Measurement and Finite Element Model Validation of Immature Porcine Brain-Skull Displacement during Rapid Sagittal Head Rotations.

PubMed

Pasquesi, Stephanie A; Margulies, Susan S

2018-01-01

Computational models are valuable tools for studying tissue-level mechanisms of traumatic brain injury, but to produce more accurate estimates of tissue deformation, these models must be validated against experimental data. In this study, we present in situ measurements of brain-skull displacement in the neonatal piglet head ( n  = 3) at the sagittal midline during six rapid non-impact rotations (two rotations per specimen) with peak angular velocities averaging 51.7 ± 1.4 rad/s. Marks on the sagittally cut brain and skull/rigid potting surfaces were tracked, and peak values of relative brain-skull displacement were extracted and found to be significantly less than values extracted from a previous axial plane model. In a finite element model of the sagittally transected neonatal porcine head, the brain-skull boundary condition was matched to the measured physical experiment data. Despite smaller sagittal plane displacements at the brain-skull boundary, the corresponding finite element boundary condition optimized for sagittal plane rotations is far less stiff than its axial counterpart, likely due to the prominent role of the boundary geometry in restricting interface movement. Finally, bridging veins were included in the finite element model. Varying the bridging vein mechanical behavior over a previously reported range had no influence on the brain-skull boundary displacements. This direction-specific sagittal plane boundary condition can be employed in finite element models of rapid sagittal head rotations.

Measurement and Finite Element Model Validation of Immature Porcine Brain–Skull Displacement during Rapid Sagittal Head Rotations

PubMed Central

Pasquesi, Stephanie A.; Margulies, Susan S.

2018-01-01

Computational models are valuable tools for studying tissue-level mechanisms of traumatic brain injury, but to produce more accurate estimates of tissue deformation, these models must be validated against experimental data. In this study, we present in situ measurements of brain–skull displacement in the neonatal piglet head (n = 3) at the sagittal midline during six rapid non-impact rotations (two rotations per specimen) with peak angular velocities averaging 51.7 ± 1.4 rad/s. Marks on the sagittally cut brain and skull/rigid potting surfaces were tracked, and peak values of relative brain–skull displacement were extracted and found to be significantly less than values extracted from a previous axial plane model. In a finite element model of the sagittally transected neonatal porcine head, the brain–skull boundary condition was matched to the measured physical experiment data. Despite smaller sagittal plane displacements at the brain–skull boundary, the corresponding finite element boundary condition optimized for sagittal plane rotations is far less stiff than its axial counterpart, likely due to the prominent role of the boundary geometry in restricting interface movement. Finally, bridging veins were included in the finite element model. Varying the bridging vein mechanical behavior over a previously reported range had no influence on the brain–skull boundary displacements. This direction-specific sagittal plane boundary condition can be employed in finite element models of rapid sagittal head rotations. PMID:29515995

UXO Discrimination in Cases with Overlapping Signatures

DTIC Science & Technology

2007-03-07

13. APPENDIX B: HFE -BIEM ..........................................................................................................290 - 7...First principals numerical solutions developed were a Hybrid Finite Element – Boundary Integral Equation Method ( HFE -BIEM) body of revolution (BOR...attacks, namely the Method of Auxiliary Sources (MAS) and the Hybrid Finite Element – Boundary Integral Equation Method ( HFE -BIEM). These work

A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.

2014-01-01

We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.

Applications of FEM and BEM in two-dimensional fracture mechanics problems

NASA Technical Reports Server (NTRS)

Min, J. B.; Steeve, B. E.; Swanson, G. R.

1992-01-01

A comparison of the finite element method (FEM) and boundary element method (BEM) for the solution of two-dimensional plane strain problems in fracture mechanics is presented in this paper. Stress intensity factors (SIF's) were calculated using both methods for elastic plates with either a single-edge crack or an inclined-edge crack. In particular, two currently available programs, ANSYS for finite element analysis and BEASY for boundary element analysis, were used.

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

A finite element: Boundary integral method for electromagnetic scattering. Ph.D. Thesis Technical Report, Feb. - Sep. 1992

NASA Technical Reports Server (NTRS)

Collins, J. D.; Volakis, John L.

1992-01-01

A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications.

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.

Calculation methods for compressible turbulent boundary layers, 1976

NASA Technical Reports Server (NTRS)

Bushnell, D. M.; Cary, A. M., Jr.; Harris, J. E.

1977-01-01

Equations and closure methods for compressible turbulent boundary layers are discussed. Flow phenomena peculiar to calculation of these boundary layers were considered, along with calculations of three dimensional compressible turbulent boundary layers. Procedures for ascertaining nonsimilar two and three dimensional compressible turbulent boundary layers were appended, including finite difference, finite element, and mass-weighted residual methods.

High-Accuracy Finite Element Method: Benchmark Calculations

NASA Astrophysics Data System (ADS)

Gusev, Alexander; Vinitsky, Sergue; Chuluunbaatar, Ochbadrakh; Chuluunbaatar, Galmandakh; Gerdt, Vladimir; Derbov, Vladimir; Góźdź, Andrzej; Krassovitskiy, Pavel

2018-02-01

We describe a new high-accuracy finite element scheme with simplex elements for solving the elliptic boundary-value problems and show its efficiency on benchmark solutions of the Helmholtz equation for the triangle membrane and hypercube.

A combined finite element-boundary element formulation for solution of axially symmetric bodies

NASA Technical Reports Server (NTRS)

Collins, Jeffrey D.; Volakis, John L.

1991-01-01

A new method is presented for the computation of electromagnetic scattering from axially symmetric bodies. To allow the simulation of inhomogeneous cross sections, the method combines the finite element and boundary element techniques. Interior to a fictitious surface enclosing the scattering body, the finite element method is used which results in a sparce submatrix, whereas along the enclosure the Stratton-Chu integral equation is enforced. By choosing the fictitious enclosure to be a right circular cylinder, most of the resulting boundary integrals are convolutional and may therefore be evaluated via the FFT with which the system is iteratively solved. In view of the sparce matrix associated with the interior fields, this reduces the storage requirement of the entire system to O(N) making the method attractive for large scale computations. The details of the corresponding formulation and its numerical implementation are described.

Experimental validation of boundary element methods for noise prediction

NASA Technical Reports Server (NTRS)

Seybert, A. F.; Oswald, Fred B.

1992-01-01

Experimental validation of methods to predict radiated noise is presented. A combined finite element and boundary element model was used to predict the vibration and noise of a rectangular box excited by a mechanical shaker. The predicted noise was compared to sound power measured by the acoustic intensity method. Inaccuracies in the finite element model shifted the resonance frequencies by about 5 percent. The predicted and measured sound power levels agree within about 2.5 dB. In a second experiment, measured vibration data was used with a boundary element model to predict noise radiation from the top of an operating gearbox. The predicted and measured sound power for the gearbox agree within about 3 dB.

A boundary element alternating method for two-dimensional mixed-mode fracture problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Krishnamurthy, T.

1992-01-01

A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.

Acoustic coupled fluid-structure interactions using a unified fast multipole boundary element method.

PubMed

Wilkes, Daniel R; Duncan, Alec J

2015-04-01

This paper presents a numerical model for the acoustic coupled fluid-structure interaction (FSI) of a submerged finite elastic body using the fast multipole boundary element method (FMBEM). The Helmholtz and elastodynamic boundary integral equations (BIEs) are, respectively, employed to model the exterior fluid and interior solid domains, and the pressure and displacement unknowns are coupled between conforming meshes at the shared boundary interface to achieve the acoustic FSI. The low frequency FMBEM is applied to both BIEs to reduce the algorithmic complexity of the iterative solution from O(N(2)) to O(N(1.5)) operations per matrix-vector product for N boundary unknowns. Numerical examples are presented to demonstrate the algorithmic and memory complexity of the method, which are shown to be in good agreement with the theoretical estimates, while the solution accuracy is comparable to that achieved by a conventional finite element-boundary element FSI model.

A combined finite element-boundary element formulation for solution of two-dimensional problems via CGFFT

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Jin, Jian-Ming; Volakis, John L.

1990-01-01

A method for the computation of electromagnetic scattering from arbitrary two-dimensional bodies is presented. The method combines the finite element and boundary element methods leading to a system for solution via the conjugate gradient Fast Fourier Transform (FFT) algorithm. Two forms of boundaries aimed at reducing the storage requirement of the boundary integral are investigated. It is shown that the boundary integral becomes convolutional when a circular enclosure is chosen, resulting in reduced storage requirement when the system is solved via the conjugate gradient FFT method. The same holds for the ogival enclosure, except that some of the boundary integrals are not convolutional and must be carefully treated to maintain O(N) memory requirement. Results for several circular and ogival structures are presented and shown to be in excellent agreement with those obtained by traditional methods.

Thermal finite-element analysis of space shuttle main engine turbine blade

NASA Technical Reports Server (NTRS)

Abdul-Aziz, Ali; Tong, Michael T.; Kaufman, Albert

1987-01-01

Finite-element, transient heat transfer analyses were performed for the first-stage blades of the space shuttle main engine (SSME) high-pressure fuel turbopump. The analyses were based on test engine data provided by Rocketdyne. Heat transfer coefficients were predicted by performing a boundary-layer analysis at steady-state conditions with the STAN5 boundary-layer code. Two different peak-temperature overshoots were evaluated for the startup transient. Cutoff transient conditions were also analyzed. A reduced gas temperature profile based on actual thermocouple data was also considered. Transient heat transfer analyses were conducted with the MARC finite-element computer code.

A class of hybrid finite element methods for electromagnetics: A review

NASA Technical Reports Server (NTRS)

Volakis, J. L.; Chatterjee, A.; Gong, J.

1993-01-01

Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.

Numerical investigation of nonlinear fluid-structure interaction dynamic behaviors under a general Immersed Boundary-Lattice Boltzmann-Finite Element method

NASA Astrophysics Data System (ADS)

Gong, Chun-Lin; Fang, Zhe; Chen, Gang

A numerical approach based on the immersed boundary (IB), lattice Boltzmann and nonlinear finite element method (FEM) is proposed to simulate hydrodynamic interactions of very flexible objects. In the present simulation framework, the motion of fluid is obtained by solving the discrete lattice Boltzmann equations on Eulerian grid, the behaviors of flexible objects are calculated through nonlinear dynamic finite element method, and the interactive forces between them are implicitly obtained using velocity correction IB method which satisfies the no-slip conditions well at the boundary points. The efficiency and accuracy of the proposed Immersed Boundary-Lattice Boltzmann-Finite Element method is first validated by a fluid-structure interaction (F-SI) benchmark case, in which a flexible filament flaps behind a cylinder in channel flow, then the nonlinear vibration mechanism of the cylinder-filament system is investigated by altering the Reynolds number of flow and the material properties of filament. The interactions between two tandem and side-by-side identical objects in a uniform flow are also investigated, and the in-phase and out-of-phase flapping behaviors are captured by the proposed method.

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

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

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk; Seaid, Mohammed; Trevelyan, Jon

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach canmore » be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.« less

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.; Woo, Alex C.; Yu, C. Long

1992-01-01

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This is due to the lack of rigorous mathematical models for conformal antenna arrays, and as a result the design of conformal arrays is primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. Herewith we shall extend this formulation for conformal arrays on large metallic cylinders. In this we develop the mathematical formulation. In particular we discuss the finite element equations, the shape elements, and the boundary integral evaluation, and it is shown how this formulation can be applied with minimal computation and memory requirements. The implementation shall be discussed in a later report.

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.

1992-01-01

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This was due to the lack of rigorous mathematical models for conformal antenna arrays. As a result, the design of conformal arrays was primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We are extending this formulation to conformal arrays on large metallic cylinders. In doing so, we will develop a mathematical formulation. In particular, we discuss the finite element equations, the shape elements, and the boundary integral evaluation. It is shown how this formulation can be applied with minimal computation and memory requirements.

Eigenvalues of Rectangular Waveguide Using FEM With Hybrid Elements

NASA Technical Reports Server (NTRS)

Deshpande, Manohar D.; Hall, John M.

2002-01-01

A finite element analysis using hybrid triangular-rectangular elements is developed to estimate eigenvalues of a rectangular waveguide. Use of rectangular vector-edge finite elements in the vicinity of the PEC boundary and triangular elements in the interior region more accurately models the physical nature of the electromagnetic field, and consequently quicken the convergence.

A finite element boundary integral formulation for radiation and scattering by cavity antennas using tetrahedral elements

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, J. L.; Chatterjee, A.; Jin, J. M.

1992-01-01

A hybrid finite element boundary integral formulation is developed using tetrahedral and/or triangular elements for discretizing the cavity and/or aperture of microstrip antenna arrays. The tetrahedral elements with edge based linear expansion functions are chosen for modeling the volume region and triangular elements are used for discretizing the aperture. The edge based expansion functions are divergenceless thus removing the requirement to introduce a penalty term and the tetrahedral elements permit greater geometrical adaptability than the rectangular bricks. The underlying theory and resulting expressions are discussed in detail together with some numerical scattering examples for comparison and demonstration.

Finite element analysis of low speed viscous and inviscid aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1977-01-01

A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC.

A multilevel correction adaptive finite element method for Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Hu, Guanghui; Xie, Hehu; Xu, Fei

2018-02-01

In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.

Books and monographs on finite element technology

NASA Technical Reports Server (NTRS)

Noor, A. K.

1985-01-01

The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.

Quadrilateral/hexahedral finite element mesh coarsening

DOEpatents

Staten, Matthew L; Dewey, Mark W; Scott, Michael A; Benzley, Steven E

2012-10-16

A technique for coarsening a finite element mesh ("FEM") is described. This technique includes identifying a coarsening region within the FEM to be coarsened. Perimeter chords running along perimeter boundaries of the coarsening region are identified. The perimeter chords are redirected to create an adaptive chord separating the coarsening region from a remainder of the FEM. The adaptive chord runs through mesh elements residing along the perimeter boundaries of the coarsening region. The adaptive chord is then extracted to coarsen the FEM.

Review of literature on the finite-element solution of the equations of two-dimensional surface-water flow in the horizontal plane

USGS Publications Warehouse

Lee, Jonathan K.; Froehlich, David C.

1987-01-01

Published literature on the application of the finite-element method to solving the equations of two-dimensional surface-water flow in the horizontal plane is reviewed in this report. The finite-element method is ideally suited to modeling two-dimensional flow over complex topography with spatially variable resistance. A two-dimensional finite-element surface-water flow model with depth and vertically averaged velocity components as dependent variables allows the user great flexibility in defining geometric features such as the boundaries of a water body, channels, islands, dikes, and embankments. The following topics are reviewed in this report: alternative formulations of the equations of two-dimensional surface-water flow in the horizontal plane; basic concepts of the finite-element method; discretization of the flow domain and representation of the dependent flow variables; treatment of boundary conditions; discretization of the time domain; methods for modeling bottom, surface, and lateral stresses; approaches to solving systems of nonlinear equations; techniques for solving systems of linear equations; finite-element alternatives to Galerkin's method of weighted residuals; techniques of model validation; and preparation of model input data. References are listed in the final chapter.

Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory

NASA Technical Reports Server (NTRS)

Putcha, N. S.; Reddy, J. N.

1986-01-01

A mixed shear flexible finite element, with relaxed continuity, is developed for the geometrically linear and nonlinear analysis of layered anisotropic plates. The element formulation is based on a refined higher order theory which satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate and requires no shear correction coefficients. The mixed finite element developed herein consists of eleven degrees of freedom per node which include three displacements, two rotations and six moment resultants. The element is evaluated for its accuracy in the analysis of the stability and vibration of anisotropic rectangular plates with different lamination schemes and boundary conditions. The mixed finite element described here for the higher order theory gives very accurate results for buckling loads and natural frequencies.

Contact Stress Analysis of Spiral Bevel Gears Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Kumar, A; Reddy, S.; Handschuh, R.

1995-01-01

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

Finite Element Models and Properties of a Stiffened Floor-Equipped Composite Cylinder

NASA Technical Reports Server (NTRS)

Grosveld, Ferdinand W.; Schiller, Noah H.; Cabell, Randolph H.

2010-01-01

Finite element models were developed of a floor-equipped, frame and stringer stiffened composite cylinder including a coarse finite element model of the structural components, a coarse finite element model of the acoustic cavities above and below the beam-supported plywood floor, and two dense models consisting of only the structural components. The report summarizes the geometry, the element properties, the material and mechanical properties, the beam cross-section characteristics, the beam element representations and the boundary conditions of the composite cylinder models. The expressions used to calculate the group speeds for the cylinder components are presented.

Frequency domain finite-element and spectral-element acoustic wave modeling using absorbing boundaries and perfectly matched layer

NASA Astrophysics Data System (ADS)

Rahimi Dalkhani, Amin; Javaherian, Abdolrahim; Mahdavi Basir, Hadi

2018-04-01

Wave propagation modeling as a vital tool in seismology can be done via several different numerical methods among them are finite-difference, finite-element, and spectral-element methods (FDM, FEM and SEM). Some advanced applications in seismic exploration benefit the frequency domain modeling. Regarding flexibility in complex geological models and dealing with the free surface boundary condition, we studied the frequency domain acoustic wave equation using FEM and SEM. The results demonstrated that the frequency domain FEM and SEM have a good accuracy and numerical efficiency with the second order interpolation polynomials. Furthermore, we developed the second order Clayton and Engquist absorbing boundary condition (CE-ABC2) and compared it with the perfectly matched layer (PML) for the frequency domain FEM and SEM. In spite of PML method, CE-ABC2 does not add any additional computational cost to the modeling except assembling boundary matrices. As a result, considering CE-ABC2 is more efficient than PML for the frequency domain acoustic wave propagation modeling especially when computational cost is high and high-level absorbing performance is unnecessary.

Finite Element A Posteriori Error Estimation for Heat Conduction. Degree awarded by George Washington Univ.

NASA Technical Reports Server (NTRS)

Lang, Christapher G.; Bey, Kim S. (Technical Monitor)

2002-01-01

This research investigates residual-based a posteriori error estimates for finite element approximations of heat conduction in single-layer and multi-layered materials. The finite element approximation, based upon hierarchical modelling combined with p-version finite elements, is described with specific application to a two-dimensional, steady state, heat-conduction problem. Element error indicators are determined by solving an element equation for the error with the element residual as a source, and a global error estimate in the energy norm is computed by collecting the element contributions. Numerical results of the performance of the error estimate are presented by comparisons to the actual error. Two methods are discussed and compared for approximating the element boundary flux. The equilibrated flux method provides more accurate results for estimating the error than the average flux method. The error estimation is applied to multi-layered materials with a modification to the equilibrated flux method to approximate the discontinuous flux along a boundary at the material interfaces. A directional error indicator is developed which distinguishes between the hierarchical modeling error and the finite element error. Numerical results are presented for single-layered materials which show that the directional indicators accurately determine which contribution to the total error dominates.

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

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

Gerritsma, Marc; Bochev, Pavel

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

DOE PAGES

Gerritsma, Marc; Bochev, Pavel

2016-03-22

Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity–vorticity–pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximatedmore » by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. Here, we also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.« less

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

NASA Technical Reports Server (NTRS)

Meade, Andrew J., Jr.

1992-01-01

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

A Hybrid Numerical Analysis Method for Structural Health Monitoring

NASA Technical Reports Server (NTRS)

Forth, Scott C.; Staroselsky, Alexander

2001-01-01

A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.

Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Kumar, A.; Reddy, S.; Handschuh, R.

1993-01-01

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

A comparative study of an ABC and an artificial absorber for truncating finite element meshes

NASA Technical Reports Server (NTRS)

Oezdemir, T.; Volakis, John L.

1993-01-01

The type of mesh termination used in the context of finite element formulations plays a major role on the efficiency and accuracy of the field solution. The performance of an absorbing boundary condition (ABC) and an artificial absorber (a new concept) for terminating the finite element mesh was evaluated. This analysis is done in connection with the problem of scattering by a finite slot array in a thick ground plane. The two approximate mesh truncation schemes are compared with the exact finite element-boundary integral (FEM-BI) method in terms of accuracy and efficiency. It is demonstrated that both approximate truncation schemes yield reasonably accurate results even when the mesh is extended only 0.3 wavelengths away from the array aperture. However, the artificial absorber termination method leads to a substantially more efficient solution. Moreover, it is shown that the FEM-BI method remains quite competitive with the FEM-artificial absorber method when the FFT is used for computing the matrix-vector products in the iterative solution algorithm. These conclusions are indeed surprising and of major importance in electromagnetic simulations based on the finite element method.

Automated quadrilateral surface discretization method and apparatus usable to generate mesh in a finite element analysis system

DOEpatents

Blacker, Teddy D.

1994-01-01

An automatic quadrilateral surface discretization method and apparatus is provided for automatically discretizing a geometric region without decomposing the region. The automated quadrilateral surface discretization method and apparatus automatically generates a mesh of all quadrilateral elements which is particularly useful in finite element analysis. The generated mesh of all quadrilateral elements is boundary sensitive, orientation insensitive and has few irregular nodes on the boundary. A permanent boundary of the geometric region is input and rows are iteratively layered toward the interior of the geometric region. Also, an exterior permanent boundary and an interior permanent boundary for a geometric region may be input and the rows are iteratively layered inward from the exterior boundary in a first counter clockwise direction while the rows are iteratively layered from the interior permanent boundary toward the exterior of the region in a second clockwise direction. As a result, a high quality mesh for an arbitrary geometry may be generated with a technique that is robust and fast for complex geometric regions and extreme mesh gradations.

A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1990-01-01

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.

A new technique for simulating composite material

NASA Technical Reports Server (NTRS)

Volakis, John L.

1991-01-01

This project dealt with the development on new methodologies and algorithms for the multi-spectrum electromagnetic characterization of large scale nonmetallic airborne vehicles and structures. A robust, low memory, and accurate methodology was developed which is particularly suited for modern machine architectures. This is a hybrid finite element method that combines two well known numerical solution approaches. That of the finite element method for modeling volumes and the boundary integral method which yields exact boundary conditions for terminating the finite element mesh. In addition, a variety of high frequency results were generated (such as diffraction coefficients for impedance surfaces and material layers) and a class of boundary conditions were developed which hold promise for more efficient simulations. During the course of this project, nearly 25 detailed research reports were generated along with an equal number of journal papers. The reports, papers, and journal articles are listed in the appendices along with their abstracts.

Finite cover method with mortar elements for elastoplasticity problems

NASA Astrophysics Data System (ADS)

Kurumatani, M.; Terada, K.

2005-06-01

Finite cover method (FCM) is extended to elastoplasticity problems. The FCM, which was originally developed under the name of manifold method, has recently been recognized as one of the generalized versions of finite element methods (FEM). Since the mesh for the FCM can be regular and squared regardless of the geometry of structures to be analyzed, structural analysts are released from a burdensome task of generating meshes conforming to physical boundaries. Numerical experiments are carried out to assess the performance of the FCM with such discretization in elastoplasticity problems. Particularly to achieve this accurately, the so-called mortar elements are introduced to impose displacement boundary conditions on the essential boundaries, and displacement compatibility conditions on material interfaces of two-phase materials or on joint surfaces between mutually incompatible meshes. The validity of the mortar approximation is also demonstrated in the elastic-plastic FCM.

Highly Accurate Beam Torsion Solutions Using the p-Version Finite Element Method

NASA Technical Reports Server (NTRS)

Smith, James P.

1996-01-01

A new treatment of the classical beam torsion boundary value problem is applied. Using the p-version finite element method with shape functions based on Legendre polynomials, torsion solutions for generic cross-sections comprised of isotropic materials are developed. Element shape functions for quadrilateral and triangular elements are discussed, and numerical examples are provided.

Finite-element numerical modeling of atmospheric turbulent boundary layer

NASA Technical Reports Server (NTRS)

Lee, H. N.; Kao, S. K.

1979-01-01

A dynamic turbulent boundary-layer model in the neutral atmosphere is constructed, using a dynamic turbulent equation of the eddy viscosity coefficient for momentum derived from the relationship among the turbulent dissipation rate, the turbulent kinetic energy and the eddy viscosity coefficient, with aid of the turbulent second-order closure scheme. A finite-element technique was used for the numerical integration. In preliminary results, the behavior of the neutral planetary boundary layer agrees well with the available data and with the existing elaborate turbulent models, using a finite-difference scheme. The proposed dynamic formulation of the eddy viscosity coefficient for momentum is particularly attractive and can provide a viable alternative approach to study atmospheric turbulence, diffusion and air pollution.

Probabilistic boundary element method

NASA Technical Reports Server (NTRS)

Cruse, T. A.; Raveendra, S. T.

1989-01-01

The purpose of the Probabilistic Structural Analysis Method (PSAM) project is to develop structural analysis capabilities for the design analysis of advanced space propulsion system hardware. The boundary element method (BEM) is used as the basis of the Probabilistic Advanced Analysis Methods (PADAM) which is discussed. The probabilistic BEM code (PBEM) is used to obtain the structural response and sensitivity results to a set of random variables. As such, PBEM performs analogous to other structural analysis codes such as finite elements in the PSAM system. For linear problems, unlike the finite element method (FEM), the BEM governing equations are written at the boundary of the body only, thus, the method eliminates the need to model the volume of the body. However, for general body force problems, a direct condensation of the governing equations to the boundary of the body is not possible and therefore volume modeling is generally required.

A 2.5D finite element and boundary element model for the ground vibration from trains in tunnels and validation using measurement data

NASA Astrophysics Data System (ADS)

Jin, Qiyun; Thompson, David J.; Lurcock, Daniel E. J.; Toward, Martin G. R.; Ntotsios, Evangelos

2018-05-01

A numerical model is presented for the ground-borne vibration produced by trains running in tunnels. The model makes use of the assumption that the geometry and material properties are invariant in the axial direction. It is based on the so-called two-and-a-half dimensional (2.5D) coupled Finite Element and Boundary Element methodology, in which a two-dimensional cross-section is discretised into finite elements and boundary elements and the third dimension is represented by a Fourier transform over wavenumbers. The model is applied to a particular case of a metro line built with a cast-iron tunnel lining. An equivalent continuous model of the tunnel is developed to allow it to be readily implemented in the 2.5D framework. The tunnel structure and the track are modelled using solid and beam finite elements while the ground is modelled using boundary elements. The 2.5D track-tunnel-ground model is coupled with a train consisting of several vehicles, which are represented by multi-body models. The response caused by the passage of a train is calculated as the sum of the dynamic component, excited by the combined rail and wheel roughness, and the quasi-static component, induced by the constant moving axle loads. Field measurements have been carried out to provide experimental validation of the model. These include measurements of the vibration of the rail, the tunnel invert and the tunnel wall. In addition, simultaneous measurements were made on the ground surface above the tunnel. Rail roughness and track characterisation measurements were also made. The prediction results are compared with measured vibration obtained during train passages, with good agreement.

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

NASA Technical Reports Server (NTRS)

Chung, T. J. (Editor); Karr, Gerald R. (Editor)

1989-01-01

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

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.

