the porous NiTi bone fixation plates with six different levels of stiffness. Finite element simulations, and mechanical tests have been done to verify the performance of the fabricated parts resulting from our design and fabrication method.

Modeling sound transmission of human middle ear and its clinical applications using finite element analysis.

PubMed

Chen, Shou-I; Lee, Ming-Hsiao; Yao, Chih-Min; Chen, Peir-Rong; Chou, Yuan-Fang; Liu, Tien-Chen; Song, Yu-Lin; Lee, Chia-Fone

2013-03-01

We have developed a new finite element (FE) model of human right ear, including the accurate geometry of middle ear ossicles, external ear canal, tympanic cavity, and mastoid cavity. The FE model would be suitable to study the dynamic behaviors of pathological middle ear conditions, including changes of stapedial ligament stiffness, tensor tympani ligament (TTL), and tympanic membrane (TM) stiffness and thickness. Increasing stiffness of stapedial ligament has substantial effect on stapes footplate movement, especially at low frequencies, but less effect on umbo movement. Softer TTL will result in increasing umbo and stapes footplate displacement, especially at low frequencies (f<1000Hz). When the TTL was detached, the vibration amplitude of umbo increased by 6dB at 600Hz and two peaks (300 and 600Hz) were found in the vibration amplitude of stapes footplate. Increasing the stiffness of tensor tympani resulted in a slightly decreased umbo amplitude at very low frequencies (f<500Hz) and significantly decreased displacement up to 12dB at middle frequencies (1000Hz1500Hz. As (TM) thickness was increased, the umbo displacement was reduced, especially at very low frequencies (f<600Hz). Otherwise, the stapes displacement was reduced at all frequencies. Copyright © 2013. Published by Elsevier B.V.

Umbilical Stiffness Matrix Characterization and Testing for Microgravity Science Payloads

NASA Technical Reports Server (NTRS)

Engberg, Robert C.

2003-01-01

This paper describes efforts of testing and analysis of various candidate cables and umbilicals for International Space Station microgravity science payloads. The effects of looping, large vs. small displacements, and umbilical mounting configurations were assessed. A 3-DOF stepper motor driven fixture was used to excite the umbilicals. Forces and moments were directly measured in all three axes with a 6-DOF load cell in order to derive suitable stiffness matrices for design and analysis of vibration isolation controllers. Data obtained from these tests were used to help determine the optimum type and configuration of umbilical cables for the International Space Station microgravity science glovebox (MSG) vibration isolation platform. The data and procedures can also be implemented into control algorithm simulations to assist in validation of actively controlled vibration isolation systems. The experimental results of this work are specific in support of the Glovebox Integrated Microgravity Isolation Technology (g-LIMIT) isolation platform, to be located in the microgravity science glovebox aboard the U.S. Destiny Laboratory Module.

Restricted Closed Shell Hartree Fock Roothaan Matrix Method Applied to Helium Atom Using Mathematica

ERIC Educational Resources Information Center

Acosta, César R.; Tapia, J. Alejandro; Cab, César

2014-01-01

Slater type orbitals were used to construct the overlap and the Hamiltonian core matrices; we also found the values of the bi-electron repulsion integrals. The Hartree Fock Roothaan approximation process starts with setting an initial guess value for the elements of the density matrix; with these matrices we constructed the initial Fock matrix.…

Immobilization of long-lived radionuclides in carbon matrices produced with the use of polyimide binders

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abdulakhatov, Murat; Bartenev, Sergey; Firsin, Nikolai

Available in abstract form only. Full text of publication follows: Conditions for immobilization of long-lived radionuclides {sup 99}Tc, {sup 129}I and {sup 241}Am in carbon matrices were investigated by using their chemical analogs. Stable isotopes of rhenium, iodine and europium were used as chemical analogs of {sup 99}Tc, {sup 129}I and {sup 241}Am, respectively. It is shown that the carbon matrices incorporating the above elements can be produced by carbonization of composites with ITA-31 polyimide binder of the following composition: equal molar ratio between dianhydride of 3,3/,4,4/-benzophenone-tetracarboxylic acid and tetraacetyl derivative of 4,4/-diaminodiphenyl ester, radionuclide being investigated or its chemicalmore » analog and carbon fabric as reinforcing component. The elements under investigation were used both in the form of salts or oxides and in the form of their complexes with ion-exchange resins. The produced composites were carbonized in inert gas (argon) or in vacuum. The physical-chemical properties of the samples were studied. It was revealed that the resultant matrices meet the requirements imposed on waste storage and final disposal. (authors)« less

Intraventricular filling under increasing left ventricular wall stiffness and heart rates

NASA Astrophysics Data System (ADS)

Samaee, Milad; Lai, Hong Kuan; Schovanec, Joseph; Santhanakrishnan, Arvind; Nagueh, Sherif

2015-11-01

Heart failure with normal ejection fraction (HFNEF) is a clinical syndrome that is prevalent in over 50% of heart failure patients. HFNEF patients show increased left ventricle (LV) wall stiffness and clinical diagnosis is difficult using ejection fraction (EF) measurements. We hypothesized that filling vortex circulation strength would decrease with increasing LV stiffness irrespective of heart rate (HR). 2D PIV and hemodynamic measurements were acquired on LV physical models of varying wall stiffness under resting and exercise HRs. The LV models were comparatively tested in an in vitro flow circuit consisting of a two-element Windkessel model driven by a piston pump. The stiffer LV models were tested in comparison with the least stiff baseline model without changing pump amplitude, circuit compliance and resistance. Increasing stiffness at resting HR resulted in diminishing cardiac output without lowering EF below 50% as in HFNEF. Increasing HR to 110 bpm in addition to stiffness resulted in lowering EF to less than 50%. The circulation strength of the intraventricular filling vortex diminished with increasing stiffness and HR. The results suggest that filling vortex circulation strength could be potentially used as a surrogate measure of LV stiffness. This research was supported by the Oklahoma Center for Advancement of Science and Technology (HR14-022).

Finite element analysis of the axial stiffness of a ball screw

NASA Astrophysics Data System (ADS)

Zhou, L.-X.; Li, P.-Y.

2018-06-01

The ball screw was developed for high speed and high precision operation; therefore, increasingly greater demands have been placed on the stiffness of the ball screw. Firstly, ANSYS software was used to compare the axial stiffness of a single-nut and single-arc ball screw and a single-nut and double-arc ball screw when the spiral angle is not considered. On this basis, the model of a single-nut ball screw was established taking into consideration the spiral lead angle, and then the variations in displacement and stiffness when the ball screw pair was subjected to an axial force were determined. The axial contact stiffness of the double-nut ball screw pair, subject to a pre-tightening force, was analyzed, according to the above-mentioned steps. The simulation results demonstrated that under the same working conditions, the stiffness of the double-arc ball screw was larger by between 5∼100 N/um than that of the single-arc ball screw. The spiral lead angle increased the axial stiffness of the ball screw pair, and the axial stiffness of the double-nut ball screw pair subject to a pre-tightening force was larger by between 790∼1360 N/um than that of the axial stiffness of the single-nut ball screw pair.

A new method for measuring the rotational accuracy of rolling element bearings

NASA Astrophysics Data System (ADS)

Chen, Ye; Zhao, Xiangsong; Gao, Weiguo; Hu, Gaofeng; Zhang, Shizhen; Zhang, Dawei

2016-12-01

The rotational accuracy of a machine tool spindle has critical influence upon the geometric shape and surface roughness of finished workpiece. The rotational performance of the rolling element bearings is a main factor which affects the spindle accuracy, especially in the ultra-precision machining. In this paper, a new method is developed to measure the rotational accuracy of rolling element bearings of machine tool spindles. Variable and measurable axial preload is applied to seat the rolling elements in the bearing races, which is used to simulate the operating conditions. A high-precision (radial error is less than 300 nm) and high-stiffness (radial stiffness is 600 N/μm) hydrostatic reference spindle is adopted to rotate the inner race of the test bearing. To prevent the outer race from rotating, a 2-degrees of freedom flexure hinge mechanism (2-DOF FHM) is designed. Correction factors by using stiffness analysis are adopted to eliminate the influences of 2-DOF FHM in the radial direction. Two capacitive displacement sensors with nano-resolution (the highest resolution is 9 nm) are used to measure the radial error motion of the rolling element bearing, without separating the profile error as the traditional rotational accuracy metrology of the spindle. Finally, experimental measurements are performed at different spindle speeds (100-4000 rpm) and axial preloads (75-780 N). Synchronous and asynchronous error motion values are evaluated to demonstrate the feasibility and repeatability of the developed method and instrument.

High precision computing with charge domain devices and a pseudo-spectral method therefor

NASA Technical Reports Server (NTRS)

Barhen, Jacob (Inventor); Toomarian, Nikzad (Inventor); Fijany, Amir (Inventor); Zak, Michail (Inventor)

1997-01-01

The present invention enhances the bit resolution of a CCD/CID MVM processor by storing each bit of each matrix element as a separate CCD charge packet. The bits of each input vector are separately multiplied by each bit of each matrix element in massive parallelism and the resulting products are combined appropriately to synthesize the correct product. In another aspect of the invention, such arrays are employed in a pseudo-spectral method of the invention, in which partial differential equations are solved by expressing each derivative analytically as matrices, and the state function is updated at each computation cycle by multiplying it by the matrices. The matrices are treated as synaptic arrays of a neural network and the state function vector elements are treated as neurons. In a further aspect of the invention, moving target detection is performed by driving the soliton equation with a vector of detector outputs. The neural architecture consists of two synaptic arrays corresponding to the two differential terms of the soliton-equation and an adder connected to the output thereof and to the output of the detector array to drive the soliton equation.

GPU-accelerated Modeling and Element-free Reverse-time Migration with Gauss Points Partition

NASA Astrophysics Data System (ADS)

Zhen, Z.; Jia, X.

2014-12-01

Element-free method (EFM) has been applied to seismic modeling and migration. Compared with finite element method (FEM) and finite difference method (FDM), it is much cheaper and more flexible because only the information of the nodes and the boundary of the study area are required in computation. In the EFM, the number of Gauss points should be consistent with the number of model nodes; otherwise the accuracy of the intermediate coefficient matrices would be harmed. Thus when we increase the nodes of velocity model in order to obtain higher resolution, we find that the size of the computer's memory will be a bottleneck. The original EFM can deal with at most 81×81 nodes in the case of 2G memory, as tested by Jia and Hu (2006). In order to solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition (GPP), and utilize the GPUs to improve the computation efficiency. Considering the characteristics of the Gaussian points, the GPP method doesn't influence the propagation of seismic wave in the velocity model. To overcome the time-consuming computation of the stiffness matrix (K) and the mass matrix (M), we also use the GPUs in our computation program. We employ the compressed sparse row (CSR) format to compress the intermediate sparse matrices and try to simplify the operations by solving the linear equations with the CULA Sparse's Conjugate Gradient (CG) solver instead of the linear sparse solver 'PARDISO'. It is observed that our strategy can significantly reduce the computational time of K and Mcompared with the algorithm based on CPU. The model tested is Marmousi model. The length of the model is 7425m and the depth is 2990m. We discretize the model with 595x298 nodes, 300x300 Gauss cells and 3x3 Gauss points in each cell. In contrast to the computational time of the conventional EFM, the GPUs-GPP approach can substantially improve the efficiency. The speedup ratio of time consumption of computing K, M is 120 and the speedup ratio time consumption of RTM is 11.5. At the same time, the accuracy of imaging is not harmed. Another advantage of the GPUs-GPP method is its easy applications in other numerical methods such as the FEM. Finally, in the GPUs-GPP method, the arrays require quite limited memory storage, which makes the method promising in dealing with large-scale 3D problems.

Accurate Simulation of Parametrically Excited Micromirrors via Direct Computation of the Electrostatic Stiffness

PubMed Central

Frangi, Attilio; Guerrieri, Andrea; Boni, Nicoló

2017-01-01

Electrostatically actuated torsional micromirrors are key elements in Micro-Opto-Electro- Mechanical-Systems. When forced by means of in-plane comb-fingers, the dynamics of the main torsional response is known to be strongly non-linear and governed by parametric resonance. Here, in order to also trace unstable branches of the mirror response, we implement a simplified continuation method with arc-length control and propose an innovative technique based on Finite Elements and the concepts of material derivative in order to compute the electrostatic stiffness; i.e., the derivative of the torque with respect to the torsional angle, as required by the continuation approach. PMID:28383483

Accurate Simulation of Parametrically Excited Micromirrors via Direct Computation of the Electrostatic Stiffness.

PubMed

Frangi, Attilio; Guerrieri, Andrea; Boni, Nicoló

2017-04-06

Electrostatically actuated torsional micromirrors are key elements in Micro-Opto-Electro- Mechanical-Systems. When forced by means of in-plane comb-fingers, the dynamics of the main torsional response is known to be strongly non-linear and governed by parametric resonance. Here, in order to also trace unstable branches of the mirror response, we implement a simplified continuation method with arc-length control and propose an innovative technique based on Finite Elements and the concepts of material derivative in order to compute the electrostatic stiffness; i.e., the derivative of the torque with respect to the torsional angle, as required by the continuation approach.

Effects of substitution on the exchange stiffness and magnetization of Co films

NASA Astrophysics Data System (ADS)

Eyrich, C.; Zamani, A.; Huttema, W.; Arora, M.; Harrison, D.; Rashidi, F.; Broun, D.; Heinrich, B.; Mryasov, O.; Ahlberg, M.; Karis, O.; Jönsson, P. E.; From, M.; Zhu, X.; Girt, E.

2014-12-01

An antiferromagnetically coupled FM/NM/FM (FM = ferromagnet, NM = normal metal) trilayer structure responds to an external magnetic field by the formation of a magnetic-moment spring within the FM layers. We show that the exchange stiffness (Aex) of an FM layer can be determined by fitting the field-dependent magnetization, M (H ) , of the FM/NM/FM trilayer to a micromagnetic model. Using this method, we have measured the exchange stiffness of thin-film Co alloyed with Cr, Fe, Ni, Pd, Pt, and Ru. The results show that the rate at which a substituent element reduces the exchange stiffness is not directly related to its effect on the magnetization of the alloy. The observed trends have been understood by material-specific modeling based on density functional theory within the local density approximation. The stiffness measurements are in agreement with Brillouin light scattering carried out on thicker Co films.

Reflection matrices with U q [osp(2) (2|2m)] symmetry

NASA Astrophysics Data System (ADS)

Vieira, R. S.; Lima-Santos, A.

2017-09-01

We propose a classification of the reflection K-matrices (solutions of the boundary Yang-Baxter equation) for the Uq[osp(2)(2\\vert 2m)]=Uq[C(2)(m+1)] vertex-model. We found four families of solutions, namely, the complete solutions, in which no elements of the reflection K-matrix is null, the block-diagonal solutions, the X-shape solutions and the diagonal solutions. We highlight that these diagonal K-matrices also hold for the Uq[osp(2)(2n+2\\vert 2m)]=Uq[D(2)(n+1, m)] vertex-model.

Modeling error analysis of stationary linear discrete-time filters

NASA Technical Reports Server (NTRS)

Patel, R.; Toda, M.

1977-01-01

The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a design can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices is available.

Artificial muscles with adjustable stiffness

NASA Astrophysics Data System (ADS)

Mutlu, Rahim; Alici, Gursel

2010-04-01

This paper reports on a stiffness enhancement methodology based on using a suitably designed contact surface with which cantilevered-type conducting polymer bending actuators are in contact during operation. The contact surface constrains the bending behaviour of the actuators. Depending on the topology of the contact surface, the resistance of the polymer actuators to deformation, i.e. stiffness, is varied. As opposed to their predecessors, these polymer actuators operate in air. Finite element analysis and modelling are used to quantify the effect of the contact surface on the effective stiffness of a trilayer cantilevered beam, which represents a one-end-free, the-other-end-fixed polypyrrole (PPy) conducting polymer actuator under a uniformly distributed load. After demonstrating the feasibility of the adjustable stiffness concept, experiments were conducted to determine the stiffness of bending-type conducting polymer actuators in contact with a range (20-40 mm in radius) of circular contact surfaces. The numerical and experimental results presented demonstrate that the stiffness of the actuators can be varied using a suitably profiled contact surface. The larger the radius of the contact surface is, the higher is the stiffness of the polymer actuators. The outcomes of this study suggest that, although the stiffness of the artificial muscles considered in this study is constant for a given geometric size, and electrical and chemical operation conditions, it can be changed in a nonlinear fashion to suit the stiffness requirement of a considered application. The stiffness enhancement methodology can be extended to other ionic-type conducting polymer actuators.

Improvement of analytical dynamic models using modal test data

NASA Technical Reports Server (NTRS)

Berman, A.; Wei, F. S.; Rao, K. V.

1980-01-01

A method developed to determine maximum changes in analytical mass and stiffness matrices to make them consistent with a set of measured normal modes and natural frequencies is presented. The corrected model will be an improved base for studies of physical changes, boundary condition changes, and for prediction of forced responses. The method features efficient procedures not requiring solutions of the eigenvalue problem, and the ability to have more degrees of freedom than the test data. In addition, modal displacements are obtained for all analytical degrees of freedom, and the frequency dependence of the coordinate transformations is properly treated.

Development of an intravascular ultrasound elastography based on a dual-element transducer

NASA Astrophysics Data System (ADS)

Shih, Cho-Chiang; Chen, Pei-Yu; Ma, Teng; Zhou, Qifa; Shung, K. Kirk; Huang, Chih-Chung

2018-04-01

The ability to measure the elastic properties of plaques and vessels would be useful in clinical diagnoses, particularly for detecting a vulnerable plaque. This study demonstrates the feasibility of the combination of intravascular ultrasound (IVUS) and acoustic radiation force elasticity imaging for detecting the distribution of stiffness within atherosclerotic arteries ex vivo. A dual-frequency IVUS transducer with two elements was used to induce the propagation of the shear wave (by the 8.5 MHz pushing element) which could be simultaneously monitored by the 31 MHz imaging element. The wave-amplitude image and the wave-velocity image were reconstructed by measuring the peak displacement and wave velocity of shear wave propagation, respectively. System performance was verified using gelatin phantoms. The phantom results demonstrate that the stiffness differences of shear modulus of 1.6 kPa can be distinguished through the wave-amplitude and wave-velocity images. The stiffness distributions of the atherosclerotic aorta from a rabbit were obtained, for which the values of peak displacement and the shear wave velocity were 3.7 ± 1.2 µm and 0.38 ± 0.19 m s-1 for the lipid-rich plaques, and 1.0 ± 0.2 µm and 3.45 ± 0.45 m s-1 for the arterial walls, respectively. These results indicate that IVUS elasticity imaging can be used to distinguish the elastic properties of plaques and vessels.

Variable stiffness corrugated composite structure with shape memory polymer for morphing skin applications

NASA Astrophysics Data System (ADS)

Gong, Xiaobo; Liu, Liwu; Scarpa, Fabrizio; Leng, Jinsong; Liu, Yanju

2017-03-01

This work presents a variable stiffness corrugated structure based on a shape memory polymer (SMP) composite with corrugated laminates as reinforcement that shows smooth aerodynamic surface, extreme mechanical anisotropy and variable stiffness for potential morphing skin applications. The smart composite corrugated structure shows a low in-plane stiffness to minimize the actuation energy, but also possess high out-of-plane stiffness to transfer the aerodynamic pressure load. The skin provides an external smooth aerodynamic surface because of the one-sided filling with the SMP. Due to variable stiffness of the shape memory polymer the morphing skin exhibits a variable stiffness with a change of temperature, which can help the skin adjust its stiffness according different service environments and also lock the temporary shape without external force. Analytical models related to the transverse and bending stiffness are derived and validated using finite element techniques. The stiffness of the morphing skin is further investigated by performing a parametric analysis against the geometry of the corrugation and various sets of SMP fillers. The theoretical and numerical models show a good agreement and demonstrate the potential of this morphing skin concept for morphing aircraft applications. We also perform a feasibility study of the use of this morphing skin in a variable camber morphing wing baseline. The results show that the morphing skin concept exhibits sufficient bending stiffness to withstand the aerodynamic load at low speed (less than 0.3 Ma), while demonstrating a large transverse stiffness variation (up to 191 times) that helps to create a maximum mechanical efficiency of the structure under varying external conditions.

On the Assessment of Psychometric Adequacy in Correlation Matrices.

ERIC Educational Resources Information Center

Dziuban, Charles D.; Shirkey, Edwin C.

Three techniques for assessing the adequacy of correlation matrices for factor analysis were applied to four examples from the literature. The methods compared were: (1) inspection of the off diagonal elements of the anti-image covariance matrix S(to the 2nd) R(to the -1) and S(to the 2nd); (2) the Measure of Sampling Adequacy (M.S.A.), and (3)…

Space of symmetry matrices with elements 0, ±1 and complete geometric description; its properties and application.

PubMed

Stróż, Kazimierz

2011-09-01

A fixed set, that is the set of all lattice metrics corresponding to the arithmetic holohedry of a primitive lattice, is a natural tool for keeping track of the symmetry changes that may occur in a deformable lattice [Ericksen (1979). Arch. Rat. Mech. Anal. 72, 1-13; Michel (1995). Symmetry and Structural Properties of Condensed Matter, edited by T. Lulek, W. Florek & S. Walcerz. Singapore: Academic Press; Pitteri & Zanzotto (1996). Acta Cryst. A52, 830-838; and references quoted therein]. For practical applications it is desirable to limit the infinite number of arithmetic holohedries, and simplify their classification and construction of the fixed sets. A space of 480 matrices with cyclic consecutive powers, determinant 1, elements from {0, ±1} and geometric description were analyzed and offered as the framework for dealing with the symmetry of reduced lattices. This matrix space covers all arithmetic holohedries of primitive lattice descriptions related to the three shortest lattice translations in direct or reciprocal spaces, and corresponds to the unique list of 39 fixed points with integer coordinates in six-dimensional space of lattice metrics. Matrices are presented by the introduced dual symbol, which sheds some light on the lattice and its symmetry-related properties, without further digging into matrices. By the orthogonal lattice distortion the lattice group-subgroup relations are easily predicted. It was proven and exemplified that new symbols enable classification of lattice groups on an absolute basis, without metric considerations. In contrast to long established but sophisticated methods for assessing the metric symmetry of a lattice, simple filtering of the symmetry operations from the predefined set is proposed. It is concluded that the space of symmetry matrices with elements from {0, ±1} is the natural environment of lattice symmetries related to the reduced cells and that complete geometric characterization of matrices in the arithmetic holohedry provides a useful tool for solving practical lattice-related problems, especially in the context of lattice deformation. © 2011 International Union of Crystallography

Crosslinkable hydrogels derived from cartilage, meniscus, and tendon tissue.

PubMed

Visser, Jetze; Levett, Peter A; te Moller, Nikae C R; Besems, Jeremy; Boere, Kristel W M; van Rijen, Mattie H P; de Grauw, Janny C; Dhert, Wouter J A; van Weeren, P René; Malda, Jos

2015-04-01

Decellularized tissues have proven to be versatile matrices for the engineering of tissues and organs. These matrices usually consist of collagens, matrix-specific proteins, and a set of largely undefined growth factors and signaling molecules. Although several decellularized tissues have found their way to clinical applications, their use in the engineering of cartilage tissue has only been explored to a limited extent. We set out to generate hydrogels from several tissue-derived matrices, as hydrogels are the current preferred cell carriers for cartilage repair. Equine cartilage, meniscus, and tendon tissue was harvested, decellularized, enzymatically digested, and functionalized with methacrylamide groups. After photo-cross-linking, these tissue digests were mechanically characterized. Next, gelatin methacrylamide (GelMA) hydrogel was functionalized with these methacrylated tissue digests. Equine chondrocytes and mesenchymal stromal cells (MSCs) (both from three donors) were encapsulated and cultured in vitro up to 6 weeks. Gene expression (COL1A1, COL2A1, ACAN, MMP-3, MMP-13, and MMP-14), cartilage-specific matrix formation, and hydrogel stiffness were analyzed after culture. The cartilage, meniscus, and tendon digests were successfully photo-cross-linked into hydrogels. The addition of the tissue-derived matrices to GelMA affected chondrogenic differentiation of MSCs, although no consequent improvement was demonstrated. For chondrocytes, the tissue-derived matrix gels performed worse compared to GelMA alone. This work demonstrates for the first time that native tissues can be processed into crosslinkable hydrogels for the engineering of tissues. Moreover, the differentiation of encapsulated cells can be influenced in these stable, decellularized matrix hydrogels.

Appendix F : finite element analysis of end region.

DOT National Transportation Integrated Search

2013-03-01

FE (finite element) modeling was conducted to 1) provide a better understanding of the : elastic behavior of the end region prior to cracking and 2) to evaluate the effects of bearing pad : stiffness and width on end region elastic stresses. The FEA ...

From deep TLS validation to ensembles of atomic models built from elemental motions. II. Analysis of TLS refinement results by explicit interpretation

DOE PAGES

Afonine, Pavel V.; Adams, Paul D.; Urzhumtsev, Alexandre

2018-06-08

TLS modelling was developed by Schomaker and Trueblood to describe atomic displacement parameters through concerted (rigid-body) harmonic motions of an atomic group [Schomaker & Trueblood (1968), Acta Cryst. B 24 , 63–76]. The results of a TLS refinement are T , L and S matrices that provide individual anisotropic atomic displacement parameters (ADPs) for all atoms belonging to the group. These ADPs can be calculated analytically using a formula that relates the elements of the TLS matrices to atomic parameters. Alternatively, ADPs can be obtained numerically from the parameters of concerted atomic motions corresponding to the TLS matrices. Both proceduresmore » are expected to produce the same ADP values and therefore can be used to assess the results of TLS refinement. Here, the implementation of this approach in PHENIX is described and several illustrations, including the use of all models from the PDB that have been subjected to TLS refinement, are provided.« less

From deep TLS validation to ensembles of atomic models built from elemental motions. II. Analysis of TLS refinement results by explicit interpretation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Afonine, Pavel V.; Adams, Paul D.; Urzhumtsev, Alexandre

TLS modelling was developed by Schomaker and Trueblood to describe atomic displacement parameters through concerted (rigid-body) harmonic motions of an atomic group [Schomaker & Trueblood (1968), Acta Cryst. B 24 , 63–76]. The results of a TLS refinement are T , L and S matrices that provide individual anisotropic atomic displacement parameters (ADPs) for all atoms belonging to the group. These ADPs can be calculated analytically using a formula that relates the elements of the TLS matrices to atomic parameters. Alternatively, ADPs can be obtained numerically from the parameters of concerted atomic motions corresponding to the TLS matrices. Both proceduresmore » are expected to produce the same ADP values and therefore can be used to assess the results of TLS refinement. Here, the implementation of this approach in PHENIX is described and several illustrations, including the use of all models from the PDB that have been subjected to TLS refinement, are provided.« less

An electric-analog simulation of elliptic partial differential equations using finite element theory

USGS Publications Warehouse

Franke, O.L.; Pinder, G.F.; Patten, E.P.

1982-01-01

Elliptic partial differential equations can be solved using the Galerkin-finite element method to generate the approximating algebraic equations, and an electrical network to solve the resulting matrices. Some element configurations require the use of networks containing negative resistances which, while physically realizable, are more expensive and time-consuming to construct. ?? 1982.