On a 3-D singularity element for computation of combined mode stress intensities

NASA Technical Reports Server (NTRS)

Atluri, S. N.; Kathiresan, K.

1976-01-01

A special three-dimensional singularity element is developed for the computation of combined modes 1, 2, and 3 stress intensity factors, which vary along an arbitrarily curved crack front in three dimensional linear elastic fracture problems. The finite element method is based on a displacement-hybrid finite element model, based on a modified variational principle of potential energy, with arbitrary element interior displacements, interelement boundary displacements, and element boundary tractions as variables. The special crack-front element used in this analysis contains the square root singularity in strains and stresses, where the stress-intensity factors K(1), K(2), and K(3) are quadratically variable along the crack front and are solved directly along with the unknown nodal displacements.

Coupled NASTRAN/boundary element formulation for acoustic scattering

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Henderson, Francis M.; Schuetz, Luise S.

1987-01-01

A coupled finite element/boundary element capability is described for calculating the sound pressure field scattered by an arbitrary submerged 3-D elastic structure. Structural and fluid impedances are calculated with no approximation other than discretization. The surface fluid pressures and normal velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior field. Far field pressures are then evaluated from the surface solution using the Helmholtz exterior integral equation. The overall approach is illustrated and validated using a known analytic solution for scattering from submerged spherical shells.

Finite elements and fluid dynamics. [instability effects on solution of nonlinear equations

NASA Technical Reports Server (NTRS)

Fix, G.

1975-01-01

Difficulties concerning a use of the finite element method in the solution of the nonlinear equations of fluid dynamics are partly related to various 'hidden' instabilities which often arise in fluid calculations. The instabilities are typically due to boundary effects or nonlinearities. It is shown that in certain cases these instabilities can be avoided if certain conservation laws are satisfied, and that the latter are often intimately related to finite elements.

On modelling three-dimensional piezoelectric smart structures with boundary spectral element method

NASA Astrophysics Data System (ADS)

Zou, Fangxin; Aliabadi, M. H.

2017-05-01

The computational efficiency of the boundary element method in elastodynamic analysis can be significantly improved by employing high-order spectral elements for boundary discretisation. In this work, for the first time, the so-called boundary spectral element method is utilised to formulate the piezoelectric smart structures that are widely used in structural health monitoring (SHM) applications. The resultant boundary spectral element formulation has been validated by the finite element method (FEM) and physical experiments. The new formulation has demonstrated a lower demand on computational resources and a higher numerical stability than commercial FEM packages. Comparing to the conventional boundary element formulation, a significant reduction in computational expenses has been achieved. In summary, the boundary spectral element formulation presented in this paper provides a highly efficient and stable mathematical tool for the development of SHM applications.

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Zapp, John; Hsa, Chang-Yu; Volakis, John L.

1990-01-01

An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Meade, Andrew James, Jr.

1989-01-01

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Stress Distribution During Deformation of Polycrystalline Aluminum by Molecular-Dynamics and Finite-Element Modeling

NASA Technical Reports Server (NTRS)

Yamakov, V.; Saether, E.; Phillips, D.; Glaessgen, E. H.

2004-01-01

In this paper, a multiscale modelling strategy is used to study the effect of grain-boundary sliding on stress localization in a polycrystalline microstructure with an uneven distribution of grain size. The development of the molecular dynamics (MD) analysis used to interrogate idealized grain microstructures with various types of grain boundaries and the multiscale modelling strategies for modelling large systems of grains is discussed. Both molecular-dynamics and finite-element (FE) simulations for idealized polycrystalline models of identical geometry are presented with the purpose of demonstrating the effectiveness of the adapted finite-element method using cohesive zone models to reproduce grain-boundary sliding and its effect on the stress distribution in a polycrystalline metal. The yield properties of the grain-boundary interface, used in the FE simulations, are extracted from a MD simulation on a bicrystal. The models allow for the study of the load transfer between adjacent grains of very different size through grain-boundary sliding during deformation. A large-scale FE simulation of 100 grains of a typical microstructure is then presented to reveal that the stress distribution due to grain-boundary sliding during uniform tensile strain can lead to stress localization of two to three times the background stress, thus suggesting a significant effect on the failure properties of the metal.

Scalable Implementation of Finite Elements by NASA _ Implicit (ScIFEi)

NASA Technical Reports Server (NTRS)

Warner, James E.; Bomarito, Geoffrey F.; Heber, Gerd; Hochhalter, Jacob D.

2016-01-01

Scalable Implementation of Finite Elements by NASA (ScIFEN) is a parallel finite element analysis code written in C++. ScIFEN is designed to provide scalable solutions to computational mechanics problems. It supports a variety of finite element types, nonlinear material models, and boundary conditions. This report provides an overview of ScIFEi (\\Sci-Fi"), the implicit solid mechanics driver within ScIFEN. A description of ScIFEi's capabilities is provided, including an overview of the tools and features that accompany the software as well as a description of the input and output le formats. Results from several problems are included, demonstrating the efficiency and scalability of ScIFEi by comparing to finite element analysis using a commercial code.

Effect of joint spacing and joint dip on the stress distribution around tunnels using different numerical methods

NASA Astrophysics Data System (ADS)

Nikadat, Nooraddin; Fatehi Marji, Mohammad; Rahmannejad, Reza; Yarahmadi Bafghi, Alireza

2016-11-01

Different conditions may affect the stability of tunnels by the geometry (spacing and orientation) of joints in the surrounded rock mass. In this study, by comparing the results obtained by the three novel numerical methods i.e. finite element method (Phase2), discrete element method (UDEC) and indirect boundary element method (TFSDDM), the effects of joint spacing and joint dips on the stress distribution around rock tunnels are numerically studied. These comparisons indicate the validity of the stress analyses around circular rock tunnels. These analyses also reveal that for a semi-continuous environment, boundary element method gives more accurate results compared to the results of finite element and distinct element methods. In the indirect boundary element method, the displacements due to joints of different spacing and dips are estimated by using displacement discontinuity (DD) formulations and the total stress distribution around the tunnel are obtained by using fictitious stress (FS) formulations.

Automated Structural Optimization System (ASTROS) Damage Tolerance Module. Volume 1 - Final Report

DTIC Science & Technology

1999-02-01

cracks in the infinite do- main subjected to the unknown crack surface loading T. The second one, denoted as PFEM [shown in Fig. 2.13(b)], has the...same finite geometry as in the original problem except that the cracks are ignored. The boundary Tu of PFEM has the prescribed displacement u, while...Because of the absence of the cracks, the problem PFEM can be solved much easier by the finite element method (or the boundary element method). To

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

Mathematical aspects of finite element methods for incompressible viscous flows

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.

1986-01-01

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

Applications of Taylor-Galerkin finite element method to compressible internal flow problems

NASA Technical Reports Server (NTRS)

Sohn, Jeong L.; Kim, Yongmo; Chung, T. J.

1989-01-01

A two-step Taylor-Galerkin finite element method with Lapidus' artificial viscosity scheme is applied to several test cases for internal compressible inviscid flow problems. Investigations for the effect of supersonic/subsonic inlet and outlet boundary conditions on computational results are particularly emphasized.

Mesh Deformation Based on Fully Stressed Design: The Method and Two-Dimensional Examples

NASA Technical Reports Server (NTRS)

Hsu, Su-Yuen; Chang, Chau-Lyan

2007-01-01

Mesh deformation in response to redefined boundary geometry is a frequently encountered task in shape optimization and analysis of fluid-structure interaction. We propose a simple and concise method for deforming meshes defined with three-node triangular or four-node tetrahedral elements. The mesh deformation method is suitable for large boundary movement. The approach requires two consecutive linear elastic finite-element analyses of an isotropic continuum using a prescribed displacement at the mesh boundaries. The first analysis is performed with homogeneous elastic property and the second with inhomogeneous elastic property. The fully stressed design is employed with a vanishing Poisson s ratio and a proposed form of equivalent strain (modified Tresca equivalent strain) to calculate, from the strain result of the first analysis, the element-specific Young s modulus for the second analysis. The theoretical aspect of the proposed method, its convenient numerical implementation using a typical linear elastic finite-element code in conjunction with very minor extra coding for data processing, and results for examples of large deformation of two-dimensional meshes are presented in this paper. KEY WORDS: Mesh deformation, shape optimization, fluid-structure interaction, fully stressed design, finite-element analysis, linear elasticity, strain failure, equivalent strain, Tresca failure criterion

A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates

NASA Technical Reports Server (NTRS)

Putcha, N. S.; Reddy, J. N.

1986-01-01

The present study is concerned with the development of a mixed shear flexible finite element with relaxed continuity for the geometrically linear and nonlinear analysis of laminated anisotropic plates. The formulation of the element is based on a refined higher-order theory. This theory satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate. Shear correction coefficients are not needed. The developed element consists of 11 degrees-of-freedom per node, taking into account three displacements, two rotations, and six moment resultants. An evaluation of the element is conducted with respect to the accuracy obtained in the bending of laminated anistropic rectangular plates with different lamination schemes, loadings, and boundary conditions.

A QR accelerated volume-to-surface boundary condition for finite element solution of eddy current problems

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

White, D; Fasenfest, B; Rieben, R

2006-09-08

We are concerned with the solution of time-dependent electromagnetic eddy current problems using a finite element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. We propose a Biot-Savart law based volume-to-surface boundary condition to meet this requirement. This Biot-Savart approach is demonstrated to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretizedmore » Biot-Savart law.« less

Shape optimization of three-dimensional stamped and solid automotive components

NASA Technical Reports Server (NTRS)

Botkin, M. E.; Yang, R.-J.; Bennett, J. A.

1987-01-01

The shape optimization of realistic, 3-D automotive components is discussed. The integration of the major parts of the total process: modeling, mesh generation, finite element and sensitivity analysis, and optimization are stressed. Stamped components and solid components are treated separately. For stamped parts a highly automated capability was developed. The problem description is based upon a parameterized boundary design element concept for the definition of the geometry. Automatic triangulation and adaptive mesh refinement are used to provide an automated analysis capability which requires only boundary data and takes into account sensitivity of the solution accuracy to boundary shape. For solid components a general extension of the 2-D boundary design element concept has not been achieved. In this case, the parameterized surface shape is provided using a generic modeling concept based upon isoparametric mapping patches which also serves as the mesh generator. Emphasis is placed upon the coupling of optimization with a commercially available finite element program. To do this it is necessary to modularize the program architecture and obtain shape design sensitivities using the material derivative approach so that only boundary solution data is needed.

Improved Finite Element Modeling of the Turbofan Engine Inlet Radiation Problem

NASA Technical Reports Server (NTRS)

Roy, Indranil Danda; Eversman, Walter; Meyer, H. D.

1993-01-01

Improvements have been made in the finite element model of the acoustic radiated field from a turbofan engine inlet in the presence of a mean flow. The problem of acoustic radiation from a turbofan engine inlet is difficult to model numerically because of the large domain and high frequencies involved. A numerical model with conventional finite elements in the near field and wave envelope elements in the far field has been constructed. By employing an irrotational mean flow assumption, both the mean flow and the acoustic perturbation problem have been posed in an axisymmetric formulation in terms of the velocity potential; thereby minimizing computer storage and time requirements. The finite element mesh has been altered in search of an improved solution. The mean flow problem has been reformulated with new boundary conditions to make it theoretically rigorous. The sound source at the fan face has been modeled as a combination of positive and negative propagating duct eigenfunctions. Therefore, a finite element duct eigenvalue problem has been solved on the fan face and the resulting modal matrix has been used to implement a source boundary condition on the fan face in the acoustic radiation problem. In the post processing of the solution, the acoustic pressure has been evaluated at Gauss points inside the elements and the nodal pressure values have been interpolated from them. This has significantly improved the results. The effect of the geometric position of the transition circle between conventional finite elements and wave envelope elements has been studied and it has been found that the transition can be made nearer to the inlet than previously assumed.

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)

On the existence and stability conditions for mixed-hybrid finite element solutions based on Reissner's variational principle

NASA Technical Reports Server (NTRS)

Karlovitz, L. A.; Atluri, S. N.; Xue, W.-M.

1985-01-01

The extensions of Reissner's two-field (stress and displacement) principle to the cases wherein the displacement field is discontinuous and/or the stress field results in unreciprocated tractions, at a finite number of surfaces ('interelement boundaries') in a domain (as, for instance, when the domain is discretized into finite elements), is considered. The conditions for the existence, uniqueness, and stability of mixed-hybrid finite element solutions based on such discontinuous fields, are summarized. The reduction of these global conditions to local ('element') level, and the attendant conditions on the ranks of element matrices, are discussed. Two examples of stable, invariant, least-order elements - a four-node square planar element and an eight-node cubic element - are discussed in detail.

Convergence of an hp-Adaptive Finite Element Strategy in Two and Three Space-Dimensions

NASA Astrophysics Data System (ADS)

Bürg, Markus; Dörfler, Willy

2010-09-01

We show convergence of an automatic hp-adaptive refinement strategy for the finite element method on the elliptic boundary value problem. The strategy is a generalization of a refinement strategy proposed for one-dimensional situations to problems in two and three space-dimensions.

Solving Fluid Structure Interaction Problems with an Immersed Boundary Method

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.

2016-01-01

An immersed boundary method for the compressible Navier-Stokes equations can be used for moving boundary problems as well as fully coupled fluid-structure interaction is presented. The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, based on the locally stabilized immersed boundary method previously presented by the authors, is extended to account for unsteady boundary motion and coupled to linear and geometrically nonlinear structural finite element solvers. The approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems. Keywords: Immersed Boundary Method, Higher-Order Finite Difference Method, Fluid Structure Interaction.

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

NASA Technical Reports Server (NTRS)

Day, Brad A.; Meade, Andrew J., Jr.

1993-01-01

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

Deformation of two-phase aggregates using standard numerical methods

NASA Astrophysics Data System (ADS)

Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.

2013-04-01

Geodynamic problems often involve the large deformation of material encompassing material boundaries. In geophysical fluids, such boundaries often coincide with a discontinuity in the viscosity (or effective viscosity) field and subsequently in the pressure field. Here, we employ popular implementations of the finite difference and finite element methods for solving viscous flow problems. On one hand, we implemented finite difference method coupled with a Lagrangian marker-in-cell technique to represent the deforming fluid. Thanks to it Eulerian nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the Lagrangian finite element method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the finite difference scheme, we ran large strain simple shear deformation of aggregates containing either weak of strong circular inclusion (1e6 viscosity ratio). The results, obtained for different grid resolutions, are compared to Lagrangian finite element results which are considered as reference solution. The comparison is then used to establish up to which strain can finite difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the Eulerian mesh.

Finite elements of nonlinear continua.

NASA Technical Reports Server (NTRS)

Oden, J. T.

1972-01-01

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Scaled boundary finite element simulation and modeling of the mechanical behavior of cracked nanographene sheets

NASA Astrophysics Data System (ADS)

Honarmand, M.; Moradi, M.

2018-06-01

In this paper, by using scaled boundary finite element method (SBFM), a perfect nanographene sheet or cracked ones were simulated for the first time. In this analysis, the atomic carbon bonds were modeled by simple bar elements with circular cross-sections. Despite of molecular dynamics (MD), the results obtained from SBFM analysis are quite acceptable for zero degree cracks. For all angles except zero, Griffith criterion can be applied for the relation between critical stress and crack length. Finally, despite the simplifications used in nanographene analysis, obtained results can simulate the mechanical behavior with high accuracy compared with experimental and MD ones.

Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation

NASA Technical Reports Server (NTRS)

Glaisner, F.; Tezduyar, T. E.

1987-01-01

Finite element procedures for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation have been implemented. For both formulations, streamline-upwind/Petrov-Galerkin techniques are used for the discretization of the transport equations. The main problem associated with the vorticity stream-function formulation is the lack of boundary conditions for vorticity at solid surfaces. Here an implicit treatment of the vorticity at no-slip boundaries is incorporated in a predictor-multicorrector time integration scheme. For the primitive variable formulation, mixed finite-element approximations are used. A nine-node element and a four-node + bubble element have been implemented. The latter is shown to exhibit a checkerboard pressure mode and a numerical treatment for this spurious pressure mode is proposed. The two methods are compared from the points of view of simulating internal and external flows and the possibilities of extensions to three dimensions.

Efficient finite element simulation of slot spirals, slot radomes and microwave structures

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, J. L.

1995-01-01

This progress report contains the following two documents: (1) 'Efficient Finite Element Simulation of Slot Antennas using Prismatic Elements' - A hybrid finite element-boundary integral (FE-BI) simulation technique is discussed to treat narrow slot antennas etched on a planar platform. Specifically, the prismatic elements are used to reduce the redundant sampling rates and ease the mesh generation process. Numerical results for an antenna slot and frequency selective surfaces are presented to demonstrate the validity and capability of the technique; and (2) 'Application and Design Guidelines of the PML Absorber for Finite Element Simulations of Microwave Packages' - The recently introduced perfectly matched layer (PML) uniaxial absorber for frequency domain finite element simulations has several advantages. In this paper we present the application of PML for microwave circuit simulations along with design guidelines to obtain a desired level of absorption. Different feeding techniques are also investigated for improved accuracy.

A collocation--Galerkin finite element model of cardiac action potential propagation.

PubMed

Rogers, J M; McCulloch, A D

1994-08-01

A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, we observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.

A mixed-penalty biphasic finite element formulation incorporating viscous fluids and material interfaces.

PubMed

Chan, B; Donzelli, P S; Spilker, R L

2000-06-01

The fluid viscosity term of the fluid phase constitutive equation and the interface boundary conditions between biphasic, solid and fluid domains have been incorporated into a mixed-penalty finite element formulation of the linear biphasic theory for hydrated soft tissue. The finite element code can now model a single-phase viscous incompressible fluid, or a single-phase elastic solid, as limiting cases of a biphasic material. Interface boundary conditions allow the solution of problems involving combinations of biphasic, fluid and solid regions. To incorporate these conditions, the volume-weighted mixture velocity is introduced as a degree of freedom at interface nodes so that the kinematic continuity conditions are satisfied by conventional finite element assembly techniques. Results comparing our numerical method with an independent, analytic solution for the problem of Couette flow over rigid and deformable porous biphasic layers show that the finite element code accurately predicts the viscous fluid flows and deformation in the porous biphasic region. Thus, the analysis can be used to model the interface between synovial fluid and articular cartilage in diarthrodial joints. This is an important step toward modeling and understanding the mechanisms of joint lubrication and another step toward fully modeling the in vivo behavior of a diarthrodial joint.

A finite-volume Eulerian-Lagrangian Localized Adjoint Method for solution of the advection-dispersion equation

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1993-01-01

A new mass-conservative method for solution of the one-dimensional advection-dispersion equation is derived and discussed. Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion-dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on Lagrangian space-time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.

A fictitious domain approach for the Stokes problem based on the extended finite element method

NASA Astrophysics Data System (ADS)

Court, Sébastien; Fournié, Michel; Lozinski, Alexei

2014-01-01

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries do not match. A mixed finite element method is used for fluid flow. The interface between the fluid and the structure is localized by a level-set function. Dirichlet boundary conditions are taken into account using Lagrange multiplier. A stabilization term is introduced to improve the approximation of the normal trace of the Cauchy stress tensor at the interface and avoid the inf-sup condition between the spaces for velocity and the Lagrange multiplier. Convergence analysis is given and several numerical tests are performed to illustrate the capabilities of the method.

Possibilities of Particle Finite Element Methods in Industrial Forming Processes

NASA Astrophysics Data System (ADS)

Oliver, J.; Cante, J. C.; Weyler, R.; Hernandez, J.

2007-04-01

The work investigates the possibilities offered by the particle finite element method (PFEM) in the simulation of forming problems involving large deformations, multiple contacts, and new boundaries generation. The description of the most distinguishing aspects of the PFEM, and its application to simulation of representative forming processes, illustrate the proposed methodology.

Evaluation and optimization of footwear comfort parameters using finite element analysis and a discrete optimization algorithm

NASA Astrophysics Data System (ADS)

Papagiannis, P.; Azariadis, P.; Papanikos, P.

2017-10-01

Footwear is subject to bending and torsion deformations that affect comfort perception. Following review of Finite Element Analysis studies of sole rigidity and comfort, a three-dimensional, linear multi-material finite element sole model for quasi-static bending and torsion simulation, overcoming boundary and optimisation limitations, is described. Common footwear materials properties and boundary conditions from gait biomechanics are used. The use of normalised strain energy for product benchmarking is demonstrated along with comfort level determination through strain energy density stratification. Sensitivity of strain energy against material thickness is greater for bending than for torsion, with results of both deformations showing positive correlation. Optimization for a targeted performance level and given layer thickness is demonstrated with bending simulations sufficing for overall comfort assessment. An algorithm for comfort optimization w.r.t. bending is presented, based on a discrete approach with thickness values set in line with practical manufacturing accuracy. This work illustrates the potential of the developed finite element analysis applications to offer viable and proven aids to modern footwear sole design assessment and optimization.

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals.

PubMed

Przybytek, Michal; Helgaker, Trygve

2013-08-07

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.

An iterative truncation method for unbounded electromagnetic problems using varying order finite elements

NASA Astrophysics Data System (ADS)

Paul, Prakash

2009-12-01

The finite element method (FEM) is used to solve three-dimensional electromagnetic scattering and radiation problems. Finite element (FE) solutions of this kind contain two main types of error: discretization error and boundary error. Discretization error depends on the number of free parameters used to model the problem, and on how effectively these parameters are distributed throughout the problem space. To reduce the discretization error, the polynomial order of the finite elements is increased, either uniformly over the problem domain or selectively in those areas with the poorest solution quality. Boundary error arises from the condition applied to the boundary that is used to truncate the computational domain. To reduce the boundary error, an iterative absorbing boundary condition (IABC) is implemented. The IABC starts with an inexpensive boundary condition and gradually improves the quality of the boundary condition as the iteration continues. An automatic error control (AEC) is implemented to balance the two types of error. With the AEC, the boundary condition is improved when the discretization error has fallen to a low enough level to make this worth doing. The AEC has these characteristics: (i) it uses a very inexpensive truncation method initially; (ii) it allows the truncation boundary to be very close to the scatterer/radiator; (iii) it puts more computational effort on the parts of the problem domain where it is most needed; and (iv) it can provide as accurate a solution as needed depending on the computational price one is willing to pay. To further reduce the computational cost, disjoint scatterers and radiators that are relatively far from each other are bounded separately and solved using a multi-region method (MRM), which leads to savings in computational cost. A simple analytical way to decide whether the MRM or the single region method will be computationally cheaper is also described. To validate the accuracy and savings in computation time, different shaped metallic and dielectric obstacles (spheres, ogives, cube, flat plate, multi-layer slab etc.) are used for the scattering problems. For the radiation problems, waveguide excited antennas (horn antenna, waveguide with flange, microstrip patch antenna) are used. Using the AEC the peak reduction in computation time during the iteration is typically a factor of 2, compared to the IABC using the same element orders throughout. In some cases, it can be as high as a factor of 4.

Combination tones along the basilar membrane in a 3D finite element model of the cochlea with acoustic boundary layer attenuation

NASA Astrophysics Data System (ADS)

Böhnke, Frank; Scheunemann, Christian; Semmelbauer, Sebastian

2018-05-01

The propagation of traveling waves along the basilar membrane is studied in a 3D finite element model of the cochlea using single and two-tone stimulation. The advantage over former approaches is the consideration of viscous-thermal boundary layer damping which makes the usual but physically unjustified assumption of Rayleigh damping obsolete. The energy loss by viscous boundary layer damping is 70 dB lower than the actually assumed power generation by outer hair cells. The space-time course with two-tone stimulation shows the traveling waves and the periodicity of the beat frequency f2 - f1.

Probabilistic finite elements for fatigue and fracture analysis

NASA Astrophysics Data System (ADS)

Belytschko, Ted; Liu, Wing Kam

Attenuation is focused on the development of Probabilistic Finite Element Method (PFEM), which combines the finite element method with statistics and reliability methods, and its application to linear, nonlinear structural mechanics problems and fracture mechanics problems. The computational tool based on the Stochastic Boundary Element Method is also given for the reliability analysis of a curvilinear fatigue crack growth. The existing PFEM's have been applied to solve for two types of problems: (1) determination of the response uncertainty in terms of the means, variance and correlation coefficients; and (2) determination the probability of failure associated with prescribed limit states.

Statistical Energy Analysis (SEA) and Energy Finite Element Analysis (EFEA) Predictions for a Floor-Equipped Composite Cylinder

NASA Technical Reports Server (NTRS)

Grosveld, Ferdinand W.; Schiller, Noah H.; Cabell, Randolph H.

2011-01-01

Comet Enflow is a commercially available, high frequency vibroacoustic analysis software founded on Energy Finite Element Analysis (EFEA) and Energy Boundary Element Analysis (EBEA). Energy Finite Element Analysis (EFEA) was validated on a floor-equipped composite cylinder by comparing EFEA vibroacoustic response predictions with Statistical Energy Analysis (SEA) and experimental results. Statistical Energy Analysis (SEA) predictions were made using the commercial software program VA One 2009 from ESI Group. The frequency region of interest for this study covers the one-third octave bands with center frequencies from 100 Hz to 4000 Hz.

Probabilistic finite elements for fatigue and fracture analysis

NASA Technical Reports Server (NTRS)

Belytschko, Ted; Liu, Wing Kam

1992-01-01

Attenuation is focused on the development of Probabilistic Finite Element Method (PFEM), which combines the finite element method with statistics and reliability methods, and its application to linear, nonlinear structural mechanics problems and fracture mechanics problems. The computational tool based on the Stochastic Boundary Element Method is also given for the reliability analysis of a curvilinear fatigue crack growth. The existing PFEM's have been applied to solve for two types of problems: (1) determination of the response uncertainty in terms of the means, variance and correlation coefficients; and (2) determination the probability of failure associated with prescribed limit states.

Hexahedral finite element mesh coarsening using pillowing technique

DOEpatents

Staten, Matthew L [Pittsburgh, PA; Woodbury, Adam C [Provo, UT; Benzley, Steven E [Provo, UT; Shepherd, Jason F [Edgewood, NM

2012-06-05

A techniques for coarsening a hexahedral mesh is described. The technique includes identifying a coarsening region within a hexahedral mesh to be coarsened. A boundary sheet of hexahedral elements is inserted into the hexahedral mesh around the coarsening region. A column of hexahedral elements is identified within the boundary sheet. The column of hexahedral elements is collapsed to create an extraction sheet of hexahedral elements contained within the coarsening region. Then, the extraction sheet of hexahedral elements is extracted to coarsen the hexahedral mesh.

NASTRAN thermal analyzer: A general purpose finite element heat transfer computer program

NASA Technical Reports Server (NTRS)

Lee, H.; Mason, J. B.