An extension of the finite cell method using boolean operations

NASA Astrophysics Data System (ADS)

Abedian, Alireza; Düster, Alexander

2017-05-01

In the finite cell method, the fictitious domain approach is combined with high-order finite elements. The geometry of the problem is taken into account by integrating the finite cell formulation over the physical domain to obtain the corresponding stiffness matrix and load vector. In this contribution, an extension of the FCM is presented wherein both the physical and fictitious domain of an element are simultaneously evaluated during the integration. In the proposed extension of the finite cell method, the contribution of the stiffness matrix over the fictitious domain is subtracted from the cell, resulting in the desired stiffness matrix which reflects the contribution of the physical domain only. This method results in an exponential rate of convergence for porous domain problems with a smooth solution and accurate integration. In addition, it reduces the computational cost, especially when applying adaptive integration schemes based on the quadtree/octree. Based on 2D and 3D problems of linear elastostatics, numerical examples serve to demonstrate the efficiency and accuracy of the proposed method.

The effect of weak interface on transverse properties of a ceramic matrix composite

NASA Technical Reports Server (NTRS)

Shimansky, R. A.; Hahn, H. T.; Salamon, N. J.

1990-01-01

Experimental studies conducted at NASA Lewis on SiC reaction-bonded Si3N4 composite system showed that transverse stiffness and strength were much lower than those predicted from existing analytical models based on good interfacial bonding. It was believed that weakened interfaces were responsible for the decrease in tranverse properties. To support this claim, a two-dimensional FEM analysis was performed for a transverse representative volume element. Specifically, the effect of fiber/matrix displacement compatibility at the interface was studied under both tensile and compressive transverse loadings. Interface debonding was represented using active gap elements connecting the fiber and matrix. The analyses show that the transverse tensile strength and stiffness are best predicted when a debonded interface is assumed for the composite. In fact, the measured properties can be predicted by simply replacing the fibers by voids. Thus, it is found that little or no interfacial bonding exists in the composite, and that an elastic analysis can predict the transverse stiffness and strength.

Development of a curved pipe capability for the NASTRAN finite element program

NASA Technical Reports Server (NTRS)

Jeter, J. W., Jr.

1977-01-01

A curved pipe element capability for the NASTRAN structural analysis program is developed using the NASTRAN dummy element feature. A description is given of the theory involved in the subroutines which describe stiffness, mass, thermal and enforced deformation loads, and force and stress recovery for the curved pipe element. Incorporation of these subroutines into NASTRAN is discussed. Test problems are proposed. Instructions on use of the new element capability are provided.

Inverse axial mounting stiffness design for lithographic projection lenses.

PubMed

Wen-quan, Yuan; Hong-bo, Shang; Wei, Zhang

2014-09-01

In order to balance axial mounting stiffness of lithographic projection lenses and the image quality under dynamic working conditions, an easy inverse axial mounting stiffness design method is developed in this article. Imaging quality deterioration at the wafer under different axial vibration levels is analyzed. The desired image quality can be determined according to practical requirements, and axial vibrational tolerance of each lens is solved with the damped least-squares method. Based on adaptive interval adjustment, a binary search algorithm, and the finite element method, the axial mounting stiffness of each lens can be traveled in a large interval, and converges to a moderate numerical solution which makes the axial vibrational amplitude of the lens converge to its axial vibrational tolerance. Model simulation is carried out to validate the effectiveness of the method.

Finite Element Analysis and Biomechanical Comparison of Short Posterior Spinal Instrumentation with Divergent Bridge Construct versus Parallel Tension Band Construct for Thoracolumbar Spine Fractures

PubMed Central

Ouellet, Jean A.; Richards, Corey; Sardar, Zeeshan M.; Giannitsios, Demetri; Noiseux, Nicholas; Strydom, Willem S.; Reindl, Rudy; Jarzem, Peter; Arlet, Vincent; Steffen, Thomas

2013-01-01

The ideal treatment for unstable thoracolumbar fractures remains controversial with posterior reduction and stabilization, anterior reduction and stabilization, combined posterior and anterior reduction and stabilization, and even nonoperative management advocated. Short segment posterior osteosynthesis of these fractures has less comorbidities compared with the other operative approaches but settles into kyphosis over time. Biomechanical comparison of the divergent bridge construct versus the parallel tension band construct was performed for anteriorly destabilized T11–L1 spine segments using three different models: (1) finite element analysis (FEA), (2) a synthetic model, and (3) a human cadaveric model. Outcomes measured were construct stiffness and ultimate failure load. Our objective was to determine if the divergent pedicle screw bridge construct would provide more resistance to kyphotic deforming forces. All three modalities showed greater stiffness with the divergent bridge construct. The FEA calculated a stiffness of 21.6 N/m for the tension band construct versus 34.1 N/m for the divergent bridge construct. The synthetic model resulted in a mean stiffness of 17.3 N/m for parallel tension band versus 20.6 N/m for the divergent bridge (p = 0.03), whereas the cadaveric model had an average stiffness of 15.2 N/m in the parallel tension band compared with 18.4 N/m for the divergent bridge (p = 0.02). Ultimate failure load with the cadaveric model was found to be 622 N for the divergent bridge construct versus 419 N (p = 0.15) for the parallel tension band construct. This study confirms our clinical experience that the short posterior divergent bridge construct provides greater stiffness for the management of unstable thoracolumbar fractures. PMID:24436856

Left ventricular filling under elevated left atrial pressure

NASA Astrophysics Data System (ADS)

Gaddam, Manikantam; Samaee, Milad; Santhanakrishnan, Arvind

2017-11-01

Left atrial pressure (LAP) is elevated in diastolic dysfunction, where left ventricular (LV) filling is impaired due to increase in ventricular stiffness. The impact of increasing LAP and LV stiffness on intraventricular filling hemodynamics remains unclear. We conducted particle image velocimetry and hemodynamics measurements in a left heart simulator (LHS) under increasing LAP and LV stiffness at a heart rate of 70 bpm. The LHS consisted of a flexible-walled LV physical model fitted within a fluid-filled chamber. LV wall motion was generated by a piston pump that imparted pressure fluctuations in the chamber. Resistance and compliance elements in the flow loop were adjusted to obtain bulk physiological hemodynamics in the least stiff LV model. Two LV models of increasing stiffness were subsequently tested under unchanged loop settings. LAP was varied between 5-20 mm Hg for each LV model, by adjusting fluid level in a reservoir upstream of the LV. For constant LV stiffness, increasing LAP lowered cardiac output (CO), while ejection fraction (EF) and E/A ratio were increased. For constant LAP, increasing LV stiffness lowered CO and EF, and increased E/A ratio. The implications of these altered hemodynamics on intraventricular filling vortex characteristics will be presented.

Analytical study of a quasi-zero stiffness coupling using a torsion magnetic spring with negative stiffness

NASA Astrophysics Data System (ADS)

Zheng, Yisheng; Zhang, Xinong; Luo, Yajun; Zhang, Yahong; Xie, Shilin

2018-02-01

By now, many translation quasi-zero stiffness (QZS) mechanisms have been proposed to overcome the restriction between the isolation frequency range and the load bearing capacity of linear isolators. The couplings of rotor systems undertake the functions of transmitting static driving torque and isolating disturbing torque simultaneously, which creates the demand of torsion QZS mechanisms. Hence a QZS coupling is presented in this paper, where a torsion magnetic spring (TMS) composed of two coaxial ring magnet arrangements in repulsive configuration is employed to produce negative torsion stiffness to counteract the positive stiffness of a rubber spring. In this paper, the expressions of magnetic torque and stiffness are given firstly and verified by finite element simulations; and the effect of geometric parameters of the TMS on its stiffness characteristic is analyzed in detail, which contributes to the optimal design of the TMS. Then dynamic analysis of the QZS coupling is performed and the analytical expression of the torque transmissibility is achieved based on the Harmonic Balance Method. Finally, simulation of the torque transmissibility is carried out to reveal how geometric parameters of the TMS affect the isolation performance.

Analysis of Dynamic Stiffness Effect of Primary Suspension Helical Springs on Railway Vehicle Vibration

NASA Astrophysics Data System (ADS)

Sun, W.; Thompson, D. J.; Zhou, J.; Gong, D.

2016-09-01

Helical springs within the primary suspension are critical components for isolating the whole vehicle system from vibration generated at the wheel/rail contact. As train speeds increase, the frequency region of excitation becomes larger, and a simplified static stiffness can no longer represent the real stiffness property in a vehicle dynamic model. Coil springs in particular exhibit strong internal resonances, which lead to high vibration amplitudes within the spring itself as well as degradation of the vibration isolation. In this paper, the dynamic stiffness matrix method is used to determine the dynamic stiffness of a helical spring from a vehicle primary suspension. Results are confirmed with a finite element analysis. Then the spring dynamic stiffness is included within a vehicle-track coupled dynamic model of a high speed train and the effect of the dynamic stiffening of the spring on the vehicle vibration is investigated. It is shown that, for frequencies above about 50 Hz, the dynamic stiffness of the helical spring changes sharply. Due to this effect, the vibration transmissibility increases considerably which results in poor vibration isolation of the primary suspension. Introducing a rubber layer in series with the coil spring can attenuate this effect.

Design of a cosmetic glove stiffness compensation mechanism for toddler-sized hand prostheses

PubMed Central

Plettenburg, Dick H.

2017-01-01

The addition of a cosmetic glove to an upper limb prosthesis has a distinct effect on the cosmetic value, but its viscoelastic behaviour adds a substantial amount of stiffness and hysteresis to the system. As a result, the overall usability of the prosthesis is degraded. A novel negative stiffness element is designed to compensate for the cosmetic glove's stiffness. A combination of linear helical springs and the concept of rolling link mechanisms has resulted in a Rolling Stiffness Compensation Mechanism (RSCM). Results show that the RSCM is capable of exerting a progressive negative stiffness characteristic and can be built small enough to fit inside a 33 mm diameter wrist. Using the RSCM, an otherwise voluntary opening toddler-sized prosthesis is converted into a voluntary closing device, reducing maximum operation forces down to 40 N with a combined efficiency of 52%. Further adjustments to the design are possible to further improve the efficiency of the mechanism. Moreover, changes in geometric relations of the mechanism offers possibilities for a wide range of prostheses and other applications. PMID:28800635

Bending response of cross-ply laminated composite plates with diagonally perturbed localized interfacial degeneration.

PubMed

Kam, Chee Zhou; Kueh, Ahmad Beng Hong

2013-01-01

A laminated composite plate element with an interface description is developed using the finite element approach to investigate the bending performance of two-layer cross-ply laminated composite plates in presence of a diagonally perturbed localized interfacial degeneration between laminae. The stiffness of the laminate is expressed through the assembly of the stiffnesses of lamina sub-elements and interface element, the latter of which is formulated adopting the well-defined virtually zero-thickness concept. To account for the extent of both shear and axial weak bonding, a degeneration ratio is introduced in the interface formulation. The model has the advantage of simulating a localized weak bonding at arbitrary locations, with various degeneration areas and intensities, under the influence of numerous boundary conditions since the interfacial description is expressed discretely. Numerical results show that the bending behavior of laminate is significantly affected by the aforementioned parameters, the greatest effect of which is experienced by those with a localized total interface degeneration, representing the case of local delamination.

Time domain contact model for tyre/road interaction including nonlinear contact stiffness due to small-scale roughness

NASA Astrophysics Data System (ADS)

Andersson, P. B. U.; Kropp, W.

2008-11-01

Rolling resistance, traction, wear, excitation of vibrations, and noise generation are all attributes to consider in optimisation of the interaction between automotive tyres and wearing courses of roads. The key to understand and describe the interaction is to include a wide range of length scales in the description of the contact geometry. This means including scales on the order of micrometres that have been neglected in previous tyre/road interaction models. A time domain contact model for the tyre/road interaction that includes interfacial details is presented. The contact geometry is discretised into multiple elements forming pairs of matching points. The dynamic response of the tyre is calculated by convolving the contact forces with pre-calculated Green's functions. The smaller-length scales are included by using constitutive interfacial relations, i.e. by using nonlinear contact springs, for each pair of contact elements. The method is presented for normal (out-of-plane) contact and a method for assessing the stiffness of the nonlinear springs based on detailed geometry and elastic data of the tread is suggested. The governing equations of the nonlinear contact problem are solved with the Newton-Raphson iterative scheme. Relations between force, indentation, and contact stiffness are calculated for a single tread block in contact with a road surface. The calculated results have the same character as results from measurements found in literature. Comparison to traditional contact formulations shows that the effect of the small-scale roughness is large; the contact stiffness is only up to half of the stiffness that would result if contact is made over the whole element directly to the bulk of the tread. It is concluded that the suggested contact formulation is a suitable model to include more details of the contact interface. Further, the presented result for the tread block in contact with the road is a suitable input for a global tyre/road interaction model that is also based on the presented contact formulation.

Static and dynamic characteristics of a piezoceramic strut

NASA Technical Reports Server (NTRS)

Pokines, Brett J.; Belvin, W. Keith; Inman, Daniel J.

1993-01-01

The experimental study of a piezoceramic active truss is presented. This active strut is unique in that the piezoceramic configurations allow the stroke length of the strut not to be dependent on the piezoceramic material's expansion range but on the deflection range of the piezoceramic bender segment. A finite element model of a piezoceramic strut segment was constructed. Piezoceramic actuation was simulated using thermally induced strains. This model yielded information on the stiffness and force range of a bender element. The static and dynamic properties of the strut were identified experimentally. Feedback control was used to vary the stiffness of the strut. The experimentally verified model was used to explore implementation possibilities of the strut.

Data Sciences Summer Institute Topology Optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Watts, Seth

DSSI_TOPOPT is a 2D topology optimization code that designs stiff structures made of a single linear elastic material and void space. The code generates a finite element mesh of a rectangular design domain on which the user specifies displacement and load boundary conditions. The code iteratively designs a structure that minimizes the compliance (maximizes the stiffness) of the structure under the given loading, subject to an upper bound on the amount of material used. Depending on user options, the code can evaluate the performance of a user-designed structure, or create a design from scratch. Output includes the finite element mesh,more » design, and visualizations of the design.« less

A Modelling Method of Bolt Joints Based on Basic Characteristic Parameters of Joint Surfaces

NASA Astrophysics Data System (ADS)

Yuansheng, Li; Guangpeng, Zhang; Zhen, Zhang; Ping, Wang

2018-02-01

Bolt joints are common in machine tools and have a direct impact on the overall performance of the tools. Therefore, the understanding of bolt joint characteristics is essential for improving machine design and assembly. Firstly, According to the experimental data obtained from the experiment, the stiffness curve formula was fitted. Secondly, a finite element model of unit bolt joints such as bolt flange joints, bolt head joints, and thread joints was constructed, and lastly the stiffness parameters of joint surfaces were implemented in the model by the secondary development of ABAQUS. The finite element model of the bolt joint established by this method can simulate the contact state very well.

Experimental Research on Seismic Performance of Four-Element Variable Cross-Sectional Concrete Filled Steel Tubular Laced Columns

NASA Astrophysics Data System (ADS)

Ou, Zhijing; Lin, Jianmao; Chen, Shengfu; Lin, Wen

2017-10-01

A total of 7 experimental tests were conducted to investigate seismic performance of four element variable cross-sectional Concrete Filled Steel Tubular (CFST) laced columns. The experimental parameters are longitudinal slope and arrangement type of lacing tubes. The rules on hysteresis loop, ductility, energy expenditure, and stiffness degradation of specimens are researched. Test results indicate that all specimens have good seismic performance; their hysteresis loops are full without obvious shrinkage. With the increase of longitudinal slope, the horizontal carrying capacity increases, energy dissipation capacity improve, and there is slightly increase in stiffness degradation. The influence of arrangement type of lacing tubes on displacement ductility of specimens is big.

Textures of Yukawa coupling matrices in the 2HDM type III

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carcamo, A. E.; Martinez, R.; Rodriguez, J.-Alexis

2008-07-02

The quark mass matrices ansatze proposed by Fritzsch, Du-Xing and Fukuyama-Nishiura in the framework of the general two Higgs doublet model are studied. The corresponding Cabbibo-Kobayashi-Maskawa matrix elements are computed in all cases and compared with their experimental values. The complex phases of the anstaze are taken into account and the CP violating phase {delta} is computed. Finally some phenomenology is discussed.

Modification of Ca isotope and trace metal composition of the major matrices involved in shell formation of Mytilus edulis

NASA Astrophysics Data System (ADS)

Heinemann, Agnes; Fietzke, Jan; Eisenhauer, Anton; Zumholz, Karsten

2008-01-01

In this study we present the first combined investigation into the composition of the major matrices involved in calcification processes (surrounding water, extrapallial fluid, aragonite, and calcite) of Mytilus edulis with respect to their calcium isotope (δ44/40Ca) and elemental compositions (Sr/Ca and Mg/Ca). Our aim was to examine the suitability of Mytilus edulis as a proxy archive and to contribute to the understanding of the process of biomineralization. Mytilus edulis specimens were live collected from the Schwentine Estuary, Kiel Fjord, and North Sea (Sylt). δ44/40Ca was determined by thermal ionization mass spectrometry (TIMS) accompanied by measurements of Mg/Ca and Sr/Ca using inductively coupled plasma-optical emission spectroscopy (ICP-OES). The elemental and isotopic compositions of the investigated matrices showed systematic offsets. The carbonates are strongly depleted in their magnesium and strontium concentrations and fractionated toward lighter calcium isotope compositions relative to the surrounding Schwentine Estuary water. The opposite is observed for the extrapallial fluid (EPF). Our findings extend the results of previous studies reporting a strong biological control and the interaction of different environmental conditions influencing biomineralization. Future studies should focus on the temporal development of the interrelation between the different matrices.

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

DOE PAGES

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter; ...

2016-06-30

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

Chapter 8 optimized test design for identification of the variation of elastic stiffness properties of Loblolly Pine (Pinus taeda) pith to bark

Treesearch

David Kretschmann; John Considine; F. Pierron

2016-01-01

This article presents the design optimization of an un-notched Iosipescu test specimen whose goal is the characterization of the material elastic stiffnesses of a Loblolly (Pinus taeda) or Lodgepole pine (Pinus contorta) sample in one single test. A series of finite element (FE) and grid simulations were conducted to determine displacement and strain fields for various...

Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads

PubMed Central

Kong, Y. S.; Omar, M. Z.; Chua, L. B.; Abdullah, S.

2013-01-01

This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability. PMID:24298209

Pore Geometry Optimization of Titanium (Ti6Al4V) Alloy, for Its Application in the Fabrication of Customized Hip Implants

PubMed Central

Roy, Sandipan; Panda, Debojyoti; Khutia, Niloy; Chowdhury, Amit Roy

2014-01-01

The present study investigates the mechanical response of representative volume elements of porous Ti-6Al-4V alloy, to arrive at a desired range of pore geometries that would optimize the reduction in stiffness necessary for biocompatibility with the stress concentration arising around the pore periphery, under physiological loading conditions with respect to orthopedic hip implants. A comparative study of the two is performed with the aid of a newly defined optimizing parameter called pore efficiency that takes into consideration both the stiffness quantity and the stress localization around pores. To perform a detailed analysis of the response of the porous structure over the entire spectrum of loading conditions that a hip implant is subjected to in vivo, the mechanical responses of 3D finite element models of cubic and rectangular parallelepiped geometries, with porosities varying over a range of 10% to 60%, are simulated under representative compressive, flexural as well as combined loading conditions. The results that are obtained are used to suggest a range of pore diameters that lower the effective stiffness and modulus of the implant to around 60% of the stiffness and modulus of dense solid implants while keeping the stress levels within permissible limits. PMID:25400663

Explicit nonlinear finite element geometric analysis of parabolic leaf springs under various loads.

PubMed

Kong, Y S; Omar, M Z; Chua, L B; Abdullah, S

2013-01-01

This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability.

Dynamic analysis of space-related linear and non-linear structures

NASA Technical Reports Server (NTRS)

Bosela, Paul A.; Shaker, Francis J.; Fertis, Demeter G.

1990-01-01

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photo-voltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic control system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

Dynamic analysis of space-related linear and non-linear structures

NASA Technical Reports Server (NTRS)

Bosela, Paul A.; Shaker, Francis J.; Fertis, Demeter G.

1990-01-01

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photovoltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic controls system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

Simulation study of amplitude-modulated (AM) harmonic motion imaging (HMI) for stiffness contrast quantification with experimental validation.

PubMed

Maleke, Caroline; Luo, Jianwen; Gamarnik, Viktor; Lu, Xin L; Konofagou, Elisa E

2010-07-01

The objective of this study is to show that Harmonic Motion Imaging (HMI) can be used as a reliable tumor-mapping technique based on the tumor's distinct stiffness at the early onset of disease. HMI is a radiation-force-based imaging method that generates a localized vibration deep inside the tissue to estimate the relative tissue stiffness based on the resulting displacement amplitude. In this paper, a finite-element model (FEM) study is presented, followed by an experimental validation in tissue-mimicking polyacrylamide gels and excised human breast tumors ex vivo. This study compares the resulting tissue motion in simulations and experiments at four different gel stiffnesses and three distinct spherical inclusion diameters. The elastic moduli of the gels were separately measured using mechanical testing. Identical transducer parameters were used in both the FEM and experimental studies, i.e., a 4.5-MHz single-element focused ultrasound (FUS) and a 7.5-MHz diagnostic (pulse-echo) transducer. In the simulation, an acoustic pressure field was used as the input stimulus to generate a localized vibration inside the target. Radiofrequency (rf) signals were then simulated using a 2D convolution model. A one-dimensional cross-correlation technique was performed on the simulated and experimental rf signals to estimate the axial displacement resulting from the harmonic radiation force. In order to measure the reliability of the displacement profiles in estimating the tissue stiffness distribution, the contrast-transfer efficiency (CTE) was calculated. For tumor mapping ex vivo, a harmonic radiation force was applied using a 2D raster-scan technique. The 2D HMI images of the breast tumor ex vivo could detect a malignant tumor (20 x 10 mm2) surrounded by glandular and fat tissues. The FEM and experimental results from both gels and breast tumors ex vivo demonstrated that HMI was capable of detecting and mapping the tumor or stiff inclusion with various diameters or stiffnesses. HMI may thus constitute a promising technique in tumor detection (>3 mm in diameter) and mapping based on its distinct stiffness.

The recurrence sequences via Sylvester matrices

NASA Astrophysics Data System (ADS)

Karaduman, Erdal; Deveci, Ömür

2017-07-01

In this work, we define the Pell-Jacobsthal-Slyvester sequence and the Jacobsthal-Pell-Slyvester sequence by using the Slyvester matrices which are obtained from the characteristic polynomials of the Pell and Jacobsthal sequences and then, we study the sequences defined modulo m. Also, we obtain the cyclic groups and the semigroups from the generating matrices of these sequences when read modulo m and then, we derive the relationships among the orders of the cyclic groups and the periods of the sequences. Furthermore, we redefine Pell-Jacobsthal-Slyvester sequence and the Jacobsthal-Pell-Slyvester sequence by means of the elements of the groups and then, we examine them in the finite groups.

Establishment and analysis of coupled dynamic model for dual-mass silicon micro-gyroscope

NASA Astrophysics Data System (ADS)

Wang, Zhanghui; Qiu, Anping; Shi, Qin; Zhang, Taoyuan

2017-12-01

This paper presents a coupled dynamic model for a dual-mass silicon micro-gyroscope (DMSG). It can quantitatively analyze the influence of left-right stiffness difference on the natural frequencies, modal matrix and modal coupling coefficient of the DMSG. The analytic results are verified by using the finite element method (FEM) simulation. The model shows that with the left-right stiffness difference of 1%, the modal coupling coefficient is 12% in the driving direction and 31% in the sensing direction. It also shows that in order to achieve good separation, the stiffness of base beam should be small enough in both the driving and sensing direction.

The Elastic Behaviour of Sintered Metallic Fibre Networks: A Finite Element Study by Beam Theory

PubMed Central

Bosbach, Wolfram A.

2015-01-01

Background The finite element method has complimented research in the field of network mechanics in the past years in numerous studies about various materials. Numerical predictions and the planning efficiency of experimental procedures are two of the motivational aspects for these numerical studies. The widespread availability of high performance computing facilities has been the enabler for the simulation of sufficiently large systems. Objectives and Motivation In the present study, finite element models were built for sintered, metallic fibre networks and validated by previously published experimental stiffness measurements. The validated models were the basis for predictions about so far unknown properties. Materials and Methods The finite element models were built by transferring previously published skeletons of fibre networks into finite element models. Beam theory was applied as simplification method. Results and Conclusions The obtained material stiffness isn’t a constant but rather a function of variables such as sample size and boundary conditions. Beam theory offers an efficient finite element method for the simulated fibre networks. The experimental results can be approximated by the simulated systems. Two worthwhile aspects for future work will be the influence of size and shape and the mechanical interaction with matrix materials. PMID:26569603

A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation

NASA Technical Reports Server (NTRS)

Crivelli, Luis A.; Felippa, Carlos A.

1992-01-01

A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.

Evaluation of carbonate diagenesis: A comparative study of minor elements, trace elements, and rare-earth elements (REE + Y) between Pleistocene corals and matrices from Grand Cayman, British West Indies

NASA Astrophysics Data System (ADS)

Li, Rong; Jones, Brian

2014-12-01

On Grand Cayman, the Pleistocene Ironshore Formation consists of six unconformity-bounded units of limestones that have been partially or completely altered to calcite by post-depositional meteoric diagenesis. In order to examine the diagenetic history from the perspective of geochemical elements, the concentrations of minor element (Sr, Na, Mg), trace elements (Ba, Fe, Mn, Al, Si), and rare-earth elements (REE) and yttrium (Y) were determined for 105 corals and 84 matrices collected from the Rogers Wreck Point (RWP), Western Onshore area (WO), and offshore George Town (GT) areas. With the transformation of aragonite to calcite, the Sr, Na, and Ba values decreased, but Mg increased, which are indicative of diagenetic alteration in an open water system. Due to intrinsic "vital effects" and the extrinsic diagenetic environment, the variations of Sr, Na, Ba, and Mg concentrations between Acropora and Montastrea from the GT area are different to those of their counterparts from RWP and WO. The signatures of Sr, Na, Ba, and Mg are in good agreement with the diagenetic history as determined from petrographic and stable isotopic criteria. The REE + Y (REY) concentrations (ΣREY) are higher in the matrices (0.2-6.9 ppm, average 2.6 ppm) than in the associated corals (0.1-5.4 ppm, average 0.6 ppm). Shale-normalized REY patterns of the Pleistocene Ironshore Formation are similar to those of oxygenated seawater, which are characterized by (1) light REE depletion relative to heavy REE (average DySN/SmSN = 1.7, n = 35), (2) positive La anomalies (average Pr/Pr* = 1.17, n = 53), and (3) negative Ce anomalies (average Ce/Ce* = 0.49, n = 53). The preserved seawater-like REY distribution pattern, the lack of correlation between ΣREY and mineralogy, and the lack of correlation between ΣREY and diagenesis-sensitive stable oxygen isotope (δ18O) indicate that meteoric diagenesis did not have a major impact on the REY distribution patterns. The matrices and corals in the GT area, compared to their counterparts from RWP and WO, have relatively less depleted LREE and lower Y in REY distribution pattern, suggesting contamination by minor amounts of detrital sediments. This is supported by the fact that limestones from the GT area contain abnormally high contents of detrital elements (Al, Si). The variations in ΣREY in carbonate rocks from locality to locality probably reflect variations that existed in the local depositional environments where these deposits originally formed.

Identification of cracks in thick beams with a cracked beam element model

NASA Astrophysics Data System (ADS)

Hou, Chuanchuan; Lu, Yong

2016-12-01

The effect of a crack on the vibration of a beam is a classical problem, and various models have been proposed, ranging from the basic stiffness reduction method to the more sophisticated model involving formulation based on the additional flexibility due to a crack. However, in the damage identification or finite element model updating applications, it is still common practice to employ a simple stiffness reduction factor to represent a crack in the identification process, whereas the use of a more realistic crack model is rather limited. In this paper, the issues with the simple stiffness reduction method, particularly concerning thick beams, are highlighted along with a review of several other crack models. A robust finite element model updating procedure is then presented for the detection of cracks in beams. The description of the crack parameters is based on the cracked beam flexibility formulated by means of the fracture mechanics, and it takes into consideration of shear deformation and coupling between translational and longitudinal vibrations, and thus is particularly suitable for thick beams. The identification procedure employs a global searching technique using Genetic Algorithms, and there is no restriction on the location, severity and the number of cracks to be identified. The procedure is verified to yield satisfactory identification for practically any configurations of cracks in a beam.

Plate/shell structure topology optimization of orthotropic material for buckling problem based on independent continuous topological variables

NASA Astrophysics Data System (ADS)

Ye, Hong-Ling; Wang, Wei-Wei; Chen, Ning; Sui, Yun-Kang

2017-10-01

The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.

Hierarchical matrices implemented into the boundary integral approaches for gravity field modelling

NASA Astrophysics Data System (ADS)

Čunderlík, Róbert; Vipiana, Francesca

2017-04-01

Boundary integral approaches applied for gravity field modelling have been recently developed to solve the geodetic boundary value problems numerically, or to process satellite observations, e.g. from the GOCE satellite mission. In order to obtain numerical solutions of "cm-level" accuracy, such approaches require very refined level of the disretization or resolution. This leads to enormous memory requirements that need to be reduced. An implementation of the Hierarchical Matrices (H-matrices) can significantly reduce a numerical complexity of these approaches. A main idea of the H-matrices is based on an approximation of the entire system matrix that is split into a family of submatrices. Large submatrices are stored in factorized representation, while small submatrices are stored in standard representation. This allows reducing memory requirements significantly while improving the efficiency. The poster presents our preliminary results of implementations of the H-matrices into the existing boundary integral approaches based on the boundary element method or the method of fundamental solution.

Texture zeros and hierarchical masses from flavour (mis)alignment

NASA Astrophysics Data System (ADS)

Hollik, W. G.; Saldana-Salazar, U. J.

2018-03-01

We introduce an unconventional interpretation of the fermion mass matrix elements. As the full rotational freedom of the gauge-kinetic terms renders a set of infinite bases called weak bases, basis-dependent structures as mass matrices are unphysical. Matrix invariants, on the other hand, provide a set of basis-independent objects which are of more relevance. We employ one of these invariants to give a new parametrisation of the mass matrices. By virtue of it, one gains control over its implicit implications on several mass matrix structures. The key element is the trace invariant which resembles the equation of a hypersphere with a radius equal to the Frobenius norm of the mass matrix. With the concepts of alignment or misalignment we can identify texture zeros with certain alignments whereas Froggatt-Nielsen structures in the matrix elements are governed by misalignment. This method allows further insights of traditional approaches to the underlying flavour geometry.

High-Throughput Screening of Vascular Endothelium-Destructive or Protective Microenvironments: Cooperative Actions of Extracellular Matrix Composition, Stiffness, and Structure.

PubMed

Ding, Yonghui; Floren, Michael; Tan, Wei

2017-06-01

Pathological modification of the subendothelial extracellular matrix (ECM) has closely been associated with endothelial activation and subsequent cardiovascular disease progression. To understand regulatory mechanisms of these matrix modifications, the majority of previous efforts have focused on the modulation of either chemical composition or matrix stiffness on 2D smooth surfaces without simultaneously probing their cooperative effects on endothelium function on in vivo like 3D fibrous matrices. To this end, a high-throughput, combinatorial microarray platform on 2D and 3D hydrogel settings to resemble the compositions, stiffness, and structure of healthy and diseased subendothelial ECM has been established, and further their respective and combined effects on endothelial attachment, proliferation, inflammation, and junctional integrity have been investigated. For the first time, the results demonstrate that 3D fibrous structure resembling native ECM is a critical endothelium-protective microenvironmental factor by maintaining the stable, quiescent endothelium with strong resistance to proinflammatory stimuli. It is also revealed that matrix stiffening, in concert with chemical compositions resembling diseased ECM, particularly collagen III, could aggravate activation of nuclear factor kappa B, disruption of endothelium integrity, and susceptibility to proinflammatory stimuli. This study elucidates cooperative effects of various microenvironmental factors on endothelial activation and sheds light on new in vitro model for cardiovascular diseases. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Active vibration control of a single-stage spur gearbox

NASA Astrophysics Data System (ADS)

Dogruer, C. U.; Pirsoltan, Abbas K.

2017-02-01

The dynamic transmission error between driving and driven gears of a gear mechanism with torsional mode is induced by periodic time-varying mesh stiffness. In this study, to minimize the adverse effect of this time-varying mesh stiffness, a nonlinear controller which adjusts the torque acting on the driving gear is proposed. The basic approach is to modulate the input torque such that it compensates the periodic change in mesh stiffness. It is assumed that gears are assembled with high precision and gearbox is analyzed by a finite element software to calculate the mesh stiffness curve. Thus, change in the mesh stiffness, which is inherently nonlinear, can be predicted and canceled by a feed-forward loop. Then, remaining linear dynamics is controlled by pole placement techniques. Under these premises, it is claimed that any acceleration and velocity profile of the input shaft can be tracked accurately. Thereby, dynamic transmission error is kept to a minimum possible value and a spur gearbox, which does not emit much noise and vibration, is designed.

Finite Element Modeling of Thermal Cycling Induced Microcracking in Carbon/Epoxy Triaxial Braided Composites

NASA Technical Reports Server (NTRS)

Zhang, Chao; Binienda, Wieslaw K.; Morscher, Gregory; Martin, Richard E.

2012-01-01

The microcrack distribution and mass change in PR520/T700s and 3502/T700s carbon/epoxy braided composites exposed to thermal cycling was evaluated experimentally. Acoustic emission was utilized to record the crack initiation and propagation under cyclic thermal loading between -55 C and 120 C. Transverse microcrack morphology was investigated using X-ray Computed Tomography. Different performance of two kinds of composites was discovered and analyzed. Based on the observations of microcrack formation, a meso-mechanical finite element model was developed to obtain the resultant mechanical properties. The simulation results exhibited a decrease in strength and stiffness with increasing crack density. Strength and stiffness reduction versus crack densities in different orientations were compared. The changes of global mechanical behavior in both axial and transverse loading conditions were studied. Keywords: Thermal cycles; Microcrack; Finite Element Model; Braided Composite

Contribution of cytoskeletal elements to the axonal mechanical properties

PubMed Central

2013-01-01

Background Microtubules, microfilaments, and neurofilaments are cytoskeletal elements that affect cell morphology, cellular processes, and mechanical structures in neural cells. The objective of the current study was to investigate the contribution of each type of cytoskeletal element to the mechanical properties of axons of dorsal root and sympathetic ganglia cells in chick embryos. Results Microtubules, microfilaments, and neurofilaments in axons were disrupted by nocodazole, cytochalasin D, and acrylamide, respectively, or a combination of the three. An atomic force microscope (AFM) was then used to compress the treated axons, and the resulting corresponding force-deformation information was analyzed to estimate the mechanical properties of axons that were partially or fully disrupted. Conclusion We have found that the mechanical stiffness was most reduced in microtubules-disrupted-axons, followed by neurofilaments-disrupted- and microfilaments-disrupted-axons. This suggests that microtubules contribute the most of the mechanical stiffness to axons. PMID:24007256

Dynamic Analysis of Geared Rotors by Finite Elements

NASA Technical Reports Server (NTRS)

Kahraman, A.; Ozguven, H. Nevzat; Houser, D. R.; Zakrajsek, J. J.

1992-01-01

A finite element model of a geared rotor system on flexible bearings has been developed. The model includes the rotary inertia of on shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis geared rotors by calculating the critical speeds and determining the response of any point on the shafts to mass unbalances, geometric eccentricities of gears, and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.

Dynamics of a 4x6-Meter Thin Film Elliptical Inflated Membrane for Space Applications

NASA Technical Reports Server (NTRS)

Casiano, Matthew J.; Hamidzadeh, Hamid R.; Tinker, Michael L.; McConnaughey, Paul R. (Technical Monitor)

2002-01-01

Dynamic characterization of a thin film inflatable elliptical structure is described in detail. A two-step finite element modeling approach in MSC/NASTRAN is utilized, consisting of (1) a nonlinear static pressurization procedure used to obtain the updated stiffness matrix, and (2) a modal "restart" eigen solution that uses the modified stiffness matrix. Unique problems encountered in modeling of this large Hexameter lightweight inflatable arc identified, including considerable difficulty in obtaining convergence in the nonlinear finite element pressurization solution. It was found that the extremely thin polyimide film material (.001 in or 1 mil) presents tremendous problems in obtaining a converged solution when internal pressure loading is applied. Approaches utilized to overcome these difficulties are described. Comparison of finite element predictions for frequency and mode shapes of the inflated structure with closed-form solutions for a flat pre-tensioned membrane indicate reasonable agreement.

Actin cytoskeleton stiffness grades metastatic potential of ovarian carcinoma Hey A8 cells via nanoindentation mapping.

PubMed

Zhou, Z L; Sun, X X; Ma, J; Tong, M H; To, S K Y; Wong, A S T; Ngan, A H W

2017-07-26

Recent studies have indicated that the nanoindentation measured stiffness of carcinoma adherent cells is in general lower than normal cells, thus suggesting that cell stiffness may serve as a bio-marker for carcinoma. However, the proper establishment of such a conclusion would require biophysical understanding of the underlying mechanism of the cell stiffness. In this work, we compared the elastic moduli of the actin cytoskeletons of Hey A8 ovarian carcinoma cells with and without metastasis (HM and NM), as measured by 2D atomic force microscopy (AFM) with low-depth nanoindentation via a rate-jump method. The results indicate clearly that HM cells showed lower actin cytoskeleton stiffness atop of their nucleus position and higher actin cytoskeleton stiffness at their rims, compared to NM cells, suggesting that the local stiffness on the cytoskeleton can reflect actin filament distribution. Immunofluorescence staining and scanning electron microscopy (SEM) also indicated that the difference in stiffness in Hey A8 cells with different metastasis is associated with their F-actin rearrangement. Finite-element modelling (FEM) shows that a migrating cell would have its actin filaments bundled together to form stress fibers, which would exhibit lower indentation stiffness than the less aligned arrangement of filaments in a non-migrating cell. The results here indicate that the actin cytoskeleton stiffness can serve as a reliable marker for grading the metastasis of adherent carcinoma cells due to their cytoskeleton change and potentially predicting the migration direction of the cells. Copyright © 2017 Elsevier Ltd. All rights reserved.

Stress stiffened silicon nitride micro bridges array as substrate with tunable stiffness for cell culture.

PubMed

Chen, Jianfeng; Liu, Guangli; Ma, Chengfu; Zhao, Gang; Du, Wenqiang; Zhu, Wulin; Chu, Jiaru

2017-06-01

Recently, interactions between one-dimensional structural stiffness of physical micro environments and cell biological process have been widely studied. However in previous studies, the influence of structural stiffness on biological process was coupled with the influence of micro fiber curvature. Therefore decoupling the influences of fiber curvature and structural stiffness on cell biological process is of prime importance. In this study, we proposed a novel cell culture substrate comprised of silicon nitride bridges whose structure stiffness can be regulated by altering the axial residual stress without changing material and geometry properties. Both theoretical calculations and finite element simulations were performed to study the influence of residual stress on structure stiffness of bridges. Then multi-positions AFM bending tests were implemented to measure local stiffness of a single micro bridge so as to verify our predictions. NIH/3T3 mouse fibroblast cells were cultured on our substrates to examine the feasibility of the substrate application for investigating cellular response to microenvironment with variable stiffness. The results showed that cells on the edge region near bridge ends were more spread, elongated and better aligned along the bridge axial direction than those on the bridge center region. The results suggest that cells can sense and respond to the differences of stiffness and stiffness gradient between the edge and the center region of the bridges, which makes this kind of substrates can be applied in some biomedical fields, such as cell migration and wound healing. Copyright © 2017 Elsevier B.V. All rights reserved.

Simultaneous structural and control optimization via linear quadratic regulator eigenstructure assignment

NASA Technical Reports Server (NTRS)

Becus, G. A.; Lui, C. Y.; Venkayya, V. B.; Tischler, V. A.

1987-01-01

A method for simultaneous structural and control design of large flexible space structures (LFSS) to reduce vibration generated by disturbances is presented. Desired natural frequencies and damping ratios for the closed loop system are achieved by using a combination of linear quadratic regulator (LQR) synthesis and numerical optimization techniques. The state and control weighing matrices (Q and R) are expressed in terms of structural parameters such as mass and stiffness. The design parameters are selected by numerical optimization so as to minimize the weight of the structure and to achieve the desired closed-loop eigenvalues. An illustrative example of the design of a two bar truss is presented.

A system identification technique based on the random decrement signatures. Part 2: Experimental results

NASA Technical Reports Server (NTRS)

Bedewi, Nabih E.; Yang, Jackson C. S.

1987-01-01

Identification of the system parameters of a randomly excited structure may be treated using a variety of statistical techniques. Of all these techniques, the Random Decrement is unique in that it provides the homogeneous component of the system response. Using this quality, a system identification technique was developed based on a least-squares fit of the signatures to estimate the mass, damping, and stiffness matrices of a linear randomly excited system. The results of an experiment conducted on an offshore platform scale model to verify the validity of the technique and to demonstrate its application in damage detection are presented.

Complex eigenvalue extraction in NASTRAN by the tridiagonal reduction (FEER) method

NASA Technical Reports Server (NTRS)

Newman, M.; Mann, F. I.

1977-01-01

An extension of the Tridiagonal Reduction (FEER) method to complex eigenvalue analysis in NASTRAN is described. As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum are extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order is much lower than that of the full size problem. The reduction process is effected automatically, and thus avoids the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admits mass, damping and stiffness matrices which are unrestricted in character, i.e., they may be real, complex, symmetric or unsymmetric, singular or non-singular.

Micromechanical contact stiffness devices and application for calibrating contact resonance atomic force microscopy.

PubMed

Rosenberger, Matthew R; Chen, Sihan; Prater, Craig B; King, William P

2017-01-27

This paper reports the design, fabrication, and characterization of micromechanical devices that can present an engineered contact stiffness to an atomic force microscope (AFM) cantilever tip. These devices allow the contact stiffness between the AFM tip and a substrate to be easily and accurately measured, and can be used to calibrate the cantilever for subsequent mechanical property measurements. The contact stiffness devices are rigid copper disks of diameters 2-18 μm integrated onto a soft silicone substrate. Analytical modeling and finite element simulations predict the elastic response of the devices. Measurements of tip-sample interactions during quasi-static force measurements compare well with modeling simulation, confirming the expected elastic response of the devices, which are shown to have contact stiffness 32-156 N m -1 . To demonstrate one application, we use the disk sample to calibrate three resonant modes of a U-shaped AFM cantilever actuated via Lorentz force, at approximately 220, 450, and 1200 kHz. We then use the calibrated cantilever to determine the contact stiffness and elastic modulus of three polymer samples at these modes. The overall approach allows cantilever calibration without prior knowledge of the cantilever geometry or its resonance modes, and could be broadly applied to both static and dynamic measurements that require AFM calibration against a known contact stiffness.

Micromechanical contact stiffness devices and application for calibrating contact resonance atomic force microscopy

NASA Astrophysics Data System (ADS)

Rosenberger, Matthew R.; Chen, Sihan; Prater, Craig B.; King, William P.

2017-01-01

This paper reports the design, fabrication, and characterization of micromechanical devices that can present an engineered contact stiffness to an atomic force microscope (AFM) cantilever tip. These devices allow the contact stiffness between the AFM tip and a substrate to be easily and accurately measured, and can be used to calibrate the cantilever for subsequent mechanical property measurements. The contact stiffness devices are rigid copper disks of diameters 2-18 μm integrated onto a soft silicone substrate. Analytical modeling and finite element simulations predict the elastic response of the devices. Measurements of tip-sample interactions during quasi-static force measurements compare well with modeling simulation, confirming the expected elastic response of the devices, which are shown to have contact stiffness 32-156 N m-1. To demonstrate one application, we use the disk sample to calibrate three resonant modes of a U-shaped AFM cantilever actuated via Lorentz force, at approximately 220, 450, and 1200 kHz. We then use the calibrated cantilever to determine the contact stiffness and elastic modulus of three polymer samples at these modes. The overall approach allows cantilever calibration without prior knowledge of the cantilever geometry or its resonance modes, and could be broadly applied to both static and dynamic measurements that require AFM calibration against a known contact stiffness.

Three new models for evaluation of standard involute spur gear mesh stiffness

NASA Astrophysics Data System (ADS)

Liang, Xihui; Zhang, Hongsheng; Zuo, Ming J.; Qin, Yong

2018-02-01

Time-varying mesh stiffness is one of the main internal excitation sources of gear dynamics. Accurate evaluation of gear mesh stiffness is crucial for gear dynamic analysis. This study is devoted to developing new models for spur gear mesh stiffness evaluation. Three models are proposed. The proposed model 1 can give very accurate mesh stiffness result but the gear bore surface must be assumed to be rigid. Enlighted by the proposed model 1, our research discovers that the angular deflection pattern of the gear bore surface of a pair of meshing gears under a constant torque basically follows a cosine curve. Based on this finding, two other models are proposed. The proposed model 2 evaluates gear mesh stiffness by using angular deflections at different circumferential angles of an end surface circle of the gear bore. The proposed model 3 requires using only the angular deflection at an arbitrary circumferential angle of an end surface circle of the gear bore but this model can only be used for a gear with the same tooth profile among all teeth. The proposed models are accurate in gear mesh stiffness evaluation and easy to use. Finite element analysis is used to validate the accuracy of the proposed models.

Processing and properties of magnesium containing a dense uniform dispersion of nanoparticles.

PubMed

Chen, Lian-Yi; Xu, Jia-Quan; Choi, Hongseok; Pozuelo, Marta; Ma, Xiaolong; Bhowmick, Sanjit; Yang, Jenn-Ming; Mathaudhu, Suveen; Li, Xiao-Chun

2015-12-24

Magnesium is a light metal, with a density two-thirds that of aluminium, is abundant on Earth and is biocompatible; it thus has the potential to improve energy efficiency and system performance in aerospace, automobile, defence, mobile electronics and biomedical applications. However, conventional synthesis and processing methods (alloying and thermomechanical processing) have reached certain limits in further improving the properties of magnesium and other metals. Ceramic particles have been introduced into metal matrices to improve the strength of the metals, but unfortunately, ceramic microparticles severely degrade the plasticity and machinability of metals, and nanoparticles, although they have the potential to improve strength while maintaining or even improving the plasticity of metals, are difficult to disperse uniformly in metal matrices. Here we show that a dense uniform dispersion of silicon carbide nanoparticles (14 per cent by volume) in magnesium can be achieved through a nanoparticle self-stabilization mechanism in molten metal. An enhancement of strength, stiffness, plasticity and high-temperature stability is simultaneously achieved, delivering a higher specific yield strength and higher specific modulus than almost all structural metals.

Power flow prediction in vibrating systems via model reduction

NASA Astrophysics Data System (ADS)

Li, Xianhui

This dissertation focuses on power flow prediction in vibrating systems. Reduced order models (ROMs) are built based on rational Krylov model reduction which preserve power flow information in the original systems over a specified frequency band. Stiffness and mass matrices of the ROMs are obtained by projecting the original system matrices onto the subspaces spanned by forced responses. A matrix-free algorithm is designed to construct ROMs directly from the power quantities at selected interpolation frequencies. Strategies for parallel implementation of the algorithm via message passing interface are proposed. The quality of ROMs is iteratively refined according to the error estimate based on residual norms. Band capacity is proposed to provide a priori estimate of the sizes of good quality ROMs. Frequency averaging is recast as ensemble averaging and Cauchy distribution is used to simplify the computation. Besides model reduction for deterministic systems, details of constructing ROMs for parametric and nonparametric random systems are also presented. Case studies have been conducted on testbeds from Harwell-Boeing collections. Input and coupling power flow are computed for the original systems and the ROMs. Good agreement is observed in all cases.

Non-continuum, anisotropic nanomechanics of random and aligned electrospun nanofiber matrices

NASA Astrophysics Data System (ADS)

Chery, Daphney; Han, Biao; Mauck, Robert; Shenoy, Vivek; Han, Lin

Polymer nanofiber assemblies are widely used in cell culture and tissue engineering, while their nanomechanical characteristics have received little attention. In this study, to understand their nanoscale structure-mechanics relations, nanofibers of polycaprolactone (PCL) and poly(vinyl alcohol) (PVA) were fabricated via electrospinning, and tested via AFM-nanoindentation with a microspherical tip (R ~10 μm) in PBS. For the hydrophobic, less-swollen PCL, a novel, non-continuum linear F-D dependence was observed, instead of the typical Hertzian F-D3/2 behavior, which is usually expected for continuum materials. This linear trend is likely resulted from the tensile stretch of a few individual nanofibers as they were indented in the normal plane. In contrast, for the hydrophilic, highly swollen PVA, the observed typical Hertzian response indicates the dominance of localized deformation within each nanofiber, which had swollen to become hydrogels. Furthermore, for both matrices, aligned fibers showed significantly higher stiffness than random fibers. These results provide a fundamental basis on the nanomechanics of biomaterials for specialized applications in cell phenotype and tissue repair.

Fractal heterogeneity in minimal matrix models of scars modulates stiff-niche stem-cell responses via nuclear exit of a mechanorepressor

NASA Astrophysics Data System (ADS)

Dingal, P. C. Dave P.; Bradshaw, Andrew M.; Cho, Sangkyun; Raab, Matthew; Buxboim, Amnon; Swift, Joe; Discher, Dennis E.

2015-09-01

Scarring is a long-lasting problem in higher animals, and reductionist approaches could aid in developing treatments. Here, we show that copolymerization of collagen I with polyacrylamide produces minimal matrix models of scars (MMMS), in which fractal-fibre bundles segregate heterogeneously to the hydrogel subsurface. Matrix stiffens locally--as in scars--while allowing separate control over adhesive-ligand density. The MMMS elicits scar-like phenotypes from mesenchymal stem cells (MSCs): cells spread and polarize quickly, increasing nucleoskeletal lamin-A yet expressing the `scar marker' smooth muscle actin (SMA) more slowly. Surprisingly, expression responses to MMMS exhibit less cell-to-cell noise than homogeneously stiff gels. Such differences from bulk-average responses arise because a strong SMA repressor, NKX2.5, slowly exits the nucleus on rigid matrices. NKX2.5 overexpression overrides rigid phenotypes, inhibiting SMA and cell spreading, whereas cytoplasm-localized NKX2.5 mutants degrade in well-spread cells. MSCs thus form a `mechanical memory' of rigidity by progressively suppressing NKX2.5, thereby elevating SMA in a scar-like state.

Exposure of Cleft Lip and Palate Patients to Toxic Elements Released during Orthodontic Treatment in the Study of Non-Invasive Matrices

PubMed Central

Mikulewicz, Marcin; Kachniarz, Krzysztof; Chojnacka, Katarzyna

2015-01-01

The Objective The aim of the study was evaluation of metal ions (nickel and chromium) released from orthodontic appliances in cleft lip and palate patients and the usefulness of non-invasive matrices (saliva and hair). Materials and Methods The material studied consisted of 100 individuals, including 59 females and 41 males of 5 to 16 years of age, which were divided into 3 groups: experimental–patients with cleft lip and palate (36 individuals, the average treatment time 5.74 years); control group–patients without cleft lip and palate, during orthodontic treatment (32 individuals, the average treatment time 1.78 years) and the control group patients without cleft lip and palate, without any orthodontic appliances (32 individuals). Samples (saliva, hair) were collected and subjects underwent a survey by questionnaire. Multi-elemental analyses of the composition of non-invasive matrices was conducted in an accredited laboratory by inductively coupled plasma spectrometry technique ICP-OES. The results were reported as mean contents of particular elements (Cd, Cr, Cu, Fe, Mn, Mo, Ni, Si) in hair and in saliva. Results The concentration of Cr, Ni, Fe and Cu ions in saliva of cleft lip and palate patients were several times higher as compared with not treated orthodontically control groups and higher than in the group with orthodontic appliances. Among the assessed matrices, hair of cleft lip and palate patients seem to be not a meaningful biomarker. Conclusion It was found that orthodontic appliances used in long-term treatment of cleft lip and palate patients do not release toxic levels of Cr and Ni ions. PMID:26544176

A triangular thin shell finite element: Nonlinear analysis. [structural analysis

NASA Technical Reports Server (NTRS)

Thomas, G. R.; Gallagher, R. H.

1975-01-01

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

Mesh refinement in finite element analysis by minimization of the stiffness matrix trace

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.

1989-01-01

Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution.

Mutation of the myosin converter domain alters cross-bridge elasticity

PubMed Central

Köhler, Jan; Winkler, Gerhard; Schulte, Imke; Scholz, Tim; McKenna, William; Brenner, Bernhard; Kraft, Theresia

2002-01-01

Elastic distortion of a structural element of the actomyosin complex is fundamental to the ability of myosin to generate motile forces. An elastic element allows strain to develop within the actomyosin complex (cross-bridge) before movement. Relief of this strain then drives filament sliding, or more generally, movement of a cargo. Even with the known crystal structure of the myosin head, however, the structural element of the actomyosin complex in which elastic distortion occurs remained unclear. To assign functional relevance to various structural elements of the myosin head, e.g., to identify the elastic element within the cross-bridge, we studied mechanical properties of muscle fibers from patients with familial hypertrophic cardiomyopathy with point mutations in the head domain of the β-myosin heavy chain. We found that the Arg-719 → Trp (Arg719Trp) mutation, which is located in the converter domain of the myosin head fragment, causes an increase in force generation and fiber stiffness under isometric conditions by 48–59%. Under rigor and relaxing conditions, fiber stiffness was 45–47% higher than in control fibers. Yet, kinetics of active cross-bridge cycling were unchanged. These findings, especially the increase in fiber stiffness under rigor conditions, indicate that cross-bridges with the Arg719Trp mutation are more resistant to elastic distortion. The data presented here strongly suggest that the converter domain that forms the junction between the catalytic and the light-chain-binding domain of the myosin head is not only essential for elastic distortion of the cross-bridge, but that the main elastic distortion may even occur within the converter domain itself. PMID:11904418

Single-strain-gage force/stiffness buckling prediction techniques on a hat-stiffened panel

NASA Technical Reports Server (NTRS)

Hudson, Larry D.; Thompson, Randolph C.