1972-01-01

The program not only can render temperature distributions in solids subjected to various thermal boundary conditions, including effects of diffuse-gray thermal radiation, but is fully compatible in capacity and in the finite-element model representation with that of its structural counterpart in the NASTRAN system. The development history of the finite-element approach for determining temperatures is summarized. The scope of analysis capability, program structure, features, and limitations are given with the objective of providing NASTRAN users with an overall veiw of the NASTRAN thermal analyzer.

Robust Hybrid Finite Element Methods for Antennas and Microwave Circuits

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, John L.

1996-01-01

One of the primary goals in this dissertation is concerned with the development of robust hybrid finite element-boundary integral (FE-BI) techniques for modeling and design of conformal antennas of arbitrary shape. Both the finite element and integral equation methods will be first overviewed in this chapter with an emphasis on recently developed hybrid FE-BI methodologies for antennas, microwave and millimeter wave applications. The structure of the dissertation is then outlined. We conclude the chapter with discussions of certain fundamental concepts and methods in electromagnetics, which are important to this study.

Development of non-linear finite element computer code

NASA Technical Reports Server (NTRS)

Becker, E. B.; Miller, T.

1985-01-01

Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein.

Solid/FEM integration at SNLA

NASA Technical Reports Server (NTRS)

Chavez, Patrick F.

1987-01-01

The effort at Sandia National Labs. on the methodologies and techniques being used to generate strict hexahedral finite element meshes from a solid model is described. The functionality of the modeler is used to decompose the solid into a set of nonintersecting meshable finite element primitives. The description of the decomposition is exported, via a Boundary Representative format, to the meshing program which uses the information for complete finite element model specification. Particular features of the program are discussed in some detail along with future plans for development which includes automation of the decomposition using artificial intelligence techniques.

Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2014-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Finite element modeling of mass transport in high-Péclet cardiovascular flows

NASA Astrophysics Data System (ADS)

Hansen, Kirk; Arzani, Amirhossein; Shadden, Shawn

2016-11-01

Mass transport plays an important role in many important cardiovascular processes, including thrombus formation and atherosclerosis. These mass transport problems are characterized by Péclet numbers of up to 108, leading to several numerical difficulties. The presence of thin near-wall concentration boundary layers requires very fine mesh resolution in these regions, while large concentration gradients within the flow cause numerical stabilization issues. In this work, we will discuss some guidelines for solving mass transport problems in cardiovascular flows using a stabilized Galerkin finite element method. First, we perform mesh convergence studies in a series of idealized and patient-specific geometries to determine the required near-wall mesh resolution for these types of problems, using both first- and second-order tetrahedral finite elements. Second, we investigate the use of several boundary condition types at outflow boundaries where backflow during some parts of the cardiac cycle can lead to convergence issues. Finally, we evaluate the effect of reducing Péclet number by increasing mass diffusivity as has been proposed by some researchers. This work was supported by the NSF GRFP and NSF Career Award #1354541.

A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis

NASA Astrophysics Data System (ADS)

Jokhio, G. A.; Izzuddin, B. A.

2015-05-01

This article presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-element, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-element along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-elements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.

Finite element analysis of thrust angle contact ball slewing bearing

NASA Astrophysics Data System (ADS)

Deng, Biao; Guo, Yuan; Zhang, An; Tang, Shengjin

2017-12-01

In view of the large heavy slewing bearing no longer follows the rigid ring hupothesis under the load condition, the entity finite element model of thrust angular contact ball bearing was established by using finite element analysis software ANSYS. The boundary conditions of the model were set according to the actual condition of slewing bearing, the internal stress state of the slewing bearing was obtained by solving and calculation, and the calculated results were compared with the numerical results based on the rigid ring assumption. The results show that more balls are loaded in the result of finite element method, and the maximum contact stresses between the ball and raceway have some reductions. This is because the finite element method considers the ferrule as an elastic body. The ring will produce structure deformation in the radial plane when the heavy load slewing bearings are subjected to external loads. The results of the finite element method are more in line with the actual situation of the slewing bearing in the engineering.

Application of laser ranging and VLBI data to a study of plate tectonic driving forces. [finite element method

NASA Technical Reports Server (NTRS)

Solomon, S. C.

1980-01-01

The measurability of changes in plate driving or resistive forces associated with plate boundary earthquakes by laser rangefinding or VLBI is considered with emphasis on those aspects of plate forces that can be characterized by such measurements. Topics covered include: (1) analytic solutions for two dimensional stress diffusion in a plate following earthquake faulting on a finite fault; (2) two dimensional finite-element solutions for the global state of stress at the Earth's surface for possible plate driving forces; and (3) finite-element solutions for three dimensional stress diffusion in a viscoelastic Earth following earthquake faulting.

Linear theory of boundary effects in open wind tunnels with finite jet lengths

NASA Technical Reports Server (NTRS)

Katzoff, S; Gardner, Clifford S; Diesendruck, Leo; Eisenstadt, Bertram J

1950-01-01

In the first part, the boundary conditions for an open wind tunnel (incompressible flow) are examined with special reference to the effects of the closed entrance and exit sections. Basic conditions are that the velocity must be continuous at the entrance lip and that the velocities in the upstream and downstream closed portions must be equal. In the second part, solutions are derived for four types of two-dimensional open tunnels, including one in which the pressures on the two free surfaces are not equal. Numerical results are given for every case. In general, if the lifting element is more than half the tunnel height from the inlet, the boundary effect at the lifting element is the same as for an infinitely long open tunnel. In the third part, a general method is given for calculating the boundary effect in an open circular wind tunnel of finite jet length. Numerical results are given for a lifting element concentrate at a point on the axis.

Three-dimensional elastic-plastic finite-element analysis of fatigue crack propagation

NASA Technical Reports Server (NTRS)

Goglia, G. L.; Chermahini, R. G.

1985-01-01

Fatigue cracks are a major problem in designing structures subjected to cyclic loading. Cracks frequently occur in structures such as aircraft and spacecraft. The inspection intervals of many aircraft structures are based on crack-propagation lives. Therefore, improved prediction of propagation lives under flight-load conditions (variable-amplitude loading) are needed to provide more realistic design criteria for these structures. The main thrust was to develop a three-dimensional, nonlinear, elastic-plastic, finite element program capable of extending a crack and changing boundary conditions for the model under consideration. The finite-element model is composed of 8-noded (linear-strain) isoparametric elements. In the analysis, the material is assumed to be elastic-perfectly plastic. The cycle stress-strain curve for the material is shown Zienkiewicz's initial-stress method, von Mises's yield criterion, and Drucker's normality condition under small-strain assumptions are used to account for plasticity. The three-dimensional analysis is capable of extending the crack and changing boundary conditions under cyclic loading.

User's Manual for FEM-BEM Method. 1.0

NASA Technical Reports Server (NTRS)

Butler, Theresa; Deshpande, M. D. (Technical Monitor)

2002-01-01

A user's manual for using FORTRAN code to perform electromagnetic analysis of arbitrarily shaped material cylinders using a hybrid method that combines the finite element method (FEM) and the boundary element method (BEM). In this method, the material cylinder is enclosed by a fictitious boundary and the Maxwell's equations are solved by FEM inside the boundary and by BEM outside the boundary. The electromagnetic scattering on several arbitrarily shaped material cylinders using this FORTRAN code is computed to as examples.

Research on Finite Element Model Generating Method of General Gear Based on Parametric Modelling

NASA Astrophysics Data System (ADS)

Lei, Yulong; Yan, Bo; Fu, Yao; Chen, Wei; Hou, Liguo

2017-06-01

Aiming at the problems of low efficiency and poor quality of gear meshing in the current mainstream finite element software, through the establishment of universal gear three-dimensional model, and explore the rules of unit and node arrangement. In this paper, a finite element model generation method of universal gear based on parameterization is proposed. Visual Basic program is used to realize the finite element meshing, give the material properties, and set the boundary / load conditions and other pre-processing work. The dynamic meshing analysis of the gears is carried out with the method proposed in this pape, and compared with the calculated values to verify the correctness of the method. The method greatly shortens the workload of gear finite element pre-processing, improves the quality of gear mesh, and provides a new idea for the FEM pre-processing.

Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities

NASA Astrophysics Data System (ADS)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-04-01

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix.

Nonlinear Structural Analysis

NASA Technical Reports Server (NTRS)

1984-01-01

Nonlinear structural analysis techniques for engine structures and components are addressed. The finite element method and boundary element method are discussed in terms of stress and structural analyses of shells, plates, and laminates.

Radiated Sound Power from a Curved Honeycomb Panel

NASA Technical Reports Server (NTRS)

Robinson, Jay H.; Buehrle, Ralph D.; Klos, Jacob; Grosveld, Ferdinand W.

2003-01-01

The validation of finite element and boundary element model for the vibro-acoustic response of a curved honeycomb core composite aircraft panel is completed. The finite element and boundary element models were previously validated separately. This validation process was hampered significantly by the method in which the panel was installed in the test facility. The fixture used was made primarily of fiberboard and the panel was held in a groove in the fiberboard by a compression fitting made of plastic tubing. The validated model is intended to be used to evaluate noise reduction concepts from both an experimental and analytic basis simultaneously. An initial parametric study of the influence of core thickness on the radiated sound power from this panel, using this numerical model was subsequently conducted. This study was significantly influenced by the presence of strong boundary condition effects but indicated that the radiated sound power from this panel was insensitive to core thickness primarily due to the offsetting effects of added mass and added stiffness in the frequency range investigated.

Finite element flow analysis; Proceedings of the Fourth International Symposium on Finite Element Methods in Flow Problems, Chuo University, Tokyo, Japan, July 26-29, 1982

NASA Astrophysics Data System (ADS)

Kawai, T.

Among the topics discussed are the application of FEM to nonlinear free surface flow, Navier-Stokes shallow water wave equations, incompressible viscous flows and weather prediction, the mathematical analysis and characteristics of FEM, penalty function FEM, convective, viscous, and high Reynolds number FEM analyses, the solution of time-dependent, three-dimensional and incompressible Navier-Stokes equations, turbulent boundary layer flow, FEM modeling of environmental problems over complex terrain, and FEM's application to thermal convection problems and to the flow of polymeric materials in injection molding processes. Also covered are FEMs for compressible flows, including boundary layer flows and transonic flows, hybrid element approaches for wave hydrodynamic loadings, FEM acoustic field analyses, and FEM treatment of free surface flow, shallow water flow, seepage flow, and sediment transport. Boundary element methods and FEM computational technique topics are also discussed. For individual items see A84-25834 to A84-25896

Boundary element analysis of post-tensioned slabs

NASA Astrophysics Data System (ADS)

Rashed, Youssef F.

2015-06-01

In this paper, the boundary element method is applied to carry out the structural analysis of post-tensioned flat slabs. The shear-deformable plate-bending model is employed. The effect of the pre-stressing cables is taken into account via the equivalent load method. The formulation is automated using a computer program, which uses quadratic boundary elements. Verification samples are presented, and finally a practical application is analyzed where results are compared against those obtained from the finite element method. The proposed method is efficient in terms of computer storage and processing time as well as the ease in data input and modifications.

Constrained and Unconstrained Variational Finite Element Formulation of Solutions to a Stress Wave Problem - a Numerical Comparison.

DTIC Science & Technology

1982-10-01

Element Unconstrained Variational Formulations," Innovativ’e Numerical Analysis For the Applied Engineering Science, R. P. Shaw, et at, Fitor...Initial Boundary Value of Gun Dynamics Solved by Finite Element Unconstrained Variational Formulations," Innovative Numerical Analysis For the Applied ... Engineering Science, R. P. Shaw, et al, Editors, University Press of Virginia, Charlottesville, pp. 733-741, 1980. 2 J. J. Wu, "Solutions to Initial

Finite element method for calculating spectral and optical characteristics of axially symmetric quantum dots

NASA Astrophysics Data System (ADS)

Gusev, A. A.; Chuluunbaatar, O.; Vinitsky, S. I.; Derbov, V. L.; Hai, L. L.; Kazaryan, E. M.; Sarkisyan, H. A.

2018-04-01

We present new calculation schemes using high-order finite element method implemented on unstructured grids with triangle elements for solving boundary-value problems that describe axially symmetric quantum dots. The efficiency of the algorithms and software is demonstrated by benchmark calculations of the energy spectrum, the envelope eigenfunctions of electron, hole and exciton states, and the direct interband light absorption in conical and spheroidal impenetrable quantum dots.

Scattering of Acoustic Waves from Ocean Boundaries

DTIC Science & Technology

2015-09-30

of buried mines and improve SONAR performance in shallow water. OBJECTIVES 1) Determination of the correct physical model of acoustic propagation... acoustic parameters in the ocean. APPROACH 1) Finite Element Modeling for Range Dependent Waveguides: Finite element modeling is applied to a...roughness measurements for reverberation modeling . GLISTEN data provide insight into the role of biology on acoustic propagation and scattering

Prediction of the thermal environment and thermal response of simple panels exposed to radiant heat

NASA Technical Reports Server (NTRS)

Turner, Travis L.; Ash, Robert L.

1989-01-01

A method of predicting the radiant heat flux distribution produced by a bank of tubular quartz heaters was applied to a radiant system consisting of a single unreflected lamp irradiating a flat metallic incident surface. In this manner, the method was experimentally verified for various radiant system parameter settings and used as a source of input for a finite element thermal analysis. Two finite element thermal analyses were applied to a thermal system consisting of a thin metallic panel exposed to radiant surface heating. A two-dimensional steady-state finite element thermal analysis algorithm, based on Galerkin's Method of Weighted Residuals (GFE), was formulated specifically for this problem and was used in comparison to the thermal analyzers of the Engineering Analysis Language (EAL). Both analyses allow conduction, convection, and radiation boundary conditions. Differences in the respective finite element formulation are discussed in terms of their accuracy and resulting comparison discrepancies. The thermal analyses are shown to perform well for the comparisons presented here with some important precautions about the various boundary condition models. A description of the experiment, corresponding analytical modeling, and resulting comparisons are presented.

Approximating the stress field within the unit cell of a fabric reinforced composite using replacement elements

NASA Technical Reports Server (NTRS)

Foye, R. L.

1993-01-01

This report concerns the prediction of the elastic moduli and the internal stresses within the unit cell of a fabric reinforced composite. In the proposed analysis no restrictions or assumptions are necessary concerning yarn or tow cross-sectional shapes or paths through the unit cell but the unit cell itself must be a right hexagonal parallelepiped. All the unit cell dimensions are assumed to be small with respect to the thickness of the composite structure that it models. The finite element analysis of a unit cell is usually complicated by the mesh generation problems and the non-standard, adjacent-cell boundary conditions. This analysis avoids these problems through the use of preprogrammed boundary conditions and replacement materials (or elements). With replacement elements it is not necessary to match all the constitutional material interfaces with finite element boundaries. Simple brick-shaped elements can be used to model the unit cell structure. The analysis predicts the elastic constants and the average stresses within each constituent material of each brick element. The application and results of this analysis are demonstrated through several example problems which include a number of composite microstructures.

Inversion of Robin coefficient by a spectral stochastic finite element approach

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

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

NOTE: Solving the ECG forward problem by means of a meshless finite element method

NASA Astrophysics Data System (ADS)

Li, Z. S.; Zhu, S. A.; He, Bin

2007-07-01

The conventional numerical computational techniques such as the finite element method (FEM) and the boundary element method (BEM) require laborious and time-consuming model meshing. The new meshless FEM only uses the boundary description and the node distribution and no meshing of the model is required. This paper presents the fundamentals and implementation of meshless FEM and the meshless FEM method is adapted to solve the electrocardiography (ECG) forward problem. The method is evaluated on a single-layer torso model, in which the analytical solution exists, and tested in a realistic geometry homogeneous torso model, with satisfactory results being obtained. The present results suggest that the meshless FEM may provide an alternative for ECG forward solutions.

Electromagnetic scattering and radiation from microstrip patch antennas and spirals residing in a cavity

NASA Technical Reports Server (NTRS)

Volakis, J. L.; Gong, J.; Alexanian, A.; Woo, A.

1992-01-01

A new hybrid method is presented for the analysis of the scattering and radiation by conformal antennas and arrays comprised of circular or rectangular elements. In addition, calculations for cavity-backed spiral antennas are given. The method employs a finite element formulation within the cavity and the boundary integral (exact boundary condition) for terminating the mesh. By virtue of the finite element discretization, the method has no restrictions on the geometry and composition of the cavity or its termination. Furthermore, because of the convolutional nature of the boundary integral and the inherent sparseness of the finite element matrix, the storage requirement is kept very low at O(n). These unique features of the method have already been exploited in other scattering applications and have permitted the analysis of large-size structures with remarkable efficiency. In this report, we describe the method's formulation and implementation for circular and rectangular patch antennas in different superstrate and substrate configurations which may also include the presence of lumped loads and resistive sheets/cards. Also, various modelling approaches are investigated and implemented for characterizing a variety of feed structures to permit the computation of the input impedance and radiation pattern. Many computational examples for rectangular and circular patch configurations are presented which demonstrate the method's versatility, modeling capability and accuracy.

Micromorphic approach for gradient-extended thermo-elastic-plastic solids in the logarithmic strain space

NASA Astrophysics Data System (ADS)

Aldakheel, Fadi

2017-11-01

The coupled thermo-mechanical strain gradient plasticity theory that accounts for microstructure-based size effects is outlined within this work. It extends the recent work of Miehe et al. (Comput Methods Appl Mech Eng 268:704-734, 2014) to account for thermal effects at finite strains. From the computational viewpoint, the finite element design of the coupled problem is not straightforward and requires additional strategies due to the difficulties near the elastic-plastic boundaries. To simplify the finite element formulation, we extend it toward the micromorphic approach to gradient thermo-plasticity model in the logarithmic strain space. The key point is the introduction of dual local-global field variables via a penalty method, where only the global fields are restricted by boundary conditions. Hence, the problem of restricting the gradient variable to the plastic domain is relaxed, which makes the formulation very attractive for finite element implementation as discussed in Forest (J Eng Mech 135:117-131, 2009) and Miehe et al. (Philos Trans R Soc A Math Phys Eng Sci 374:20150170, 2016).

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

NASA Technical Reports Server (NTRS)

Noor, A. K. (Editor); Hayduk, R. J. (Editor)

1985-01-01

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Moving Particles Through a Finite Element Mesh

PubMed Central

Peskin, Adele P.; Hardin, Gary R.

1998-01-01

We present a new numerical technique for modeling the flow around multiple objects moving in a fluid. The method tracks the dynamic interaction between each particle and the fluid. The movements of the fluid and the object are directly coupled. A background mesh is designed to fit the geometry of the overall domain. The mesh is designed independently of the presence of the particles except in terms of how fine it must be to track particles of a given size. Each particle is represented by a geometric figure that describes its boundary. This figure overlies the mesh. Nodes are added to the mesh where the particle boundaries intersect the background mesh, increasing the number of nodes contained in each element whose boundary is intersected. These additional nodes are then used to describe and track the particle in the numerical scheme. Appropriate element shape functions are defined to approximate the solution on the elements with extra nodes. The particles are moved through the mesh by moving only the overlying nodes defining the particles. The regular finite element grid remains unchanged. In this method, the mesh does not distort as the particles move. Instead, only the placement of particle-defining nodes changes as the particles move. Element shape functions are updated as the nodes move through the elements. This method is especially suited for models of moderate numbers of moderate-size particles, where the details of the fluid-particle coupling are important. Both the complications of creating finite element meshes around appreciable numbers of particles, and extensive remeshing upon movement of the particles are simplified in this method. PMID:28009377

[3-D finite element modeling of internal fixation of mandibular mental fracture and the design of boundary constraints].

PubMed

Luo, Xiaohui; Wang, Hang; Fan, Yubo

2007-04-01

This study was aimed to develop a 3-D finite element (3-D FE) model of the mental fractured mandible and design the boundary constrains. The CT images from a health volunteer were used as the original information and put into ANSYS program to build a 3-D FE model. The model of the miniplate and screw which were used for the internal fixation was established by Pro/E. The boundary constrains of different muscle loadings were used to simulate the 3 functional conditions of the mandible. A 3-D FE model of mental fractured mandible under the miniplate-screw internal fixation system was constructed. And by the boundary constraints, the 3 biting conditions were simulated and the model could serve as a foundation on which to analyze the biomechanical behavior of the fractured mandible.

Survey of the status of finite element methods for partial differential equations

NASA Technical Reports Server (NTRS)

Temam, Roger

1986-01-01

The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

Failure modes for compression loaded angle-ply plates with holes

NASA Technical Reports Server (NTRS)

Burns, S. W.; Herakovich, C. T.; Williams, J. G.

1987-01-01

A combined theoretical-experimental investigation of failure in notched, graphite-epoxy, angle-ply laminates subjected to far-field compression loading indicates that failure generally initiates on the hole boundary and propagates along a line parallel to the fiber orientation of the laminate. The strength of notched laminates with specimen width-to-hole diameter ratios of 5 and 10 are compared to the strength of unnotched laminates. The experimental results are complemented by a three-dimensional finite element stress analysis that includes interlaminar stresses around holes in (+/- theta)s laminates. The finite element predictions indicate that failure is initiated by shear stresses at the hole boundary.

Electrodiffusion: a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution.

PubMed

Lu, Benzhuo; Zhou, Y C; Huber, Gary A; Bond, Stephen D; Holst, Michael J; McCammon, J Andrew

2007-10-07

A computational framework is presented for the continuum modeling of cellular biomolecular diffusion influenced by electrostatic driving forces. This framework is developed from a combination of state-of-the-art numerical methods, geometric meshing, and computer visualization tools. In particular, a hybrid of (adaptive) finite element and boundary element methods is adopted to solve the Smoluchowski equation (SE), the Poisson equation (PE), and the Poisson-Nernst-Planck equation (PNPE) in order to describe electrodiffusion processes. The finite element method is used because of its flexibility in modeling irregular geometries and complex boundary conditions. The boundary element method is used due to the convenience of treating the singularities in the source charge distribution and its accurate solution to electrostatic problems on molecular boundaries. Nonsteady-state diffusion can be studied using this framework, with the electric field computed using the densities of charged small molecules and mobile ions in the solvent. A solution for mesh generation for biomolecular systems is supplied, which is an essential component for the finite element and boundary element computations. The uncoupled Smoluchowski equation and Poisson-Boltzmann equation are considered as special cases of the PNPE in the numerical algorithm, and therefore can be solved in this framework as well. Two types of computations are reported in the results: stationary PNPE and time-dependent SE or Nernst-Planck equations solutions. A biological application of the first type is the ionic density distribution around a fragment of DNA determined by the equilibrium PNPE. The stationary PNPE with nonzero flux is also studied for a simple model system, and leads to an observation that the interference on electrostatic field of the substrate charges strongly affects the reaction rate coefficient. The second is a time-dependent diffusion process: the consumption of the neurotransmitter acetylcholine by acetylcholinesterase, determined by the SE and a single uncoupled solution of the Poisson-Boltzmann equation. The electrostatic effects, counterion compensation, spatiotemporal distribution, and diffusion-controlled reaction kinetics are analyzed and different methods are compared.

Broadband ground motion simulation using a paralleled hybrid approach of Frequency Wavenumber and Finite Difference method

NASA Astrophysics Data System (ADS)

Chen, M.; Wei, S.

2016-12-01

The serious damage of Mexico City caused by the 1985 Michoacan earthquake 400 km away indicates that urban areas may be affected by remote earthquakes. To asses earthquake risk of urban areas imposed by distant earthquakes, we developed a hybrid Frequency Wavenumber (FK) and Finite Difference (FD) code implemented with MPI, since the computation of seismic wave propagation from a distant earthquake using a single numerical method (e.g. Finite Difference, Finite Element or Spectral Element) is very expensive. In our approach, we compute the incident wave field (ud) at the boundaries of the excitation box, which surrounding the local structure, using a paralleled FK method (Zhu and Rivera, 2002), and compute the total wave field (u) within the excitation box using a parallelled 2D FD method. We apply perfectly matched layer (PML) absorbing condition to the diffracted wave field (u-ud). Compared to previous Generalized Ray Theory and Finite Difference (Wen and Helmberger, 1998), Frequency Wavenumber and Spectral Element (Tong et al., 2014), and Direct Solution Method and Spectral Element hybrid method (Monteiller et al., 2013), our absorbing boundary condition dramatically suppress the numerical noise. The MPI implementation of our method can greatly speed up the calculation. Besides, our hybrid method also has a potential use in high resolution array imaging similar to Tong et al. (2014).

Guidelines and Recommendations on the Use of Higher Order Finite Elements for Bending Analysis of Plates

NASA Astrophysics Data System (ADS)

Carrera, E.; Miglioretti, F.; Petrolo, M.

2011-11-01

This paper compares and evaluates various plate finite elements to analyse the static response of thick and thin plates subjected to different loading and boundary conditions. Plate elements are based on different assumptions for the displacement distribution along the thickness direction. Classical (Kirchhoff and Reissner-Mindlin), refined (Reddy and Kant), and other higher-order displacement fields are implemented up to fourth-order expansion. The Unified Formulation UF by the first author is used to derive finite element matrices in terms of fundamental nuclei which consist of 3×3 arrays. The MITC4 shear-locking free type formulation is used for the FE approximation. Accuracy of a given plate element is established in terms of the error vs. thickness-to-length parameter. A significant number of finite elements for plates are implemented and compared using displacement and stress variables for various plate problems. Reduced models that are able to detect the 3D solution are built and a Best Plate Diagram (BPD) is introduced to give guidelines for the construction of plate theories based on a given accuracy and number of terms. It is concluded that the UF is a valuable tool to establish, for a given plate problem, the most accurate FE able to furnish results within a certain accuracy range. This allows us to obtain guidelines and recommendations in building refined elements in the bending analysis of plates for various geometries, loadings, and boundary conditions.

Sensitivity analysis on the effective stiffness properties of 3-D orthotropic honeycomb cores

NASA Astrophysics Data System (ADS)

Karakoç, Alp

2018-01-01

The present study investigates the influences of representative volume element RVE mesh and material parameters, here cell wall elastic moduli, on the effective stiffness properties of three dimensional orthotropic honeycomb cores through strain driven computational homogenization in the finite element framework. For this purpose, case studies were carried out, for which hexagonal cellular RVEs were generated, meshed with eight node linear brick finite elements of varying numbers. Periodic boundary conditions were then implemented on the RVE boundaries by using one-to-one nodal match for the corresponding corners, edges and surfaces for the imposed macroscopic strains. As a novelty, orthotropic material properties were assigned for each cell wall by means of the transformation matrices following the cell wall orientations. Thereafter, simulations were conducted and volume averaged macroscopic stresses were obtained. Eventually, effective stiffness properties were obtained, through which RVE sensitivity analysis was carried out. The investigations indicate that there is a strong relation between number of finite elements and most of the effective stiffness parameters. In addition to this, cell wall elastic moduli also play critical role on the effective properties of the investigated materials.