1991-01-01

Predicting the buckling characteristics of a test panel is necessary to ensure panel integrity during a test program. A single-strain-gage buckling prediction method was developed on a hat-stiffened, monolithic titanium buckling panel. The method is an adaptation of the original force/stiffness method which requires back-to-back gages. The single-gage method was developed because the test panel did not have back-to-back gages. The method was used to predict buckling loads and temperatures under various heating and loading conditions. The results correlated well with a finite element buckling analysis. The single-gage force/stiffness method was a valid real-time and post-test buckling prediction technique.

Arterial waveguide model for shear wave elastography: implementation and in vitro validation

NASA Astrophysics Data System (ADS)

Vaziri Astaneh, Ali; Urban, Matthew W.; Aquino, Wilkins; Greenleaf, James F.; Guddati, Murthy N.

2017-07-01

Arterial stiffness is found to be an early indicator of many cardiovascular diseases. Among various techniques, shear wave elastography has emerged as a promising tool for estimating local arterial stiffness through the observed dispersion of guided waves. In this paper, we develop efficient models for the computational simulation of guided wave dispersion in arterial walls. The models are capable of considering fluid-loaded tubes, immersed in fluid or embedded in a solid, which are encountered in in vitro/ex vivo, and in vivo experiments. The proposed methods are based on judiciously combining Fourier transformation and finite element discretization, leading to a significant reduction in computational cost while fully capturing complex 3D wave propagation. The developed methods are implemented in open-source code, and verified by comparing them with significantly more expensive, fully 3D finite element models. We also validate the models using the shear wave elastography of tissue-mimicking phantoms. The computational efficiency of the developed methods indicates the possibility of being able to estimate arterial stiffness in real time, which would be beneficial in clinical settings.

Mechanics of microtubules: effects of protofilament orientation.

PubMed

Donhauser, Zachary J; Jobs, William B; Binka, Edem C

2010-09-08

Microtubules are hollow cylindrical polymers of the protein tubulin that play a number of important dynamic and structural roles in eukaryotic cells. Both in vivo and in vitro microtubules can exist in several possible configurations, differing in the number of protofilaments, helical rise of tubulin dimers, and protofilament skew angle with respect to the main tube axis. Here, finite element modeling is applied to examine the mechanical response of several known microtubule types when subjected to radial deformation. The data presented here provide an important insight into microtubule stiffness and reveal that protofilament orientation does not affect radial stiffness. Rather, stiffness is primarily dependent on the effective Young's modulus of the polymerized material and the effective radius of the microtubule. These results are also directly correlated to atomic force microscopy nanoindentation measurements to allow a more detailed interpretation of previous experiments. When combined with experimental data that show a significant difference between microtubules stabilized with a slowly hydrolyzable GTP analog and microtubules stabilized with paclitaxel, the finite element data suggest that paclitaxel increases the overall radial flexibility of the microtubule wall. Copyright 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Mechanics of Microtubules: Effects of Protofilament Orientation

PubMed Central

Donhauser, Zachary J.; Jobs, William B.; Binka, Edem C.

2010-01-01

Microtubules are hollow cylindrical polymers of the protein tubulin that play a number of important dynamic and structural roles in eukaryotic cells. Both in vivo and in vitro microtubules can exist in several possible configurations, differing in the number of protofilaments, helical rise of tubulin dimers, and protofilament skew angle with respect to the main tube axis. Here, finite element modeling is applied to examine the mechanical response of several known microtubule types when subjected to radial deformation. The data presented here provide an important insight into microtubule stiffness and reveal that protofilament orientation does not affect radial stiffness. Rather, stiffness is primarily dependent on the effective Young's modulus of the polymerized material and the effective radius of the microtubule. These results are also directly correlated to atomic force microscopy nanoindentation measurements to allow a more detailed interpretation of previous experiments. When combined with experimental data that show a significant difference between microtubules stabilized with a slowly hydrolyzable GTP analog and microtubules stabilized with paclitaxel, the finite element data suggest that paclitaxel increases the overall radial flexibility of the microtubule wall. PMID:20816081

Analysis of Foundation of Tall R/C Chimney Incorporating Flexibility of Soil

NASA Astrophysics Data System (ADS)

Jayalekshmi, B. R.; Jisha, S. V.; Shivashankar, R.

2017-09-01

Three dimensional Finite Element (FE) analysis was carried out for 100 and 400 m high R/C chimneys having piled annular raft and annular raft foundations considering the flexibility of soil subjected to across-wind load. Stiffness of supporting soil and foundation were varied to evaluate the significance of Soil-Structure Interaction (SSI). The integrated chimney-foundation-soil system was analysed by finite element software ANSYS based on direct method of SSI assuming linear elastic material behaviour. FE analyses were carried out for two cases of SSI namely, (1) chimney with annular raft foundation and (2) chimney with piled annular raft foundation. The responses in raft such as bending moments and settlements were evaluated for both the cases and compared to those obtained from the conventional method of analysis of annular raft foundation. It is found that the responses in raft vary considerably depending on the stiffness of the underlying soil and the stiffness of foundation. Piled raft foundations are better suited for tall chimneys to be constructed in loose or medium sand.

Integrated technology rotor/flight research rotor concept definition study

NASA Technical Reports Server (NTRS)

Carlson, R. G.; Beno, E. A.; Ulisnik, H. D.

1983-01-01

As part of the Integrated Technology Rotor/Flight Research Rotor (ITR/FRR) Program a number of advanced rotor system designs were conceived and investigated. From these, several were chosen that best meet the started ITR goals with emphasis on stability, reduced weight and hub drag, simplicity, low head moment stiffness, and adequate strength and fatigue life. It was concluded that obtaining low hub moment stiffness was difficult when only the blade flexibility of bearingless rotor blades is considered, unacceptably low fatigue life being the primary problem. Achieving a moderate hub moment stiffness somewhat higher than state of the art articulated rotors in production today is possible within the fatigue life constraint. Alternatively, low stiffness is possible when additional rotor elements, besides the blades themselves, provide part of the rotor flexibility. Two primary designs evolved as best meeting the general ITR requirements that presently exist. An I shaped flexbeam with an external torque tube can satisfy the general goals but would have either higher stiffness or reduced fatigue life. The elastic gimbal rotor can achieve a better combination of low stiffness and high fatigue life but would be a somewhat heavier design and possibly exhibit a higher risk of aeromechanical instability.

Foundation stiffness in the linear modeling of wind turbines

NASA Astrophysics Data System (ADS)

Chiang, Chih-Hung; Yu, Chih-Peng; Chen, Yan-Hao; Lai, Jiunnren; Hsu, Keng-Tsang; Cheng, Chia-Chi

2017-04-01

Effects of foundation stiffness on the linear vibrations of wind turbine systems are of concerns for both planning and construction of wind turbine systems. Current study performed numerical modeling for such a problem using linear spectral finite elements. The effects of foundation stiffness were investigated for various combinations of shear wave velocity of soil, size of tower base plate, and pile length. Multiple piles are also included in the models such that the foundation stiffness can be analyzed more realistically. The results indicate that the shear wave velocity of soil and the size of tower base plate have notable effects on the dominant frequency of the turbine-tower system. The larger the lateral dimension, the stiffer the foundation. Large pile cap and multiple spaced piles result in higher stiffness than small pile cap and a mono-pile. The lateral stiffness of a mono-pile mainly depends on the shear wave velocity of soil with the exception for a very short pile that the end constraints may affect the lateral vibration of the superstructure. Effective pile length may be determined by comparing the simulation results of the frictional pile to those of the end-bearing pile.

Optimization of a Hybrid Magnetic Bearing for a Magnetically Levitated Blood Pump via 3-D FEA

PubMed Central

Cheng, Shanbao; Olles, Mark W.; Burger, Aaron F.; Day, Steven W.

2011-01-01

In order to improve the performance of a magnetically levitated (maglev) axial flow blood pump, three-dimensional (3-D) finite element analysis (FEA) was used to optimize the design of a hybrid magnetic bearing (HMB). Radial, axial, and current stiffness of multiple design variations of the HMB were calculated using a 3-D FEA package and verified by experimental results. As compared with the original design, the optimized HMB had twice the axial stiffness with the resulting increase of negative radial stiffness partially compensated for by increased current stiffness. Accordingly, the performance of the maglev axial flow blood pump with the optimized HMBs was improved: the maximum pump speed was increased from 6000 rpm to 9000 rpm (50%). The radial, axial and current stiffness of the HMB was found to be linear at nominal operational position from both 3-D FEA and empirical measurements. Stiffness values determined by FEA and empirical measurements agreed well with one another. The magnetic flux density distribution and flux loop of the HMB were also visualized via 3-D FEA which confirms the designers’ initial assumption about the function of this HMB. PMID:22065892

Optimization of a Hybrid Magnetic Bearing for a Magnetically Levitated Blood Pump via 3-D FEA.

PubMed

Cheng, Shanbao; Olles, Mark W; Burger, Aaron F; Day, Steven W

2011-10-01

In order to improve the performance of a magnetically levitated (maglev) axial flow blood pump, three-dimensional (3-D) finite element analysis (FEA) was used to optimize the design of a hybrid magnetic bearing (HMB). Radial, axial, and current stiffness of multiple design variations of the HMB were calculated using a 3-D FEA package and verified by experimental results. As compared with the original design, the optimized HMB had twice the axial stiffness with the resulting increase of negative radial stiffness partially compensated for by increased current stiffness. Accordingly, the performance of the maglev axial flow blood pump with the optimized HMBs was improved: the maximum pump speed was increased from 6000 rpm to 9000 rpm (50%). The radial, axial and current stiffness of the HMB was found to be linear at nominal operational position from both 3-D FEA and empirical measurements. Stiffness values determined by FEA and empirical measurements agreed well with one another. The magnetic flux density distribution and flux loop of the HMB were also visualized via 3-D FEA which confirms the designers' initial assumption about the function of this HMB.

Broken flavor 2↔3 symmetry and phenomenological approach for universal quark and lepton mass matrices

NASA Astrophysics Data System (ADS)

Matsuda, Koichi; Nishiura, Hiroyuki

2006-01-01

A phenomenological approach for the universal mass matrix model with a broken flavor 2↔3 symmetry is explored by introducing the 2↔3 antisymmetric parts of mass matrices for quarks and charged leptons. We present explicit texture components of the mass matrices, which are consistent with all the neutrino oscillation experiments and quark mixing data. The mass matrices have a common structure for quarks and leptons, while the large lepton mixings and the small quark mixings are derived with no fine-tuning due to the difference of the phase factors. The model predicts a value 2.4×10-3 for the lepton mixing matrix element square |U13|2, and also ⟨mν⟩=(0.89-1.4)×10-4eV for the averaged neutrino mass which appears in the neutrinoless double beta decay.

A decentralized linear quadratic control design method for flexible structures

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1990-01-01

A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass and stiffness properties.

Ablative and transport fractionation of trace elements during laser sampling of glass and copper

NASA Astrophysics Data System (ADS)

Outridge, P. M.; Doherty, W.; Gregoire, D. C.

1997-12-01

The fractionation of trace elements due to ablation and transport processes was quantified during Q-switched infrared laser sampling of glass and copper reference materials. Filter-trapping of the ablated product at different points in the sample introduction system showed ablation and transport sometimes caused opposing fractionation effects, leading to a confounded measure of overall (ablative + transport) fractionation. An unexpected result was the greater ablative fractionation of some elements (Au, Ag, Bi, Te in glass and Au, Be, Bi, Ni, Te in copper) at a higher laser fluence of 1.35 × 10 4W cm -2 than at 0.62 × 10 4W cm -2, which contradicted predictions from modelling studies of ablation processes. With glass, there was an inverse logarithmic relationship between the extent of ablative and overall fractionation and element oxide melting point (OMPs), with elements with OMPs < 1000° C exhibiting overall concentration increases of 20-1340%. Fractionation during transport was quantitatively important for most certified elements in copper, and for the most volatile elements (Au, Ag, Bi, Te) in glass. Elements common to both matrices showed 50-100% higher ablative fractionation in copper, possibly because of greater heat conductance away from the ablation site causing increased element volatilisation or zone refinement. These differences between matrices indicate that non-matrix-matched standardisation is likely to provide inaccurate calibration of laser ablation inductively coupled plasma-mass spectrometry analyses of at least some elements.

Research on damping properties optimization of variable-stiffness plate

NASA Astrophysics Data System (ADS)

Wen-kai, QI; Xian-tao, YIN; Cheng, SHEN

2016-09-01

This paper investigates damping optimization design of variable-stiffness composite laminated plate, which means fibre paths can be continuously curved and fibre angles are distinct for different regions. First, damping prediction model is developed based on modal dissipative energy principle and verified by comparing with modal testing results. Then, instead of fibre angles, the element stiffness and damping matrixes are translated to be design variables on the basis of novel Discrete Material Optimization (DMO) formulation, thus reducing the computation time greatly. Finally, the modal damping capacity of arbitrary order is optimized using MMA (Method of Moving Asymptotes) method. Meanwhile, mode tracking technique is employed to investigate the variation of modal shape. The convergent performance of interpolation function, first order specific damping capacity (SDC) optimization results and variation of modal shape in different penalty factor are discussed. The results show that the damping properties of the variable-stiffness plate can be increased by 50%-70% after optimization.

Seismic analysis of the frame structure reformed by cutting off column and jacking based on stiffness ratio

NASA Astrophysics Data System (ADS)

Zhao, J. K.; Xu, X. S.

2017-11-01

The cutting off column and jacking technology is a method for increasing story height, which has been widely used and paid much attention in engineering. The stiffness will be changed after the process of cutting off column and jacking, which directly affects the overall seismic performance. It is usually necessary to take seismic strengthening measures to enhance the stiffness. A five story frame structure jacking project in Jinan High-tech Zone was taken as an example, and three finite element models were established which contains the frame model before lifting, after lifting and after strengthening. Based on the stiffness, the dynamic time-history analysis was carried out to research its seismic performance under the EL-Centro seismic wave, the Taft seismic wave and the Tianjin artificial seismic wave. The research can provide some guidance for the design and construction of the entire jack lifting structure.

Finite Element Simulation and Additive Manufacturing of Stiffness-Matched NiTi Fixation Hardware for Mandibular Reconstruction Surgery

PubMed Central

Jahadakbar, Ahmadreza; Shayesteh Moghaddam, Narges; Amerinatanzi, Amirhesam; Dean, David; Karaca, Haluk E.; Elahinia, Mohammad

2016-01-01

Process parameters and post-processing heat treatment techniques have been developed to produce both shape memory and superelastic NiTi using Additive Manufacturing. By introducing engineered porosity, the stiffness of NiTi can be tuned to the level closely matching cortical bone. Using additively manufactured porous superelastic NiTi, we have proposed the use of patient-specific, stiffness-matched fixation hardware, for mandible skeletal reconstructive surgery. Currently, Ti-6Al-4V is the most commonly used material for skeletal fixation devices. Although this material offers more than sufficient strength for immobilization during the bone healing process, the high stiffness of Ti-6Al-4V implants can cause stress shielding. In this paper, we present a study of mandibular reconstruction that uses a dry cadaver mandible to validate our geometric and biomechanical design and fabrication (i.e., 3D printing) of NiTi skeletal fixation hardware. Based on the reference-dried mandible, we have developed a Finite Element model to evaluate the performance of the proposed fixation. Our results show a closer-to-normal stress distribution and an enhanced contact pressure at the bone graft interface than would be in the case with Ti-6Al-4V off-the-shelf fixation hardware. The porous fixation plates used in this study were fabricated by selective laser melting. PMID:28952598

Ability of Magnetic Resonance Elastography to Assess Taut Bands

PubMed Central

Chen, Qingshan; Basford, Jeffery; An, Kai-Nan

2008-01-01

Background Myofascial taut bands are central to diagnosis of myofascial pain. Despite their importance, we still lack either a laboratory test or imaging technique capable of objectively confirming either their nature or location. This study explores the ability of magnetic resonance elastography to localize and investigate the mechanical properties of myofascial taut bands on the basis of their effects on shear wave propagation. Methods This study was conducted in three phases. The first involved the imaging of taut bands in gel phantoms, the second a finite element modeling of the phantom experiment, and the third a preliminary evaluation involving eight human subjects-four of whom had, and four of whom did not have myofascial pain. Experiments were performed with a 1.5 Tesla magnetic resonance imaging scanner. Shear wave propagation was imaged and shear stiffness was reconstructed using matched filtering stiffness inversion algorithms. Findings The gel phantom imaging and finite element calculation experiments supported our hypothesis that taut bands can be imaged based on its outstanding shear stiffness. The preliminary human study showed a statistically significant 50-100% (p=0.01) increase of shear stiffness in the taut band regions of the involved subjects relative to that of the controls or in nearby uninvolved muscle. Interpretation This study suggests that magnetic resonance elastography may have a potential for objectively characterizing myofascial taut bands that have been up to now detectable only by the clinician's fingers. PMID:18206282

Finite Element Simulation and Additive Manufacturing of Stiffness-Matched NiTi Fixation Hardware for Mandibular Reconstruction Surgery.

PubMed

Jahadakbar, Ahmadreza; Shayesteh Moghaddam, Narges; Amerinatanzi, Amirhesam; Dean, David; Karaca, Haluk E; Elahinia, Mohammad

2016-12-19

Process parameters and post-processing heat treatment techniques have been developed to produce both shape memory and superelastic NiTi using Additive Manufacturing. By introducing engineered porosity, the stiffness of NiTi can be tuned to the level closely matching cortical bone. Using additively manufactured porous superelastic NiTi, we have proposed the use of patient-specific, stiffness-matched fixation hardware, for mandible skeletal reconstructive surgery. Currently, Ti-6Al-4V is the most commonly used material for skeletal fixation devices. Although this material offers more than sufficient strength for immobilization during the bone healing process, the high stiffness of Ti-6Al-4V implants can cause stress shielding. In this paper, we present a study of mandibular reconstruction that uses a dry cadaver mandible to validate our geometric and biomechanical design and fabrication (i.e., 3D printing) of NiTi skeletal fixation hardware. Based on the reference-dried mandible, we have developed a Finite Element model to evaluate the performance of the proposed fixation. Our results show a closer-to-normal stress distribution and an enhanced contact pressure at the bone graft interface than would be in the case with Ti-6Al-4V off-the-shelf fixation hardware. The porous fixation plates used in this study were fabricated by selective laser melting.

Efficient techniques for forced response involving linear modal components interconnected by discrete nonlinear connection elements

NASA Astrophysics Data System (ADS)

Avitabile, Peter; O'Callahan, John

2009-01-01

Generally, response analysis of systems containing discrete nonlinear connection elements such as typical mounting connections require the physical finite element system matrices to be used in a direct integration algorithm to compute the nonlinear response analysis solution. Due to the large size of these physical matrices, forced nonlinear response analysis requires significant computational resources. Usually, the individual components of the system are analyzed and tested as separate components and their individual behavior may essentially be linear when compared to the total assembled system. However, the joining of these linear subsystems using highly nonlinear connection elements causes the entire system to become nonlinear. It would be advantageous if these linear modal subsystems could be utilized in the forced nonlinear response analysis since much effort has usually been expended in fine tuning and adjusting the analytical models to reflect the tested subsystem configuration. Several more efficient techniques have been developed to address this class of problem. Three of these techniques given as: equivalent reduced model technique (ERMT);modal modification response technique (MMRT); andcomponent element method (CEM); are presented in this paper and are compared to traditional methods.

Decomposition of diverse solid inorganic matrices with molten ammonium bifluoride salt for constituent elemental analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Hara, Matthew J.; Kellogg, Cyndi M.; Parker, Cyrena M.

Ammonium bifluoride (ABF, NH4F·HF) is a well-known reagent for converting metal oxides to fluorides and for its applications in breaking down minerals and ores in order to extract useful components. It has been more recently applied to the decomposition of inorganic matrices prior to elemental analysis. Herein, a sample decomposition method that employs molten ABF sample treatment in the initial step is systematically evaluated across a range of inorganic sample types: glass, quartz, zircon, soil, and pitchblende ore. Method performance is evaluated across the two variables: duration of molten ABF treatment and ABF reagent mass to sample mass ratio. Themore » degree of solubilization of these sample classes are compared to the fluoride stoichiometry that is theoretically necessary to enact complete fluorination of the sample types. Finally, the sample decomposition method is performed on several soil and pitchblende ore standard reference materials, after which elemental constituent analysis is performed by ICP-OES and ICP-MS. Elemental recoveries are compared to the certified values; results indicate good to excellent recoveries across a range of alkaline earth, rare earth, transition metal, and actinide elements.« less

Deformations of temporary wooden supports used to reduce building deflections in mining areas

NASA Astrophysics Data System (ADS)

Gromysz, Krzysztof

2018-04-01

Temporary supports, consisting of a stack of wooden elements and a hydraulic jack, are used in the process of removing deflections in buildings with one to three aboveground floors in mining areas. During uneven raising, the supports are loaded monotonically, unloaded and loaded cyclically. Laboratory tests were designed for the supports. For the investigated range of loads of 0 to 400 kN, under a growing load, a linear relationship exists between a load and the change in the stack length, which signifies that the deformations of wooden elements and displacements related to their mutual interactions increase proportionally. A seemingly higher stack stiffness is seen at the beginning of the unloading process and for cyclical loads, meaning that in this phase of loading, the material deformation of the wooden elements and the jack is responsible for changing the jack length in this load phase, with a negligible presence of mutual displacements of wooden elements. The support, after being unloaded, returns to the initial position and its permanent deformations are not observed. The stiffness of a temporary support decreases as the height of the stack of wooden elements increases.

An analysis of cross-coupling of a multicomponent jet engine test stand using finite element modeling techniques

NASA Technical Reports Server (NTRS)

Schweikhard, W. G.; Singnoi, W. N.

1985-01-01

A two axis thrust measuring system was analyzed by using a finite a element computer program to determine the sensitivities of the thrust vectoring nozzle system to misalignment of the load cells and applied loads, and the stiffness of the structural members. Three models were evaluated: (1) the basic measuring element and its internal calibration load cells; (2) the basic measuring element and its external load calibration equipment; and (3) the basic measuring element, external calibration load frame and the altitude facility support structure. Alignment of calibration loads was the greatest source of error for multiaxis thrust measuring systems. Uniform increases or decreases in stiffness of the members, which might be caused by the selection of the materials, have little effect on the accuracy of the measurements. It is found that the POLO-FINITE program is a viable tool for designing and analyzing multiaxis thrust measurement systems. The response of the test stand to step inputs that might be encountered with thrust vectoring tests was determined. The dynamic analysis show a potential problem for measuring the dynamic response characteristics of thrust vectoring systems because of the inherently light damping of the test stand.

Modification of a Macromechanical Finite-Element Based Model for Impact Analysis of Triaxially-Braided Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Blinzler, Brina J.; Binienda, Wieslaw K.

2010-01-01

A macro level finite element-based model has been developed to simulate the mechanical and impact response of triaxially-braided polymer matrix composites. In the analytical model, the triaxial braid architecture is simulated by using four parallel shell elements, each of which is modeled as a laminated composite. For the current analytical approach, each shell element is considered to be a smeared homogeneous material. The commercial transient dynamic finite element code LS-DYNA is used to conduct the simulations, and a continuum damage mechanics model internal to LS-DYNA is used as the material constitutive model. The constitutive model requires stiffness and strength properties of an equivalent unidirectional composite. Simplified micromechanics methods are used to determine the equivalent stiffness properties, and results from coupon level tests on the braided composite are utilized to back out the required strength properties. Simulations of quasi-static coupon tests of several representative braided composites are conducted to demonstrate the correlation of the model. Impact simulations of a represented braided composites are conducted to demonstrate the capability of the model to predict the penetration velocity and damage patterns obtained experimentally.

NASTRAN thermal analyzer: Theory and application including a guide to modeling engineering problems, volume 1. [thermal analyzer manual

NASA Technical Reports Server (NTRS)

Lee, H. P.

1977-01-01

The NASTRAN Thermal Analyzer Manual describes the fundamental and theoretical treatment of the finite element method, with emphasis on the derivations of the constituent matrices of different elements and solution algorithms. Necessary information and data relating to the practical applications of engineering modeling are included.

BIPAD: A web server for modeling bipartite sequence elements

PubMed Central

Bi, Chengpeng; Rogan, Peter K

2006-01-01

Background Many dimeric protein complexes bind cooperatively to families of bipartite nucleic acid sequence elements, which consist of pairs of conserved half-site sequences separated by intervening distances that vary among individual sites. Results We introduce the Bipad Server [1], a web interface to predict sequence elements embedded within unaligned sequences. Either a bipartite model, consisting of a pair of one-block position weight matrices (PWM's) with a gap distribution, or a single PWM matrix for contiguous single block motifs may be produced. The Bipad program performs multiple local alignment by entropy minimization and cyclic refinement using a stochastic greedy search strategy. The best models are refined by maximizing incremental information contents among a set of potential models with varying half site and gap lengths. Conclusion The web service generates information positional weight matrices, identifies binding site motifs, graphically represents the set of discovered elements as a sequence logo, and depicts the gap distribution as a histogram. Server performance was evaluated by generating a collection of bipartite models for distinct DNA binding proteins. PMID:16503993

On the performance of explicit and implicit algorithms for transient thermal analysis

NASA Astrophysics Data System (ADS)

Adelman, H. M.; Haftka, R. T.

1980-09-01

The status of an effort to increase the efficiency of calculating transient temperature fields in complex aerospace vehicle structures is described. The advantages and disadvantages of explicit and implicit algorithms are discussed. A promising set of implicit algorithms, known as the GEAR package is described. Four test problems, used for evaluating and comparing various algorithms, have been selected and finite element models of the configurations are discribed. These problems include a space shuttle frame component, an insulated cylinder, a metallic panel for a thermal protection system and a model of the space shuttle orbiter wing. Calculations were carried out using the SPAR finite element program, the MITAS lumped parameter program and a special purpose finite element program incorporating the GEAR algorithms. Results generally indicate a preference for implicit over explicit algorithms for solution of transient structural heat transfer problems when the governing equations are stiff. Careful attention to modeling detail such as avoiding thin or short high-conducting elements can sometimes reduce the stiffness to the extent that explicit methods become advantageous.

A preliminary investigation of finite-element modeling for composite rotor blades

NASA Technical Reports Server (NTRS)

Lake, Renee C.; Nixon, Mark W.

1988-01-01

The results from an initial phase of an in-house study aimed at improving the dynamic and aerodynamic characteristics of composite rotor blades through the use of elastic couplings are presented. Large degree of freedom shell finite element models of an extension twist coupled composite tube were developed and analyzed using MSC/NASTRAN. An analysis employing a simplified beam finite element representation of the specimen with the equivalent engineering stiffness was additionally performed. Results from the shell finite element normal modes and frequency analysis were compared to those obtained experimentally, showing an agreement within 13 percent. There was appreciable degradation in the frequency prediction for the torsional mode, which is elastically coupled. This was due to the absence of off-diagonal coupling terms in the formulation of the equivalent engineering stiffness. Parametric studies of frequency variation due to small changes in ply orientation angle and ply thickness were also performed. Results showed linear frequency variations less than 2 percent per 1 degree variation in the ply orientation angle, and 1 percent per 0.0001 inch variation in the ply thickness.

A method for accounting for test fixture compliance when estimating proximal femur stiffness.

PubMed

Rossman, Timothy; Dragomir-Daescu, Dan

2016-09-06

Fracture testing of cadaveric femora to obtain strength and stiffness information is an active area of research in developing tools for diagnostic prediction of bone strength. These measurements are often used in the estimation and validation of companion finite element models constructed from the femora CT scan data, therefore, the accuracy of the data is of paramount importance. However, experimental stiffness calculated from force-displacement data has largely been ignored by most researchers due to inherent error in the differential displacement measurement obtained when not accounting for testing apparatus compliance. However, having such information is necessary for validation of computational models. Even in the few cases when fixture compliance was considered the measurements showed large lab-to-lab variation due to lack of standardization in fixture design. We examined the compliance of our in-house designed cadaveric femur test fixture to determine the errors we could expect when calculating stiffness from the collected experimental force-displacement data and determined the stiffness of the test fixture to be more than 10 times the stiffness of the stiffest femur in a sample of 44 femora. When correcting the apparent femur stiffness derived from the original data, we found that the largest stiffness was underestimated by about 10%. The study confirmed that considering test fixture compliance is a necessary step in improving the accuracy of fracture test data for characterizing femur stiffness, and highlighted the need for test fixture design standardization for proximal femur fracture testing. Copyright © 2016 Elsevier Ltd. All rights reserved.

Aortic root dimension and arterial stiffness in arterial hypertension: the Campania Salute Network.

PubMed

Lønnebakken, Mai Tone; Izzo, Raffaele; Mancusi, Costantino; Losi, Maria Angela; Stabile, Eugenio; Rozza, Francesco; Gerdts, Eva; Trimarco, Bruno; de Luca, Nicola; de Simone, Giovanni

2016-06-01

The relation between aortic root dimension (ARD) and measures of arterial stiffness is uncertain. Accordingly, we studied the relation between ARD and an estimate of arterial stiffness in 12 392 hypertensive patients (age 53 ± 12 years, 43% women) free of prevalent cardiovascular disease and with ejection fraction at least 50%, from the Campania Salute Network Registry. Echocardiographic ARD was measured and compared with the value predicted by age, sex and height by using a z-score. Arterial stiffness was assessed by the pulse pressure/stroke index. The highest population tertile of pulse pressure/stroke index was considered 'high arterial stiffness'. High arterial stiffness was more common in women than in men (P < 0.001) and associated with older age, diabetes, longer duration of hypertension and less frequent smoking habit (all P less than 0.01). Patients with high arterial stiffness had smaller ARD, higher carotid intima-media thickness and plasma cholesterol, and lower BMI and glomerular filtration rate (all P less than 0.01). In multivariable logistic analysis, high arterial stiffness was associated with both lower ARD z-score [OR 0.83 (95% confidence interval 0.79-0.88)] and higher carotid intima-media thickness [OR 1.36 (95% confidence interval 1.26-1.47); both P less than 0.0001], independent of significant associations with age, female sex, body size, DBP, heart rate, duration of hypertension, diabetes and smoking habit. Small ARD, together with atherosclerotic modifications of conduit arteries, is associated with increased 2-element Windkessel model of arterial stiffness in hypertension, independently of the significant effect of confounders.

Numerical Methods for 2-Dimensional Modeling

DTIC Science & Technology

1980-12-01

high-order finite element methods, and a multidimensional version of the method of lines, both utilizing an optimized stiff integrator for the time...integration. The finite element methods have proved disappointing, but the method of lines has provided an unexpectedly large gain in speed. Two...diffusion problems with the same number of unknowns (a 21 x 41 grid), solved by second-order finite element methods, took over seven minutes on the Cray-i

Numerical model of glulam beam delamination in dependence on cohesive strength

NASA Astrophysics Data System (ADS)

Kawecki, Bartosz; Podgórski, Jerzy

2018-01-01

This paper presents an attempt of using a finite element method for predicting delamination of a glue laminated timber beam through a cohesive layer. There were used cohesive finite elements, quadratic stress damage initiation criterion and mixed mode energy release rate failure model. Finite element damage was equal to its complete stiffness degradation. Timber material was considered to be an orthotropic with plastic behaviour after reaching bending limit.

The mechanics of tessellations - bioinspired strategies for fracture resistance.

PubMed

Fratzl, Peter; Kolednik, Otmar; Fischer, F Dieter; Dean, Mason N

2016-01-21

Faced with a comparatively limited palette of minerals and organic polymers as building materials, evolution has arrived repeatedly on structural solutions that rely on clever geometric arrangements to avoid mechanical trade-offs in stiffness, strength and flexibility. In this tutorial review, we highlight the concept of tessellation, a structural motif that involves periodic soft and hard elements arranged in series and that appears in a vast array of invertebrate and vertebrate animal biomaterials. We start from basic mechanics principles on the effects of material heterogeneities in hypothetical structures, to derive common concepts from a diversity of natural examples of one-, two- and three-dimensional tilings/layerings. We show that the tessellation of a hard, continuous surface - its atomization into discrete elements connected by a softer phase - can theoretically result in maximization of material toughness, with little expense to stiffness or strength. Moreover, the arrangement of soft/flexible and hard/stiff elements into particular geometries can permit surprising functions, such as signal filtering or 'stretch and catch' responses, where the constrained flexibility of systems allows a built-in safety mechanism for ensuring that both compressive and tensile loads are managed well. Our analysis unites examples ranging from exoskeletal materials (fish scales, arthropod cuticle, turtle shell) to endoskeletal materials (bone, shark cartilage, sponge spicules) to attachment devices (mussel byssal threads), from both invertebrate and vertebrate animals, while spotlighting success and potential for bio-inspired manmade applications.

Morphing hybrid honeycomb (MOHYCOMB) with in situ Poisson’s ratio modulation

NASA Astrophysics Data System (ADS)

Heath, Callum J. C.; Neville, Robin M.; Scarpa, Fabrizio; Bond, Ian P.; Potter, Kevin D.

2016-08-01

Electrostatic adhesion can be used as a means of reversible attachment. Through application of high voltage (~2 kV) across closely spaced parallel plate electrodes, significant shear stresses (11 kPa) can be generated. The highest levels of electrostatic holding force can be achieved through close contact of connection surfaces; this is facilitated by flexible electrodes which can conform to reduce air gaps. Cellular structures are comprised of thin walled elements, making them ideal host structures for electrostatic adhesive elements. The reversible adhesion provides control of the internal connectivity of the cellular structure, and determines the effective cell geometry. This would offer variable stiffness and control of the effective Poisson’s ratio of the global cellular array. Using copper-polyimide thin film laminates and PVDF thin film dielectrics, double lap shear electrostatic adhesive elements have been introduced to a cellular geometry. By activating different groups of reversible adhesive interfaces, the cellular array can assume four different cell configurations. A maximum stiffness modulation of 450% between the ‘All off’ and ‘All on’ cell morphologies has been demonstrated. This structure is also capable of in situ effective Poisson’s ratio variations, with the ability to switch between values of -0.45 and 0.54. Such a structure offers the potential for tuneable vibration absorption (due to its variable stiffness properties), or as a smart honeycomb with controllable curvature and is termed morphing hybrid honeycomb.

Stiffness of the endplate boundary layer and endplate surface topography are associated with brittleness of human whole vertebral bodies

PubMed Central

Nekkanty, Srikant; Yerramshetty, Janardhan; Kim, Do-Gyoon; Zauel, Roger; Johnson, Evan; Cody, Dianna D.; Yeni, Yener N.

2013-01-01

Stress magnitude and variability as estimated from large scale finite element (FE) analyses have been associated with compressive strength of human vertebral cancellous cores but these relationships have not been explored for whole vertebral bodies. In this study, the objectives were to investigate the relationship of FE-calculated stress distribution parameters with experimentally determined strength, stiffness, and displacement based ductility measures in human whole vertebral bodies, investigate the effect of endplate loading conditions on vertebral stiffness, strength, and ductility and test the hypothesis that endplate topography affects vertebral ductility and stress distributions. Eighteen vertebral bodies (T6-L3 levels; 4 female and 5 male cadavers, aged 40-98 years) were scanned using a flat panel CT system and followed with axial compression testing with Wood’s metal as filler material to maintain flat boundaries between load plates and specimens. FE models were constructed using reconstructed CT images and filler material was added digitally. Two different FE models with different filler material modulus simulating Wood’s metal and intervertebral disc (W-layer and D-layer models) were used. Element material modulus to cancellous bone was based on image gray value. Average, standard deviation, and coefficient of variation of von Mises stress in vertebral bone for W-layer and D-layer models and also the ratios of FE parameters from the two models (W/D) were calculated. Inferior and superior endplate surface topographical distribution parameters were calculated. Experimental stiffness, maximum load and work to fracture had the highest correlation with FE-calculated stiffness while experimental ductility measures had highest correlations with FE-calculated average von Mises stress and W-layer to D-layer stiffness ratio. Endplate topography of the vertebra was also associated with its structural ductility and the distribution parameter that best explained this association was kurtosis of inferior endplate topography. Our results indicate that endplate topography variations may provide insight into the mechanisms responsible for vertebral fractures. PMID:20633709

Condition number estimation of preconditioned matrices.

PubMed

Kushida, Noriyuki

2015-01-01

The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.

Identification of delaminations in composite: structural health monitoring software based on spectral estimation and hierarchical genetic algorithm

NASA Astrophysics Data System (ADS)

Nag, A.; Mahapatra, D. Roy; Gopalakrishnan, S.

2003-10-01

A hierarchical Genetic Algorithm (GA) is implemented in a high peformance spectral finite element software for identification of delaminations in laminated composite beams. In smart structural health monitoring, the number of delaminations (or any other modes of damage) as well as their locations and sizes are no way completely known. Only known are the healthy structural configuration (mass, stiffness and damping matrices updated from previous phases of monitoring), sensor measurements and some information about the load environment. To handle such enormous complexity, a hierarchical GA is used to represent heterogeneous population consisting of damaged structures with different number of delaminations and their evolution process to identify the correct damage configuration in the structures under monitoring. We consider this similarity with the evolution process in heterogeneous population of species in nature to develop an automated procedure to decide on what possible damaged configuration might have produced the deviation in the measured signals. Computational efficiency of the identification task is demonstrated by considering a single delamination. The behavior of fitness function in GA, which is an important factor for fast convergence, is studied for single and multiple delaminations. Several advantages of the approach in terms of computational cost is discussed. Beside tackling different other types of damage configurations, further scope of research for development of hybrid soft-computing modules are highlighted.

2D and 3D Matrices to Study Linear Invadosome Formation and Activity.

PubMed

Di Martino, Julie; Henriet, Elodie; Ezzoukhry, Zakaria; Mondal, Chandrani; Bravo-Cordero, Jose Javier; Moreau, Violaine; Saltel, Frederic

2017-06-02

Cell adhesion, migration, and invasion are involved in many physiological and pathological processes. For example, during metastasis formation, tumor cells have to cross anatomical barriers to invade and migrate through the surrounding tissue in order to reach blood or lymphatic vessels. This requires the interaction between cells and the extracellular matrix (ECM). At the cellular level, many cells, including the majority of cancer cells, are able to form invadosomes, which are F-actin-based structures capable of degrading ECM. Invadosomes are protrusive actin structures that recruit and activate matrix metalloproteinases (MMPs). The molecular composition, density, organization, and stiffness of the ECM are crucial in regulating invadosome formation and activation. In vitro, a gelatin assay is the standard assay used to observe and quantify invadosome degradation activity. However, gelatin, which is denatured collagen I, is not a physiological matrix element. A novel assay using type I collagen fibrils was developed and used to demonstrate that this physiological matrix is a potent inducer of invadosomes. Invadosomes that form along the collagen fibrils are known as linear invadosomes due to their linear organization on the fibers. Moreover, molecular analysis of linear invadosomes showed that the discoidin domain receptor 1 (DDR1) is the receptor involved in their formation. These data clearly demonstrate the importance of using a physiologically relevant matrix in order to understand the complex interactions between cells and the ECM.

A survey of the core-congruential formulation for geometrically nonlinear TL finite elements

NASA Technical Reports Server (NTRS)

Felippa, Carlos A.; Crivelli, Luis A.; Haugen, Bjorn

1994-01-01

This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.

Membrane triangles with corner drilling freedoms. I - The EFF element

NASA Technical Reports Server (NTRS)

Alvin, Ken; De La Fuente, Horacio M.; Haugen, Bjorn; Felippa, Carlos A.

1992-01-01

The formulation of 3-node 9-DOF membrane elements with normal-to-element-plane rotations (drilling freedoms) is examined in the context of parametrized variational principles. In particular, attention is given to the application of the extended free formulation (EFF) to the construction of a triangular membrane element with drilling freedoms that initially has complete quadratic polynomial expansions in each displacement component. The main advantage of the EFF over the free formulation triangle is that an explicit form is obtained for the higher-order stiffness.

A mixed shear flexible finite element for the analysis of laminated plates

NASA Technical Reports Server (NTRS)

Putcha, N. S.; Reddy, J. N.

1984-01-01

A mixed shear flexible finite element based on the Hencky-Mindlin type shear deformation theory of laminated plates is presented and their behavior in bending is investigated. The element consists of three displacements, two rotations, and three moments as the generalized degrees of freedom per node. The numerical convergence and accuracy characteristics of the element are investigated by comparing the finite element solutions with the exact solutions. The present study shows that reduced-order integration of the stiffness coefficients due to shear is necessary to obtain accurate results for thin plates.

Optical matrix-matrix multiplication method demonstrated by the use of a multifocus hololens

NASA Technical Reports Server (NTRS)

Liu, H. K.; Liang, Y.-Z.

1984-01-01

A method of optical matrix-matrix multiplication is presented. The feasibility of the method is also experimentally demonstrated by the use of a dichromated-gelatin multifocus holographic lens (hololens). With the specific values of matrices chosen, the average percentage error between the theoretical and experimental data of the elements of the output matrix of the multiplication of some specific pairs of 3 x 3 matrices is 0.4 percent, which corresponds to an 8-bit accuracy.

Finite Element Analysis of Single Cell Stiffness Measurements Using PZT-Integrated Buckling Nanoneedles.

PubMed

Rad, Maryam Alsadat; Tijjani, Auwal Shehu; Ahmad, Mohd Ridzuan; Auwal, Shehu Muhammad

2016-12-23

This paper proposes a new technique for real-time single cell stiffness measurement using lead zirconate titanate (PZT)-integrated buckling nanoneedles. The PZT and the buckling part of the nanoneedle have been modelled and validated using the ABAQUS software. The two parts are integrated together to function as a single unit. After calibration, the stiffness, Young's modulus, Poisson's ratio and sensitivity of the PZT-integrated buckling nanoneedle have been determined to be 0.7100 N·m -1 , 123.4700 GPa, 0.3000 and 0.0693 V·m·N -1 , respectively. Three Saccharomyces cerevisiae cells have been modelled and validated based on compression tests. The average global stiffness and Young's modulus of the cells are determined to be 10.8867 ± 0.0094 N·m -1 and 110.7033 ± 0.0081 MPa, respectively. The nanoneedle and the cell have been assembled to measure the local stiffness of the single Saccharomyces cerevisiae cells The local stiffness, Young's modulus and PZT output voltage of the three different size Saccharomyces cerevisiae have been determined at different environmental conditions. We investigated that, at low temperature the stiffness value is low to adapt to the change in the environmental condition. As a result, Saccharomyces cerevisiae becomes vulnerable to viral and bacterial attacks. Therefore, the proposed technique will serve as a quick and accurate process to diagnose diseases at early stage in a cell for effective treatment.

Analysis of Flexible Car Body of Straddle Monorail Vehicle

NASA Astrophysics Data System (ADS)

Zhong, Yuanmu

2018-03-01

Based on the finite element model of straddle monorail vehicle, a rigid-flexible coupling dynamic model considering vehicle body’s flexibility is established. The influence of vertical stiffness and vertical damping of the running wheel on the modal parameters of the car body is analyzed. The effect of flexible car body on modal parameters and vehicle ride quality is also studied. The results show that when the vertical stiffness of running wheel is less than 1 MN / m, the car body bounce and pitch frequency increase with the increasing of the vertical stiffness of the running wheel, when the running wheel vertical stiffness is 1MN / m or more, car body bounce and pitch frequency remained unchanged; When the vertical stiffness of the running wheel is below 1.8 MN / m, the vehicle body bounce and pitch damping ratio increase with the increasing of the vertical stiffness of the running wheel; When the running wheel vertical stiffness is 1.8MN / m or more, the car body bounce and pitch damping ratio remained unchanged; The running wheel vertical damping on the car body bounce and pitch frequency has no effect; Car body bounce and pitch damping ratio increase with the increasing of the vertical damping of the running wheel. The flexibility of the car body has no effect on the modal parameters of the car, which will improve the vehicle ride quality index.

Progress report 3 of cooperative program for design, fabrication, and testing of high modulus composite helicopter shafting

NASA Technical Reports Server (NTRS)

Wright, C. C.; Baker, D. J.

1980-01-01

This report describes the third phase of work, the objective of which was to overcome the excessive brittleness of the previously developed UH-1 helicopter tail rotor drive shaft design which demonstrated a shaft train weight savings of 53.1% over the current 2024-T3 aluminum shaft train. A materials impact program demonstrated exceptionally noteworthy performance of two woven constructions containing E-glass and PRD 49-III (designation later changed to KEVLAR 49) fibers in an epoxy resin matrix. Thermoplastic matrices and PRD 49-III fiber provided impact resistance at low weight which was superior to composites having the same fiber in a thermoset resin matrix. A design, fabrication, and test program showed that shaft impact resistance could be improved over the previously developed graphite composite design at a cost in shaft train rate savings. The shaft train weight savings of the most impact tolerant construction was 4.0% over the current aluminum shaft train. Alternating plies of graphite and glass appear to provide substantially greater tube impact durability than that provided by hybridization of the two fibers into one tape wound to a ply design equivalent in strength and stiffness to that of the alternating ply design. Recommendations were made to continue research work to exploit the potential for more impact-durable structures through the use of KEVLAR 49 fiber, woven structures, thermoplastic matrices and THORNEL 50-S/KEVLAR 49 blends with thermoset matrices.

Coal fly ash-slag-based geopolymers: microstructure and metal leaching.

PubMed

Izquierdo, Maria; Querol, Xavier; Davidovits, Joseph; Antenucci, Diano; Nugteren, Henk; Fernández-Pereira, Constantino

2009-07-15

This study deals with the use of fly ash as a starting material for geopolymeric matrices. The leachable concentrations of geopolymers were compared with those of the starting fly ash to evaluate the retention of potentially harmful elements within the geopolymer matrix. Geopolymer matrices give rise to a leaching scenario characterised by a highly alkaline environment, which inhibits the leaching of heavy metals but may enhance the mobilization of certain oxyanionic species. Thus, fly ash-based geopolymers were found to immobilize a number of trace pollutants such as Be, Bi, Cd, Co, Cr, Cu, Nb, Ni, Pb, Sn, Th, U, Y, Zr and rare earth elements. However, the leachable levels of elements occurring in their oxyanionic form such as As, B, Mo, Se, V and W were increased after geopolymerization. This suggests that an optimal dosage, synthesis and curing conditions are essential in order to obtain a long-term stable final product that ensures an efficient physical encapsulation.

Elastin-like Protein-Hyaluronic acid (ELP-HA) Hydrogels with Decoupled Mechanical and Biochemical cues for Cartilage Regeneration

PubMed Central

Zhu, Danqing; Wang, Huiyuan; Trinh, Pavin; Heilshorn, Sarah C.; Yang, Fan

2018-01-01

Hyaluronic acid (HA) is a major component of cartilage extracellular matrix and is an attractive material for use as 3D injectable matrices for cartilage regeneration. While previous studies have shown the promise of HA-based hydrogels to support cell-based cartilage formation, varying HA concentration generally led to simultaneous changes in both biochemical cues and stiffness. How cells respond to the change of biochemical content of HA remains largely unknown. Here we report an adaptable elastin-like protein-hyaluronic acid (ELP-HA) hydrogel platform using dynamic covalent chemistry, which allows varyiation of HA concentration without affecting matrix stiffness. ELP-HA hydrogels were created through dynamic hydrazone bonds via the reaction between hydrazine-modified ELP (ELP-HYD) and aldehyde-modified HA (HA-ALD). By tuning the stoichiometric ratio of aldehyde groups to hydrazine groups while maintaining ELP-HYD concentration constant, hydrogels with variable HA concentration (1.5%, 3%, or 5%) (w/v) were fabricated with comparable stiffness. To evaluate the effects of HA concentration on cell-based cartilage regeneration, chondrocytes were encapsulated within ELP-HA hydrogels with varying HA concentration. Increasing HA concentration led to a dose-dependent increase in cartilage-marker gene expression and enhanced sGAG deposition while minimizing undesirable fibrocartilage phenotype. The use of adaptable protein hydrogels formed via dynamic covalent chemistry may be broadly applicable as 3D scaffolds with decoupled niche properties to guide other desirable cell fates and tissue repair. PMID:28268018

Elastin-like protein-hyaluronic acid (ELP-HA) hydrogels with decoupled mechanical and biochemical cues for cartilage regeneration.

PubMed

Zhu, Danqing; Wang, Huiyuan; Trinh, Pavin; Heilshorn, Sarah C; Yang, Fan

2017-05-01

Hyaluronic acid (HA) is a major component of cartilage extracellular matrix and is an attractive material for use as 3D injectable matrices for cartilage regeneration. While previous studies have shown the promise of HA-based hydrogels to support cell-based cartilage formation, varying HA concentration generally led to simultaneous changes in both biochemical cues and stiffness. How cells respond to the change of biochemical content of HA remains largely unknown. Here we report an adaptable elastin-like protein-hyaluronic acid (ELP-HA) hydrogel platform using dynamic covalent chemistry, which allows variation of HA concentration without affecting matrix stiffness. ELP-HA hydrogels were created through dynamic hydrazone bonds via the reaction between hydrazine-modified ELP (ELP-HYD) and aldehyde-modified HA (HA-ALD). By tuning the stoichiometric ratio of aldehyde groups to hydrazine groups while maintaining ELP-HYD concentration constant, hydrogels with variable HA concentration (1.5%, 3%, or 5%) (w/v) were fabricated with comparable stiffness. To evaluate the effects of HA concentration on cell-based cartilage regeneration, chondrocytes were encapsulated within ELP-HA hydrogels with varying HA concentration. Increasing HA concentration led to a dose-dependent increase in cartilage-marker gene expression and enhanced sGAG deposition while minimizing undesirable fibrocartilage phenotype. The use of adaptable protein hydrogels formed via dynamic covalent chemistry may be broadly applicable as 3D scaffolds with decoupled niche properties to guide other desirable cell fates and tissue repair. Copyright © 2017 Elsevier Ltd. All rights reserved.

Finite element, modal co-ordinate analysis of structures subjected to moving loads

NASA Astrophysics Data System (ADS)

Olsson, M.

1985-03-01

Some of the possibilities of the finite element method in the moving load problem are demonstrated. The bridge-vehicle interaction phenomenon is considered by deriving a general bridge-vehicle element which is believed to be novel. This element may be regarded as a finite element with time-dependent and unsymmetric element matrices. The bridge response is formulated in modal co-ordinates thereby reducing the number of equations to be solved within each time step. Illustrative examples are shown for the special case of a beam bridge model and a one-axle vehicle model.

Light weight high-stiffness stage platen

DOEpatents

Spence, Paul A.

2001-01-01

An improved light weight, stiff stage platen for photolithography is provided. The high stiffness of the stage platen is exemplified by a relatively high first resonant vibrational mode as determined, for instance, by finite element modal analysis. The stage platen can be employed to support a chuck that is designed to secure a mask or wafer. The stage platen includes a frame that has interior walls that define an interior region and that has exterior walls wherein the outer surfaces of at least two adjacent walls are reflective mirror surfaces; and a matrix of ribs within the interior region that is connected to the interior walls wherein the stage platen exhibits a first vibrational mode at a frequency of greater than about 1000 Hz.

Virtual reality robotic telesurgery simulations using MEMICA haptic system

NASA Technical Reports Server (NTRS)

Bar-Cohen, Yoseph; Mavroidis, Constantinos; Bouzit, Mourad; Dolgin, Benjamin; Harm, Deborah L.; Kopchok, George E.; White, Rodney

2001-01-01

The authors conceived a haptic mechanism called MEMICA (Remote Mechanical Mirroring using Controlled stiffness and Actuators) that can enable the design of high dexterity, rapid response, and large workspace haptic system. The development of a novel MEMICA gloves and virtual reality models are being explored to allow simulation of telesurgery and other applications. The MEMICA gloves are being designed to provide intuitive mirroring of the conditions at a virtual site where a robot simulates the presence of a human operator. The key components of MEMICA are miniature electrically controlled stiffness (ECS) elements and electrically controlled force and stiffness (ECFS) actuators that are based on the use of Electro-Rheological Fluids (ERF. In this paper the design of the MEMICA system and initial experimental results are presented.

Derivation of stiffness matrix in constitutive modeling of magnetorheological elastomer

NASA Astrophysics Data System (ADS)

Leng, D.; Sun, L.; Sun, J.; Lin, Y.

2013-02-01

Magnetorheological elastomers (MREs) are a class of smart materials whose mechanical properties change instantly by the application of a magnetic field. Based on the specially orthotropic, transversely isotropic stress-strain relationships and effective permeability model, the stiffness matrix of constitutive equations for deformable chain-like MRE is considered. To valid the components of shear modulus in this stiffness matrix, the magnetic-structural simulations with finite element method (FEM) are presented. An acceptable agreement is illustrated between analytical equations and numerical simulations. For the specified magnetic field, sphere particle radius, distance between adjacent particles in chains and volume fractions of ferrous particles, this constitutive equation is effective to engineering application to estimate the elastic behaviour of chain-like MRE in an external magnetic field.

Error associated with a reduced order linear model of a spur gear pair

NASA Technical Reports Server (NTRS)

Kahraman, A.; Singh, R.

1991-01-01

The paper proposes a reduced-order analytical model of a spur gear pair which consists of two identical spur gears, two identical flexible shafts, and four identical rolling element bearings of a given radial stiffness. The error associated with the undamped eigensolution is estimated by a comparison with a benchmark finite element model.

An influence coefficient method for the application of the modal technique to wing flutter suppression of the DAST ARW-1 wing

NASA Technical Reports Server (NTRS)

Pines, S.

1981-01-01

The methods used to compute the mass, structural stiffness, and aerodynamic forces in the form of influence coefficient matrices as applied to a flutter analysis of the Drones for Aerodynamic and Structural Testing (DAST) Aeroelastic Research Wing. The DAST wing was chosen because wind tunnel flutter test data and zero speed vibration data of the modes and frequencies exist and are available for comparison. A derivation of the equations of motion that can be used to apply the modal method for flutter suppression is included. A comparison of the open loop flutter predictions with both wind tunnel data and other analytical methods is presented.

A system identification technique based on the random decrement signatures. Part 1: Theory and simulation

NASA Technical Reports Server (NTRS)

Bedewi, Nabih E.; Yang, Jackson C. S.