Analysis of cylindrical wrap-around and doubly conformal patch antennas by way of the finite element-artificial absorber method

NASA Technical Reports Server (NTRS)

Volakis, J. L.; Kempel, L. C.; Sliva, R.; Wang, H. T. G.; Woo, A. G.

1994-01-01

The goal of this project was to develop analysis codes for computing the scattering and radiation of antennas on cylindrically and doubly conformal platforms. The finite element-boundary integral (FE-BI) method has been shown to accurately model the scattering and radiation of cavity-backed patch antennas. Unfortunately extension of this rigorous technique to coated or doubly curved platforms is cumbersome and inefficient. An alternative approximate approach is to employ an absorbing boundary condition (ABC) for terminating the finite element mesh thus avoiding use of a Green's function. A FE-ABC method is used to calculate the radar cross section (RCS) and radiation pattern of a cavity-backed patch antenna which is recessed within a metallic surface. It is shown that this approach is accurate for RCS and antenna pattern calculations with an ABC surface displaced as little as 0.3 lambda from the cavity aperture. These patch antennas may have a dielectric overlay which may also be modeled with this technique.

Hybrid finite difference/finite element immersed boundary method.

PubMed

E Griffith, Boyce; Luo, Xiaoyu

2017-12-01

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.

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.

The Model Experiments and Finite Element Analysis on Deformation and Failure by Excavation of Grounds in Foregoing-roof Method

NASA Astrophysics Data System (ADS)

Sotokoba, Yasumasa; Okajima, Kenji; Iida, Toshiaki; Tanaka, Tadatsugu

We propose the trenchless box culvert construction method to construct box culverts in small covering soil layers while keeping roads or tracks open. When we use this construction method, it is necessary to clarify deformation and shear failure by excavation of grounds. In order to investigate the soil behavior, model experiments and elasto-plactic finite element analysis were performed. In the model experiments, it was shown that the shear failure was developed from the end of the roof to the toe of the boundary surface. In the finite element analysis, a shear band effect was introduced. Comparing the observed shear bands in model experiments with computed maximum shear strain contours, it was found that the observed direction of the shear band could be simulated reasonably by the finite element analysis. We may say that the finite element method used in this study is useful tool for this construction method.

Models and finite element approximations for interacting nanosized piezoelectric bodies and acoustic medium

NASA Astrophysics Data System (ADS)

Nasedkin, A. V.

2017-01-01

This research presents the new size-dependent models of piezoelectric materials oriented to finite element applications. The proposed models include the facilities of taking into account different mechanisms of damping for mechanical and electric fields. The coupled models also incorporate the equations of the theory of acoustics for viscous fluids. In particular cases, these models permit to use the mode superposition method with full separation of the finite element systems into independent equations for the independent modes for transient and harmonic problems. The main boundary conditions were supplemented with the facilities of taking into account the coupled surface effects, allowing to explore the nanoscale piezoelectric materials in the framework of theories of continuous media with surface stresses and their generalizations. For the considered problems we have implemented the finite element technologies and various numerical algorithms to maintain a symmetrical structure of the finite element quasi-definite matrices (matrix structure for the problems with a saddle point).

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

Performance of low-rank QR approximation of the finite element Biot-Savart law

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

White, D A; Fasenfest, B J

2006-01-12

We are concerned with the computation of magnetic fields from known electric currents in the finite element setting. In finite element eddy current simulations it is necessary to prescribe the magnetic field (or potential, depending upon the formulation) on the conductor boundary. In situations where the magnetic field is due to a distributed current density, the Biot-Savart law can be used, eliminating the need to mesh the nonconducting regions. Computation of the Biot-Savart law can be significantly accelerated using a low-rank QR approximation. We review the low-rank QR method and report performance on selected problems.

ICAN/PART: Particulate composite analyzer, user's manual and verification studies

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Murthy, Pappu L. N.; Mital, Subodh K.

1996-01-01

A methodology for predicting the equivalent properties and constituent microstresses for particulate matrix composites, based on the micromechanics approach, is developed. These equations are integrated into a computer code developed to predict the equivalent properties and microstresses of fiber reinforced polymer matrix composites to form a new computer code, ICAN/PART. Details of the flowchart, input and output for ICAN/PART are described, along with examples of the input and output. Only the differences between ICAN/PART and the original ICAN code are described in detail, and the user is assumed to be familiar with the structure and usage of the original ICAN code. Detailed verification studies, utilizing dim dimensional finite element and boundary element analyses, are conducted in order to verify that the micromechanics methodology accurately models the mechanics of particulate matrix composites. ne equivalent properties computed by ICAN/PART fall within bounds established by the finite element and boundary element results. Furthermore, constituent microstresses computed by ICAN/PART agree in average sense with results computed using the finite element method. The verification studies indicate that the micromechanics programmed into ICAN/PART do indeed accurately model the mechanics of particulate matrix composites.

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1988-01-01

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

Finite element modelling of creep cavity filling by solute diffusion

NASA Astrophysics Data System (ADS)

Versteylen, C. D.; Szymański, N. K.; Sluiter, M. H. F.; van Dijk, N. H.

2018-04-01

In recently discovered self healing creep steels, open-volume creep cavities are filled by the precipitation of supersaturated solute. These creep cavities form on the grain boundaries oriented perpendicular to the applied stress. The presence of a free surface triggers a flux of solute from the matrix, over the grain boundaries towards the creep cavities. We studied the creep cavity filling by finite element modelling and found that the filling time critically depends on (i) the ratio of diffusivities in the grain boundary and the bulk, and (ii) on the ratio of the intercavity distance and the cavity size. For a relatively large intercavity spacing 3D transport is observed when the grain boundary and volume diffusivities are of a similar order of magnitude, while a 2D behaviour is observed when the grain boundary diffusivity is dominant. Instead when the intercavity distance is small, the transport behaviour tends to a 1D behaviour in all cases, as the amount of solute available in the grain boundary is insufficient. A phase diagram with the transition lines is constructed.

New Developments in the Embedded Statistical Coupling Method: Atomistic/Continuum Crack Propagation

NASA Technical Reports Server (NTRS)

Saether, E.; Yamakov, V.; Glaessgen, E.

2008-01-01

A concurrent multiscale modeling methodology that embeds a molecular dynamics (MD) region within a finite element (FEM) domain has been enhanced. The concurrent MD-FEM coupling methodology uses statistical averaging of the deformation of the atomistic MD domain to provide interface displacement boundary conditions to the surrounding continuum FEM region, which, in turn, generates interface reaction forces that are applied as piecewise constant traction boundary conditions to the MD domain. The enhancement is based on the addition of molecular dynamics-based cohesive zone model (CZM) elements near the MD-FEM interface. The CZM elements are a continuum interpretation of the traction-displacement relationships taken from MD simulations using Cohesive Zone Volume Elements (CZVE). The addition of CZM elements to the concurrent MD-FEM analysis provides a consistent set of atomistically-based cohesive properties within the finite element region near the growing crack. Another set of CZVEs are then used to extract revised CZM relationships from the enhanced embedded statistical coupling method (ESCM) simulation of an edge crack under uniaxial loading.

Structural and Acoustic Numerical Modeling of a Curved Composite Honeycomb Panel

NASA Technical Reports Server (NTRS)

Grosveld, Ferdinand W.; Buehrle, Ralph D.; Robinson, Jay H.

2001-01-01

The finite and boundary element modeling of the curved section of a composite honeycomb aircraft fuselage sidewall was validated for both structural response and acoustic radiation. The curved panel was modeled in the pre-processor MSC/PATRAN. Geometry models of the curved panel were constructed based on the physical dimensions of the test article. Material properties were obtained from the panel manufacturer. Finite element models were developed to predict the modal parameters for free and supported panel boundary conditions up to a frequency of 600 Hz. Free boundary conditions were simulated by providing soft foam support under the four comers of the panel or by suspending the panel from elastic bands. Supported boundary conditions were obtained by clamping the panel between plastic tubing seated in grooves along the perimeter of a stiff and heavy frame. The frame was installed in the transmission loss window of the Structural Acoustic Loads and Transmission (SALT) facility at NASA Langley Research Center. The structural response of the curved panel due to point force excitation was predicted using MSC/NASTRAN and the radiated sound was computed with COMET/Acoustics. The predictions were compared with the results from experimental modal surveys and forced response tests on the fuselage panel. The finite element models were refined and updated to provide optimum comparison with the measured modal data. Excellent agreement was obtained between the numerical and experimental modal data for the free as well as for the supported boundary conditions. Frequency response functions (FRF) were computed relating the input force excitation at one panel location to the surface acceleration response at five panel locations. Frequency response functions were measured at the same locations on the test specimen and were compared with the calculated FRF values. Good agreement was obtained for the real and imaginary parts of the transfer functions when modal participation was allowed up to 3000 Hz. The validated finite element model was used to predict the surface velocities due to the point force excitation. Good agreement was obtained between the spatial characteristics of the predicted and measured surface velocities. The measured velocity data were input into the acoustic boundary element code to compute the sound radiated by the panel. The predicted sound pressure levels in the far-field of the panel agreed well with the sound pressure levels measured at the same location.

Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

NASA Technical Reports Server (NTRS)

Sutjahjo, Edhi; Chamis, Christos C.

1993-01-01

Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

[Finite Element Modelling of the Eye for the Investigation of Accommodation].

PubMed

Martin, H; Stachs, O; Guthoff, R; Grabow, N

2016-12-01

Background: Accommodation research increasingly uses engineering methods. This article presents the use of the finite element method in accommodation research. Material and Methods: Geometry, material data and boundary conditions are prerequisites for the application of the finite element method. Published data on geometry and materials are reviewed. It is shown how boundary conditions are important and how they influence the results. Results: Two dimensional and three dimensional models of the anterior chamber of the eye are presented. With simple two dimensional models, it is shown that realistic results for the accommodation amplitude can always be achieved. More complex three dimensional models of the accommodation mechanism - including the ciliary muscle - require further investigations of the material data and of the morphology of the ciliary muscle, if they are to achieve realistic results for accommodation. Discussion and Conclusion: The efficiency and the limitations of the finite element method are especially clear for accommodation. Application of the method requires extensive preparation, including acquisition of geometric and material data and experimental validation. However, a validated model can be used as a basis for parametric studies, by systematically varying material data and geometric dimensions. This allows systematic investigation of how essential input parameters influence the results. Georg Thieme Verlag KG Stuttgart · New York.

Structural Noise and Acoustic Characteristics Improvement of Transport Power Plants

NASA Astrophysics Data System (ADS)

Chaynov, N. D.; Markov, V. A.; Savastenko, A. A.

2018-03-01

Noise reduction generated during the operation of various machines and mechanisms is an urgent task with regard to the power plants and, in particular, to internal combustion engines. Sound emission from the surfaces vibration of body parts is one of the main noise manifestations of the running engine and it is called a structural noise. The vibration defining of the outer surfaces of complex body parts and the calculation of their acoustic characteristics are determined with numerical methods. At the same time, realization of finite and boundary elements methods combination turned out to be very effective. The finite element method is used in calculating the structural elements vibrations, and the boundary elements method is used in the structural noise calculation. The main conditions of the methodology and the results of the structural noise analysis applied to a number of automobile engines are shown.

A parametric study of hard tissue injury prediction using finite elements: consideration of geometric complexity, subfailure material properties, CT-thresholding, and element characteristics.

PubMed

Arregui-Dalmases, Carlos; Del Pozo, Eduardo; Duprey, Sonia; Lopez-Valdes, Francisco J; Lau, Anthony; Subit, Damien; Kent, Richard

2010-06-01

The objectives of this study were to examine the axial response of the clavicle under quasistatic compressions replicating the body boundary conditions and to quantify the sensitivity of finite element-predicted fracture in the clavicle to several parameters. Clavicles were harvested from 14 donors (age range 14-56 years). Quasistatic axial compression tests were performed using a custom rig designed to replicate in situ boundary conditions. Prior to testing, high-resolution computed tomography (CT) scans were taken of each clavicle. From those images, finite element models were constructed. Factors varied parametrically included the density used to threshold cortical bone in the CT scans, the presence of trabecular bone, the mesh density, Young's modulus, the maximum stress, and the element type (shell vs. solid, triangular vs. quadrilateral surface elements). The experiments revealed significant variability in the peak force (2.41 +/- 0.72 kN) and displacement to peak force (4.9 +/- 1.1 mm), with age (p < .05) and with some geometrical traits of the specimens. In the finite element models, the failure force and location were moderately dependent upon the Young's modulus. The fracture force was highly sensitive to the yield stress (80-110 MPa). Neither fracture location nor force was strongly dependent on mesh density as long as the element size was less than 5 x 5 mm(2). Both the fracture location and force were strongly dependent upon the threshold density used to define the thickness of the cortical shell.

Frequency response function (FRF) based updating of a laser spot welded structure

NASA Astrophysics Data System (ADS)

Zin, M. S. Mohd; Rani, M. N. Abdul; Yunus, M. A.; Sani, M. S. M.; Wan Iskandar Mirza, W. I. I.; Mat Isa, A. A.

2018-04-01

The objective of this paper is to present frequency response function (FRF) based updating as a method for matching the finite element (FE) model of a laser spot welded structure with a physical test structure. The FE model of the welded structure was developed using CQUAD4 and CWELD element connectors, and NASTRAN was used to calculate the natural frequencies, mode shapes and FRF. Minimization of the discrepancies between the finite element and experimental FRFs was carried out using the exceptional numerical capability of NASTRAN Sol 200. The experimental work was performed under free-free boundary conditions using LMS SCADAS. Avast improvement in the finite element FRF was achieved using the frequency response function (FRF) based updating with two different objective functions proposed.

ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve☆

PubMed Central

Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk

2014-01-01

In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) [52] are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly singular and hyper-singular integral equations and prove, in particular, convergence of the related adaptive mesh-refining algorithms. Throughout, the theoretical findings are underlined by numerical experiments. PMID:24748725

Multiscale Modeling of Intergranular Fracture in Aluminum: Constitutive Relation For Interface Debonding

NASA Technical Reports Server (NTRS)

Yamakov, V.; Saether, E.; Glaessgen, E. H.

2008-01-01

Intergranular fracture is a dominant mode of failure in ultrafine grained materials. In the present study, the atomistic mechanisms of grain-boundary debonding during intergranular fracture in aluminum are modeled using a coupled molecular dynamics finite element simulation. Using a statistical mechanics approach, a cohesive-zone law in the form of a traction-displacement constitutive relationship, characterizing the load transfer across the plane of a growing edge crack, is extracted from atomistic simulations and then recast in a form suitable for inclusion within a continuum finite element model. The cohesive-zone law derived by the presented technique is free of finite size effects and is statistically representative for describing the interfacial debonding of a grain boundary (GB) interface examined at atomic length scales. By incorporating the cohesive-zone law in cohesive-zone finite elements, the debonding of a GB interface can be simulated in a coupled continuum-atomistic model, in which a crack starts in the continuum environment, smoothly penetrates the continuum-atomistic interface, and continues its propagation in the atomistic environment. This study is a step towards relating atomistically derived decohesion laws to macroscopic predictions of fracture and constructing multiscale models for nanocrystalline and ultrafine grained materials.

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

Discontinuous dual-primal mixed finite elements for elliptic problems

NASA Technical Reports Server (NTRS)

Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo

2000-01-01

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

Benchmark model correction of monitoring system based on Dynamic Load Test of Bridge

NASA Astrophysics Data System (ADS)

Shi, Jing-xian; Fan, Jiang

2018-03-01

Structural health monitoring (SHM) is a field of research in the area, and it’s designed to achieve bridge safety and reliability assessment, which needs to be carried out on the basis of the accurate simulation of the finite element model. Bridge finite element model is simplified of the structural section form, support conditions, material properties and boundary condition, which is based on the design and construction drawings, and it gets the calculation models and the results.But according to the design and specification requirements established finite element model due to its cannot fully reflect the true state of the bridge, so need to modify the finite element model to obtain the more accurate finite element model. Based on Da-guan river crossing of Ma - Zhao highway in Yunnan province as the background to do the dynamic load test test, we find that the impact coefficient of the theoretical model of the bridge is very different from the coefficient of the actual test, and the change is different; according to the actual situation, the calculation model is adjusted to get the correct frequency of the bridge, the revised impact coefficient found that the modified finite element model is closer to the real state, and provides the basis for the correction of the finite model.

A combined finite element-boundary integral formulation for solution of two-dimensional scattering problems via CGFFT. [Conjugate Gradient Fast Fourier Transformation

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Volakis, John L.; Jin, Jian-Ming

1990-01-01

A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principal advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.

A combined finite element and boundary integral formulation for solution via CGFFT of 2-dimensional scattering problems

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Volakis, John L.

1989-01-01

A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principle advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.

Probabilistic Structural Analysis Theory Development

NASA Technical Reports Server (NTRS)

Burnside, O. H.

1985-01-01

The objective of the Probabilistic Structural Analysis Methods (PSAM) project is to develop analysis techniques and computer programs for predicting the probabilistic response of critical structural components for current and future space propulsion systems. This technology will play a central role in establishing system performance and durability. The first year's technical activity is concentrating on probabilistic finite element formulation strategy and code development. Work is also in progress to survey critical materials and space shuttle mian engine components. The probabilistic finite element computer program NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) is being developed. The final probabilistic code will have, in the general case, the capability of performing nonlinear dynamic of stochastic structures. It is the goal of the approximate methods effort to increase problem solving efficiency relative to finite element methods by using energy methods to generate trial solutions which satisfy the structural boundary conditions. These approximate methods will be less computer intensive relative to the finite element approach.

ESCHER: An interactive mesh-generating editor for preparing finite-element input

NASA Technical Reports Server (NTRS)

Oakes, W. R., Jr.

1984-01-01

ESCHER is an interactive mesh generation and editing program designed to help the user create a finite-element mesh, create additional input for finite-element analysis, including initial conditions, boundary conditions, and slidelines, and generate a NEUTRAL FILE that can be postprocessed for input into several finite-element codes, including ADINA, ADINAT, DYNA, NIKE, TSAAS, and ABUQUS. Two important ESCHER capabilities, interactive geometry creation and mesh archival storge are described in detail. Also described is the interactive command language and the use of interactive graphics. The archival storage and restart file is a modular, entity-based mesh data file. Modules of this file correspond to separate editing modes in the mesh editor, with data definition syntax preserved between the interactive commands and the archival storage file. Because ESCHER was expected to be highly interactive, extensive user documentation was provided in the form of an interactive HELP package.

Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1983-01-01

A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.

TORO II: A finite element computer program for nonlinear quasi-static problems in electromagnetics: Part 1, Theoretical background

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

Gartling, D.K.

The theoretical and numerical background for the finite element computer program, TORO II, is presented in detail. TORO II is designed for the multi-dimensional analysis of nonlinear, electromagnetic field problems described by the quasi-static form of Maxwell`s equations. A general description of the boundary value problems treated by the program is presented. The finite element formulation and the associated numerical methods used in TORO II are also outlined. Instructions for the use of the code are documented in SAND96-0903; examples of problems analyzed with the code are also provided in the user`s manual. 24 refs., 8 figs.

A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain

NASA Astrophysics Data System (ADS)

Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V.

2018-05-01

The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form $\\Delta t\\le C$, where $C$ depends only on problem data, and $h^{2m_u+2}\\le c\\,\\Delta t$, $m_u$ is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

Transient conduction-radiation analysis of an absolute active cavity radiometer using finite elements

NASA Technical Reports Server (NTRS)

Mahan, J. R.; Kowsary, F.; Tira, N.; Gardiner, B. D.

1987-01-01

A NASA-developed finite element-based model of a generic active cavity radiometer (ACR) has been developed in order to study the dependence on operating temperature of the closed-loop and open-loop transient response of the instrument. Transient conduction within the sensing element is explored, and the transient temperature distribution resulting from the application of a time-varying radiative boundary condition is calculated. The results verify the prediction that operation of an ACR at cryogenic temperatures results in large gains in frequency response.

Prediction of response of aircraft panels subjected to acoustic and thermal loads

NASA Technical Reports Server (NTRS)

Mei, Chuh

1992-01-01

The primary effort of this research project has been focused on the development of analytical methods for the prediction of random response of structural panels subjected to combined and intense acoustic and thermal loads. The accomplishments on various acoustic fatigue research activities are described first, then followed by publications and theses. Topics covered include: transverse shear deformation; finite element models of vibrating composite laminates; large deflection vibration modeling; finite element analysis of thermal buckling; and prediction of three dimensional duct using boundary element method.

ANALYZING NUMERICAL ERRORS IN DOMAIN HEAT TRANSPORT MODELS USING THE CVBEM.

USGS Publications Warehouse

Hromadka, T.V.; ,

1985-01-01

Besides providing an exact solution for steady-state heat conduction processes (Laplace Poisson equations), the CVBEM (complex variable boundary element method) can be used for the numerical error analysis of domain model solutions. For problems where soil water phase change latent heat effects dominate the thermal regime, heat transport can be approximately modeled as a time-stepped steady-state condition in the thawed and frozen regions, respectively. The CVBEM provides an exact solution of the two-dimensional steady-state heat transport problem, and also provides the error in matching the prescribed boundary conditions by the development of a modeling error distribution or an approximative boundary generation. This error evaluation can be used to develop highly accurate CVBEM models of the heat transport process, and the resulting model can be used as a test case for evaluating the precision of domain models based on finite elements or finite differences.

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

NASA Astrophysics Data System (ADS)

Heumann, Holger; Rapetti, Francesca

2017-04-01

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.

Significance of Strain in Formulation in Theory of Solid Mechanics

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.

2003-01-01

The basic theory of solid mechanics was deemed complete circa 1860 when St. Venant provided the strain formulation or the field compatibility condition. The strain formulation was incomplete. The missing portion has been formulated and identified as the boundary compatibility condition (BCC). The BCC, derived through a variational formulation, has been verified through integral theorem and solution of problems. The BCC, unlike the field counterpart, do not trivialize when expressed in displacements. Navier s method and the stiffness formulation have to account for the extra conditions especially at the inter-element boundaries in a finite element model. Completion of the strain formulation has led to the revival of the direct force calculation methods: the Integrated Force Method (IFM) and its dual (IFMD) for finite element analysis, and the completed Beltrami-Michell formulation (CBMF) in elasticity. The benefits from the new methods in elasticity, in finite element analysis, and in design optimization are discussed. Existing solutions and computer codes may have to be adjusted for the compliance of the new conditions. Complacency because the discipline is over a century old and computer codes have been developed for half a century can lead to stagnation of the discipline.

Computer aided stress analysis of long bones utilizing computer tomography

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

Marom, S.A.

1986-01-01

A computer aided analysis method, utilizing computed tomography (CT) has been developed, which together with a finite element program determines the stress-displacement pattern in a long bone section. The CT data file provides the geometry, the density and the material properties for the generated finite element model. A three-dimensional finite element model of a tibial shaft is automatically generated from the CT file by a pre-processing procedure for a finite element program. The developed pre-processor includes an edge detection algorithm which determines the boundaries of the reconstructed cross-sectional images of the scanned bone. A mesh generation procedure than automatically generatesmore » a three-dimensional mesh of a user-selected refinement. The elastic properties needed for the stress analysis are individually determined for each model element using the radiographic density (CT number) of each pixel with the elemental borders. The elastic modulus is determined from the CT radiographic density by using an empirical relationship from the literature. The generated finite element model, together with applied loads, determined from existing gait analysis and initial displacements, comprise a formatted input for the SAP IV finite element program. The output of this program, stresses and displacements at the model elements and nodes, are sorted and displayed by a developed post-processor to provide maximum and minimum values at selected locations in the model.« less

Rigorous joining of advanced reduced-dimensional beam models to three-dimensional finite element models

NASA Astrophysics Data System (ADS)

Song, Huimin

In the aerospace and automotive industries, many finite element analyses use lower-dimensional finite elements such as beams, plates and shells, to simplify the modeling. These simplified models can greatly reduce the computation time and cost; however, reduced-dimensional models may introduce inaccuracies, particularly near boundaries and near portions of the structure where reduced-dimensional models may not apply. Another factor in creation of such models is that beam-like structures frequently have complex geometry, boundaries and loading conditions, which may make them unsuitable for modeling with single type of element. The goal of this dissertation is to develop a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. The first chapter of the thesis gives the background of the present work and some related previous work. The second chapter is focused on formulating a system of equations that govern the joining of a 2D model with a beam model for planar deformation. The essential aspect of this formulation is to find the transformation matrices to achieve deflection and load continuity on the interface. Three approaches are provided to obtain the transformation matrices. An example based on joining a beam to a 2D finite element model is examined, and the accuracy of the analysis is studied by comparing joint results with the full 2D analysis. The third chapter is focused on formulating the system of equations for joining a beam to a 3D finite element model for static and free-vibration problems. The transition between the 3D elements and beam elements is achieved by use of the stress recovery technique of the variational-asymptotic method as implemented in VABS (the Variational Asymptotic Beam Section analysis). The formulations for an interface transformation matrix and the generalized Timoshenko beam are discussed in this chapter. VABS is also used to obtain the beam constitutive properties and warping functions for stress recovery. Several 3D-beam joint examples are presented to show the convergence and accuracy of the analysis. Accuracy is accessed by comparing the joint results with the full 3D analysis. The fourth chapter provides conclusions from present studies and recommendations for future work.

Finite element analysis of inviscid subsonic boattail flow

NASA Technical Reports Server (NTRS)

Chima, R. V.; Gerhart, P. M.

1981-01-01

A finite element code for analysis of inviscid subsonic flows over arbitrary nonlifting planar or axisymmetric bodies is described. The code solves a novel primitive variable formulation of the coupled irrotationality and compressible continuity equations. Results for flow over a cylinder, a sphere, and a NACA 0012 airfoil verify the code. Computed subcritical flows over an axisymmetric boattailed afterbody compare well with finite difference results and experimental data. Interative coupling with an integral turbulent boundary layer code shows strong viscous effects on the inviscid flow. Improvements in code efficiency and extensions to transonic flows are discussed.

Coupled Structural, Thermal, Phase-change and Electromagnetic Analysis for Superconductors, Volume 2

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Park, K. C.; Militello, C.; Schuler, J. J.

1996-01-01

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromag subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermel and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. Volume 1 describes mostly formulation specific problems. Volume 2 describes generalization of those formulations.

A Three-Dimensional Finite-Element Model for Simulating Water Flow in Variably Saturated Porous Media

NASA Astrophysics Data System (ADS)

Huyakorn, Peter S.; Springer, Everett P.; Guvanasen, Varut; Wadsworth, Terry D.