1987-01-01

Identification of the system parameters of a randomly excited structure may be treated using a variety of statistical techniques. Of all these techniques, the Random Decrement is unique in that it provides the homogeneous component of the system response. Using this quality, a system identification technique was developed based on a least-squares fit of the signatures to estimate the mass, damping, and stiffness matrices of a linear randomly excited system. The mathematics of the technique is presented in addition to the results of computer simulations conducted to demonstrate the prediction of the response of the system and the random forcing function initially introduced to excite the system.

Solution of quadratic matrix equations for free vibration analysis of structures.

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1973-01-01

An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.

Sensitivity of corneal biomechanical and optical behavior to material parameters using design of experiments method.

PubMed

Xu, Mengchen; Lerner, Amy L; Funkenbusch, Paul D; Richhariya, Ashutosh; Yoon, Geunyoung

2018-02-01

The optical performance of the human cornea under intraocular pressure (IOP) is the result of complex material properties and their interactions. The measurement of the numerous material parameters that define this material behavior may be key in the refinement of patient-specific models. The goal of this study was to investigate the relative contribution of these parameters to the biomechanical and optical responses of human cornea predicted by a widely accepted anisotropic hyperelastic finite element model, with regional variations in the alignment of fibers. Design of experiments methods were used to quantify the relative importance of material properties including matrix stiffness, fiber stiffness, fiber nonlinearity and fiber dispersion under physiological IOP. Our sensitivity results showed that corneal apical displacement was influenced nearly evenly by matrix stiffness, fiber stiffness and nonlinearity. However, the variations in corneal optical aberrations (refractive power and spherical aberration) were primarily dependent on the value of the matrix stiffness. The optical aberrations predicted by variations in this material parameter were sufficiently large to predict clinically important changes in retinal image quality. Therefore, well-characterized individual variations in matrix stiffness could be critical in cornea modeling in order to reliably predict optical behavior under different IOPs or after corneal surgery.

Pneumatic Variable Series Elastic Actuator.

PubMed

Zheng, Hao; Wu, Molei; Shen, Xiangrong

2016-08-01

Inspired by human motor control theory, stiffness control is highly effective in manipulation and human-interactive tasks. The implementation of stiffness control in robotic systems, however, has largely been limited to closed-loop control, and suffers from multiple issues such as limited frequency range, potential instability, and lack of contribution to energy efficiency. Variable-stiffness actuator represents a better solution, but the current designs are complex, heavy, and bulky. The approach in this paper seeks to address these issues by using pneumatic actuator as a variable series elastic actuator (VSEA), leveraging the compressibility of the working fluid. In this work, a pneumatic actuator is modeled as an elastic element with controllable stiffness and equilibrium point, both of which are functions of air masses in the two chambers. As such, for the implementation of stiffness control in a robotic system, the desired stiffness/equilibrium point can be converted to the desired chamber air masses, and a predictive pressure control approach is developed to control the timing of valve switching to obtain the desired air mass while minimizing control action. Experimental results showed that the new approach in this paper requires less expensive hardware (on-off valve instead of proportional valve), causes less control action in implementation, and provides good control performance by leveraging the inherent dynamics of the actuator.

Variable Stiffness Panel Structural Analyses With Material Nonlinearity and Correlation With Tests

NASA Technical Reports Server (NTRS)

Wu, K. Chauncey; Gurdal, Zafer

2006-01-01

Results from structural analyses of three tow-placed AS4/977-3 composite panels with both geometric and material nonlinearities are presented. Two of the panels have variable stiffness layups where the fiber orientation angle varies as a continuous function of location on the panel planform. One variable stiffness panel has overlapping tow bands of varying thickness, while the other has a theoretically uniform thickness. The third panel has a conventional uniform-thickness [plus or minus 45](sub 5s) layup with straight fibers, providing a baseline for comparing the performance of the variable stiffness panels. Parametric finite element analyses including nonlinear material shear are first compared with material characterization test results for two orthotropic layups. This nonlinear material model is incorporated into structural analysis models of the variable stiffness and baseline panels with applied end shortenings. Measured geometric imperfections and mechanical prestresses, generated by forcing the variable stiffness panels from their cured anticlastic shapes into their flatter test configurations, are also modeled. Results of these structural analyses are then compared to the measured panel structural response. Good correlation is observed between the analysis results and displacement test data throughout deep postbuckling up to global failure, suggesting that nonlinear material behavior is an important component of the actual panel structural response.

Pneumatic Variable Series Elastic Actuator

PubMed Central

Zheng, Hao; Wu, Molei; Shen, Xiangrong

2016-01-01

Inspired by human motor control theory, stiffness control is highly effective in manipulation and human-interactive tasks. The implementation of stiffness control in robotic systems, however, has largely been limited to closed-loop control, and suffers from multiple issues such as limited frequency range, potential instability, and lack of contribution to energy efficiency. Variable-stiffness actuator represents a better solution, but the current designs are complex, heavy, and bulky. The approach in this paper seeks to address these issues by using pneumatic actuator as a variable series elastic actuator (VSEA), leveraging the compressibility of the working fluid. In this work, a pneumatic actuator is modeled as an elastic element with controllable stiffness and equilibrium point, both of which are functions of air masses in the two chambers. As such, for the implementation of stiffness control in a robotic system, the desired stiffness/equilibrium point can be converted to the desired chamber air masses, and a predictive pressure control approach is developed to control the timing of valve switching to obtain the desired air mass while minimizing control action. Experimental results showed that the new approach in this paper requires less expensive hardware (on–off valve instead of proportional valve), causes less control action in implementation, and provides good control performance by leveraging the inherent dynamics of the actuator. PMID:27354755

Linear Parameter Varying Identification of Dynamic Joint Stiffness during Time-Varying Voluntary Contractions

PubMed Central

Golkar, Mahsa A.; Sobhani Tehrani, Ehsan; Kearney, Robert E.

2017-01-01

Dynamic joint stiffness is a dynamic, nonlinear relationship between the position of a joint and the torque acting about it, which can be used to describe the biomechanics of the joint and associated limb(s). This paper models and quantifies changes in ankle dynamic stiffness and its individual elements, intrinsic and reflex stiffness, in healthy human subjects during isometric, time-varying (TV) contractions of the ankle plantarflexor muscles. A subspace, linear parameter varying, parallel-cascade (LPV-PC) algorithm was used to identify the model from measured input position perturbations and output torque data using voluntary torque as the LPV scheduling variable (SV). Monte-Carlo simulations demonstrated that the algorithm is accurate, precise, and robust to colored measurement noise. The algorithm was then used to examine stiffness changes associated with TV isometric contractions. The SV was estimated from the Soleus EMG using a Hammerstein model of EMG-torque dynamics identified from unperturbed trials. The LPV-PC algorithm identified (i) a non-parametric LPV impulse response function (LPV IRF) for intrinsic stiffness and (ii) a LPV-Hammerstein model for reflex stiffness consisting of a LPV static nonlinearity followed by a time-invariant state-space model of reflex dynamics. The results demonstrated that: (a) intrinsic stiffness, in particular ankle elasticity, increased significantly and monotonically with activation level; (b) the gain of the reflex pathway increased from rest to around 10–20% of subject's MVC and then declined; and (c) the reflex dynamics were second order. These findings suggest that in healthy human ankle, reflex stiffness contributes most at low muscle contraction levels, whereas, intrinsic contributions monotonically increase with activation level. PMID:28579954

Estimating Human Trabecular Meshwork Stiffness by Numerical Modeling and Advanced OCT Imaging.

PubMed

Wang, Ke; Johnstone, Murray A; Xin, Chen; Song, Shaozhen; Padilla, Steven; Vranka, Janice A; Acott, Ted S; Zhou, Kai; Schwaner, Stephen A; Wang, Ruikang K; Sulchek, Todd; Ethier, C Ross

2017-09-01

The purpose of this study was to estimate human trabecular meshwork (hTM) stiffness, thought to be elevated in glaucoma, using a novel indirect approach, and to compare results with direct en face atomic force microscopy (AFM) measurements. Postmortem human eyes were perfused to measure outflow facility and identify high- and low-flow regions (HF, LF) by tracer. Optical coherence tomography (OCT) images were obtained as Schlemm's canal luminal pressure was directly manipulated. TM stiffness was deduced by an inverse finite element modeling (FEM) approach. A series of AFM forcemaps was acquired along a line traversing the anterior angle on a radially cut flat-mount corneoscleral wedge with TM facing upward. The elastic modulus of normal hTM estimated by inverse FEM was 70 ± 20 kPa (mean ± SD), whereas glaucomatous hTM was slightly stiffer (98 ± 19 kPa). This trend was consistent with TM stiffnesses measured by AFM: normal hTM stiffness = 1.37 ± 0.56 kPa, which was lower than glaucomatous hTM stiffness (2.75 ± 1.19 kPa). None of these differences were statistically significant. TM in HF wedges was softer than that in LF wedges for both normal and glaucomatous eyes based on the inverse FEM approach but not by AFM. Outflow facility was significantly correlated with TM stiffness estimated by FEM in six human eyes (P = 0.018). TM stiffness is higher, but only modestly so, in glaucomatous patients. Outflow facility in both normal and glaucomatous human eyes appears to associate with TM stiffness. This evidence motivates further studies to investigate factors underlying TM biomechanical property regulation.

Symmetry of semi-reduced lattices.

PubMed

Stróż, Kazimierz

2015-05-01

The main result of this work is extension of the famous characterization of Bravais lattices according to their metrical, algebraic and geometric properties onto a wide class of primitive lattices (including Buerger-reduced, nearly Buerger-reduced and a substantial part of Delaunay-reduced) related to low-restricted semi-reduced descriptions (s.r.d.'s). While the `geometric' operations in Bravais lattices map the basis vectors into themselves, the `arithmetic' operators in s.r.d. transform the basis vectors into cell vectors (basis vectors, face or space diagonals) and are represented by matrices from the set {\\bb V} of all 960 matrices with the determinant ±1 and elements {0, ±1} of the matrix powers. A lattice is in s.r.d. if the moduli of off-diagonal elements in both the metric tensors M and M(-1) are smaller than corresponding diagonal elements sharing the same column or row. Such lattices are split into 379 s.r.d. types relative to the arithmetic holohedries. Metrical criteria for each type do not need to be explicitly given but may be modelled as linear derivatives {\\bb M}(p,q,r), where {\\bb M} denotes the set of 39 highest-symmetry metric tensors, and p,q,r describe changes of appropriate interplanar distances. A sole filtering of {\\bb V} according to an experimental s.r.d. metric and subsequent geometric interpretation of the filtered matrices lead to mathematically stable and rich information on the Bravais-lattice symmetry and deviations from the exact symmetry. The emphasis on the crystallographic features of lattices was obtained by shifting the focus (i) from analysis of a lattice metric to analysis of symmetry matrices [Himes & Mighell (1987). Acta Cryst. A43, 375-384], (ii) from the isometric approach and invariant subspaces to the orthogonality concept {some ideas in Le Page [J. Appl. Cryst. (1982), 15, 255-259]} and splitting indices [Stróż (2011). Acta Cryst. A67, 421-429] and (iii) from fixed cell transformations to transformations derivable via geometric information (Himes & Mighell, 1987; Le Page, 1982). It is illustrated that corresponding arithmetic and geometric holohedries share space distribution of symmetry elements. Moreover, completeness of the s.r.d. types reveals their combinatorial structure and simplifies the crystallographic description of structural phase transitions, especially those observed with the use of powder diffraction. The research proves that there are excellent theoretical and practical reasons for looking at crystal lattice symmetry from an entirely new and surprising point of view - the combinatorial set {\\bb V} of matrices, their semi-reduced lattice context and their geometric properties.

A chemo-mechanical free-energy-based approach to model durotaxis and extracellular stiffness-dependent contraction and polarization of cells.

PubMed

Shenoy, Vivek B; Wang, Hailong; Wang, Xiao

2016-02-06

We propose a chemo-mechanical model based on stress-dependent recruitment of myosin motors to describe how the contractility, polarization and strain in cells vary with the stiffness of their surroundings and their shape. A contractility tensor, which depends on the distribution of myosin motors, is introduced to describe the chemical free energy of the cell due to myosin recruitment. We explicitly include the contributions to the free energy that arise from mechanosensitive signalling pathways (such as the SFX, Rho-Rock and MLCK pathways) through chemo-mechanical coupling parameters. Taking the variations of the total free energy, which consists of the chemical and mechanical components, in accordance with the second law of thermodynamics provides equations for the temporal evolution of the active stress and the contractility tensor. Following this approach, we are able to recover the well-known Hill relation for active stresses, based on the fundamental principles of irreversible thermodynamics rather than phenomenology. We have numerically implemented our free energy-based approach to model spatial distribution of strain and contractility in (i) cells supported by flexible microposts, (ii) cells on two-dimensional substrates, and (iii) cells in three-dimensional matrices. We demonstrate how the polarization of the cells and the orientation of stress fibres can be deduced from the eigenvalues and eigenvectors of the contractility tensor. Our calculations suggest that the chemical free energy of the cell decreases with the stiffness of the extracellular environment as the cytoskeleton polarizes in response to stress-dependent recruitment of molecular motors. The mechanical energy, which includes the strain energy and motor potential energy, however, increases with stiffness, but the overall energy is lower for cells in stiffer environments. This provides a thermodynamic basis for durotaxis, whereby cells preferentially migrate towards stiffer regions of the extracellular environment. Our models also explain, from an energetic perspective, why the shape of the cells can change in response to stiffness of the surroundings. The effect of the stiffness of the nucleus on its shape and the orientation of the stress fibres is also studied for all the above geometries. Along with making testable predictions, we have estimated the magnitudes of the chemo-mechanical coupling parameters for myofibroblasts based on data reported in the literature.

A chemo-mechanical free-energy-based approach to model durotaxis and extracellular stiffness-dependent contraction and polarization of cells

PubMed Central

Shenoy, Vivek B.; Wang, Hailong; Wang, Xiao

2016-01-01

We propose a chemo-mechanical model based on stress-dependent recruitment of myosin motors to describe how the contractility, polarization and strain in cells vary with the stiffness of their surroundings and their shape. A contractility tensor, which depends on the distribution of myosin motors, is introduced to describe the chemical free energy of the cell due to myosin recruitment. We explicitly include the contributions to the free energy that arise from mechanosensitive signalling pathways (such as the SFX, Rho-Rock and MLCK pathways) through chemo-mechanical coupling parameters. Taking the variations of the total free energy, which consists of the chemical and mechanical components, in accordance with the second law of thermodynamics provides equations for the temporal evolution of the active stress and the contractility tensor. Following this approach, we are able to recover the well-known Hill relation for active stresses, based on the fundamental principles of irreversible thermodynamics rather than phenomenology. We have numerically implemented our free energy-based approach to model spatial distribution of strain and contractility in (i) cells supported by flexible microposts, (ii) cells on two-dimensional substrates, and (iii) cells in three-dimensional matrices. We demonstrate how the polarization of the cells and the orientation of stress fibres can be deduced from the eigenvalues and eigenvectors of the contractility tensor. Our calculations suggest that the chemical free energy of the cell decreases with the stiffness of the extracellular environment as the cytoskeleton polarizes in response to stress-dependent recruitment of molecular motors. The mechanical energy, which includes the strain energy and motor potential energy, however, increases with stiffness, but the overall energy is lower for cells in stiffer environments. This provides a thermodynamic basis for durotaxis, whereby cells preferentially migrate towards stiffer regions of the extracellular environment. Our models also explain, from an energetic perspective, why the shape of the cells can change in response to stiffness of the surroundings. The effect of the stiffness of the nucleus on its shape and the orientation of the stress fibres is also studied for all the above geometries. Along with making testable predictions, we have estimated the magnitudes of the chemo-mechanical coupling parameters for myofibroblasts based on data reported in the literature. PMID:26855753

Condition Number Estimation of Preconditioned Matrices

PubMed Central

Kushida, Noriyuki

2015-01-01

The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager’s method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei’s matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei’s matrix, and matrices generated with the finite element method. PMID:25816331

Glass microneedles for force measurements: a finite-element analysis model

PubMed Central

Ayittey, Peter N.; Walker, John S.; Rice, Jeremy J.; de Tombe, Pieter P.

2010-01-01

Changes in developed force (0.1–3.0 μN) observed during contraction of single myofibrils in response to rapidly changing calcium concentrations can be measured using glass microneedles. These microneedles are calibrated for stiffness and deflect on response to developed myofibril force. The precision and accuracy of kinetic measurements are highly dependent on the structural and mechanical characteristics of the microneedles, which are generally assumed to have a linear force–deflection relationship. We present a finite-element analysis (FEA) model used to simulate the effects of measurable geometry on stiffness as a function of applied force and validate our model with actual measured needle properties. In addition, we developed a simple heuristic constitutive equation that best describes the stiffness of our range of microneedles used and define limits of geometry parameters within which our predictions hold true. Our model also maps a relation between the geometry parameters and natural frequencies in air, enabling optimum parametric combinations for microneedle fabrication that would reflect more reliable force measurement in fluids and physiological environments. We propose a use for this model to aid in the design of microneedles to improve calibration time, reproducibility, and precision for measuring myofibrillar, cellular, and supramolecular kinetic forces. PMID:19104827

A probability distribution model of tooth pits for evaluating time-varying mesh stiffness of pitting gears

NASA Astrophysics Data System (ADS)

Lei, Yaguo; Liu, Zongyao; Wang, Delong; Yang, Xiao; Liu, Huan; Lin, Jing

2018-06-01

Tooth damage often causes a reduction in gear mesh stiffness. Thus time-varying mesh stiffness (TVMS) can be treated as an indication of gear health conditions. This study is devoted to investigating the mesh stiffness variations of a pair of external spur gears with tooth pitting, and proposes a new model for describing tooth pitting based on probability distribution. In the model, considering the appearance and development process of tooth pitting, we model the pitting on the surface of spur gear teeth as a series of pits with a uniform distribution in the direction of tooth width and a normal distribution in the direction of tooth height, respectively. In addition, four pitting degrees, from no pitting to severe pitting, are modeled. Finally, influences of tooth pitting on TVMS are analyzed in details and the proposed model is validated by comparing with a finite element model. The comparison results show that the proposed model is effective for the TVMS evaluations of pitting gears.

Buckling and Post-Buckling Behaviors of a Variable Stiffness Composite Laminated Wing Box Structure

NASA Astrophysics Data System (ADS)

Wang, Peiyan; Huang, Xinting; Wang, Zhongnan; Geng, Xiaoliang; Wang, Yuansheng

2018-04-01

The buckling and post-buckling behaviors of variable stiffness composite laminates (VSCL) with curvilinear fibers were investigated and compared with constant stiffness composite laminates (CSCL) with straight fibers. A VSCL box structure was evaluated under a pure bending moment. The results of the comparative test showed that the critical buckling load of the VSCL box was approximately 3% higher than that of the CSCL box. However, the post-buckling load-bearing capacity was similar due to the layup angle and the immature status of the material processing technology. The properties of the VSCL and CSCL boxes under a pure bending moment were simulated using the Hashin criterion and cohesive interface elements. The simulation results are consistent with the experimental results in stiffness, critical buckling load and failure modes but not in post-buckling load capacity. The results of the experiment, the simulation and laminated plate theory show that VSCL greatly improves the critical buckling load but has little influence on the post-buckling load-bearing capacity.

One-dimensional analysis of thin-walled beams with diaphragms and its application to optimization for stiffness reinforcement

NASA Astrophysics Data System (ADS)

Jung, Joon Hee; Jang, Gang-Won; Shin, Dongil; Kim, Yoon Young

2018-03-01

This paper presents a method to analyze thin-walled beams with quadrilateral cross sections reinforced with diaphragms using a one-dimensional higher-order beam theory. The effect of a diaphragm is reflected focusing on the increase of static stiffness. The deformations on the beam-interfacing boundary of a thin diaphragm are described by using deformation modes of the beam cross section while the deformations inside the diaphragm are approximated in the form of complete cubic polynomials. By using the principle of minimum potential energy, its stiffness that significantly affects distortional deformation of a thin-walled beam can be considered in the one-dimensional beam analysis. It is shown that the accuracy of the resulting one-dimensional analysis is comparable with that by a shell element based analysis. As a means to demonstrate the usefulness of the present approach for design, position optimization problems of diaphragms for stiffness reinforcement of an automotive side frame are solved.

Normalized stiffness ratios for mechanical characterization of isotropic acoustic foams.

PubMed

Sahraoui, Sohbi; Brouard, Bruno; Benyahia, Lazhar; Parmentier, Damien; Geslain, Alan

2013-12-01

This paper presents a method for the mechanical characterization of isotropic foams at low frequency. The objective of this study is to determine the Young's modulus, the Poisson's ratio, and the loss factor of commercially available foam plates. The method is applied on porous samples having square and circular sections. The main idea of this work is to perform quasi-static compression tests of a single foam sample followed by two juxtaposed samples having the same dimensions. The load and displacement measurements lead to a direct extraction of the elastic constants by means of normalized stiffness and normalized stiffness ratio which depend on Poisson's ratio and shape factor. The normalized stiffness is calculated by the finite element method for different Poisson ratios. The no-slip boundary conditions imposed by the loading rigid plates create interfaces with a complex strain distribution. Beforehand, compression tests were performed by means of a standard tensile machine in order to determine the appropriate pre-compression rate for quasi-static tests.

Spacecraft Pointing and Position Control,

DTIC Science & Technology

1981-11-01

GEOSTATIONARY ELEMENTS As the classical set of Keplerian elements (a,e,i,a,Q, M ) is inappropriate for geosta- tionary orbits because the angular...instead of E., the set E + AE (34) - a - -LP(t 0 is obtained. Since the orbital element vector has to be computed for each measurement time, a simple orbit ...depends on the stiffness terms effected by kinematic coupling with the orbit rate 0o and the set gain K The x-component of the disturbance torque, this

Electrostatically tunable resonance frequency beam utilizing a stress-sensitive film

DOEpatents

Thundat, Thomas G.; Wachter, Eric A.; Davis, J. Kenneth

2001-01-01

Methods and apparatus for detecting particular frequencies of acoustic vibration utilize an electrostatically-tunable beam element having a stress-sensitive coating and means for providing electrostatic force to controllably deflect the beam element thereby changing its stiffness and its resonance frequency. It is then determined from the response of the electrostatically-tunable beam element to the acoustical vibration to which the beam is exposed whether or not a particular frequency or frequencies of acoustic vibration are detected.

Magnetically tunable resonance frequency beam utilizing a stress-sensitive film

DOEpatents

Davis, J. Kenneth; Thundat, Thomas G.; Wachter, Eric A.

2001-01-01

Methods and apparatus for detecting particular frequencies of vibration utilize a magnetically-tunable beam element having a stress-sensitive coating and means for providing magnetic force to controllably deflect the beam element thereby changing its stiffness and its resonance frequency. It is then determined from the response of the magnetically-tunable beam element to the vibration to which the beam is exposed whether or not a particular frequency or frequencies of vibration are detected.

A numerical method for interface problems in elastodynamics

NASA Technical Reports Server (NTRS)

Mcghee, D. S.

1984-01-01

The numerical implementation of a formulation for a class of interface problems in elastodynamics is discussed. This formulation combines the use of the finite element and boundary integral methods to represent the interior and the exteriro regions, respectively. In particular, the response of a semicylindrical alluvial valley in a homogeneous halfspace to incident antiplane SH waves is considered to determine the accuracy and convergence of the numerical procedure. Numerical results are obtained from several combinations of the incidence angle, frequency of excitation, and relative stiffness between the inclusion and the surrounding halfspace. The results tend to confirm the theoretical estimates that the convergence is of the order H(2) for the piecewise linear elements used. It was also observed that the accuracy descreases as the frequency of excitation increases or as the relative stiffness of the inclusion decreases.

Flutter: A finite element program for aerodynamic instability analysis of general shells of revolution with thermal prestress

NASA Technical Reports Server (NTRS)

Fallon, D. J.; Thornton, E. A.

1983-01-01

Documentation for the computer program FLUTTER is presented. The theory of aerodynamic instability with thermal prestress is discussed. Theoretical aspects of the finite element matrices required in the aerodynamic instability analysis are also discussed. General organization of the computer program is explained, and instructions are then presented for the execution of the program.

Convergence rates for finite element problems with singularities. Part 1: Antiplane shear. [crack

NASA Technical Reports Server (NTRS)

Plunkett, R.

1980-01-01

The problem of a finite crack in an infinite medium under antiplane shear load is considered. It is shown that the nodal forces at the tip of the crack accurately gives the order of singularity, that n energy release methods can give the strength to better than 1 percent with element size 1/10 the crack length, and that nodal forces give a much better estimate of the stress field than do the elements themselves. The finite element formulation and the factoring of tridiagonal matrices are discussed.

DYCAST: A finite element program for the crash analysis of structures

NASA Technical Reports Server (NTRS)

Pifko, A. B.; Winter, R.; Ogilvie, P.

1987-01-01

DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors.

Vibroacoustic Model Validation for a Curved Honeycomb Composite Panel

NASA Technical Reports Server (NTRS)

Buehrle, Ralph D.; Robinson, Jay H.; Grosveld, Ferdinand W.

2001-01-01

Finite element and boundary element models are developed to investigate the vibroacoustic response of a curved honeycomb composite sidewall panel. Results from vibroacoustic tests conducted in the NASA Langley Structural Acoustic Loads and Transmission facility are used to validate the numerical predictions. The sidewall panel is constructed from a flexible honeycomb core sandwiched between carbon fiber reinforced composite laminate face sheets. This type of construction is being used in the development of an all-composite aircraft fuselage. In contrast to conventional rib-stiffened aircraft fuselage structures, the composite panel has nominally uniform thickness resulting in a uniform distribution of mass and stiffness. Due to differences in the mass and stiffness distribution, the noise transmission mechanisms for the composite panel are expected to be substantially different from those of a conventional rib-stiffened structure. The development of accurate vibroacoustic models will aide in the understanding of the dominant noise transmission mechanisms and enable optimization studies to be performed that will determine the most beneficial noise control treatments. Finite element and boundary element models of the sidewall panel are described. Vibroacoustic response predictions are presented for forced vibration input and the results are compared with experimental data.

Teaching Fourier optics through ray matrices

NASA Astrophysics Data System (ADS)

Moreno, I.; Sánchez-López, M. M.; Ferreira, C.; Davis, J. A.; Mateos, F.

2005-03-01

In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics.

Finite Element Analysis of Single Cell Stiffness Measurements Using PZT-Integrated Buckling Nanoneedles

PubMed Central

Rad, Maryam Alsadat; Tijjani, Auwal Shehu; Ahmad, Mohd Ridzuan; Auwal, Shehu Muhammad

2016-01-01

This paper proposes a new technique for real-time single cell stiffness measurement using lead zirconate titanate (PZT)-integrated buckling nanoneedles. The PZT and the buckling part of the nanoneedle have been modelled and validated using the ABAQUS software. The two parts are integrated together to function as a single unit. After calibration, the stiffness, Young’s modulus, Poisson’s ratio and sensitivity of the PZT-integrated buckling nanoneedle have been determined to be 0.7100 N·m−1, 123.4700 GPa, 0.3000 and 0.0693 V·m·N−1, respectively. Three Saccharomyces cerevisiae cells have been modelled and validated based on compression tests. The average global stiffness and Young’s modulus of the cells are determined to be 10.8867 ± 0.0094 N·m−1 and 110.7033 ± 0.0081 MPa, respectively. The nanoneedle and the cell have been assembled to measure the local stiffness of the single Saccharomyces cerevisiae cells The local stiffness, Young’s modulus and PZT output voltage of the three different size Saccharomyces cerevisiae have been determined at different environmental conditions. We investigated that, at low temperature the stiffness value is low to adapt to the change in the environmental condition. As a result, Saccharomyces cerevisiae becomes vulnerable to viral and bacterial attacks. Therefore, the proposed technique will serve as a quick and accurate process to diagnose diseases at early stage in a cell for effective treatment. PMID:28025571

Deformation Analysis of RC Ties Externally Strengthened with FRP Sheets

NASA Astrophysics Data System (ADS)

Gribniak, V.; Arnautov, A. K.; Kaklauskas, G.; Jakstaite, R.; Tamulenas, V.; Gudonis, E.