1986-12-01

A three-dimensional finite-element model for simulating water flow in variably saturated porous media is presented. The model formulation is general and capable of accommodating complex boundary conditions associated with seepage faces and infiltration or evaporation on the soil surface. Included in this formulation is an improved Picard algorithm designed to cope with severely nonlinear soil moisture relations. The algorithm is formulated for both rectangular and triangular prism elements. The element matrices are evaluated using an "influence coefficient" technique that avoids costly numerical integration. Spatial discretization of a three-dimensional region is performed using a vertical slicing approach designed to accommodate complex geometry with irregular boundaries, layering, and/or lateral discontinuities. Matrix solution is achieved using a slice successive overrelaxation scheme that permits a fairly large number of nodal unknowns (on the order of several thousand) to be handled efficiently on small minicomputers. Six examples are presented to verify and demonstrate the utility of the proposed finite-element model. The first four examples concern one- and two-dimensional flow problems used as sample problems to benchmark the code. The remaining examples concern three-dimensional problems. These problems are used to illustrate the performance of the proposed algorithm in three-dimensional situations involving seepage faces and anisotropic soil media.

Interior Noise Predictions in the Preliminary Design of the Large Civil Tiltrotor (LCTR2)

NASA Technical Reports Server (NTRS)

Grosveld, Ferdinand W.; Cabell, Randolph H.; Boyd, David D.

2013-01-01

A prediction scheme was established to compute sound pressure levels in the interior of a simplified cabin model of the second generation Large Civil Tiltrotor (LCTR2) during cruise conditions, while being excited by turbulent boundary layer flow over the fuselage, or by tiltrotor blade loading and thickness noise. Finite element models of the cabin structure, interior acoustic space, and acoustically absorbent (poro-elastic) materials in the fuselage were generated and combined into a coupled structural-acoustic model. Fluctuating power spectral densities were computed according to the Efimtsov turbulent boundary layer excitation model. Noise associated with the tiltrotor blades was predicted in the time domain as fluctuating surface pressures and converted to power spectral densities at the fuselage skin finite element nodes. A hybrid finite element (FE) approach was used to compute the low frequency acoustic cabin response over the frequency range 6-141 Hz with a 1 Hz bandwidth, and the Statistical Energy Analysis (SEA) approach was used to predict the interior noise for the 125-8000 Hz one-third octave bands.

Implementation of Nonhomogeneous Dirichlet Boundary Conditions in the p- Version of the Finite Element Method

DTIC Science & Technology

1988-09-01

Institute for Physical Science and Teennology rUniversity of Maryland o College Park, MD 20742 B. Gix) Engineering Mechanics Research Corporation Troy...OF THE FINITE ELEMENT METHOD by Ivo Babuska Institute for Physical Science and Technology University of Maryland College Park, MD 20742 B. Guo 2...2Research partially supported by the National Science Foundation under Grant DMS-85-16191 during the stay at the Institute for Physical Science and

Elastic-plastic analysis of a propagating crack under cyclic loading

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Armen, H., Jr.

1974-01-01

Development and application of a two-dimensional finite-element analysis to predict crack-closure and crack-opening stresses during specified histories of cyclic loading. An existing finite-element computer program which accounts for elastic-plastic material behavior under cyclic loading was modified to account for changing boundary conditions - crack growth and intermittent contact of crack surfaces. This program was subsequently used to study the crack-closure behavior under constant-amplitude and simple block-program loading.

The Perfectly Matched Layer absorbing boundary for fluid-structure interactions using the Immersed Finite Element Method.

PubMed

Yang, Jubiao; Yu, Feimi; Krane, Michael; Zhang, Lucy T

2018-01-01

In this work, a non-reflective boundary condition, the Perfectly Matched Layer (PML) technique, is adapted and implemented in a fluid-structure interaction numerical framework to demonstrate that proper boundary conditions are not only necessary to capture correct wave propagations in a flow field, but also its interacted solid behavior and responses. While most research on the topics of the non-reflective boundary conditions are focused on fluids, little effort has been done in a fluid-structure interaction setting. In this study, the effectiveness of the PML is closely examined in both pure fluid and fluid-structure interaction settings upon incorporating the PML algorithm in a fully-coupled fluid-structure interaction framework, the Immersed Finite Element Method. The performance of the PML boundary condition is evaluated and compared to reference solutions with a variety of benchmark test cases including known and expected solutions of aeroacoustic wave propagation as well as vortex shedding and advection. The application of the PML in numerical simulations of fluid-structure interaction is then investigated to demonstrate the efficacy and necessity of such boundary treatment in order to capture the correct solid deformation and flow field without the requirement of a significantly large computational domain.

Approximate minimum-time trajectories for 2-link flexible manipulators

NASA Technical Reports Server (NTRS)

Eisler, G. R.; Segalman, D. J.; Robinett, R. D.

1989-01-01

Powell's nonlinear programming code, VF02AD, was used to generate approximate minimum-time tip trajectories for 2-link semi-rigid and flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for an n-link, m-joint system with horizontal-plane bending only. Constraints on the trajectory include boundary conditions on position and energy for a rest-to-rest maneuver, straight-line tracking between boundary positions, and motor torque limits. Trajectory comparisons utilize a change in the link stiffness, EI, to transition from the semi-rigid to flexible case. Results show the level of compliance necessary to excite significant modal behavior. Quiescence of the final configuration is examined with the finite-element model.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 2: Derivation of finite-element equations and comparisons with analytical solutions

USGS Publications Warehouse

Cooley, Richard L.

1992-01-01

MODFE, a modular finite-element model for simulating steady- or unsteady-state, area1 or axisymmetric flow of ground water in a heterogeneous anisotropic aquifer is documented in a three-part series of reports. In this report, part 2, the finite-element equations are derived by minimizing a functional of the difference between the true and approximate hydraulic head, which produces equations that are equivalent to those obtained by either classical variational or Galerkin techniques. Spatial finite elements are triangular with linear basis functions, and temporal finite elements are one dimensional with linear basis functions. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining units; (3) specified recharge or discharge at points, along lines, or areally; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining units combined with aquifer dewatering, and evapotranspiration. The matrix equations produced by the finite-element method are solved by the direct symmetric-Doolittle method or the iterative modified incomplete-Cholesky conjugate-gradient method. The direct method can be efficient for small- to medium-sized problems (less than about 500 nodes), and the iterative method is generally more efficient for larger-sized problems. Comparison of finite-element solutions with analytical solutions for five example problems demonstrates that the finite-element model can yield accurate solutions to ground-water flow problems.

Three-dimensional analysis of chevron-notched specimens by boundary integral method

NASA Technical Reports Server (NTRS)

Mendelson, A.; Ghosn, L.

1983-01-01

The chevron-notched short bar and short rod specimens was analyzed by the boundary integral equations method. This method makes use of boundary surface elements in obtaining the solution. The boundary integral models were composed of linear triangular and rectangular surface segments. Results were obtained for two specimens with width to thickness ratios of 1.45 and 2.00 and for different crack length to width ratios ranging from 0.4 to 0.7. Crack opening displacement and stress intensity factors determined from displacement calculations along the crack front and compliance calculations were compared with experimental values and with finite element analysis.

Experimental validation of a numerical model for subway induced vibrations

NASA Astrophysics Data System (ADS)

Gupta, S.; Degrande, G.; Lombaert, G.

2009-04-01

This paper presents the experimental validation of a coupled periodic finite element-boundary element model for the prediction of subway induced vibrations. The model fully accounts for the dynamic interaction between the train, the track, the tunnel and the soil. The periodicity or invariance of the tunnel and the soil in the longitudinal direction is exploited using the Floquet transformation, which allows for an efficient formulation in the frequency-wavenumber domain. A general analytical formulation is used to compute the response of three-dimensional invariant or periodic media that are excited by moving loads. The numerical model is validated by means of several experiments that have been performed at a site in Regent's Park on the Bakerloo line of London Underground. Vibration measurements have been performed on the axle boxes of the train, on the rail, the tunnel invert and the tunnel wall, and in the free field, both at the surface and at a depth of 15 m. Prior to these vibration measurements, the dynamic soil characteristics and the track characteristics have been determined. The Bakerloo line tunnel of London Underground has been modelled using the coupled periodic finite element-boundary element approach and free field vibrations due to the passage of a train at different speeds have been predicted and compared to the measurements. The correspondence between the predicted and measured response in the tunnel is reasonably good, although some differences are observed in the free field. The discrepancies are explained on the basis of various uncertainties involved in the problem. The variation in the response with train speed is similar for the measurements as well as the predictions. This study demonstrates the applicability of the coupled periodic finite element-boundary element model to make realistic predictions of the vibrations from underground railways.

Implementation of the glacial rebound prestress advection correction in general-purpose finite element analysis software: Springs versus foundations

NASA Astrophysics Data System (ADS)

Schmidt, Peter; Lund, Björn; Hieronymus, Christoph

2012-03-01

When general-purpose finite element analysis software is used to model glacial isostatic adjustment (GIA), the first-order effect of prestress advection has to be accounted for by the user. We show here that the common use of elastic foundations at boundaries between materials of different densities will produce incorrect displacements, unless the boundary is perpendicular to the direction of gravity. This is due to the foundations always acting perpendicular to the surface to which they are attached, while the body force they represent always acts in the direction of gravity. If prestress advection is instead accounted for by the use of elastic spring elements in the direction of gravity, the representation will be correct. The use of springs adds a computation of the spring constants to the analysis. The spring constant for a particular node is defined by the product of the density contrast at the boundary, the gravitational acceleration, and the area supported by the node. To be consistent with the finite element formulation, the area is evaluated by integration of the nodal shape functions. We outline an algorithm for the calculation and include a Python script that integrates the shape functions over a bilinear quadrilateral element. For linear rectangular and triangular elements, the area supported by each node is equal to the element area divided the number of defining nodes, thereby simplifying the computation. This is, however, not true in the general nonrectangular case, and we demonstrate this with a simple 1-element model. The spring constant calculation is simple and performed in the preprocessing stage of the analysis. The time spent on the calculation is more than compensated for by a shorter analysis time, compared to that for a model with foundations. We illustrate the effects of using springs versus foundations with a simple two-dimensional GIA model of glacial loading, where the Earth model has an inclined boundary between the overlying elastic layer and the lower viscoelastic layer. Our example shows that the error introduced by the use of foundations is large enough to affect an analysis based on high-accuracy geodetic data.

Parametric Instability of Static Shafts-Disk System Using Finite Element Method

NASA Astrophysics Data System (ADS)

Wahab, A. M.; Rasid, Z. A.; Abu, A.

2017-10-01

Parametric instability condition is an important consideration in design process as it can cause failure in machine elements. In this study, parametric instability behaviour was studied for a simple shaft and disk system that was subjected to axial load under pinned-pinned boundary condition. The shaft was modelled based on the Nelson’s beam model, which considered translational and rotary inertias, transverse shear deformation and torsional effect. The Floquet’s method was used to estimate the solution for Mathieu equation. Finite element codes were developed using MATLAB to establish the instability chart. The effect of additional disk mass on the stability chart was investigated for pinned-pinned boundary conditions. Numerical results and illustrative examples are given. It is found that the additional disk mass decreases the instability region during static condition. The location of the disk as well has significant effect on the instability region of the shaft.

State-constrained booster trajectory solutions via finite elements and shooting

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.; Seywald, Hans

1993-01-01

This paper presents an extension of a FEM formulation based on variational principles. A general formulation for handling internal boundary conditions and discontinuities in the state equations is presented, and the general formulation is modified for optimal control problems subject to state-variable inequality constraints. Solutions which only touch the state constraint and solutions which have a boundary arc of finite length are considered. Suitable shape and test functions are chosen for a FEM discretization. All element quadrature (equivalent to one-point Gaussian quadrature over each element) may be done in closed form. The final form of the algebraic equations is then derived. A simple state-constrained problem is solved. Then, for a practical application of the use of the FEM formulation, a launch vehicle subject to a dynamic pressure constraint (a first-order state inequality constraint) is solved. The results presented for the launch-vehicle trajectory have some interesting features, including a touch-point solution.

The finite element method in low speed aerodynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1975-01-01

The finite element procedure is shown to be of significant impact in design of the 'computational wind tunnel' for low speed aerodynamics. The uniformity of the mathematical differential equation description, for viscous and/or inviscid, multi-dimensional subsonic flows about practical aerodynamic system configurations, is utilized to establish the general form of the finite element algorithm. Numerical results for inviscid flow analysis, as well as viscous boundary layer, parabolic, and full Navier Stokes flow descriptions verify the capabilities and overall versatility of the fundamental algorithm for aerodynamics. The proven mathematical basis, coupled with the distinct user-orientation features of the computer program embodiment, indicate near-term evolution of a highly useful analytical design tool to support computational configuration studies in low speed aerodynamics.

Geometrical and topological issues in octree based automatic meshing

NASA Technical Reports Server (NTRS)

Saxena, Mukul; Perucchio, Renato

1987-01-01

Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is discussed. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary representation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractor. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.

Octree based automatic meshing from CSG models

NASA Technical Reports Server (NTRS)

Perucchio, Renato

1987-01-01

Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is emphasized. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary respresentation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractors. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.

A new approach to implement absorbing boundary condition in biomolecular electrostatics.

PubMed

Goni, Md Osman

2013-01-01

This paper discusses a novel approach to employ the absorbing boundary condition in conjunction with the finite-element method (FEM) in biomolecular electrostatics. The introduction of Bayliss-Turkel absorbing boundary operators in electromagnetic scattering problem has been incorporated by few researchers. However, in the area of biomolecular electrostatics, this boundary condition has not been investigated yet. The objective of this paper is twofold. First, to solve nonlinear Poisson-Boltzmann equation using Newton's method and second, to find an efficient and acceptable solution with minimum number of unknowns. In this work, a Galerkin finite-element formulation is used along with a Bayliss-Turkel absorbing boundary operator that explicitly accounts for the open field problem by mapping the Sommerfeld radiation condition from the far field to near field. While the Bayliss-Turkel condition works well when the artificial boundary is far from the scatterer, an acceptable tolerance of error can be achieved with the second order operator. Numerical results on test case with simple sphere show that the treatment is able to reach the same level of accuracy achieved by the analytical method while using a lower grid density. Bayliss-Turkel absorbing boundary condition (BTABC) combined with the FEM converges to the exact solution of scattering problems to within discretization error.

Smoothed Particle Hydrodynamics Continuous Boundary Force method for Navier-Stokes equations subject to Robin boundary condition

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

Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.

2014-02-15

Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel Continuous Boundary Force (CBF) method is proposed for solving the Navier-Stokes equations subject to Robin boundary condition. In the CBF method, the Robin boundary condition at boundary is replaced by the homogeneous Neumann boundary condition at the boundary and a volumetric force term added to the momentum conservation equation. Smoothed Particle Hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two-dimensional and three-dimensional flows in domains bounded by flat and curved boundaries subject to variousmore » forms of the Robin boundary condition. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite element method. Taken the no-slip boundary condition as a special case of slip boundary condition, we demonstrate that the SPH-CBF method describes accurately both no-slip and slip conditions.« less

Finite element stress, vibration, and buckling analysis of laminated beams with the use of refined elements

NASA Astrophysics Data System (ADS)

Borovkov, Alexei I.; Avdeev, Ilya V.; Artemyev, A.

1999-05-01

In present work, the stress, vibration and buckling finite element analysis of laminated beams is performed. Review of the equivalent single-layer (ESL) laminate theories is done. Finite element algorithms and procedures integrated into the original FEA program system and based on the classical laminated plate theory (CLPT), first-order shear deformation theory (FSDT), third-order theory of Reddy (TSDT-R) and third- order theory of Kant (TSDT-K) with the use of the Lanczos method for solving of the eigenproblem are developed. Several numerical tests and examples of bending, free vibration and buckling of multilayered and sandwich beams with various material, geometry properties and boundary conditions are solved. New effective higher-order hierarchical element for the accurate calculation of transverse shear stress is proposed. The comparative analysis of results obtained by the considered models and solutions of 2D problems of the heterogeneous anisotropic elasticity is fulfilled.

Moving finite elements in 2-D

NASA Technical Reports Server (NTRS)

Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.

1983-01-01

The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.

The h-p Version of the Finite Element Method for Problems with Nonhomogeneous Essential Boundary Condition.

DTIC Science & Technology

1987-09-01

one commercial code based on the p and h-p version of the finite element, the program PROBE of NOETIC Technologies (St. Louis, MO). PROBE deals with two...Standards. o To be an international center of study and research for foreign students in numerical mathematics who are supported by foreign govern- ments or...ment agencies such as the National Bureau of Standards. o To be an international center of study and research for foreign students in numerical

Finite element analysis of Mercury slosh in the solar electric propulsion stage

NASA Technical Reports Server (NTRS)

Singh, J. N.

1975-01-01

The static equilibrium shapes of the neoprene bladder have been established corresponding to various ullage and gravity configurations under specified boundary conditions. The hemispherical bladder is taken to be attached at the diametral plane of the sphere with zero relative slope. With these shapes, the spherical tank with bladder and mercury has been modeled as an assemblage of finite elements. The properties of these elements have then been calculated using a linear displacement field. The dynamic characteristics were obtained to be used to define a mechanical analog which will reproduce the sloshing phenomenon of the system.

Subject-specific finite element modelling of the human foot complex during walking: sensitivity analysis of material properties, boundary and loading conditions.

PubMed

Akrami, Mohammad; Qian, Zhihui; Zou, Zhemin; Howard, David; Nester, Chris J; Ren, Lei

2018-04-01

The objective of this study was to develop and validate a subject-specific framework for modelling the human foot. This was achieved by integrating medical image-based finite element modelling, individualised multi-body musculoskeletal modelling and 3D gait measurements. A 3D ankle-foot finite element model comprising all major foot structures was constructed based on MRI of one individual. A multi-body musculoskeletal model and 3D gait measurements for the same subject were used to define loading and boundary conditions. Sensitivity analyses were used to investigate the effects of key modelling parameters on model predictions. Prediction errors of average and peak plantar pressures were below 10% in all ten plantar regions at five key gait events with only one exception (lateral heel, in early stance, error of 14.44%). The sensitivity analyses results suggest that predictions of peak plantar pressures are moderately sensitive to material properties, ground reaction forces and muscle forces, and significantly sensitive to foot orientation. The maximum region-specific percentage change ratios (peak stress percentage change over parameter percentage change) were 1.935-2.258 for ground reaction forces, 1.528-2.727 for plantar flexor muscles and 4.84-11.37 for foot orientations. This strongly suggests that loading and boundary conditions need to be very carefully defined based on personalised measurement data.

A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains

NASA Technical Reports Server (NTRS)

Kandil, Osama A.

1998-01-01

Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.

A Semianalytical Model for Pumping Tests in Finite Heterogeneous Confined Aquifers With Arbitrarily Shaped Boundary

NASA Astrophysics Data System (ADS)

Wang, Lei; Dai, Cheng; Xue, Liang

2018-04-01

This study presents a Laplace-transform-based boundary element method to model the groundwater flow in a heterogeneous confined finite aquifer with arbitrarily shaped boundaries. The boundary condition can be Dirichlet, Neumann or Robin-type. The derived solution is analytical since it is obtained through the Green's function method within the domain. However, the numerical approximation is required on the boundaries, which essentially renders it a semi-analytical solution. The proposed method can provide a general framework to derive solutions for zoned heterogeneous confined aquifers with arbitrarily shaped boundary. The requirement of the boundary element method presented here is that the Green function must exist for a specific PDE equation. In this study, the linear equations for the two-zone and three-zone confined aquifers with arbitrarily shaped boundary is established in Laplace space, and the solution can be obtained by using any linear solver. Stehfest inversion algorithm can be used to transform it back into time domain to obtain the transient solution. The presented solution is validated in the two-zone cases by reducing the arbitrarily shaped boundaries to circular ones and comparing it with the solution in Lin et al. (2016, https://doi.org/10.1016/j.jhydrol.2016.07.028). The effect of boundary shape and well location on dimensionless drawdown in two-zone aquifers is investigated. Finally the drawdown distribution in three-zone aquifers with arbitrarily shaped boundary for constant-rate tests (CRT) and flow rate distribution for constant-head tests (CHT) are analyzed.

Avalanches, loading and finite size effects in 2D amorphous plasticity: results from a finite element model

NASA Astrophysics Data System (ADS)

Sandfeld, Stefan; Budrikis, Zoe; Zapperi, Stefano; Fernandez Castellanos, David

2015-02-01

Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand—where the concept of linear lattice defects is not applicable—still are lagging behind. We introduce an eigenstrain-based finite element lattice model for simulations of shear band formation and strain avalanches. Our model allows us to study the influence of surfaces and finite size effects on the statistics of avalanches. We find that even with relatively complex loading conditions and open boundary conditions, critical exponents describing avalanche statistics are unchanged, which validates the use of simpler scalar lattice-based models to study these phenomena.

Development of an integrated BEM approach for hot fluid structure interaction

NASA Technical Reports Server (NTRS)

Dargush, G. F.; Banerjee, P. K.; Shi, Y.

1990-01-01

A comprehensive boundary element method is presented for transient thermoelastic analysis of hot section Earth-to-Orbit engine components. This time-domain formulation requires discretization of only the surface of the component, and thus provides an attractive alternative to finite element analysis for this class of problems. In addition, steep thermal gradients, which often occur near the surface, can be captured more readily since with a boundary element approach there are no shape functions to constrain the solution in the direction normal to the surface. For example, the circular disc analysis indicates the high level of accuracy that can be obtained. In fact, on the basis of reduced modeling effort and improved accuracy, it appears that the present boundary element method should be the preferred approach for general problems of transient thermoelasticity.

Application of the boundary element method to the micromechanical analysis of composite materials

NASA Technical Reports Server (NTRS)

Goldberg, R. K.; Hopkins, D. A.

1995-01-01

A new boundary element formulation for the micromechanical analysis of composite materials is presented in this study. A unique feature of the formulation is the use of circular shape functions to convert the two-dimensional integrations of the composite fibers to one-dimensional integrations. To demonstrate the applicability of the formulations, several example problems including elastic and thermal analysis of laminated composites and elastic analyses of woven composites are presented and the boundary element results compared to experimental observations and/or results obtained through alternate analytical procedures. While several issues remain to be addressed in order to make the methodology more robust, the formulations presented here show the potential in providing an alternative to traditional finite element methods, particularly for complex composite architectures.

Coupled thermomechanical behavior of graphene using the spring-based finite element approach

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

Georgantzinos, S. K., E-mail: sgeor@mech.upatras.gr; Anifantis, N. K., E-mail: nanif@mech.upatras.gr; Giannopoulos, G. I., E-mail: ggiannopoulos@teiwest.gr

The prediction of the thermomechanical behavior of graphene using a new coupled thermomechanical spring-based finite element approach is the aim of this work. Graphene sheets are modeled in nanoscale according to their atomistic structure. Based on molecular theory, the potential energy is defined as a function of temperature, describing the interatomic interactions in different temperature environments. The force field is approached by suitable straight spring finite elements. Springs simulate the interatomic interactions and interconnect nodes located at the atomic positions. Their stiffness matrix is expressed as a function of temperature. By using appropriate boundary conditions, various different graphene configurations aremore » analyzed and their thermo-mechanical response is approached using conventional finite element procedures. A complete parametric study with respect to the geometric characteristics of graphene is performed, and the temperature dependency of the elastic material properties is finally predicted. Comparisons with available published works found in the literature demonstrate the accuracy of the proposed method.« less

Definition of NASTRAN sets by use of parametric geometry

NASA Technical Reports Server (NTRS)

Baughn, Terry V.; Tiv, Mehran

1989-01-01

Many finite element preprocessors describe finite element model geometry with points, lines, surfaces and volumes. One method for describing these basic geometric entities is by use of parametric cubics which are useful for representing complex shapes. The lines, surfaces and volumes may be discretized for follow on finite element analysis. The ability to limit or selectively recover results from the finite element model is extremely important to the analyst. Equally important is the ability to easily apply boundary conditions. Although graphical preprocessors have made these tasks easier, model complexity may not lend itself to easily identify a group of grid points desired for data recovery or application of constraints. A methodology is presented which makes use of the assignment of grid point locations in parametric coordinates. The parametric coordinates provide a convenient ordering of the grid point locations and a method for retrieving the grid point ID's from the parent geometry. The selected grid points may then be used for the generation of the appropriate set and constraint cards.

[Stress analysis of femoral stems in cementless total hip arthroplasty by two-dimensional finite element method using boundary friction layer].

PubMed

Oomori, H; Imura, S; Gesso, H

1992-04-01

To develop stem design achieving primary fixation of stems and effective load transfer to the femur, we studied stress analysis of stems in cementless total hip arthroplasty by two-dimensional finite element method using boundary friction layer in stem-bone interface. The results of analyses of stem-bone interface stresses and von Mises stresses at the cortical bones indicated that ideal stem design features would be as follows: 1) Sufficient length, with the distal end extending beyond the isthmus region. 2) Maximum possible width, to contact the cortical bones in the isthmus region. 3) No collars but a lateral shoulder at the proximal portion. 4) A distal tip, to contact the cortical bones at the distal portion.

Finite element method formulation in polar coordinates for transient heat conduction problems

NASA Astrophysics Data System (ADS)

Duda, Piotr

2016-04-01

The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method (FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.

Coupled Structural, Thermal, Phase-Change and Electromagnetic Analysis for Superconductors. Volume 1

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Park, K. C.; Militello, C.; Schuler, J. J.

1996-01-01

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermal and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. This volume, Volume 1, describes mostly formulations for specific problems. Volume 2 describes generalization of those formulations.

Propagating plane harmonic waves through finite length plates of variable thickness using finite element techniques

NASA Technical Reports Server (NTRS)

Clark, J. H.; Kalinowski, A. J.; Wagner, C. A.

1983-01-01

An analysis is given using finite element techniques which addresses the propagaton of a uniform incident pressure wave through a finite diameter axisymmetric tapered plate immersed in a fluid. The approach utilized in developing a finite element solution to this problem is based upon a technique for axisymmetric fluid structure interaction problems. The problem addressed is that of a 10 inch diameter axisymmetric fixed plate totally immersed in a fluid. The plate increases in thickness from approximately 0.01 inches thick at the center to 0.421 inches thick at a radius of 5 inches. Against each face of the tapered plate a cylindrical fluid volume was represented extending five wavelengths off the plate in the axial direction. The outer boundary of the fluid and plate regions were represented as a rigid encasement cylinder as was nearly the case in the physical problem. The primary objective of the analysis is to determine the form of the transmitted pressure distribution on the downstream side of the plate.

Numeric simulation model for long-term orthodontic tooth movement with contact boundary conditions using the finite element method.

PubMed

Hamanaka, Ryo; Yamaoka, Satoshi; Anh, Tuan Nguyen; Tominaga, Jun-Ya; Koga, Yoshiyuki; Yoshida, Noriaki

2017-11-01

Although many attempts have been made to simulate orthodontic tooth movement using the finite element method, most were limited to analyses of the initial displacement in the periodontal ligament and were insufficient to evaluate the effect of orthodontic appliances on long-term tooth movement. Numeric simulation of long-term tooth movement was performed in some studies; however, neither the play between the brackets and archwire nor the interproximal contact forces were considered. The objectives of this study were to simulate long-term orthodontic tooth movement with the edgewise appliance by incorporating those contact conditions into the finite element model and to determine the force system when the space is closed with sliding mechanics. We constructed a 3-dimensional model of maxillary dentition with 0.022-in brackets and 0.019 × 0.025-in archwire. Forces of 100 cN simulating sliding mechanics were applied. The simulation was accomplished on the assumption that bone remodeling correlates with the initial tooth displacement. This method could successfully represent the changes in the moment-to-force ratio: the tooth movement pattern during space closure. We developed a novel method that could simulate the long-term orthodontic tooth movement and accurately determine the force system in the course of time by incorporating contact boundary conditions into finite element analysis. It was also suggested that friction is progressively increased during space closure in sliding mechanics. Copyright © 2017. Published by Elsevier Inc.

Including fluid shear viscosity in a structural acoustic finite element model using a scalar fluid representation

PubMed Central

Cheng, Lei; Li, Yizeng; Grosh, Karl

2013-01-01

An approximate boundary condition is developed in this paper to model fluid shear viscosity at boundaries of coupled fluid-structure system. The effect of shear viscosity is approximated by a correction term to the inviscid boundary condition, written in terms of second order in-plane derivatives of pressure. Both thin and thick viscous boundary layer approximations are formulated; the latter subsumes the former. These approximations are used to develop a variational formation, upon which a viscous finite element method (FEM) model is based, requiring only minor modifications to the boundary integral contributions of an existing inviscid FEM model. Since this FEM formulation has only one degree of freedom for pressure, it holds a great computational advantage over the conventional viscous FEM formulation which requires discretization of the full set of linearized Navier-Stokes equations. The results from thick viscous boundary layer approximation are found to be in good agreement with the prediction from a Navier-Stokes model. When applicable, thin viscous boundary layer approximation also gives accurate results with computational simplicity compared to the thick boundary layer formulation. Direct comparison of simulation results using the boundary layer approximations and a full, linearized Navier-Stokes model are made and used to evaluate the accuracy of the approximate technique. Guidelines are given for the parameter ranges over which the accurate application of the thick and thin boundary approximations can be used for a fluid-structure interaction problem. PMID:23729844

Including fluid shear viscosity in a structural acoustic finite element model using a scalar fluid representation.

PubMed

Cheng, Lei; Li, Yizeng; Grosh, Karl

2013-08-15

An approximate boundary condition is developed in this paper to model fluid shear viscosity at boundaries of coupled fluid-structure system. The effect of shear viscosity is approximated by a correction term to the inviscid boundary condition, written in terms of second order in-plane derivatives of pressure. Both thin and thick viscous boundary layer approximations are formulated; the latter subsumes the former. These approximations are used to develop a variational formation, upon which a viscous finite element method (FEM) model is based, requiring only minor modifications to the boundary integral contributions of an existing inviscid FEM model. Since this FEM formulation has only one degree of freedom for pressure, it holds a great computational advantage over the conventional viscous FEM formulation which requires discretization of the full set of linearized Navier-Stokes equations. The results from thick viscous boundary layer approximation are found to be in good agreement with the prediction from a Navier-Stokes model. When applicable, thin viscous boundary layer approximation also gives accurate results with computational simplicity compared to the thick boundary layer formulation. Direct comparison of simulation results using the boundary layer approximations and a full, linearized Navier-Stokes model are made and used to evaluate the accuracy of the approximate technique. Guidelines are given for the parameter ranges over which the accurate application of the thick and thin boundary approximations can be used for a fluid-structure interaction problem.

Competing Grain Boundary and Interior Deformation Mechanisms with Varying Sizes

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

Zhang, Wei; Gao, Yanfei; Nieh, T. G.

In typical coarse-grained alloys, the dominant plastic deformations are dislocation gliding or climbing, and material strengths can be tuned by dislocation interactions with grain boundaries, precipitates, solid solutions, and other defects. With the reduction of grain size, the increase of material strengths follows the classic Hall-Petch relationship up to nano-grained materials. Even at room temperatures, nano-grained materials exhibit strength softening, or called the inverse Hall-Petch effect, as grain boundary processes take over as the dominant deformation mechanisms. On the other hand, at elevated temperatures, grain boundary processes compete with grain interior deformation mechanisms over a wide range of the appliedmore » stress and grain sizes. This book chapter reviews and compares the rate equation model and the microstructure-based finite element simulations. The latter explicitly accounts for the grain boundary sliding, grain boundary diffusion and migration, as well as the grain interior dislocation creep. Therefore the explicit finite element method has clear advantages in problems where microstructural heterogeneities play a critical role, such as in the gradient microstructure in shot peening or weldment. Furthermore, combined with the Hall-Petch effect and its breakdown, the above competing processes help construct deformation mechanism maps by extending from the classic Frost-Ashby type to the ones with the dependence of grain size.« less

Analysis Software

NASA Technical Reports Server (NTRS)

1994-01-01

General Purpose Boundary Element Solution Technology (GPBEST) software employs the boundary element method of mechanical engineering analysis, as opposed to finite element. It is, according to one of its developers, 10 times faster in data preparation and more accurate than other methods. Its use results in less expensive products because the time between design and manufacturing is shortened. A commercial derivative of a NASA-developed computer code, it is marketed by Best Corporation to solve problems in stress analysis, heat transfer, fluid analysis and yielding and cracking of solids. Other applications include designing tractor and auto parts, household appliances and acoustic analysis.

Stress concentration investigations using NASTRAN

NASA Technical Reports Server (NTRS)

Gillcrist, M. C.; Parnell, L. A.

1986-01-01

Parametic investigations are performed using several two dimensional finite element formulations to determine their suitability for use in predicting extremum stresses in marine propellers. Comparisons are made of two NASTRAN elements (CTRIM6 and CTRAIA2) wherein elasticity properties have been modified to yield plane strain results. The accuracy of the elements is investigated by comparing finite element stress predictions with experimentally determined stresses in two classical cases: (1) tension in a flat plate with a circular hole; and (2) a filleted flat bar subjected to in-plane bending. The CTRIA2 element is found to provide good results. The displacement field from a three dimensional finite element model of a representative marine propeller is used as the boundary condition for the two dimensional plane strain investigations of stresses in the propeller blade and fillet. Stress predictions from the three dimensional analysis are compared with those from the two dimensional models. The validity of the plane strain modifications to the NASTRAN element is checked by comparing the modified CTRIA2 element stress predictions with those of the ABAQUS plane strain element, CPE4.

Design and Stress Analysis of Low-Noise Adjusted Bearing Contact Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Fuentes, A.; Litvin, F. L.; Mullins, B. R.; Woods, R.; Handschuh, R. F.; Lewicki, David G.

2002-01-01

An integrated computerized approach for design and stress analysis of low-noise spiral bevel gear drives with adjusted bearing contact is proposed. The procedure of computations is an iterative process that requires four separate procedures and provide: (a) a parabolic function of transmission errors that is able to reduce the effect of errors of alignment on noise and vibration, and (b) reduction of the shift of bearing contact caused by misalignment. Application of finite element analysis enables us to determine the contact and bending stresses and investigate the formation of the bearing contact. The design of finite element models and boundary conditions is automated and does not require intermediate CAD computer programs for application of general purpose computer program for finite element analysis.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

Heat transfer monitoring by means of the hot wire technique and finite element analysis software.

PubMed

Hernández Wong, J; Suarez, V; Guarachi, J; Calderón, A; Rojas-Trigos, J B; Juárez, A G; Marín, E

2014-01-01

It is reported the study of the radial heat transfer in a homogeneous and isotropic substance with a heat linear source in its axial axis. For this purpose, the hot wire characterization technique has been used, in order to obtain the temperature distribution as a function of radial distance from the axial axis and time exposure. Also, the solution of the transient heat transport equation for this problem was obtained under appropriate boundary conditions, by means of finite element technique. A comparison between experimental, conventional theoretical model and numerical simulated results is done to demonstrate the utility of the finite element analysis simulation methodology in the investigation of the thermal response of substances. Copyright © 2013 Elsevier Ltd. All rights reserved.

A domain decomposition approach to implementing fault slip in finite-element models of quasi-static and dynamic crustal deformation

USGS Publications Warehouse

Aagaard, Brad T.; Knepley, M.G.; Williams, C.A.

2013-01-01

We employ a domain decomposition approach with Lagrange multipliers to implement fault slip in a finite-element code, PyLith, for use in both quasi-static and dynamic crustal deformation applications. This integrated approach to solving both quasi-static and dynamic simulations leverages common finite-element data structures and implementations of various boundary conditions, discretization schemes, and bulk and fault rheologies. We have developed a custom preconditioner for the Lagrange multiplier portion of the system of equations that provides excellent scalability with problem size compared to conventional additive Schwarz methods. We demonstrate application of this approach using benchmarks for both quasi-static viscoelastic deformation and dynamic spontaneous rupture propagation that verify the numerical implementation in PyLith.

Scattering and radiation analysis of three-dimensional cavity arrays via a hybrid finite element method

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1992-01-01

A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three-dimensional cavity arrays recessed in a ground plane. The technique combines the finite element and boundary integral methods and invokes Floquet's representation to formulate a system of equations for the fields at the apertures and those inside the cavities. The system is solved via the conjugate gradient method in conjunction with the Fast Fourier Transform (FFT) thus achieving an O(N) storage requirement. By virtue of the finite element method, the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics. Several numerical results are presented, along with new measured data, which demonstrate the validity, efficiency, and capability of the technique.

Pretest 3-D finite element modeling of the wedge pillar portion of the WIPP (Waste Isolation Pilot Plant) Geomechanical Evaluation (Room G) in situ experiment. [Waste Isolation Pilot Plant

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

Preece, D.S.

Pretest 3-D finite element calculations have been performed on the wedge pillar portion of the WIPP Geomechanical Evaluation Experiment. The wedge pillar separates two drifts that intersect at an angle of 7.5/sup 0/. Purpose of the experiment is to provide data on the creep behavior of the wedge and progressive failure at the tip. The first set of calculations utilized a symmetry plane on the center-line of the wedge which allowed treatment of the entire configuration by modeling half of the geometry. Two 3-D calculations in this first set were performed with different drift widths to study the influence ofmore » drift size on closure and maximum stress. A cross-section perpendicular to the wedge was also analyzed with 2-D finite element models and the results compared to the 3-D results. In another set of 3-D calculations both drifts were modeled but with less distance between the drifts and the outer boundaries. Results of these calculations are compared with results from the other calculations to better understand the influence of boundary conditions.« less

Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes

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

De Corato, M., E-mail: marco.decorato@unina.it; Slot, J.J.M., E-mail: j.j.m.slot@tue.nl; Hütter, M., E-mail: m.huetter@tue.nl

In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered withinmore » the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.« less

Free vibration analysis of elastic structures submerged in an infinite or semi-infinite fluid domain by means of a coupled FE-BE solver

NASA Astrophysics Data System (ADS)

Zheng, Chang-Jun; Bi, Chuan-Xing; Zhang, Chuanzeng; Gao, Hai-Feng; Chen, Hai-Bo

2018-04-01

The vibration behavior of thin elastic structures can be noticeably influenced by the surrounding water, which represents a kind of heavy fluid. Since the feedback of the acoustic pressure onto the structure cannot be neglected in this case, a strong coupled scheme between the structural and fluid domains is usually required. In this work, a coupled finite element and boundary element (FE-BE) solver is developed for the free vibration analysis of structures submerged in an infinite fluid domain or a semi-infinite fluid domain with a free water surface. The structure is modeled by the finite element method (FEM). The compressibility of the fluid is taken into account, and hence the Helmholtz equation serves as the governing equation of the fluid domain. The boundary element method (BEM) is employed to model the fluid domain, and a boundary integral formulation with a half-space fundamental solution is used to satisfy the Dirichlet boundary condition on the free water surface exactly. The resulting nonlinear eigenvalue problem (NEVP) is converted into a small linear one by using a contour integral method. Adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenfrequencies of interest. The Burton-Miller method is used to filter out the fictitious eigenfrequencies of the boundary integral formulations. Numerical examples are given to demonstrate the accuracy and applicability of the developed eigensolver, and also show that the fluid-loading effect strongly depends on both the water depth and the mode shapes.

An efficient structural finite element for inextensible flexible risers

NASA Astrophysics Data System (ADS)

Papathanasiou, T. K.; Markolefas, S.; Khazaeinejad, P.; Bahai, H.

2017-12-01

A core part of all numerical models used for flexible riser analysis is the structural component representing the main body of the riser as a slender beam. Loads acting on this structural element are self-weight, buoyant and hydrodynamic forces, internal pressure and others. A structural finite element for an inextensible riser with a point-wise enforcement of the inextensibility constrain is presented. In particular, the inextensibility constraint is applied only at the nodes of the meshed arc length parameter. Among the virtues of the proposed approach is the flexibility in the application of boundary conditions and the easy incorporation of dissipative forces. Several attributes of the proposed finite element scheme are analysed and computation times for the solution of some simplified examples are discussed. Future developments aim at the appropriate implementation of material and geometric parameters for the beam model, i.e. flexural and torsional rigidity.

Micromechanical predictions of crack propagation and fracture energy in a single fiber boron/aluminum model composite

NASA Technical Reports Server (NTRS)

Adams, D. F.; Mahishi, J. M.

1982-01-01

The axisymmetric finite element model and associated computer program developed for the analysis of crack propagation in a composite consisting of a single broken fiber in an annular sheath of matrix material was extended to include a constant displacement boundary condition during an increment of crack propagation. The constant displacement condition permits the growth of a stable crack, as opposed to the catastropic failure in an earlier version. The finite element model was refined to respond more accurately to the high stresses and steep stress gradients near the broken fiber end. The accuracy and effectiveness of the conventional constant strain axisymmetric element for crack problems was established by solving the classical problem of a penny-shaped crack in a thick cylindrical rod under axial tension. The stress intensity factors predicted by the present finite element model are compared with existing continuum results.

An Embedded Statistical Method for Coupling Molecular Dynamics and Finite Element Analyses

NASA Technical Reports Server (NTRS)

Saether, E.; Glaessgen, E.H.; Yamakov, V.

2008-01-01

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

A New Concurrent Multiscale Methodology for Coupling Molecular Dynamics and Finite Element Analyses

NASA Technical Reports Server (NTRS)

Yamakov, Vesselin; Saether, Erik; Glaessgen, Edward H/.

2008-01-01

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

A three dimensional finite element formulation for thermoviscoelastic orthotropic media

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

Zocher, M.A.

1997-12-31

A numerical algorithm for the efficient solution of the uncoupled quasistatic initial/boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation is briefly outlined.

TECHNICAL NOTE: Direct finite-element analysis of the frequency response of a Y-Z lithium niobate SAW filter

NASA Astrophysics Data System (ADS)

Xu, Guanshui

2000-12-01

A direct finite-element model is developed for the full-scale analysis of the electromechanical phenomena involved in surface acoustic wave (SAW) devices. The equations of wave propagation in piezoelectric materials are discretized using the Galerkin method, in which an implicit algorithm of the Newmark family with unconditional stability is implemented. The Rayleigh damping coefficients are included in the elements near the boundary to reduce the influence of the reflection of waves. The performance of the model is demonstrated by the analysis of the frequency response of a Y-Z lithium niobate filter with two uniform ports, with emphasis on the influence of the number of electrodes. The frequency response of the filter is obtained through the Fourier transform of the impulse response, which is solved directly from the finite-element simulation. It shows that the finite-element results are in good agreement with the characteristic frequency response of the filter predicted by the simple phase-matching argument. The ability of the method to evaluate the influence of the bulk waves at the high-frequency end of the filter passband and the influence of the number of electrodes on insertion loss is noteworthy. We conclude that the direct finite-element analysis of SAW devices can be used as an effective tool for the design of high-performance SAW devices. Some practical computational challenges of finite-element modeling of SAW devices are discussed.

A probabilistic Hu-Washizu variational principle

NASA Technical Reports Server (NTRS)

Liu, W. K.; Belytschko, T.; Besterfield, G. H.

1987-01-01

A Probabilistic Hu-Washizu Variational Principle (PHWVP) for the Probabilistic Finite Element Method (PFEM) is presented. This formulation is developed for both linear and nonlinear elasticity. The PHWVP allows incorporation of the probabilistic distributions for the constitutive law, compatibility condition, equilibrium, domain and boundary conditions into the PFEM. Thus, a complete probabilistic analysis can be performed where all aspects of the problem are treated as random variables and/or fields. The Hu-Washizu variational formulation is available in many conventional finite element codes thereby enabling the straightforward inclusion of the probabilistic features into present codes.

Critical temperatures of hybrid laminates using finite elements

NASA Astrophysics Data System (ADS)

Chockalingam, S.; Mathew, T. C.; Singh, G.; Rao, G. V.

1992-06-01

Thermal buckling of antisymmetric cross-ply hybrid laminates is investigated. A one-dimensional finite element based on first-order shear deformation theory, having two nodes and six degrees of freedom per node, namely axial displacement, transverse displacements and rotation of the normal to the beam axis and their derivatives with respect to beam coordinate axis, is employed for this purpose. Various types of hybrid laminates with different combination of glass/epoxy, Kevlar/epoxy and carbon/epoxy are considered. Effects of slenderness ratio, boundary conditions and lay-ups are studied in detail.

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.

Development of an integrated BEM approach for hot fluid structure interaction: BEST-FSI: Boundary Element Solution Technique for Fluid Structure Interaction

NASA Technical Reports Server (NTRS)

Dargush, G. F.; Banerjee, P. K.; Shi, Y.

1992-01-01

As part of the continuing effort at NASA LeRC to improve both the durability and reliability of hot section Earth-to-orbit engine components, significant enhancements must be made in existing finite element and finite difference methods, and advanced techniques, such as the boundary element method (BEM), must be explored. The BEM was chosen as the basic analysis tool because the critical variables (temperature, flux, displacement, and traction) can be very precisely determined with a boundary-based discretization scheme. Additionally, model preparation is considerably simplified compared to the more familiar domain-based methods. Furthermore, the hyperbolic character of high speed flow is captured through the use of an analytical fundamental solution, eliminating the dependence of the solution on the discretization pattern. The price that must be paid in order to realize these advantages is that any BEM formulation requires a considerable amount of analytical work, which is typically absent in the other numerical methods. All of the research accomplishments of a multi-year program aimed toward the development of a boundary element formulation for the study of hot fluid-structure interaction in Earth-to-orbit engine hot section components are detailed. Most of the effort was directed toward the examination of fluid flow, since BEM's for fluids are at a much less developed state. However, significant strides were made, not only in the analysis of thermoviscous fluids, but also in the solution of the fluid-structure interaction problem.

Optical frequency selective surface design using a GPU accelerated finite element boundary integral method

NASA Astrophysics Data System (ADS)

Ashbach, Jason A.

Periodic metallodielectric frequency selective surface (FSS) designs have historically seen widespread use in the microwave and radio frequency spectra. By scaling the dimensions of an FSS unit cell for use in a nano-fabrication process, these concepts have recently been adapted for use in optical applications as well. While early optical designs have been limited to wellunderstood geometries or optimized pixelated screens, nano-fabrication, lithographic and interconnect technology has progressed to a point where it is possible to fabricate metallic screens of arbitrary geometries featuring curvilinear or even three-dimensional characteristics that are only tens of nanometers wide. In order to design an FSS featuring such characteristics, it is important to have a robust numerical solver that features triangular elements in purely two-dimensional geometries and prismatic or tetrahedral elements in three-dimensional geometries. In this dissertation, a periodic finite element method code has been developed which features prismatic elements whose top and bottom boundaries are truncated by numerical integration of the boundary integral as opposed to an approximate representation found in a perfectly matched layer. However, since no exact solution exists for the calculation of triangular elements in a boundary integral, this process can be time consuming. To address this, these calculations were optimized for parallelization such that they may be done on a graphics processor, which provides a large increase in computational speed. Additionally, a simple geometrical representation using a Bezier surface is presented which provides generality with few variables. With a fast numerical solver coupled with a lowvariable geometric representation, a heuristic optimization algorithm has been used to develop several optical designs such as an absorber, a circular polarization filter, a transparent conductive surface and an enhanced, optical modulator.

A coupled sharp-interface immersed boundary-finite-element method for flow-structure interaction with application to human phonation.

PubMed

Zheng, X; Xue, Q; Mittal, R; Beilamowicz, S

2010-11-01

A new flow-structure interaction method is presented, which couples a sharp-interface immersed boundary method flow solver with a finite-element method based solid dynamics solver. The coupled method provides robust and high-fidelity solution for complex flow-structure interaction (FSI) problems such as those involving three-dimensional flow and viscoelastic solids. The FSI solver is used to simulate flow-induced vibrations of the vocal folds during phonation. Both two- and three-dimensional models have been examined and qualitative, as well as quantitative comparisons, have been made with established results in order to validate the solver. The solver is used to study the onset of phonation in a two-dimensional laryngeal model and the dynamics of the glottal jet in a three-dimensional model and results from these studies are also presented.

Coupled BE/FE/BE approach for scattering from fluid-filled structures

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Cheng, Raymond S.

1990-01-01

NASHUA is a coupled finite element/boundary element capability built around NASTRAN for calculating the low frequency far-field acoustic pressure field radiated or scattered by an arbitrary, submerged, three-dimensional, elastic structure subjected to either internal time-harmonic mechanical loads or external time-harmonic incident loadings. Described here are the formulation and use of NASHUA for solving such structural acoustics problems when the structure is fluid-filled. NASTRAN is used to generate the structural finite element model and to perform most of the required matrix operations. Both fluid domains are modeled using the boundary element capability in NASHUA, whose matrix formulation (and the associated NASTRAN DMAP) for evacuated structures can be used with suitable interpretation of the matrix definitions. After computing surface pressures and normal velocities, far-field pressures are evaluated using an asymptotic form of the Helmholtz exterior integral equation. The proposed numerical approach is validated by comparing the acoustic field scattered from a submerged fluid-filled spherical thin shell to that obtained with a series solution, which is also derived here.

Local mesh adaptation technique for front tracking problems

NASA Astrophysics Data System (ADS)

Lock, N.; Jaeger, M.; Medale, M.; Occelli, R.

1998-09-01

A numerical model is developed for the simulation of moving interfaces in viscous incompressible flows. The model is based on the finite element method with a pseudo-concentration technique to track the front. Since a Eulerian approach is chosen, the interface is advected by the flow through a fixed mesh. Therefore, material discontinuity across the interface cannot be described accurately. To remedy this problem, the model has been supplemented with a local mesh adaptation technique. This latter consists in updating the mesh at each time step to the interface position, such that element boundaries lie along the front. It has been implemented for unstructured triangular finite element meshes. The outcome of this technique is that it allows an accurate treatment of material discontinuity across the interface and, if necessary, a modelling of interface phenomena such as surface tension by using specific boundary elements. For illustration, two examples are computed and presented in this paper: the broken dam problem and the Rayleigh-Taylor instability. Good agreement has been obtained in the comparison of the numerical results with theory or available experimental data.

Accurate Solution of Multi-Region Continuum Biomolecule Electrostatic Problems Using the Linearized Poisson-Boltzmann Equation with Curved Boundary Elements

PubMed Central

Altman, Michael D.; Bardhan, Jaydeep P.; White, Jacob K.; Tidor, Bruce

2009-01-01

We present a boundary-element method (BEM) implementation for accurately solving problems in biomolecular electrostatics using the linearized Poisson–Boltzmann equation. Motivating this implementation is the desire to create a solver capable of precisely describing the geometries and topologies prevalent in continuum models of biological molecules. This implementation is enabled by the synthesis of four technologies developed or implemented specifically for this work. First, molecular and accessible surfaces used to describe dielectric and ion-exclusion boundaries were discretized with curved boundary elements that faithfully reproduce molecular geometries. Second, we avoided explicitly forming the dense BEM matrices and instead solved the linear systems with a preconditioned iterative method (GMRES), using a matrix compression algorithm (FFTSVD) to accelerate matrix-vector multiplication. Third, robust numerical integration methods were employed to accurately evaluate singular and near-singular integrals over the curved boundary elements. Finally, we present a general boundary-integral approach capable of modeling an arbitrary number of embedded homogeneous dielectric regions with differing dielectric constants, possible salt treatment, and point charges. A comparison of the presented BEM implementation and standard finite-difference techniques demonstrates that for certain classes of electrostatic calculations, such as determining absolute electrostatic solvation and rigid-binding free energies, the improved convergence properties of the BEM approach can have a significant impact on computed energetics. We also demonstrate that the improved accuracy offered by the curved-element BEM is important when more sophisticated techniques, such as non-rigid-binding models, are used to compute the relative electrostatic effects of molecular modifications. In addition, we show that electrostatic calculations requiring multiple solves using the same molecular geometry, such as charge optimization or component analysis, can be computed to high accuracy using the presented BEM approach, in compute times comparable to traditional finite-difference methods. PMID:18567005

Modeling boundary measurements of scattered light using the corrected diffusion approximation

PubMed Central

Lehtikangas, Ossi; Tarvainen, Tanja; Kim, Arnold D.

2012-01-01

We study the modeling and simulation of steady-state measurements of light scattered by a turbid medium taken at the boundary. In particular, we implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation. PMID:22435102

Finite element simulation of texture evolution and Swift effect in NiAl under torsion

NASA Astrophysics Data System (ADS)

Böhlke, Thomas; Glüge, Rainer; Klöden, Burghardt; Skrotzki, Werner; Bertram, Albrecht

2007-09-01

The texture evolution and the Swift effect in NiAl under torsion at 727 °C are studied by finite element simulations for two different initial textures. The material behaviour is modelled by an elastic-viscoplastic Taylor model. In order to overcome the well-known shortcomings of Taylor's approach, the texture evolution is also investigated by a representative volume element (RVE) with periodic boundary conditions and a compatible microstructure at the opposite faces of the RVE. Such a representative volume element takes into account the grain morphology and the grain interaction. The numerical results are compared with experimental data. It is shown that the modelling of a finite element based RVE leads to a better prediction of the final textures. However, the texture evolution path is not accounted for correctly. The simulated Swift effect depends much more on the initial orientation distribution than observed in experiment. Deviations between simulation and experiment may be due to continuous dynamic recrystallization.

Evaluation of finite-element models and stress-intensity factors for surface cracks emanating from stress concentrations

NASA Technical Reports Server (NTRS)

Tan, P. W.; Raju, I. S.; Shivakumar, K. N.; Newman, J. C., Jr.

1990-01-01

A re-evaluation of the 3-D finite-element models and methods used to analyze surface crack at stress concentrations is presented. Previous finite-element models used by Raju and Newman for surface and corner cracks at holes were shown to have ill-shaped elements at the intersection of the hole and crack boundaries. Improved models, without these ill-shaped elements, were developed for a surface crack at a circular hole and at a semi-circular edge notch. Stress-intensity factors were calculated by both the nodal-force and virtual-crack-closure methods. Comparisons made between the previously developed stress-intensity factor equations and the results from the improved models agreed well except for configurations with large notch-radii-to-plate-thickness ratios. Stress-intensity factors for a semi-elliptical surface crack located at the center of a semi-circular edge notch in a plate subjected to remote tensile loadings were calculated using the improved models.