2014-11-01

The current study has two objectives: to validate the ability of the Atena finite-element software to estimate the deformations of reinforced concrete (RC) elements strengthened with fiber-reinforced polymer (FRP) sheets and to assess the effect of FRP-to-concrete bond strength on the results of numerical simulation. It is shown that the bond strength has to be selected according to the overall stiffness of the composite element. The numerical results found are corroborated experimentally by tensile tests of RC elements strengthened with basalt FRP sheets.

Composite alginate gels for tunable cellular microenvironment mechanics

NASA Astrophysics Data System (ADS)

Khavari, Adele; Nydén, Magnus; Weitz, David A.; Ehrlicher, Allen J.

2016-08-01

The mechanics of the cellular microenvironment can be as critical as biochemistry in directing cell behavior. Many commonly utilized materials derived from extra-cellular-matrix create excellent scaffolds for cell growth, however, evaluating the relative mechanical and biochemical effects independently in 3D environments has been difficult in frequently used biopolymer matrices. Here we present 3D sodium alginate hydrogel microenvironments over a physiological range of stiffness (E = 1.85 to 5.29 kPa), with and without RGD binding sites or collagen fibers. We use confocal microscopy to measure the growth of multi-cellular aggregates (MCAs), of increasing metastatic potential in different elastic moduli of hydrogels, with and without binding factors. We find that the hydrogel stiffness regulates the growth and morphology of these cell clusters; MCAs grow larger and faster in the more rigid environments similar to cancerous breast tissue (E = 4-12 kPa) as compared to healthy tissue (E = 0.4-2 kpa). Adding binding factors from collagen and RGD peptides increases growth rates, and change maximum MCA sizes. These findings demonstrate the utility of these independently tunable mechanical/biochemistry gels, and that mechanical confinement in stiffer microenvironments may increase cell proliferation.

Index Cohesive Force Analysis Reveals That the US Market Became Prone to Systemic Collapses Since 2002

PubMed Central

Kenett, Dror Y.; Shapira, Yoash; Madi, Asaf; Bransburg-Zabary, Sharron; Gur-Gershgoren, Gitit; Ben-Jacob, Eshel

2011-01-01

Background The 2007–2009 financial crisis, and its fallout, has strongly emphasized the need to define new ways and measures to study and assess the stock market dynamics. Methodology/Principal Findings The S&P500 dynamics during 4/1999–4/2010 is investigated in terms of the index cohesive force (ICF - the balance between the stock correlations and the partial correlations after subtraction of the index contribution), and the Eigenvalue entropy of the stock correlation matrices. We found a rapid market transition at the end of 2001 from a flexible state of low ICF into a stiff (nonflexible) state of high ICF that is prone to market systemic collapses. The stiff state is also marked by strong effect of the market index on the stock-stock correlations as well as bursts of high stock correlations reminiscence of epileptic brain activity. Conclusions/Significance The market dynamical states, stability and transition between economic states was studies using new quantitative measures. Doing so shed new light on the origin and nature of the current crisis. The new approach is likely to be applicable to other classes of complex systems from gene networks to the human brain. PMID:21556323

Development of procedures for calculating stiffness and damping properties of elastomers in engineering applications. Part 4: Testing of elastomers under a rotating load. [resonance testing

NASA Technical Reports Server (NTRS)

Darlow, M. S.; Smalley, A. J.

1977-01-01

A test rig designed to measure stiffness and damping of elastomer cartridges under a rotating load excitation is described. The test rig employs rotating unbalance in a rotor which runs to 60,000 RPM as the excitation mechanism. A variable resonant mass is supported on elastomer elements and the dynamic characteristics are determined from measurements of input and output acceleration. Five different cartridges are considered: three of these are buttons cartridges having buttons located in pairs, with 120 between each pair. Two of the cartridges consist of 360 elastomer rings with rectangular cross-sections. Dynamic stiffness and damping are measured for each cartridge and compared with predictions at different frequencies and different strains.

Effect of damage on elastically tailored composite laminates

NASA Technical Reports Server (NTRS)

Armanios, Erian; Badir, Ashraf; Berdichevsky, Victor

1991-01-01

A variationally consistent theory is derived in order to predict the response of anisotropic thin-walled closed sections subjected to axial load, torsion and bending. The theory is valid for arbitrary cross-sections made of laminated composite materials with variable thickness and stiffness. Closed form expressions for the stiffness coefficients are provided as integrals in terms of lay-ups parameters and cross-sectional geometry. A comparison of stiffness coefficients and response with finite element predictions and a closed form solution is performed. The theory is applied to the investigation of the effect of damage on the extension-twist coupling in a thin-walled closed section beam. The damage is simulated as a progressive ply-by-ply failure. Results show that damage can have a significant effect on the extension-twist coupling.

Development of a method for fabricating polypropylene non-articulated dorsiflexion assist ankle foot orthoses with predetermined stiffness.

PubMed

Ramsey, Jason Allan

2011-03-01

A non-articulated plantarflexion resist ankle foot orthosis (AFO), commonly known as a posterior leaf spring AFO, is indicated for patients with motor impairment to the dorsiflexors. The AFO is often custom molded to a patient's lower limb anatomy and fabricated from polypropylene. There are no established guidelines for fabricating this type of AFO with predetermined stiffness of the ankle region for normal walking speeds. Therefore an AFO may not meet the biomechanical needs of the patient. Quantify the biomechanical ankle stiffness requirement for an individual with complete dorsiflexor impairment and develop a method for fabricating an AFO with ankle stiffness to meet that requirement. Experimental, bench research. The literature on sagittal biomechanics of non-pathological adults was reviewed to derive the stiffness of the ankle during loading response. Computer models of 144 AFOs were created with geometric variations to account for differences in human anthropometrics. Computer-based finite element analysis was employed to determine the stiffness and safety factor of the models. Stiffness of the AFOs ranged from 0.04 to 1.8 Nm/deg. This ample range is expected to account for the stiffness required for most adults with complete dorsiflexor impairment. At 5° deflection the factor of safety (ratio of strength to stress) ranged from 2.8 to 9.1. A computer program was generated that computes AFO stiffness from user-input variables of AFO geometry. The stiffness is compared to a theoretically appropriate stiffness based on the patient mass. The geometric variables can be modified until there is a close match, resulting in AFO design specification that is appropriate for the patient. Through validation on human subjects, this method may benefit patient outcomes in clinical practice by avoiding the current uncertainty surrounding AFO performance and reducing the labor and time involved in rectifying a custom AFO post-fabrication. This method provides an avenue for improving patient outcomes by avoiding the current uncertainty surrounding non-articulated plantarflexion resist ankle foot orthosis performance. The ability to quantify the biomechanical ankle stiffness requirement for an individual with complete dorsiflexor impairment provides insight into how other AFO types should be designed as well.

A direct correlation of x-ray diffraction orientation distributions to the in-plane stiffness of semi-crystalline organic semiconducting films

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Bingxiao; Awartani, Omar; O'Connor, Brendan

2016-05-02

Large charge mobilities of semi-crystalline organic semiconducting films could be obtained by mechanically aligning the material phases of the film with the loading axis. A key element is to utilize the inherent stiffness of the material for optimal or desired alignment. However, experimentally determining the moduli of semi-crystalline organic thin films for different loading directions is difficult, if not impossible, due to film thickness and material anisotropy. In this paper, we address these challenges by presenting an approach based on combining a composite mechanics stiffness orientation formulation with a Gaussian statistical distribution to directly estimate the in-plane stiffness (transverse isotropy)more » of aligned semi-crystalline polymer films based on crystalline orientation distributions obtained by X-ray diffraction experimentally at different applied strains. Our predicted results indicate that the in-plane stiffness of an annealing film was initially isotropic, and then it evolved to transverse isotropy with increasing mechanical strains. This study underscores the significance of accounting for the crystalline orientation distributions of the film to obtain an accurate understanding and prediction of the elastic anisotropy of semi-crystalline polymer films.« less

Modeling and dynamic properties of dual-chamber solid and liquid mixture vibration isolator

NASA Astrophysics Data System (ADS)

Li, F. S.; Chen, Q.; Zhou, J. H.

2016-07-01

The dual-chamber solid and liquid mixture (SALiM) vibration isolator, mainly proposed for vibration isolation of heavy machines with low frequency, consists of four principle parts: SALiM working media including elastic elements and incompressible oil, multi-layers bellows container, rigid reservoir and the oil tube connecting the two vessels. The isolation system under study is governed by a two-degrees-of-freedom (2-DOF) nonlinear equation including quadratic damping. Simplifying the nonlinear damping into viscous damping, the equivalent stiffness and damping model is derived from the equation for the response amplitude. Theoretical analysis and numerical simulation reveal that the isolator's stiffness and damping have multiple properties with different parameters, among which the effects of exciting frequency, vibrating amplitude, quadratic damping coefficient and equivalent stiffness of the two chambers on the isolator's dynamics are discussed in depth. Based on the boundary characteristics of stiffness and damping and the main causes for stiffness hardening effect, improvement strategies are proposed to obtain better dynamic properties. At last, experiments were implemented and the test results were generally consistent with the theoretical ones, which verified the reliability of the nonlinear dynamic model.

Interfacial contact stiffness of fractal rough surfaces.

PubMed

Zhang, Dayi; Xia, Ying; Scarpa, Fabrizio; Hong, Jie; Ma, Yanhong

2017-10-09

In this work we describe a theoretical model that predicts the interfacial contact stiffness of fractal rough surfaces by considering the effects of elastic and plastic deformations of the fractal asperities. We also develop an original test rig that simulates dovetail joints for turbo machinery blades, which can fine tune the normal contact load existing between the contacting surfaces of the blade root. The interfacial contact stiffness is obtained through an inverse identification method in which finite element simulations are fitted to the experimental results. Excellent agreement is observed between the contact stiffness predicted by the theoretical model and by the analogous experimental results. We demonstrate that the contact stiffness is a power law function of the normal contact load with an exponent α within the whole range of fractal dimension D(1 < D < 2). We also show that for 1 < D < 1.5 the Pohrt-Popov behavior (α = 1/(3 - D)) is valid, however for 1.5 < D < 2, the exponent α is different and equal to 2(D - 1)/D. The diversity between the model developed in the work and the Pohrt-Popov one is explained in detail.

Effects of tooth profile modification on dynamic responses of a high speed gear-rotor-bearing system

NASA Astrophysics Data System (ADS)

Hu, Zehua; Tang, Jinyuan; Zhong, Jue; Chen, Siyu; Yan, Haiyan

2016-08-01

A finite element node dynamic model of a high speed gear-rotor-bearing system considering the time-varying mesh stiffness, backlash, gyroscopic effect and transmission error excitation is developed. Different tooth profile modifications are introduced into the gear pair and corresponding time-varying mesh stiffness curves are obtained. Effects of the tooth profile modification on mesh stiffness are analyzed, and the natural frequencies and mode shapes of the gear-rotor-bearing transmission system are given. The dynamic responses with respect to a wide input speed region including dynamic factor, vibration amplitude near the bearing and dynamic transmission error are obtained by introducing the time-varying mesh stiffness in different tooth profile modification cases into the gear-rotor-bearing dynamic system. Effects of the tooth profile modification on the dynamic responses are studied in detail. The numerical simulation results show that both the short profile modification and the long profile modification can affect the mutation of the mesh stiffness when the number of engaging tooth pairs changes. A short profile modification with an appropriate modification amount can improve the dynamic property of the system in certain work condition.

Analysis of stiffness and stress in I-bar clasps.

PubMed

Sato, Y; Tsuga, K; Abe, Y; Asahara, S; Akagawa, Y

2001-06-01

An I-bar clasp is one of the most popular direct retainers for distal-extension removable partial dentures. However, no adequate information is available on the shape associated with biomechanics. This study aimed (1) to establish a three-dimensional (3D) finite-element modelling method of I-bar clasps, and (2) to clarify the effect of the shape on the stress and stiffness of I-bar clasps. 3D computer models of I-bar clasps were created with vertical and horizontal straight sections connected with a curved section with six parameters: thickness of the clasp tip (T), width of the clasp tip (W), radius of the curvature (R), horizontal distance between the base and the vertical axis (H), vertical dimension between the tip and the horizontal axis (V), taper (change of width per unit length along the axis)(Tp). Stress decreased as T, W, R and Tp increased, and as V decreased. Stiffness (which is proportional to retention) increased as T, W, R and Tp increased, and as H and V decreased. In both stress and stiffness, the effects of T and Tp were especially large. From the results, a systematic formula between the clasp shape and the stiffness was derived.

Matrix Rigidity Regulates Cancer Cell Growth by Modulating Cellular Metabolism and Protein Synthesis

PubMed Central

Tilghman, Robert W.; Blais, Edik M.; Cowan, Catharine R.; Sherman, Nicholas E.; Grigera, Pablo R.; Jeffery, Erin D.; Fox, Jay W.; Blackman, Brett R.; Tschumperlin, Daniel J.; Papin, Jason A.; Parsons, J. Thomas

2012-01-01

Background Tumor cells in vivo encounter diverse types of microenvironments both at the site of the primary tumor and at sites of distant metastases. Understanding how the various mechanical properties of these microenvironments affect the biology of tumor cells during disease progression is critical in identifying molecular targets for cancer therapy. Methodology/Principal Findings This study uses flexible polyacrylamide gels as substrates for cell growth in conjunction with a novel proteomic approach to identify the properties of rigidity-dependent cancer cell lines that contribute to their differential growth on soft and rigid substrates. Compared to cells growing on more rigid/stiff substrates (>10,000 Pa), cells on soft substrates (150–300 Pa) exhibited a longer cell cycle, due predominantly to an extension of the G1 phase of the cell cycle, and were metabolically less active, showing decreased levels of intracellular ATP and a marked reduction in protein synthesis. Using stable isotope labeling of amino acids in culture (SILAC) and mass spectrometry, we measured the rates of protein synthesis of over 1200 cellular proteins under growth conditions on soft and rigid/stiff substrates. We identified cellular proteins whose syntheses were either preferentially inhibited or preserved on soft matrices. The former category included proteins that regulate cytoskeletal structures (e.g., tubulins) and glycolysis (e.g., phosphofructokinase-1), whereas the latter category included proteins that regulate key metabolic pathways required for survival, e.g., nicotinamide phosphoribosyltransferase, a regulator of the NAD salvage pathway. Conclusions/Significance The cellular properties of rigidity-dependent cancer cells growing on soft matrices are reminiscent of the properties of dormant cancer cells, e.g., slow growth rate and reduced metabolism. We suggest that the use of relatively soft gels as cell culture substrates would allow molecular pathways to be studied under conditions that reflect the different mechanical environments encountered by cancer cells upon metastasis to distant sites. PMID:22623999

Biomechanical characteristics of fixation methods for floating pubic symphysis.

PubMed

Song, Wenhao; Zhou, Dongsheng; He, Yu

2017-03-07

Floating pubic symphysis (FPS) is a relatively rare injury caused by high-energy mechanisms. There are several fixation methods used to treat FPS, including external fixation, subcutaneous fixation, internal fixation, and percutaneous cannulated screw fixation. To choose the appropriate fixation, it is necessary to study the biomechanical performance of these different methods. The goal of this study was to compare the biomechanical characteristics of six methods by finite element analysis. A three-dimensional finite element model of FPS was simulated. Six methods were used in the FPS model, including external fixation (Ext), subcutaneous rod fixation (Sub-rod), subcutaneous plate fixation (Sub-plate), superior pectineal plate fixation (Int-sup), infrapectineal plate fixation (Int-ifa), and cannulated screw fixation (Int-scr). Compressive and rotational loads were then applied in all models. Biomechanical characteristics that were recorded and analyzed included construct stiffness, micromotion of the fracture gaps, von Mises stress, and stress distribution. The construct stiffness of the anterior pelvic ring was decreased dramatically when FPS occurred. Compressive stiffness was restored by the three internal fixation and Sub-rod methods. Unfortunately, rotational stiffness was not restored satisfactorily by the six methods. For micromotion of the fracture gaps, the displacement was reduced significantly by the Int-sup and Int-ifa methods under compression. The internal fixation methods and Sub-plate method performed well under rotation. The maximum von Mises stress of the implants was not large. For the plate-screw system, the maximum von Mises stress occurred over the region of the fracture and plate-screw joints. The maximum von Mises stress appeared on the rod-screw and screw-bone interfaces for the rod-screw system. The present study showed the biomechanical advantages of internal fixation methods for FPS from a finite element view. Superior stabilization of the anterior pelvic ring and fracture gaps was obtained by internal fixation. Subcutaneous fixation had satisfactory outcomes as well. Sub-rod fixation offered good anti-compression, while the Sub-plate fixation provided favorable anti-rotational capacity.

Pelvic modelling and the comparison between plate position for double pelvic osteotomy using artificial cancellous bone and finite element analysis.

PubMed

McCartney, William; MacDonald, Bryan; Ober, Ciprian Andrei; Lostado-Lorza, Rubén; Gómez, Fátima Somovilla

2018-03-20

Finite element analysis was used to compare fixation methods for double pelvic osteotomy (DPO). Using 3D scanning a stereolithography (stl) image was produced of a canine pelvis and this was subsequently refined in computer aided design (CAD). Using the CAD files, the images were imported in MSC Marc software to produce a working finite element (FE) model with 3 dimensional tetrahedral elements with linear shaped functions. The dimensions of a precontoured pelvic osteotomy plate with eight screws and a twisted seven screw straight plate were used to build the 2 fixations implants for the FE models. An equivalent load of 300 N was applied progressively on all FE models in order to facilitate its convergence. The load was applied in a distributed manner on the femur-hip joint contact area in order to simulate the actual behavior of the joint. The aim of the present study was to analyze the difference in stiffness and behavior under loading between a lateral vs ventral plate fixation, with unlocked screws and different gap scenarios, for stabilization of a pelvic osteotomy using finite element analysis. From both configurations the maximum displacement of the ventral plate with 7 screws without gap had a value of 1.988 mm, while in the DPO plate had a maximum displacement of 2.191 mm. The load applied for each of the different configurations studied when a gap of 1° was considered and also when a condition of no gap was considered. The ventral plate was stiffer than the lateral plate when a gap was not present. When the gap was closed in the ventral plate, the stiffness increased until a point that remained constant. Ventral plate fixation can be as or more stiff as lateral plate fixation and provides flexible fixation. This behavior should reduce screw loosening. Using ventral plate fixation is recommended to reduce screw loosening or failure.

[Establishment and validation of normal human L1-L5 lumbar three-dimensional finite element model].

PubMed

Zhu, Zhenqi; Liu, Chenjun; Wang, Jiefu; Wang, Kaifeng; Huang, Zhixin; Wang, Weida; Liu, Haiying

2014-10-14

To create and validate a L1-L5 lumbar three-dimensional finite element model. The L1-L5 lumbar spines of a male healthy volunteer were scanned with computed tomography (CT). And a L1-L5 lumbar three-dimensional finite element model was created with the aid of software packages of Mimics, Geomagic and Ansys. Then border conditions were set, unit type was determined, finite element mesh was divided and a model was established for loading and calculating. Average model stiffness under the conditions of flexion, extension, lateral bending and axial rotation was calculated and compared with the outcomes of former articles for validation. A normal human L1-L5 lumbar three-dimensional finite element model was established to include 459 340 elements and 661 938 nodes. After constraining the inferior endplate of L5 vertebral body, 500 kg × m × s⁻² compressive loading was imposed averagely on the superior endplate of L1 vertebral body. Then 10 kg × m² × s⁻² moment simulating flexion, extension, lateral bending and axial rotation were imposed on the superior endplate of L1 vertebral body. Eventually the average stiffness of all directions was calculated and it was similar to the outcomes of former articles. The L1-L5 lumbar three-dimensional finite element model is validated so that it may used with biomechanical simulation and analysis of normal or surgical models.

Vibrations of a thin cylindrical shell stiffened by rings with various stiffness

NASA Astrophysics Data System (ADS)

Nesterchuk, G. A.

2018-05-01

The problem of vibrations of a thin-walled elastic cylindrical shell reinforced by frames of different rigidity is investigated. The solution for the case of the clamped shell edges was obtained by asymptotic methods and refined by the finite element method. Rings with zero eccentricity and stiffness varying along the generatrix of the shell cylinder are considered. Varying the optimal coefficients of the distribution functions of the rigidity of the frames and finding more precise parameters makes it possible to find correction factors for analytical formulas of approximate calculation.

On optimization of a composite bone plate using the selective stress shielding approach.

PubMed

Samiezadeh, Saeid; Tavakkoli Avval, Pouria; Fawaz, Zouheir; Bougherara, Habiba

2015-02-01

Bone fracture plates are used to stabilize fractures while allowing for adequate compressive force on the fracture ends. Yet the high stiffness of conventional bone plates significantly reduces compression at the fracture site, and can lead to subsequent bone loss upon healing. Fibre-reinforced composite bone plates have been introduced to address this drawback. However, no studies have optimized their configurations to fulfill the requirements of proper healing. In the present study, classical laminate theory and the finite element method were employed for optimization of a composite bone plate. A hybrid composite made of carbon fibre/epoxy with a flax/epoxy core, which was introduced previously, was optimized by varying the laminate stacking sequence and the contribution of each material, in order to minimize the axial stiffness and maximize the torsional stiffness for a given range of bending stiffness. The initial 14×4(14) possible configurations were reduced to 13 after applying various design criteria. A comprehensive finite element model, validated against a previous experimental study, was used to evaluate the mechanical performance of each composite configuration in terms of its fracture stability, load sharing, and strength in transverse and oblique Vancouver B1 fracture configurations at immediately post-operative, post-operative, and healed bone stages. It was found that a carbon fibre/epoxy plate with an axial stiffness of 4.6 MN, and bending and torsional stiffness of 13 and 14 N·m(2), respectively, showed an overall superiority compared with other laminate configurations. It increased the compressive force at the fracture site up to 14% when compared to a conventional metallic plate, and maintained fracture stability by ensuring the fracture fragments' relative motions were comparable to those found during metallic plate fixation. The healed stage results revealed that implantation of the titanium plate caused a 40.3% reduction in bone stiffness, while the composite plate lowered the stiffness by 32.9% as compared to the intact femur. This study proposed a number of guidelines for the design of composite bone plates. The findings suggest that a composite bone plate could be customized to allow for moderate compressive force on the fracture ends, while remaining relatively rigid in bending and torsion and strong enough to withstand external loads when a fracture gap is present. The results indicate that the proposed composite bone plate could be a potential candidate for bone fracture plate applications. Copyright © 2014 Elsevier Ltd. All rights reserved.

Advance finite element modeling of rotor blade aeroelasticity

NASA Technical Reports Server (NTRS)

Straub, F. K.; Sangha, K. B.; Panda, B.

1994-01-01

An advanced beam finite element has been developed for modeling rotor blade dynamics and aeroelasticity. This element is part of the Element Library of the Second Generation Comprehensive Helicopter Analysis System (2GCHAS). The element allows modeling of arbitrary rotor systems, including bearingless rotors. It accounts for moderately large elastic deflections, anisotropic properties, large frame motion for maneuver simulation, and allows for variable order shape functions. The effects of gravity, mechanically applied and aerodynamic loads are included. All kinematic quantities required to compute airloads are provided. In this paper, the fundamental assumptions and derivation of the element matrices are presented. Numerical results are shown to verify the formulation and illustrate several features of the element.

Activated phosphors having matrices of yttrium-transition metal compound

DOEpatents

De Kalb, E.L.; Fassel, V.A.

1975-07-01

A method is described for preparing a phosphor composition containing a lanthanide activator element with a host matrix having a transition element as a major component. The host matrix is composed of certain rare earth phosphates or vanadates such as YPO$sub 4$ with a portion of the rare earth replaced with one or more of the transition elements. On x-ray or other electromagnetic excitation, trace lanthanide impurities or additives within the phosphor are spectrometrically determined from their characteristic luminescence. (auth)

Piezoelectrically tunable resonance frequency beam utilizing a stress-sensitive film

DOEpatents

Thundat, Thomas G.; Wachter, Eric A.

2002-01-01

Methods and apparatus for detecting particular frequencies of acoustic vibration utilize a piezoelectrically-tunable beam element having a piezoelectric layer and a stress sensitive layer and means for providing an electrical potential across the piezoelectric layer to controllably change the beam's stiffness and thereby change its resonance frequency. It is then determined from the response of the piezoelectrically-tunable beam element to the acoustical vibration to which the beam element is exposed whether or not a particular frequency or frequencies of acoustic vibration are detected.

Incorporating general race and housing flexibility and deadband in rolling element bearing analysis

NASA Technical Reports Server (NTRS)

Davis, R. R.; Vallance, C. S.

1989-01-01

Methods for including the effects of general race and housing compliance and outer race-to-housing deadband (clearance) in rolling element bearing mechanics analysis is presented. It is shown that these effects can cause significant changes in bearing stiffness characteristics, which are of major importance in rotordynamic response of turbomachinery and other rotating systems. Preloading analysis is demonstrated with the finite element/contact mechanics hybrid method applied to a 45 mm angular contact ball bearing.

Development of Finite Elements for Two-Dimensional Structural Analysis Using the Integrated Force Method

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Patnaik, Surya N.; Hopkins, Dale A.

1996-01-01

The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

The influence of matrix composition and reinforcement type on the properties of polysialate composites

NASA Astrophysics Data System (ADS)

Hammell, James A.

There is a critical need for the development of materials for eliminating fire as a cause of death in aircraft accidents. Currently available composites that use organic matrices not only deteriorate at temperatures above 300°C but also emit toxic fumes. The results presented in this dissertation focus on the development of an inorganic matrix that does not burn or emit toxic fumes. The matrix, known as polysialate, can withstand temperatures in excess of 1000°C. The matrix behaves like a ceramic, but does not need high curing temperatures, so it can be processed like many common organic matrices. The major parameters evaluated in this dissertation are: (i) Influence of reinforcement type, (ii) Matrix formulation for both wet-dry durability and high temperature resistance, (iii) Influence of processing variables such as moisture reduction and storage, (iv) Tensile strain capacity of modified matrices and matrices reinforced with ceramic microfibers and discrete carbon fibers, and (v) analytical modeling of mechanical properties. For the reinforcement type; carbon, glass, and stainless steel wire fabrics were investigated. Carbon fabrics with 1, 3, 12, and 50k tows were used. A matrix chemical formulation that can withstand wetting and drying was developed. This formulation was tested at high temperatures to ascertain its stability above 400°C. On the topic of processing, shelf life of prepregged fabric layers and efficient moisture removal methods were studied. An analytical model based on layered reinforcement was developed for analyzing flexural specimens. It is shown that the new inorganic matrix can withstand wetting and drying, and also high temperature. The layered reinforcement concept provides accurate prediction of strength and stiffness for composites reinforced with 1k and 3k tows. The prepregged fabric layers can be stored for 14 days at -15°C without losing strength.