Discontinuous finite element method for vector radiative transfer

NASA Astrophysics Data System (ADS)

Wang, Cun-Hai; Yi, Hong-Liang; Tan, He-Ping

2017-03-01

The discontinuous finite element method (DFEM) is applied to solve the vector radiative transfer in participating media. The derivation in a discrete form of the vector radiation governing equations is presented, in which the angular space is discretized by the discrete-ordinates approach with a local refined modification, and the spatial domain is discretized into finite non-overlapped discontinuous elements. The elements in the whole solution domain are connected by modelling the boundary numerical flux between adjacent elements, which makes the DFEM numerically stable for solving radiative transfer equations. Several various problems of vector radiative transfer are tested to verify the performance of the developed DFEM, including vector radiative transfer in a one-dimensional parallel slab containing a Mie/Rayleigh/strong forward scattering medium and a two-dimensional square medium. The fact that DFEM results agree very well with the benchmark solutions in published references shows that the developed DFEM in this paper is accurate and effective for solving vector radiative transfer problems.

Finite element approximation of the fields of bulk and interfacial line defects

NASA Astrophysics Data System (ADS)

Zhang, Chiqun; Acharya, Amit; Puri, Saurabh

2018-05-01

A generalized disclination (g.disclination) theory (Acharya and Fressengeas, 2015) has been recently introduced that goes beyond treating standard translational and rotational Volterra defects in a continuously distributed defects approach; it is capable of treating the kinematics and dynamics of terminating lines of elastic strain and rotation discontinuities. In this work, a numerical method is developed to solve for the stress and distortion fields of g.disclination systems. Problems of small and finite deformation theory are considered. The fields of a single disclination, a single dislocation treated as a disclination dipole, a tilt grain boundary, a misfitting grain boundary with disconnections, a through twin boundary, a terminating twin boundary, a through grain boundary, a star disclination/penta-twin, a disclination loop (with twist and wedge segments), and a plate, a lenticular, and a needle inclusion are approximated. It is demonstrated that while the far-field topological identity of a dislocation of appropriate strength and a disclination-dipole plus a slip dislocation comprising a disconnection are the same, the latter microstructure is energetically favorable. This underscores the complementary importance of all of topology, geometry, and energetics in understanding defect mechanics. It is established that finite element approximations of fields of interfacial and bulk line defects can be achieved in a systematic and routine manner, thus contributing to the study of intricate defect microstructures in the scientific understanding and predictive design of materials. Our work also represents one systematic way of studying the interaction of (g.)disclinations and dislocations as topological defects, a subject of considerable subtlety and conceptual importance (Aharoni et al., 2017; Mermin, 1979).

A combined application of boundary-element and Runge-Kutta methods in three-dimensional elasticity and poroelasticity

NASA Astrophysics Data System (ADS)

Igumnov, Leonid; Ipatov, Aleksandr; Belov, Aleksandr; Petrov, Andrey

2015-09-01

The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary) and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.

Elasto-Plastic Analysis of Tee Joints Using HOT-SMAC

NASA Technical Reports Server (NTRS)

Arnold, Steve M. (Technical Monitor); Bednarcyk, Brett A.; Yarrington, Phillip W.

2004-01-01

The Higher Order Theory - Structural/Micro Analysis Code (HOT-SMAC) software package is applied to analyze the linearly elastic and elasto-plastic response of adhesively bonded tee joints. Joints of this type are finding an increasing number of applications with the increased use of composite materials within advanced aerospace vehicles, and improved tools for the design and analysis of these joints are needed. The linearly elastic results of the code are validated vs. finite element analysis results from the literature under different loading and boundary conditions, and new results are generated to investigate the inelastic behavior of the tee joint. The comparison with the finite element results indicates that HOT-SMAC is an efficient and accurate alternative to the finite element method and has a great deal of potential as an analysis tool for a wide range of bonded joints.

Design and Stress Analysis of Low-Noise Adjusted Bearing Contact Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Litvin, Faydor L.; Fuentes, Alfonso; Mullins, Baxter R.; Woods, Ron

2002-01-01

An integrated computerized approach for design and stress analysis of low-noise spiral bevel gear drives with adjusted bearing contact has been developed. The computation procedure is an iterative process, requiring four separate steps that provide: (a) a parabolic function of transmission errors that is able to reduce the effect of errors of alignment, and (b) reduction of the shift of bearing contact caused by misalignment. Application of finite element analysis permits the contact and bending stresses to be determined and investigate the formation of the bearing contact. The design of finite element models and boundary conditions is automated and does not require an intermediate CAD computer program. A commercially available finite element analysis computer program with contact capability was used to conduct the stress analysis. The theory developed is illustrated with numerical examples.

Calculation of skin-stiffener interface stresses in stiffened composite panels

NASA Technical Reports Server (NTRS)

Cohen, David; Hyer, Michael W.

1987-01-01

A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. Accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. Using this analysis procedure, the influence of geometric nonlinearities and stiffener parameters on the skin-stiffener interface stresses is evaluated.

Free vibrations of thin-walled semicircular graphite-epoxy composite frames

NASA Technical Reports Server (NTRS)

Carden, Huey D.; Noor, Ahmed K.; Peters, Jeanne M.

1990-01-01

A detailed study is made of the effects of variations in lamination and material parameters of thin walled composite frames on their vibrational characteristics. The structures considered are semicircular thin walled frames with I and J sections. The flanges and webs of the frames are modeled by using 2-D shell and plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The frequencies and modes predicted by the 2-D finite element model are compared with those obtained from experiments, as well as with the predictions of a non-dimensional thin walled beam finite element model. A detailed study is made of the sensitivity of the vibrational response to variations in the fiber orientation, material properties of the individual layers, and boundary conditions.

Free vibrations of thin-walled semicircular graphite-epoxy composite frames

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Carden, Huey D.; Peters, Jeanne M.

1990-01-01

A detailed study is made of the effects of variations in lamination and material parameters of thin walled composite frames on their vibrational characteristics. The structures considered are semicircular thin walled frames with I and J sections. The flanges and webs of the frames are modelled by using 2-D shell and plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frames. The frequencies and modes predicted by the 2-D finite element model are compared with those obtained from experiments, as well as with the predictions of a 1-D thin walled beam finite element model. A detailed study is made of the sensitivity of the vibrational response to variations in the fiber orientation, material properties of the individual layers, and boundary conditions.

Generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

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

Gao, Kai; Fu, Shubin; Gibson, Richard L.

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

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

Gao, Kai, E-mail: kaigao87@gmail.com; Fu, Shubin, E-mail: shubinfu89@gmail.com; Gibson, Richard L., E-mail: gibson@tamu.edu

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

DOE PAGES

Gao, Kai; Fu, Shubin; Gibson, Richard L.; ...

2015-04-14

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Effect of boundary conditions on the numerical solutions of representative volume element problems for random heterogeneous composite microstructures

NASA Astrophysics Data System (ADS)

Cho, Yi Je; Lee, Wook Jin; Park, Yong Ho

2014-11-01

Aspects of numerical results from computational experiments on representative volume element (RVE) problems using finite element analyses are discussed. Two different boundary conditions (BCs) are examined and compared numerically for volume elements with different sizes, where tests have been performed on the uniaxial tensile deformation of random particle reinforced composites. Structural heterogeneities near model boundaries such as the free-edges of particle/matrix interfaces significantly influenced the overall numerical solutions, producing force and displacement fluctuations along the boundaries. Interestingly, this effect was shown to be limited to surface regions within a certain distance of the boundaries, while the interior of the model showed almost identical strain fields regardless of the applied BCs. Also, the thickness of the BC-affected regions remained constant with varying volume element sizes in the models. When the volume element size was large enough compared to the thickness of the BC-affected regions, the structural response of most of the model was found to be almost independent of the applied BC such that the apparent properties converged to the effective properties. Finally, the mechanism that leads a RVE model for random heterogeneous materials to be representative is discussed in terms of the size of the volume element and the thickness of the BC-affected region.

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

NASA Technical Reports Server (NTRS)

Winget, J. M.; Hughes, T. J. R.

1985-01-01

The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

On 3-D inelastic analysis methods for hot section components (base program)

NASA Technical Reports Server (NTRS)

Wilson, R. B.; Bak, M. J.; Nakazawa, S.; Banerjee, P. K.

1986-01-01

A 3-D Inelastic Analysis Method program is described. This program consists of a series of new computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of: (1) combustor liners, (2) turbine blades, and (3) turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain)and global (dynamics, buckling) structural behavior of the three selected components. Three computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (Marc-Hot Section Technology), and BEST (Boundary Element Stress Technology), have been developed and are briefly described in this report.

Fast Boundary Element Method for acoustics with the Sparse Cardinal Sine Decomposition

NASA Astrophysics Data System (ADS)

Alouges, François; Aussal, Matthieu; Parolin, Emile

2017-07-01

This paper presents the newly proposed method Sparse Cardinal Sine Decomposition that allows fast convolution on unstructured grids. We focus on its use when coupled with finite element techniques to solve acoustic problems with the (compressed) Boundary Element Method. In addition, we also compare the computational performances of two equivalent Matlab® and Python implementations of the method. We show validation test cases in order to assess the precision of the approach. Eventually, the performance of the method is illustrated by the computation of the acoustic target strength of a realistic submarine from the Benchmark Target Strength Simulation international workshop.

Using Floquet periodicity to easily calculate dispersion curves and wave structures of homogeneous waveguides

NASA Astrophysics Data System (ADS)

Hakoda, Christopher; Rose, Joseph; Shokouhi, Parisa; Lissenden, Clifford

2018-04-01

Dispersion curves are essential to any guided-wave-related project. The Semi-Analytical Finite Element (SAFE) method has become the conventional way to compute dispersion curves for homogeneous waveguides. However, only recently has a general SAFE formulation for commercial and open-source software become available, meaning that until now SAFE analyses have been variable and more time consuming than desirable. Likewise, the Floquet boundary conditions enable analysis of waveguides with periodicity and have been an integral part of the development of metamaterials. In fact, we have found the use of Floquet boundary conditions to be an extremely powerful tool for homogeneous waveguides, too. The nuances of using periodic boundary conditions for homogeneous waveguides that do not exhibit periodicity are discussed. Comparisons between this method and SAFE are made for selected homogeneous waveguide applications. The COMSOL Multiphysics software is used for the results shown, but any standard finite element software that can implement Floquet periodicity (user-defined or built-in) should suffice. Finally, we identify a number of complex waveguides for which dispersion curves can be found with relative ease by using the periodicity inherent to the Floquet boundary conditions.

Semi-analytical discontinuous Galerkin finite element method for the calculation of dispersion properties of guided waves in plates.

PubMed

Hebaz, Salah-Eddine; Benmeddour, Farouk; Moulin, Emmanuel; Assaad, Jamal

2018-01-01

The development of reliable guided waves inspection systems is conditioned by an accurate knowledge of their dispersive properties. The semi-analytical finite element method has been proven to be very practical for modeling wave propagation in arbitrary cross-section waveguides. However, when it comes to computations on complex geometries to a given accuracy, it still has a major drawback: the high consumption of resources. Recently, discontinuous Galerkin finite element method (DG-FEM) has been found advantageous over the standard finite element method when applied as well in the frequency domain. In this work, a high-order method for the computation of Lamb mode characteristics in plates is proposed. The problem is discretised using a class of DG-FEM, namely, the interior penalty methods family. The analytical validation is performed through the homogeneous isotropic case with traction-free boundary conditions. Afterwards, functionally graded material plates are analysed and a numerical example is presented. It was found that the obtained results are in good agreement with those found in the literature.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 1: Model Description and User's Manual

USGS Publications Warehouse

Torak, L.J.

1993-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or bead-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration. The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems; Part 1, Model description and user's manual

USGS Publications Warehouse

Torak, Lynn J.

1992-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration.The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE PAGES

Bunting, Gregory; Prakash, Arun; Walsh, Timothy; ...

2018-01-26

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

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

Bunting, Gregory; Prakash, Arun; Walsh, Timothy

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Computation of three-dimensional nozzle-exhaust flow fields with the GIM code

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Anderson, P. G.

1978-01-01

A methodology is introduced for constructing numerical analogs of the partial differential equations of continuum mechanics. A general formulation is provided which permits classical finite element and many of the finite difference methods to be derived directly. The approach, termed the General Interpolants Method (GIM), can combined the best features of finite element and finite difference methods. A quasi-variational procedure is used to formulate the element equations, to introduce boundary conditions into the method and to provide a natural assembly sequence. A derivation is given in terms of general interpolation functions from this procedure. Example computations for transonic and supersonic flows in two and three dimensions are given to illustrate the utility of GIM. A three-dimensional nozzle-exhaust flow field is solved including interaction with the freestream and a coupled treatment of the shear layer. Potential applications of the GIM code to a variety of computational fluid dynamics problems is then discussed in terms of existing capability or by extension of the methodology.

A finite-element model for simulation of two-dimensional steady-state ground-water flow in confined aquifers

USGS Publications Warehouse

Kuniansky, E.L.

1990-01-01

A computer program based on the Galerkin finite-element method was developed to simulate two-dimensional steady-state ground-water flow in either isotropic or anisotropic confined aquifers. The program may also be used for unconfined aquifers of constant saturated thickness. Constant head, constant flux, and head-dependent flux boundary conditions can be specified in order to approximate a variety of natural conditions, such as a river or lake boundary, and pumping well. The computer program was developed for the preliminary simulation of ground-water flow in the Edwards-Trinity Regional aquifer system as part of the Regional Aquifer-Systems Analysis Program. Results of the program compare well to analytical solutions and simulations .from published finite-difference models. A concise discussion of the Galerkin method is presented along with a description of the program. Provided in the Supplemental Data section are a listing of the computer program, definitions of selected program variables, and several examples of data input and output used in verifying the accuracy of the program.

The Impact of Varying the Physics Grid Resolution Relative to the Dynamical Core Resolution in CAM-SE-CSLAM

NASA Astrophysics Data System (ADS)

Herrington, A. R.; Lauritzen, P. H.; Reed, K. A.

2017-12-01

The spectral element dynamical core of the Community Atmosphere Model (CAM) has recently been coupled to an approximately isotropic, finite-volume grid per implementation of the conservative semi-Lagrangian multi-tracer transport scheme (CAM-SE-CSLAM; Lauritzen et al. 2017). In this framework, the semi-Lagrangian transport of tracers are computed on the finite-volume grid, while the adiabatic dynamics are solved using the spectral element grid. The physical parameterizations are evaluated on the finite-volume grid, as opposed to the unevenly spaced Gauss-Lobatto-Legendre nodes of the spectral element grid. Computing the physics on the finite-volume grid reduces numerical artifacts such as grid imprinting, possibly because the forcing terms are no longer computed at element boundaries where the resolved dynamics are least smooth. The separation of the physics grid and the dynamics grid allows for a unique opportunity to understand the resolution sensitivity in CAM-SE-CSLAM. The observed large sensitivity of CAM to horizontal resolution is a poorly understood impediment to improved simulations of regional climate using global, variable resolution grids. Here, a series of idealized moist simulations are presented in which the finite-volume grid resolution is varied relative to the spectral element grid resolution in CAM-SE-CSLAM. The simulations are carried out at multiple spectral element grid resolutions, in part to provide a companion set of simulations, in which the spectral element grid resolution is varied relative to the finite-volume grid resolution, but more generally to understand if the sensitivity to the finite-volume grid resolution is consistent across a wider spectrum of resolved scales. Results are interpreted in the context of prior ideas regarding resolution sensitivity of global atmospheric models.

Least-squares solution of incompressible Navier-Stokes equations with the p-version of finite elements

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Sonnad, Vijay

1991-01-01

A p-version of the least squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady state incompressible viscous flow problems. The resulting system of symmetric and positive definite linear equations can be solved satisfactorily with the conjugate gradient method. In conjunction with the use of rapid operator application which avoids the formation of either element of global matrices, it is possible to achieve a highly compact and efficient solution scheme for the incompressible Navier-Stokes equations. Numerical results are presented for two-dimensional flow over a backward facing step. The effectiveness of simple outflow boundary conditions is also demonstrated.

A combined dislocation fan-finite element (DF-FE) method for stress field simulation of dislocations emerging at the free surfaces of 3D elastically anisotropic crystals

NASA Astrophysics Data System (ADS)

Balusu, K.; Huang, H.

2017-04-01

A combined dislocation fan-finite element (DF-FE) method is presented for efficient and accurate simulation of dislocation nodal forces in 3D elastically anisotropic crystals with dislocations intersecting the free surfaces. The finite domain problem is decomposed into half-spaces with singular traction stresses, an infinite domain, and a finite domain with non-singular traction stresses. As such, the singular and non-singular parts of the traction stresses are addressed separately; the dislocation fan (DF) method is introduced to balance the singular traction stresses in the half-spaces while the finite element method (FEM) is employed to enforce the non-singular boundary conditions. The accuracy and efficiency of the DF method is demonstrated using a simple isotropic test case, by comparing it with the analytical solution as well as the FEM solution. The DF-FE method is subsequently used for calculating the dislocation nodal forces in a finite elastically anisotropic crystal, which produces dislocation nodal forces that converge rapidly with increasing mesh resolutions. In comparison, the FEM solution fails to converge, especially for nodes closer to the surfaces.

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.

Variational formulation of hybrid problems for fully 3-D transonic flow with shocks in rotor

NASA Technical Reports Server (NTRS)

Liu, Gao-Lian

1991-01-01

Based on previous research, the unified variable domain variational theory of hybrid problems for rotor flow is extended to fully 3-D transonic rotor flow with shocks, unifying and generalizing the direct and inverse problems. Three variational principles (VP) families were established. All unknown boundaries and flow discontinuities (such as shocks, free trailing vortex sheets) are successfully handled via functional variations with variable domain, converting almost all boundary and interface conditions, including the Rankine Hugoniot shock relations, into natural ones. This theory provides a series of novel ways for blade design or modification and a rigorous theoretical basis for finite element applications and also constitutes an important part of the optimal design theory of rotor bladings. Numerical solutions to subsonic flow by finite elements with self-adapting nodes given in Refs., show good agreement with experimental results.

Unsteady combustion of solid propellants

NASA Astrophysics Data System (ADS)

Chung, T. J.; Kim, P. K.

The oscillatory motions of all field variables (pressure, temperature, velocity, density, and fuel fractions) in the flame zone of solid propellant rocket motors are calculated using the finite element method. The Arrhenius law with a single step forward chemical reaction is used. Effects of radiative heat transfer, impressed arbitrary acoustic wave incidence, and idealized mean flow velocities are also investigated. Boundary conditions are derived at the solid-gas interfaces and at the flame edges which are implemented via Lagrange multipliers. Perturbation expansions of all governing conservation equations up to and including the second order are carried out so that nonlinear oscillations may be accommodated. All excited frequencies are calculated by means of eigenvalue analyses, and the combustion response functions corresponding to these frequencies are determined. It is shown that the use of isoparametric finite elements, Gaussian quadrature integration, and the Lagrange multiplier boundary matrix scheme offers a convenient approach to two-dimensional calculations.

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

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

McGhee, J.M.; Roberts, R.M.; Morel, J.E.

1997-06-01

A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner formore » scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.« less

Modelling crystal plasticity by 3D dislocation dynamics and the finite element method: The Discrete-Continuous Model revisited

NASA Astrophysics Data System (ADS)

Vattré, A.; Devincre, B.; Feyel, F.; Gatti, R.; Groh, S.; Jamond, O.; Roos, A.

2014-02-01

A unified model coupling 3D dislocation dynamics (DD) simulations with the finite element (FE) method is revisited. The so-called Discrete-Continuous Model (DCM) aims to predict plastic flow at the (sub-)micron length scale of materials with complex boundary conditions. The evolution of the dislocation microstructure and the short-range dislocation-dislocation interactions are calculated with a DD code. The long-range mechanical fields due to the dislocations are calculated by a FE code, taking into account the boundary conditions. The coupling procedure is based on eigenstrain theory, and the precise manner in which the plastic slip, i.e. the dislocation glide as calculated by the DD code, is transferred to the integration points of the FE mesh is described in full detail. Several test cases are presented, and the DCM is applied to plastic flow in a single-crystal Nickel-based superalloy.

A discontinuous control volume finite element method for multi-phase flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Salinas, P.; Pavlidis, D.; Xie, Z.; Osman, H.; Pain, C. C.; Jackson, M. D.

2018-01-01

We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media.

Elasto visco-plastic flow with special attention to boundary conditions

NASA Technical Reports Server (NTRS)

Shimazaki, Y.; Thompson, E. G.

1981-01-01

A simple but nontrivial steady-state creeping elasto visco-plastic (Maxwell fluid) radial flow problem is analyzed, with special attention given to the effects of the boundary conditions. Solutions are obtained through integration of a governing equation on stress using the Runge-Kutta method for initial value problems and finite differences for boundary value problems. A more general approach through the finite element method, an approach that solves for the velocity field rather than the stress field and that is applicable to a wide range of problems, is presented and tested using the radial flow example. It is found that steady-state flows of elasto visco-plastic materials are strongly influenced by the state of stress of material as it enters the region of interest. The importance of this boundary or initial condition in analyses involving materials coming into control volumes from unusual stress environments is emphasized.

Chemorheology of reactive systems: Finite element analysis

NASA Technical Reports Server (NTRS)

Douglas, C.; Roylance, D.

1982-01-01

The equations which govern the nonisothermal flow of reactive fluids are outlined, and the means by which finite element analysis is used to solve these equations for the sort of arbitrary boundary conditions encountered in industrial practice are described. The performance of the computer code is illustrated by several trial problems, selected more for their value in providing insight to polymer processing flows than as practical production problems. Although a good deal remains to be learned as to the performance and proper use of this numerical technique, it is undeniably useful in providing better understanding of today's complicated polymer processing problems.

Domain decomposition for a mixed finite element method in three dimensions

USGS Publications Warehouse

Cai, Z.; Parashkevov, R.R.; Russell, T.F.; Wilson, J.D.; Ye, X.

2003-01-01

We consider the solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions. Based on a decomposition of the velocity space, these equations can be reduced to a discrete elliptic problem by eliminating the pressure through the use of substructures of the domain. The practicality of the reduction relies on a local basis, presented here, for the divergence-free subspace of the velocity space. We consider additive and multiplicative domain decomposition methods for solving the reduced elliptic problem, and their uniform convergence is established.

Stress analysis and buckling of J-stiffened graphite-epoxy panel

NASA Technical Reports Server (NTRS)

Davis, R. C.

1980-01-01

A graphite epoxy shear panel with bonded on J stiffeners was investigated. The panel, loaded to buckling in a picture frame shear test is described. Two finite element models, each of which included the doubler material bonded to the panel skin under the stiffeners and at the panel edges, were used to make a stress analysis of the panel. The shear load distributions in the panel from two commonly used boundary conditions, applied shear load and applied displacement, were compared with the results from one of the finite element models that included the picture frame test fixture.

On the Interconnection of Incompatible Solid Finite Element Meshes Using Multipoint Constraints

NASA Technical Reports Server (NTRS)

Fox, G. L.

1985-01-01

Incompatible meshes, i.e., meshes that physically must have a common boundary, but do not necessarily have coincident grid points, can arise in the course of a finite element analysis. For example, two substructures may have been developed at different times for different purposes and it becomes necessary to interconnect the two models. A technique that uses only multipoint constraints, i.e., MPC cards (or MPCS cards in substructuring), is presented. Since the method uses only MPC's, the procedure may apply at any stage in an analysis; no prior planning or special data is necessary.

Three-dimensional electrical impedance tomography: a topology optimization approach.

PubMed

Mello, Luís Augusto Motta; de Lima, Cícero Ribeiro; Amato, Marcelo Britto Passos; Lima, Raul Gonzalez; Silva, Emílio Carlos Nelli

2008-02-01

Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

A NURBS-enhanced finite volume solver for steady Euler equations

NASA Astrophysics Data System (ADS)

Meng, Xucheng; Hu, Guanghui

2018-04-01

In Hu and Yi (2016) [20], a non-oscillatory k-exact reconstruction method was proposed towards the high-order finite volume methods for steady Euler equations, which successfully demonstrated the high-order behavior in the simulations. However, the degeneracy of the numerical accuracy of the approximate solutions to problems with curved boundary can be observed obviously. In this paper, the issue is resolved by introducing the Non-Uniform Rational B-splines (NURBS) method, i.e., with given discrete description of the computational domain, an approximate NURBS curve is reconstructed to provide quality quadrature information along the curved boundary. The advantages of using NURBS include i). both the numerical accuracy of the approximate solutions and convergence rate of the numerical methods are improved simultaneously, and ii). the NURBS curve generation is independent of other modules of the numerical framework, which makes its application very flexible. It is also shown in the paper that by introducing more elements along the normal direction for the reconstruction patch of the boundary element, significant improvement in the convergence to steady state can be achieved. The numerical examples confirm the above features very well.

Burton-Miller-type singular boundary method for acoustic radiation and scattering

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Gu, Yan

2014-08-01

This paper proposes the singular boundary method (SBM) in conjunction with Burton and Miller's formulation for acoustic radiation and scattering. The SBM is a strong-form collocation boundary discretization technique using the singular fundamental solutions, which is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors (SIFs) to eliminate the singularities of the fundamental solutions. Therefore, it avoids singular numerical integrals in the boundary element method (BEM) and circumvents the troublesome placement of the fictitious boundary in the method of fundamental solutions (MFS). In the present method, we derive the SIFs of exterior Helmholtz equation by means of the SIFs of exterior Laplace equation owing to the same order of singularities between the Laplace and Helmholtz fundamental solutions. In conjunction with the Burton-Miller formulation, the SBM enhances the quality of the solution, particularly in the vicinity of the corresponding interior eigenfrequencies. Numerical illustrations demonstrate efficiency and accuracy of the present scheme on some benchmark examples under 2D and 3D unbounded domains in comparison with the analytical solutions, the boundary element solutions and Dirichlet-to-Neumann finite element solutions.

STARS: A general-purpose finite element computer program for analysis of engineering structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1984-01-01

STARS (Structural Analysis Routines) is primarily an interactive, graphics-oriented, finite-element computer program for analyzing the static, stability, free vibration, and dynamic responses of damped and undamped structures, including rotating systems. The element library consists of one-dimensional (1-D) line elements, two-dimensional (2-D) triangular and quadrilateral shell elements, and three-dimensional (3-D) tetrahedral and hexahedral solid elements. These elements enable the solution of structural problems that include truss, beam, space frame, plane, plate, shell, and solid structures, or any combination thereof. Zero, finite, and interdependent deflection boundary conditions can be implemented by the program. The associated dynamic response analysis capability provides for initial deformation and velocity inputs, whereas the transient excitation may be either forces or accelerations. An effective in-core or out-of-core solution strategy is automatically employed by the program, depending on the size of the problem. Data input may be at random within a data set, and the program offers certain automatic data-generation features. Input data are formatted as an optimal combination of free and fixed formats. Interactive graphics capabilities enable convenient display of nodal deformations, mode shapes, and element stresses.