Modeling spanwise nonuniformity in the cross-sectional analysis of composite beams

NASA Astrophysics Data System (ADS)

Ho, Jimmy Cheng-Chung

Spanwise nonuniformity effects are modeled in the cross-sectional analysis of beam theory. This modeling adheres to an established numerical framework on cross-sectional analysis of uniform beams with arbitrary cross-sections. This framework is based on two concepts: decomposition of the rotation tensor and the variational-asymptotic method. Allowance of arbitrary materials and geometries in the cross-section is from discretization of the warping field by finite elements. By this approach, dimensional reduction from three-dimensional elasticity is performed rigorously and the sectional strain energy is derived to be asymptotically-correct. Elastic stiffness matrices are derived for inputs into the global beam analysis. Recovery relations for the displacement, stress, and strain fields are also derived with care to be consistent with the energy. Spanwise nonuniformity effects appear in the form of pointwise and sectionwise derivatives, which are approximated by finite differences. The formulation also accounts for the effects of spanwise variations in initial twist and/or curvature. A linearly tapered isotropic strip is analyzed to demonstrate spanwise nonuniformity effects on the cross-sectional analysis. The analysis is performed analytically by the variational-asymptotic method. Results from beam theory are validated against solutions from plane stress elasticity. These results demonstrate that spanwise nonuniformity effects become significant as the rate at which the cross-sections vary increases. The modeling of transverse shear modes of deformation is accomplished by transforming the strain energy into generalized Timoshenko form. Approximations in this transformation procedure from previous works, when applied to uniform beams, are identified. The approximations are not used in the present work so as to retain more accuracy. Comparison of present results with those previously published shows that these approximations sometimes change the results measurably and thus are inappropriate. Static and dynamic results, from the global beam analysis, are calculated to show the differences between using stiffness constants from previous works and the present work. As a form of validation of the transformation procedure, calculations from the global beam analysis of initially twisted isotropic beams from using curvilinear coordinate axes featuring twist are shown to be equivalent to calculations using Cartesian coordinates.

Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method.

PubMed

Gómez, Fátima Somovilla; Lorza, Rubén Lostado; Bobadilla, Marina Corral; García, Rubén Escribano

2017-09-21

The kinematic behavior of models that are based on the finite element method (FEM) for modeling the human body depends greatly on an accurate estimate of the parameters that define such models. This task is complex, and any small difference between the actual biomaterial model and the simulation model based on FEM can be amplified enormously in the presence of nonlinearities. The current paper attempts to demonstrate how a combination of the FEM and the MRS methods with desirability functions can be used to obtain the material parameters that are most appropriate for use in defining the behavior of Finite Element (FE) models of the healthy human lumbar intervertebral disc (IVD). The FE model parameters were adjusted on the basis of experimental data from selected standard tests (compression, flexion, extension, shear, lateral bending, and torsion) and were developed as follows: First, three-dimensional parameterized FE models were generated on the basis of the mentioned standard tests. Then, 11 parameters were selected to define the proposed parameterized FE models. For each of the standard tests, regression models were generated using MRS to model the six stiffness and nine bulges of the healthy IVD models that were created by changing the parameters of the FE models. The optimal combination of the 11 parameters was based on three different adjustment criteria. The latter, in turn, were based on the combination of stiffness and bulges that were obtained from the standard test FE simulations. The first adjustment criteria considered stiffness and bulges to be equally important in the adjustment of FE model parameters. The second adjustment criteria considered stiffness as most important, whereas the third considered the bulges to be most important. The proposed adjustment methods were applied to a medium-sized human IVD that corresponded to the L3-L4 lumbar level with standard dimensions of width = 50 mm, depth = 35 mm, and height = 10 mm. Agreement between the kinematic behavior that was obtained with the optimized parameters and that obtained from the literature demonstrated that the proposed method is a powerful tool with which to adjust healthy IVD FE models when there are many parameters, stiffnesses, and bulges to which the models must adjust.

Investigations of the effects of particle properties on the wear resistance of the particle reinforced composites using a novel wear model

NASA Astrophysics Data System (ADS)

Prabhu, T. Ram

2016-08-01

A wear model is developed based on the discrete lattice spring-mass approach to study the effects of particle volume fraction, size, and stiffness on the wear resistance of particle reinforced composites. To study these effects, we have considered three volume fractions (10%, 20% and 30%), two sizes (10 × 10 and 4 × 4 sites), and two different stiffness of particles embedded in the matrix in a regular pattern. In this model, we have discretized the composite system (400 × 100 sites) into the lumped masses connected with interaction spring elements in two dimensions. The interaction elements are assumed as linear elastic and ideal plastic under applied forces. Each mass is connected to its first and second nearest neighbors by springs. The matrix and particles sites are differentiated by choosing the different stiffness values. The counter surface is simulated as a rigid body that moves on the composite material at a constant sliding speed along the horizontal direction. The governing equations are formed by equating the spring force between the pair of sites given by Hooke’s law plus external contact forces and the force due to the motion of the site given by the equation of motion. The equations are solved for the plastic strain accumulated in the springs using an explicit time stepping procedure based on a finite difference form of the above equations. If the total strain accumulated in the spring elements connected to a lump mass site exceeds the failure strain, the springs are considered to be broken, and the mass site is removed or worn away from the lattice and accounts as a wear loss. The model predicts that (i) increasing volume fraction, reducing particle size and increasing particle stiffness enhance the wear resistance of the particle reinforced composites, (ii) the particle stiffness is the most significant factor affecting the wear resistance of the composites, and (iii) the wear resistance reduced above the critical volume fraction (Vc), and Vc increases with increasing particle size. Finally, we have qualitatively compared the model results with our previously published experimental results to prove the effectiveness of the model to analysis the complex wear systems.

Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method

PubMed Central

Somovilla Gómez, Fátima

2017-01-01

The kinematic behavior of models that are based on the finite element method (FEM) for modeling the human body depends greatly on an accurate estimate of the parameters that define such models. This task is complex, and any small difference between the actual biomaterial model and the simulation model based on FEM can be amplified enormously in the presence of nonlinearities. The current paper attempts to demonstrate how a combination of the FEM and the MRS methods with desirability functions can be used to obtain the material parameters that are most appropriate for use in defining the behavior of Finite Element (FE) models of the healthy human lumbar intervertebral disc (IVD). The FE model parameters were adjusted on the basis of experimental data from selected standard tests (compression, flexion, extension, shear, lateral bending, and torsion) and were developed as follows: First, three-dimensional parameterized FE models were generated on the basis of the mentioned standard tests. Then, 11 parameters were selected to define the proposed parameterized FE models. For each of the standard tests, regression models were generated using MRS to model the six stiffness and nine bulges of the healthy IVD models that were created by changing the parameters of the FE models. The optimal combination of the 11 parameters was based on three different adjustment criteria. The latter, in turn, were based on the combination of stiffness and bulges that were obtained from the standard test FE simulations. The first adjustment criteria considered stiffness and bulges to be equally important in the adjustment of FE model parameters. The second adjustment criteria considered stiffness as most important, whereas the third considered the bulges to be most important. The proposed adjustment methods were applied to a medium-sized human IVD that corresponded to the L3–L4 lumbar level with standard dimensions of width = 50 mm, depth = 35 mm, and height = 10 mm. Agreement between the kinematic behavior that was obtained with the optimized parameters and that obtained from the literature demonstrated that the proposed method is a powerful tool with which to adjust healthy IVD FE models when there are many parameters, stiffnesses, and bulges to which the models must adjust. PMID:28934161

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

NASA Astrophysics Data System (ADS)

Nadkarni, Neel; Daraio, Chiara; Kochmann, Dennis M.

2014-08-01

We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.

Reduced-order modeling approach for frictional stick-slip behaviors of joint interface

NASA Astrophysics Data System (ADS)

Wang, Dong; Xu, Chao; Fan, Xuanhua; Wan, Qiang

2018-03-01

The complex frictional stick-slip behaviors of mechanical joint interface have a great effect on the dynamic properties of assembled structures. In this paper, a reduced-order modeling approach based on the constitutive Iwan model is proposed to describe the stick-slip behaviors of joint interface. An improved Iwan model is developed to describe the non-zero residual stiffness at macro-slip regime and smooth transition of joint stiffness from micro-slip to macro-slip regime, and the power-law relationship of energy dissipation during the micro-slip regime. In allusion to these nonlinear behaviors, the finite element method is used to calculate the recycle force under monolithic loading and the energy dissipation per cycle under oscillatory loading. The proposed model is then used to predict the nonlinear stick-slip behaviors of joint interface by curve-fitting to the results of finite element analysis, and the results show good agreements with the finite element analysis. A comparison with the experiment results in literature is also made. The proposed model agrees very well with the experiment results.

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Bare laser-synthesized Si nanoparticles as functional elements for chitosan nanofiber-based tissue engineering platforms

NASA Astrophysics Data System (ADS)

Popov, Anton A.; Al-Kattan, Ahmed; Nirwan, Viraj P.; Munnier, Emilie; Tselikov, Gleb I.; Ryabchikov, Yury V.; Chourpa, Igor; Fahmi, Amir; Kabashin, A. V.

2018-02-01

Methods of femtosecond laser ablation were used to fabricate bare (ligand-free) silicon (Si) nanoparticles in deionized water. The nanoparticles were round in shape, crystalline, free of any impurities, and water-dissolvable, while the dissolution rate depended on the concentration of oxygen defects in their composition. The nanoparticles were then eletrospun with chitosan to form nanoparticle decorated nanofibrous matrices. We found that the functionalization of nanofibers by the nanoparticles can affect the morphology and physico-chemical characteristics of resulting nanostructures. In particular, the presence of Si nanoparticles led to the reduction of fibers thickness, suggesting a potential improvement of fiber's surface reactivity. We also observed the improvement of thermal stability of hybrid nanofibers. We believe that the incorporated Si nanoparticles can serve as functional elements to improve characteristics of chitosan-based matrices for cellular growth, as well as to enable novel imaging or therapeutic functionalities for tissue engineering applications.

Electron microprobe mineral analysis guide

NASA Technical Reports Server (NTRS)

Brown, R. W.

1980-01-01

Electron microprobe mineral analysis guide is a compilation of X-ray tables and spectra recorded from various mineral matrices. Spectra were obtained using electron microprobe, equipped with LiF geared, curved crystal X-ray spectrometers, utilizing typical analytical operating conditions: 15 Kv acceleration potential, 0.02 microampere sample current as measured on a clinopyroxene standard (CP19). Tables and spectra are presented for the majority of elements, fluorine through uranium, occurring in mineral samples from lunar, meteoritic and terrestrial sources. Tables for each element contain relevant analytical information, i.e., analyzing crystal, X-ray peak, background and relative intensity information, X-ray interferences and a section containing notes on the measurement. Originally intended to cover silicates and oxide minerals the tables and spectra have been expanded to cover other mineral phases. Electron microprobe mineral analysis guide is intended as a spectral base to which additional spectra can be added as the analyst encounters new mineral matrices.

Scattering matrix elements of biological particles measured in a flow through system: theory and practice.

PubMed

Sloot, P M; Hoekstra, A G; van der Liet, H; Figdor, C G

1989-05-15

Light scattering techniques (including depolarization experiments) applied to biological cells provide a fast nondestructive probe that is very sensitive to small morphological differences. Until now quantitative measurement of these scatter phenomena were only described for particles in suspension. In this paper we discuss the symmetry conditions applicable to the scattering matrices of monodisperse biological cells in a flow cytometer and provide evidence that quantitative measurement of the elements of these scattering matrices is possible in flow through systems. Two fundamental extensions to the theoretical description of conventional scattering experiments are introduced: large cone integration of scattering signals and simultaneous implementation of the localization principle to account for scattering by a sharply focused laser beam. In addition, a specific calibration technique is proposed to account for depolarization effects of the highly specialized optics applied in flow through equipment.

A new mathematical neck model for a low-velocity rear-end impact dummy: evaluation of components influencing head kinematics.

PubMed

Linder, A

2000-03-01

A mathematical model of a new rear-end impact dummy neck was implemented using MADYMO. The main goal was to design a model with a human-like response of the first extension motion in the crash event. The new dummy neck was modelled as a series of rigid bodies (representing the seven cervical vertebrae and the uppermost thoracic element, T1) connected by pin joints, and supplemented by two muscle substitutes. The joints had non-linear stiffness characteristics and the muscle elements possessed both elastic stiffness and damping properties. The new model was compared with two neck models with the same number of vertebrae, but without muscle substitutes. The properties of the muscle substitutes and the need of these were evaluated by using three different modified neck models. The motion of T1 in the simulations was prescribed using displacement data obtained from volunteer tests. In a sensitivity analysis of the mathematical model the influence of different factors on the head-neck kinematics was evaluated. The neck model was validated against kinematics data from volunteer tests: linear displacement, angular displacement, and acceleration of the head relative to the upper torso at 7 km/h velocity change. The response of the new model was within the corridor of the volunteer tests for the main part of the time history plot. This study showed that a combination of elastic stiffness and damping in the muscle substitutes, together with a non-linear joint stiffness, resulted in a head-neck response similar to human volunteers, and superior to that of other tested neck models.

On the Stiffness of the Mesh and Urethral Mobility: A Finite Element Analysis.

PubMed

Brandão, Sofia; Parente, Marco; Da Roza, Thuane Huyer; Silva, Elisabete; Ramos, Isabel Maria; Mascarenhas, Teresa; Natal Jorge, Renato Manuel

2017-08-01

Midurethral slings are used to correct urethral hypermobility in female stress urinary incontinence (SUI), defined as the complaint of involuntary urine leakage when the intra-abdominal pressure (IAP) is increased. Structural and thermal features influence their mechanical properties, which may explain postoperative complications, e.g., erosion and urethral obstruction. We studied the effect of the mesh stiffness on urethral mobility at Valsalva maneuver, under impairment of the supporting structures (levator ani and/or ligaments), by using a numerical model. For that purpose, we modeled a sling with "lower" versus "higher" stiffness and evaluated the mobility of the bladder and urethra, that of the urethrovesical junction (the α-angle), and the force exerted at the fixation of the sling. The effect of impaired levator ani or pubourethral ligaments (PUL) alone on the organs displacement and α-angle opening was similar, showing their important role together on urethral stabilization. When the levator ani and all the ligaments were simulated as impaired, the descent of the bladder and urethra went up to 25.02 mm, that of the bladder neck was 14.57 mm, and the α-angle was 129.7 deg, in the range of what was found in women with SUI. Both meshes allowed returning to normal positioning, although at the cost of higher force exerted by the mesh with higher stiffness (3.4 N against 2.3 N), which can relate to tissue erosion. This finite element analysis allowed mimicking the biomechanical response of the pelvic structures in response to changing a material property of the midurethral synthetic mesh.

Protective Performance of Plate-Cell Rubber Tiles against Childhood Head Injury on Playground Surfaces — A Finite Element Analysis

NASA Astrophysics Data System (ADS)

Chang, Li-Tung; Huang, Tsai-Jeon

Rubber tiles are commonly used in playgrounds as protective surfacing to reduce the incidence of head injuries in children caused by falling from equipment. This study developed a rubber tile model consisting of a surface layer of solid and a base layer of plate-cell and used it to investigate head injury protective performance. An explicit finite element method based on the experimental data was used to simulate head impact on the rubber tile. The peak acceleration and head injury criterion (HIC) were employed to assess the shock-absorbing capability of the tile. The results showed that compared to the peak acceleration, use of the HIC index provided a more conservative assessment of the shock absorption ability, and ultimately the protection against head injuries. This study supports the feasibility of using rubber tile with plate-cell construction to improve shock-absorbing capability. The plate-cell structure provided an excellent cushioning effect via a lower axial shear stiffness of the surface layer and lower transverse shearing stiffness of the core. The core's dimensions were an important parameter in determining the shearing stiffness. The analysis suggested that the cushioning effect would significantly reduce the peak force on the head from a fall and delay the occurrence of the peak value during impact, resulting in a marked reduction in the peak acceleration and HIC values of the head. Two plate-cell constructions with honeycomb and box-like cores were proposed and validated in this study. The better protective ability of the honeycomb core was attributed to its lower transverse shearing stiffness.

Biomechanics of bone-fracture fixation by stiffness-graded plates in comparison with stainless-steel plates

PubMed Central

Ganesh, VK; Ramakrishna, K; Ghista, Dhanjoo N

2005-01-01

Background In the internal fixation of fractured bone by means of bone-plates fastened to the bone on its tensile surface, an on-going concern has been the excessive stress-shielding of the bone by the excessively-stiff stainless-steel plate. The compressive stress-shielding at the fracture-interface immediately after fracture-fixation delays callus formation and bone healing. Likewise, the tensile stress-shielding of the layer of the bone underneath the plate can cause osteoporosis and decrease in tensile strength of this layer. Method In order to address this problem, we propose to use stiffness-graded plates. Accordingly, we have computed (by finite-element analysis) the stress distribution in the fractured bone fixed by composite plates, whose stiffness is graded both longitudinally and transversely. Results It can be seen that the stiffness-graded composite-plates cause less stress-shielding (as an example: at 50% of the healing stage, stress at the fracture interface is compressive in nature i.e. 0.002 GPa for stainless steel plate whereas stiffness graded plates provides tensile stress of 0.002 GPa. This means that stiffness graded plate is allowing the 50% healed bone to participate in loadings). Stiffness-graded plates are more flexible, and hence permit more bending of the fractured bone. This results in higher compressive stresses induced at the fractured faces accelerate bone-healing. On the other hand, away from the fracture interface the reduced stiffness and elastic modulus of the plate causes the neutral axis of the composite structure to be lowered into the bone resulting in the higher tensile stress in the bone-layer underneath the plate, wherein is conducive to the bone preserving its tensile strength. Conclusion Stiffness graded plates (with in-built variable stiffness) are deemed to offer less stress-shielding to the bone, providing higher compressive stress at the fractured interface (to induce accelerated healing) as well as higher tensile stress in the intact portion of the bone (to prevent bone remodeling and osteoporosis). PMID:16045807

Optimal Shakedown of the Thin-Wall Metal Structures Under Strength and Stiffness Constraints

NASA Astrophysics Data System (ADS)

Alawdin, Piotr; Liepa, Liudas

2017-06-01

Classical optimization problems of metal structures confined mainly with 1st class cross-sections. But in practice it is common to use the cross-sections of higher classes. In this paper, a new mathematical model for described shakedown optimization problem for metal structures, which elements are designed from 1st to 4th class cross-sections, under variable quasi-static loads is presented. The features of limited plastic redistribution of forces in the structure with thin-walled elements there are taken into account. Authors assume the elastic-plastic flexural buckling in one plane without lateral torsional buckling behavior of members. Design formulae for Methods 1 and 2 for members are analyzed. Structures stiffness constrains are also incorporated in order to satisfy the limit serviceability state requirements. With the help of mathematical programming theory and extreme principles the structure optimization algorithm is developed and justified with the numerical experiment for the metal plane frames.

Development of 1-m primary mirror for a spaceborne camera

NASA Astrophysics Data System (ADS)

Kihm, Hagyong; Yang, Ho-Soon; Rhee, Hyug-Gyo; Lee, Yun-Woo

2015-09-01

We present the development of a 1-m lightweight mirror system for a spaceborne electro-optical camera. The mirror design was optimized to satisfy the performance requirements under launch loads and space environment. The mirror made of Zerodur® has pockets at the back surface and three square bosses at the rim. Metallic bipod flexures support the mirror at the bosses and adjust the mirror's surface distortion due to gravity. We also show an analytical formulation of the bipod flexure, where compliance and stiffness matrices of the bipod flexure are derived to estimate theoretical performance and to make initial design guidelines. Optomechanical performances such as surface distortions due to gravity is explained. Environmental verification of the mirror is achieved by vibration tests.

A concise guide for the determination of less-studied technology-critical elements (Nb, Ta, Ga, In, Ge, Te) by inductively coupled plasma mass spectrometry in environmental samples

NASA Astrophysics Data System (ADS)

Filella, Montserrat; Rodushkin, Ilia

2018-03-01

There is an increasing demand for analytical techniques able to measure so-called 'technology-critical elements', a set of chemical elements increasingly used in technological applications, in environmental matrices. Nowadays, inductively coupled plasma-mass spectrometry (ICP-MS) has become the technique of choice for measuring trace element concentrations. However, its application is often less straightforward than often assumed. The hints and drawbacks of ICP-MS application to the measurement of a set of less-studied technology-critical elements (Nb, Ta, Ga, In, Ge and Te) is discussed here and concise guidelines given.

An attempt to diagnose cancer by PIXE

NASA Astrophysics Data System (ADS)

Uda, M.; Maeda, K.; Sasa, Y.; Kusuyama, H.; Yokode, Y.

1987-03-01

PIXE is suitable especially for trace elemental analysis for atoms with high atomic numbers, which are contained in matrices composed mainly of light elements such as biological materials. An attempt has been made to distinguish elemental concentrations of cancer tissues from those of normal ones. Kidney, testis and urinary bladder cancer tissues were examined by PIXE. Key elements to diagnose these cancers were Ca, Ti, Cr, Fe and Zn. Enrichment of Fe and Ti, and deficiency of Zn could be seen in the kidney cancer. An opposite tendency was observed in the testicular cancer. Imbalance of these elemental concentrations in characteristic organs might give us a possibility for cancer diagnosis.

Optimisation of support stiffness at railway crossings

NASA Astrophysics Data System (ADS)

Grossoni, Ilaria; Bezin, Yann; Neves, Sergio

2018-07-01

Turnouts are a key element of the railway system. They are also the part of the system with the highest number of degradation modes and associated failures. There are a number of reasons for this, including high dynamic loads resulting from non-uniform rail geometry and track support stiffness. The main aim of this study is to propose a methodology to optimise the pad stiffness along a crossing panel in order to achieve a decrease in the indicators of the most common failure modes. A three-dimensional vehicle/track interaction model has been established, considering a detailed description of the crossing panel support structure. A genetic algorithm has been applied to two main types of constructions, namely direct and indirect fixing, to find the optimum combinations of resilient pad characteristics for various cases of travelling direction, travelling speed and support conditions.

On the micro-indentation of plant cells in a tissue context

NASA Astrophysics Data System (ADS)

Mosca, Gabriella; Sapala, Aleksandra; Strauss, Soeren; Routier-Kierzkowska, Anne-Lise; Smith, Richard S.

2017-02-01

The effect of geometry on cell stiffness measured with micro-indentation techniques has been explored in single cells, however it is unclear if results on single cells can be readily transferred to indentation experiments performed on a tissue in vivo. Here we explored this question by using simulation models of osmotic treatments and micro-indentation experiments on 3D multicellular tissues with the finite element method. We found that the cellular context does affect measured cell stiffness, and that several cells of context in each direction are required for optimal results. We applied the model to micro-indentation data obtained with cellular force microscopy on the sepal of A. thaliana, and found that differences in measured stiffness could be explained by cellular geometry, and do not necessarily indicate differences in cell wall material properties or turgor pressure.

Aeroelastic Model of Vocal-Fold Vibrating Element for Studying the Phonation Threshold

NASA Astrophysics Data System (ADS)

Horáček, J.; Švec, J. G.

2002-10-01

An original theoretical model for vibration onset of the vocal folds in the air-flow coming from the human subglottal tract is designed, which allows studying the influence of the physical properties of the vocal folds (e.g., geometrical shape, mass, viscosity) on their vibration characteristics (such as the natural frequencies, mode shapes of vibration and the thresholds of instability). The mathematical model of the vocal fold is designed as a simplified dynamic system of two degrees of freedom (rotation and translation) vibrating on an elastic foundation in the wall of a channel conveying air. An approximate unsteady one-dimensional flow theory for the inviscid incompressible fluid is presented for the phonatory air-flow. A generally defined shape of the vocal-fold surface is considered for expressing the unsteady aerodynamic forces in the glottis. The parameters of the mechanical part of the model, i.e., the mass, stiffness and damping matrices, are related to the geometry and material density of the vocal folds as well as to the fundamental natural frequency and damping known from experiments. The coupled numerical solution yields the vibration characteristics (natural frequencies, damping and mode shapes of vibration), including the instability thresholds of the aeroelastic system. The vibration characteristics obtained from the coupled numerical solution of the system appear to be in reasonable qualitative agreement with the physiological data and clinical observations. The model is particularly suitable for studying the phonation threshold, i.e., the onset of vibration of the vocal folds.

Bézier B¯ projection

NASA Astrophysics Data System (ADS)

Miao, Di; Borden, Michael J.; Scott, Michael A.; Thomas, Derek C.

2018-06-01

In this paper we demonstrate the use of B\\'{e}zier projection to alleviate locking phenomena in structural mechanics applications of isogeometric analysis. Interpreting the well-known $\\bar{B}$ projection in two different ways we develop two formulations for locking problems in beams and nearly incompressible elastic solids. One formulation leads to a sparse symmetric symmetric system and the other leads to a sparse non-symmetric system. To demonstrate the utility of B\\'{e}zier projection for both geometry and material locking phenomena we focus on transverse shear locking in Timoshenko beams and volumetric locking in nearly compressible linear elasticity although the approach can be applied generally to other types of locking phenemona as well. B\\'{e}zier projection is a local projection technique with optimal approximation properties, which in many cases produces solutions that are comparable to global $L^2$ projection. In the context of $\\bar{B}$ methods, the use of B\\'ezier projection produces sparse stiffness matrices with only a slight increase in bandwidth when compared to standard displacement-based methods. Of particular importance is that the approach is applicable to any spline representation that can be written in B\\'ezier form like NURBS, T-splines, LR-splines, etc. We discuss in detail how to integrate this approach into an existing finite element framework with minimal disruption through the use of B\\'ezier extraction operators and a newly introduced dual basis for the B\\'{e}zierprojection operator. We then demonstrate the behavior of the two proposed formulations through several challenging benchmark problems.

Parametric design of pressure-relieving foot orthosis using statistics-based finite element method.

PubMed

Cheung, Jason Tak-Man; Zhang, Ming

2008-04-01

Custom-molded foot orthoses are frequently prescribed in routine clinical practice to prevent or treat plantar ulcers in diabetes by reducing the peak plantar pressure. However, the design and fabrication of foot orthosis vary among clinical practitioners and manufacturers. Moreover, little information about the parametric effect of different combinations of design factors is available. As an alternative to the experimental approach, therefore, computational models of the foot and footwear can provide efficient evaluations of different combinations of structural and material design factors on plantar pressure distribution. In this study, a combined finite element and Taguchi method was used to identify the sensitivity of five design factors (arch type, insole and midsole thickness, insole and midsole stiffness) of foot orthosis on peak plantar pressure relief. From the FE predictions, the custom-molded shape was found to be the most important design factor in reducing peak plantar pressure. Besides the use of an arch-conforming foot orthosis, the insole stiffness was found to be the second most important factor for peak pressure reduction. Other design factors, such as insole thickness, midsole stiffness and midsole thickness, contributed to less important roles in peak pressure reduction in the given order. The statistics-based FE method was found to be an effective approach in evaluating and optimizing the design of foot orthosis.