Modelling to very high strains

NASA Astrophysics Data System (ADS)

Bons, P. D.; Jessell, M. W.; Griera, A.; Evans, L. A.; Wilson, C. J. L.

2009-04-01

Ductile strains in shear zones often reach extreme values, resulting in typical structures, such as winged porphyroclasts and several types of shear bands. The numerical simulation of the development of such structures has so far been inhibited by the low maximum strains that numerical models can normally achieve. Typical numerical models collapse at shear strains in the order of one to three. We have implemented a number of new functionalities in the numerical platform "Elle" (Jessell et al. 2001), which significantly increases the amount of strain that can be achieved and simultaneously reduces boundary effects that become increasingly disturbing at higher strain. Constant remeshing, while maintaining the polygonal phase regions, is the first step to avoid collapse of the finite-element grid required by finite-element solvers, such as Basil (Houseman et al. 2008). The second step is to apply a grain-growth routine to the boundaries of polygons that represent phase regions. This way, the development of sharp angles is avoided. A second advantage is that phase regions may merge or become separated (boudinage). Such topological changes are normally not possible in finite element deformation codes. The third step is the use of wrapping vertical model boundaries, with which optimal and unchanging model boundaries are maintained for the application of stress or velocity boundary conditions. The fourth step is to shift the model by a random amount in the vertical direction every time step. This way, the fixed horizontal boundary conditions are applied to different material points within the model every time step. Disturbing boundary effects are thus averaged out over the whole model and not localised to e.g. top and bottom of the model. Reduction of boundary effects has the additional advantage that model can be smaller and, therefore, numerically more efficient. Owing to the combination of these existing and new functionalities it is now possible to simulate the development of very high-strain structures. Jessell, M.W., Bons, P.D., Evans, L., Barr, T., Stüwe, K. 2001. Elle: a micro-process approach to the simulation of microstructures. Computers & Geosciences 27, 17-30. Houseman, G., Barr, T., Evans, L. 2008. Basil: stress and deformation in a viscous material. In: P.D. Bons, D. Koehn & M.W.Jessell (Eds.) Microdynamics Simulation. Lecture Notes in Earth Sciences 106, Springer, Berlin, 405p.

Fiber-reinforced materials: finite elements for the treatment of the inextensibility constraint

NASA Astrophysics Data System (ADS)

Auricchio, Ferdinando; Scalet, Giulia; Wriggers, Peter

2017-12-01

The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

NASA Technical Reports Server (NTRS)

Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard

1996-01-01

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

A finite element solution algorithm for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.

A Novel Arterial Constitutive Model in a Commercial Finite Element Package: Application to Balloon Angioplasty

PubMed Central

Zhao, Xuefeng; Liu, Yi; Zhang, Wei; Wang, Cong; Kassab, Ghassan S.

2011-01-01

Recently, a novel linearized constitutive model with a new strain measure that absorbs the material nonlinearity was validated for arteries. In this study, the linearized arterial stress-strain relationship is implemented into a finite element method package ANSYS, via the user subroutine USERMAT. The reference configuration is chosen to be the closed cylindrical tube (no-load state) rather than the open sector (zero-stress state). The residual strain is taken into account by analytic calculation and the incompressibility condition is enforced with Lagrange penalty method. Axisymmetric finite element analyses are conducted to demonstrate potential applications of this approach in a complex boundary value problem where angioplasty balloon interacts with the vessel wall. The model predictions of transmural circumferential and compressive radial stress distributions were also validated against an exponential-type Fung model, and the mean error was found to be within 6%. PMID:21689665

Adaptive Meshing of Ship Air-Wake Flowfields

DTIC Science & Technology

2014-10-21

performs cut- cell operations at geometry boundaries. A second-order spatial finite-volume scheme has been incorporated with explicit first order...The cells intersected by the geometry are handled using the “cut- cell ” approach, which is basically creating arbitrary polyhedral elements with...appropriate surface boundary conditions. Any cells completely outside the computational domain are tagged external and not solved in the flow solution

Design of Software for Design of Finite Element for Structural Analysis. Ph.D. Thesis - Stuttgart Univ., 22 Nov. 1983

NASA Technical Reports Server (NTRS)

Helfrich, Reinhard

1987-01-01

The concepts of software engineering which allow a user of the finite element method to describe a model, to collect and to check the model data in a data base as well as to form the matrices required for a finite element calculation are examined. Next the components of the model description are conceived including the mesh tree, the topology, the configuration, the kinematic boundary conditions, the data for each element, and the loads. The possibilities for description and review of the data are considered. The concept of the segments for the modularization of the programs follows the components of the model description. The significance of the mesh tree as a globular guiding structure will be understood in view of the principle of the unity of the model, the mesh tree, and the data base. The user-friendly aspects of the software system will be summarized: the principle of language communication, the data generators, error processing, and data security.

Numerical modeling of guided ultrasonic waves generated and received by piezoelectric wafer in a Delaminated composite beam

NASA Astrophysics Data System (ADS)

Xu, G. D.; Xu, B. Q.; Xu, C. G.; Luo, Y.

2017-05-01

A spectral finite element method (SFEM) is developed to analyze guided ultrasonic waves in a delaminated composite beam excited and received by a pair of surface-bonded piezoelectric wafers. The displacements of the composite beam and the piezoelectric wafer are represented by Timoshenko beam and Euler Bernoulli theory respectively. The linear piezoelectricity is used to model the electrical-mechanical coupling between the piezoelectric wafer and the beam. The coupled governing equations and the boundary conditions in time domain are obtained by using the Hamilton's principle, and then the SFEM are formulated by transforming the coupled governing equations into frequency domain via the discrete Fourier transform. The guided waves are analyzed while the interaction of waves with delamination is also discussed. The elements needed in SFEM is far fewer than those for finite element method (FEM), which result in a much faster solution speed in this study. The high accuracy of the present SFEM is verified by comparing with the finite element results.

Experimental validation of finite element and boundary element methods for predicting structural vibration and radiated noise

NASA Technical Reports Server (NTRS)

Seybert, A. F.; Wu, T. W.; Wu, X. F.

1994-01-01

This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis; noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: sound power predicted by the BEM model using vibration data measured on the surface of the box; sound power predicted by the FEM/BEM model; and sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. The predicted vibration and radiated noise were then validated through experimentation.

The Overshoot Phenomenon in Geodynamics Codes

NASA Astrophysics Data System (ADS)

Kommu, R. K.; Heien, E. M.; Kellogg, L. H.; Bangerth, W.; Heister, T.; Studley, E. H.

2013-12-01

The overshoot phenomenon is a common occurrence in numerical software when a continuous function on a finite dimensional discretized space is used to approximate a discontinuous jump, in temperature and material concentration, for example. The resulting solution overshoots, and undershoots, the discontinuous jump. Numerical simulations play an extremely important role in mantle convection research. This is both due to the strong temperature and stress dependence of viscosity and also due to the inaccessibility of deep earth. Under these circumstances, it is essential that mantle convection simulations be extremely accurate and reliable. CitcomS and ASPECT are two finite element based mantle convection simulations developed and maintained by the Computational Infrastructure for Geodynamics. CitcomS is a finite element based mantle convection code that is designed to run on multiple high-performance computing platforms. ASPECT, an adaptive mesh refinement (AMR) code built on the Deal.II library, is also a finite element based mantle convection code that scales well on various HPC platforms. CitcomS and ASPECT both exhibit the overshoot phenomenon. One attempt at controlling the overshoot uses the Entropy Viscosity method, which introduces an artificial diffusion term in the energy equation of mantle convection. This artificial diffusion term is small where the temperature field is smooth. We present results from CitcomS and ASPECT that quantify the effect of the Entropy Viscosity method in reducing the overshoot phenomenon. In the discontinuous Galerkin (DG) finite element method, the test functions used in the method are continuous within each element but are discontinuous across inter-element boundaries. The solution space in the DG method is discontinuous. FEniCS is a collection of free software tools that automate the solution of differential equations using finite element methods. In this work we also present results from a finite element mantle convection simulation implemented in FEniCS that investigates the effect of using DG elements in reducing the overshoot problem.

Finite Element Analysis of Geodesically Stiffened Cylindrical Composite Shells Using a Layerwise Theory

NASA Technical Reports Server (NTRS)

Gerhard, Craig Steven; Gurdal, Zafer; Kapania, Rakesh K.

1996-01-01

Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases.

Finite element modeling of the residual stress evolution in forged and direct-aged alloy 718 turbine disks during manufacturing and its experimental validation

NASA Astrophysics Data System (ADS)

Drexler, Andreas; Ecker, Werner; Hessert, Roland; Oberwinkler, Bernd; Gänser, Hans-Peter; Keckes, Jozef; Hofmann, Michael; Fischersworring-Bunk, Andreas

2017-10-01

In this work the evolution of the residual stress field in a forged and heat treated turbine disk of Alloy 718 and its subsequent relaxation during machining was simulated and measured. After forging at around 1000 °C the disks were natural air cooled to room temperature and direct aged in a furnace at 720 °C for 8 hours and at 620 °C for 8 hours. The machining of the Alloy 718 turbine disk was performed in two steps: The machining of the Alloy 718 turbine disk was performed in two steps: First, from the forging contour to a contour used for ultra-sonic testing. Second, from the latter to the final contour. The thermal boundary conditions in the finite element model for air cooling and furnace heating were estimated based on analytical equations from literature. A constitutive model developed for the unified description of rate dependent and rate independent mechanical material behavior of Alloy 718 under in-service conditions up to temperatures of 1000 °C was extended and parametrized to meet the manufacturing conditions with temperatures up to 1000 °C. The results of the finite element model were validated with measurements on real-scale turbine disks. The thermal boundary conditions were validated in-field with measured cooling curves. For that purpose holes were drilled at different positions into the turbine disk and thermocouples were mounted in these holes to record the time-temperature curves during natural cooling and heating. The simulated residual stresses were validated by using the hole drilling method and the neutron diffraction technique. The accuracy of the finite element model for the final manufacturing step investigated was ±50 MPa.

A finite element-based algorithm for rubbing induced vibration prediction in rotors

NASA Astrophysics Data System (ADS)

Behzad, Mehdi; Alvandi, Mehdi; Mba, David; Jamali, Jalil

2013-10-01

In this paper, an algorithm is developed for more realistic investigation of rotor-to-stator rubbing vibration, based on finite element theory with unilateral contact and friction conditions. To model the rotor, cross sections are assumed to be radially rigid. A finite element discretization based on traditional beam theories which sufficiently accounts for axial and transversal flexibility of the rotor is used. A general finite element discretization model considering inertial and viscoelastic characteristics of the stator is used for modeling the stator. Therefore, for contact analysis, only the boundary of the stator is discretized. The contact problem is defined as the contact between the circular rigid cross section of the rotor and “nodes” of the stator only. Next, Gap function and contact conditions are described for the contact problem. Two finite element models of the rotor and the stator are coupled via the Lagrange multipliers method in order to obtain the constrained equation of motion. A case study of the partial rubbing is simulated using the algorithm. The synchronous and subsynchronous responses of the partial rubbing are obtained for different rotational speeds. In addition, a sensitivity analysis is carried out with respect to the initial clearance, the stator stiffness, the damping parameter, and the coefficient of friction. There is a good agreement between the result of this research and the experimental result in the literature.

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.

Finite-Element Analysis of a Mach-8 Flight Test Article Using Nonlinear Contact Elements

NASA Technical Reports Server (NTRS)

Richards, W. Lance

1997-01-01

A flight test article, called a glove, is required for a Mach-8 boundary-layer experiment to be conducted on a flight mission of the air-launched Pegasus(reg) space booster. The glove is required to provide a smooth, three-dimensional, structurally stable, aerodynamic surface and includes instrumentation to determine when and where boundary-layer transition occurs during the hypersonic flight trajectory. A restraint mechanism has been invented to attach the glove to the wing of the space booster. The restraint mechanism securely attaches the glove to the wing in directions normal to the wing/glove interface surface, but allows the glove to thermally expand and contract to alleviate stresses in directions parallel to the interface surface. A finite-element analysis has been performed using nonlinear contact elements to model the complex behavior of the sliding restraint mechanism. This paper provides an overview of the glove design and presents details of the analysis that were essential to demonstrate the flight worthiness of the wing-glove test article. Results show that all glove components are well within the allowable stress and deformation requirements to satisfy the objectives of the flight research experiment.

International Conference on Numerical Methods in Fluid Dynamics, 7th, Stanford University, Stanford and Moffett Field, CA, June 23-27, 1980, Proceedings

NASA Technical Reports Server (NTRS)

Reynolds, W. C. (Editor); Maccormack, R. W.

1981-01-01

Topics discussed include polygon transformations in fluid mechanics, computation of three-dimensional horseshoe vortex flow using the Navier-Stokes equations, an improved surface velocity method for transonic finite-volume solutions, transonic flow calculations with higher order finite elements, the numerical calculation of transonic axial turbomachinery flows, and the simultaneous solutions of inviscid flow and boundary layer at transonic speeds. Also considered are analytical solutions for the reflection of unsteady shock waves and relevant numerical tests, reformulation of the method of characteristics for multidimensional flows, direct numerical simulations of turbulent shear flows, the stability and separation of freely interacting boundary layers, computational models of convective motions at fluid interfaces, viscous transonic flow over airfoils, and mixed spectral/finite difference approximations for slightly viscous flows.

Surface cracks in a plate of finite width under tension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

The problem of a finite plate containing collinear surface cracks is considered and solved by using the line spring model with plane elasticity and Reissner's plate theory. The main focus is on the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors in an effort to provide extensive numerical results which may be useful in applications. Some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks, and two corner cracks for wide range of relative dimensions. Particularly in corner cracks, the agreement with the finite element solution is surprisingly very good. The results are obtained for semi-elliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

Surface cracks in a plate of finite width under extension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

In this paper the problem of a finite plate containing collinear surface cracks is considered. The problem is solved by using the line spring model with plane elasticity and Reissner's plate theory. The main purpose of the study is to investigate the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors and to provide extensive numerical results which may be useful in applications. First, some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks and two corner cracks for wide range of relative dimensions. Particularly in corner cracks the agreement with the finite element solution is surprisingly very good. The results are obtained for semielliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

3-D thermal analysis using finite difference technique with finite element model for improved design of components of rocket engine turbomachines for Space Shuttle Main Engine SSME

NASA Technical Reports Server (NTRS)

Sohn, Kiho D.; Ip, Shek-Se P.

1988-01-01

Three-dimensional finite element models were generated and transferred into three-dimensional finite difference models to perform transient thermal analyses for the SSME high pressure fuel turbopump's first stage nozzles and rotor blades. STANCOOL was chosen to calculate the heat transfer characteristics (HTCs) around the airfoils, and endwall effects were included at the intersections of the airfoils and platforms for the steady-state boundary conditions. Free and forced convection due to rotation effects were also considered in hollow cores. Transient HTCs were calculated by taking ratios of the steady-state values based on the flow rates and fluid properties calculated at each time slice. Results are presented for both transient plots and three-dimensional color contour isotherm plots; they were also converted into universal files to be used for FEM stress analyses.

Probabilistic structural analysis methods for select space propulsion system components

NASA Technical Reports Server (NTRS)

Millwater, H. R.; Cruse, T. A.

1989-01-01

The Probabilistic Structural Analysis Methods (PSAM) project developed at the Southwest Research Institute integrates state-of-the-art structural analysis techniques with probability theory for the design and analysis of complex large-scale engineering structures. An advanced efficient software system (NESSUS) capable of performing complex probabilistic analysis has been developed. NESSUS contains a number of software components to perform probabilistic analysis of structures. These components include: an expert system, a probabilistic finite element code, a probabilistic boundary element code and a fast probability integrator. The NESSUS software system is shown. An expert system is included to capture and utilize PSAM knowledge and experience. NESSUS/EXPERT is an interactive menu-driven expert system that provides information to assist in the use of the probabilistic finite element code NESSUS/FEM and the fast probability integrator (FPI). The expert system menu structure is summarized. The NESSUS system contains a state-of-the-art nonlinear probabilistic finite element code, NESSUS/FEM, to determine the structural response and sensitivities. A broad range of analysis capabilities and an extensive element library is present.

Deformation behaviour of Rheocast A356 Al alloy at microlevel considering approximated RVEs

NASA Astrophysics Data System (ADS)

Islam, Sk. Tanbir; Das, Prosenjit; Das, Santanu

2015-03-01

A micromechanical approach is considered here to predict the deformation behaviour of Rheocast A356 (Al-Si-Mg) alloy. Two representative volume elements (RVEs) are modelled in the finite element (FE) framework. Two dimensional approximated microstructures are generated assuming elliptic grains, based on the grain size, shape factor and area fraction of the primary Al phase of the said alloy at different processing condition. Plastic instability is shown using stress and strain distribution between the Al rich primary and Si rich eutectic phases under different boundary conditions. Boundary conditions are applied on the approximated RVEs in such a manner, so that they represent the real life situation depending on their position on a cylindrical tensile test sample. FE analysis is carried out using commercial finite element code ABAQUS without specifying any damage or failure criteria. Micro-level in-homogeneity leads to incompatible deformation between the constituent phases of the rheocast alloy and steers plastic strain localisation. Plastic stain localised regions within the RVEs are predicted as the favourable sites for void nucleation. Subsequent growth of nucleated voids leads to final failure of the materials under investigation.

Three dimensional grain boundary modeling in polycrystalline plasticity

NASA Astrophysics Data System (ADS)

Yalçinkaya, Tuncay; Özdemir, Izzet; Fırat, Ali Osman

2018-05-01

At grain scale, polycrystalline materials develop heterogeneous plastic deformation fields, localizations and stress concentrations due to variation of grain orientations, geometries and defects. Development of inter-granular stresses due to misorientation are crucial for a range of grain boundary (GB) related failure mechanisms, such as stress corrosion cracking (SCC) and fatigue cracking. Local crystal plasticity finite element modelling of polycrystalline metals at micron scale results in stress jumps at the grain boundaries. Moreover, the concepts such as the transmission of dislocations between grains and strength of the grain boundaries are not included in the modelling. The higher order strain gradient crystal plasticity modelling approaches offer the possibility of defining grain boundary conditions. However, these conditions are mostly not dependent on misorientation of grains and can define only extreme cases. For a proper definition of grain boundary behavior in plasticity, a model for grain boundary behavior should be incorporated into the plasticity framework. In this context, a particular grain boundary model ([l]) is incorporated into a strain gradient crystal plasticity framework ([2]). In a 3-D setting, both bulk and grain boundary models are implemented as user-defined elements in Abaqus. The strain gradient crystal plasticity model works in the bulk elements and considers displacements and plastic slips as degree of freedoms. Interface elements model the plastic slip behavior, yet they do not possess any kind of mechanical cohesive behavior. The physical aspects of grain boundaries and the performance of the model are addressed through numerical examples.

Continuum calculations of continental deformation in transcurrent environments

NASA Technical Reports Server (NTRS)

Sonder, L. J.; England, P. C.; Houseman, G. A.

1986-01-01

A thin viscous sheet approximation is used to investigate continental deformation near a strike-slip boundary. The vertically averaged velocity field is calculated for a medium characterized by a power law rheology with stress exponent n. Driving stresses include those applied along boundaries of the sheet and those arising from buoyancy forces related to lateral differences in crustal thickness. Exact and approximate analytic solutions for a region with a sinusoidal strike-slip boundary condition are compared with solutions for more geologically relevant boundary conditions obtained using a finite element technique. The across-strike length scale of the deformation is approximately 1/4pi x sq rt n times the dominant wavelength of the imposed strike-slip boundary condition for both the analytic and the numerical solutions; this result is consistent with length scales observed in continental regions of large-scale transcurrent faulting. An approximate, linear relationship between displacement and rotation is found that depends only on the deformation length scale and the rheology. Calculated displacements, finite rotations, and distribution of crustal thicknesses are consistent with those observed in the region of the Pacific-North America plate boundary in California.

A High Order Discontinuous Galerkin Method for 2D Incompressible Flows

NASA Technical Reports Server (NTRS)

Liu, Jia-Guo; Shu, Chi-Wang

1999-01-01

In this paper we introduce a high order discontinuous Galerkin method for two dimensional incompressible flow in vorticity streamfunction formulation. The momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method The streamfunction is obtained by a standard Poisson solver using continuous finite elements. There is a natural matching between these two finite element spaces, since the normal component of the velocity field is continuous across element boundaries. This allows for a correct upwinding gluing in the discontinuous Galerkin framework, while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability The method is suitable for inviscid or high Reynolds number flows. Optimal error estimates are proven and verified by numerical experiments.

A 3-D turbulent flow analysis using finite elements with k-ɛ model

NASA Astrophysics Data System (ADS)

Okuda, H.; Yagawa, G.; Eguchi, Y.

1989-03-01

This paper describes the finite element turbulent flow analysis, which is suitable for three-dimensional large scale problems. The k-ɛ turbulence model as well as the conservation equations of mass and momentum are discretized in space using rather low order elements. Resulting coefficient matrices are evaluated by one-point quadrature in order to reduce the computational storage and the CPU cost. The time integration scheme based on the velocity correction method is employed to obtain steady state solutions. For the verification of this FEM program, two-dimensional plenum flow is simulated and compared with experiment. As the application to three-dimensional practical problems, the turbulent flows in the upper plenum of the fast breeder reactor are calculated for various boundary conditions.

Computation of leaky guided waves dispersion spectrum using vibroacoustic analyses and the Matrix Pencil Method: a validation study for immersed rectangular waveguides.

PubMed

Mazzotti, M; Bartoli, I; Castellazzi, G; Marzani, A

2014-09-01

The paper aims at validating a recently proposed Semi Analytical Finite Element (SAFE) formulation coupled with a 2.5D Boundary Element Method (2.5D BEM) for the extraction of dispersion data in immersed waveguides of generic cross-section. To this end, three-dimensional vibroacoustic analyses are carried out on two waveguides of square and rectangular cross-section immersed in water using the commercial Finite Element software Abaqus/Explicit. Real wavenumber and attenuation dispersive data are extracted by means of a modified Matrix Pencil Method. It is demonstrated that the results obtained using the two techniques are in very good agreement. Copyright © 2014 Elsevier B.V. All rights reserved.

Selecting boundary conditions in physiological strain analysis of the femur: Balanced loads, inertia relief method and follower load.

PubMed

Heyland, Mark; Trepczynski, Adam; Duda, Georg N; Zehn, Manfred; Schaser, Klaus-Dieter; Märdian, Sven

2015-12-01

Selection of boundary constraints may influence amount and distribution of loads. The purpose of this study is to analyze the potential of inertia relief and follower load to maintain the effects of musculoskeletal loads even under large deflections in patient specific finite element models of intact or fractured bone compared to empiric boundary constraints which have been shown to lead to physiological displacements and surface strains. The goal is to elucidate the use of boundary conditions in strain analyses of bones. Finite element models of the intact femur and a model of clinically relevant fracture stabilization by locking plate fixation were analyzed with normal walking loading conditions for different boundary conditions, specifically re-balanced loading, inertia relief and follower load. Peak principal cortex surface strains for different boundary conditions are consistent (maximum deviation 13.7%) except for inertia relief without force balancing (maximum deviation 108.4%). Influence of follower load on displacements increases with higher deflection in fracture model (from 3% to 7% for force balanced model). For load balanced models, follower load had only minor influence, though the effect increases strongly with higher deflection. Conventional constraints of fixed nodes in space should be carefully reconsidered because their type and position are challenging to justify and for their potential to introduce relevant non-physiological reaction forces. Inertia relief provides an alternative method which yields physiological strain results. Copyright © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.

Finite element analysis of the effect of a non-planar solid-liquid interface on the lateral solute segregation during unidirectional solidification

NASA Technical Reports Server (NTRS)

Carlson, F. M.; Chin, L.-Y.; Fripp, A. L.; Crouch, R. K.

1982-01-01

The effect of solid-liquid interface shape on lateral solute segregation during steady-state unidirectional solidification of a binary mixture is calculated under the assumption of no convection in the liquid. A finite element technique is employed to compute the concentration field in the liquid and the lateral segregation in the solid with a curved boundary between the liquid and solid phases. The computational model is constructed assuming knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The influence of interface curvature on the lateral compositional variation is investigated over a range of system parameters including diffusivity, growth speed, distribution coefficient, and geometric factors of the system. In the limiting case of a slightly nonplanar interface, numerical results from the finite element technique are in good agreement with the analytical solutions of Coriell and Sekerka obtained by using linear theory. For the general case of highly non-planar interface shapes, the linear theory fails and the concentration field in the liquid as well as the lateral solute segregation in the solid can be calculated by using the finite element method.

Multiscale Modeling of Polycrystalline NiTi Shape Memory Alloy under Various Plastic Deformation Conditions by Coupling Microstructure Evolution and Macroscopic Mechanical Response

PubMed Central

Jiang, Shuyong; Zhou, Tao; Tu, Jian; Shi, Laixin; Chen, Qiang; Yang, Mingbo

2017-01-01

Numerical modeling of microstructure evolution in various regions during uniaxial compression and canning compression of NiTi shape memory alloy (SMA) are studied through combined macroscopic and microscopic finite element simulation in order to investigate plastic deformation of NiTi SMA at 400 °C. In this approach, the macroscale material behavior is modeled with a relatively coarse finite element mesh, and then the corresponding deformation history in some selected regions in this mesh is extracted by the sub-model technique of finite element code ABAQUS and subsequently used as boundary conditions for the microscale simulation by means of crystal plasticity finite element method (CPFEM). Simulation results show that NiTi SMA exhibits an inhomogeneous plastic deformation at the microscale. Moreover, regions that suffered canning compression sustain more homogeneous plastic deformation by comparison with the corresponding regions subjected to uniaxial compression. The mitigation of inhomogeneous plastic deformation contributes to reducing the statistically stored dislocation (SSD) density in polycrystalline aggregation and also to reducing the difference of stress level in various regions of deformed NiTi SMA sample, and therefore sustaining large plastic deformation in the canning compression process. PMID:29027925

Multiscale Modeling of Polycrystalline NiTi Shape Memory Alloy under Various Plastic Deformation Conditions by Coupling Microstructure Evolution and Macroscopic Mechanical Response.

PubMed

Hu, Li; Jiang, Shuyong; Zhou, Tao; Tu, Jian; Shi, Laixin; Chen, Qiang; Yang, Mingbo

2017-10-13

Numerical modeling of microstructure evolution in various regions during uniaxial compression and canning compression of NiTi shape memory alloy (SMA) are studied through combined macroscopic and microscopic finite element simulation in order to investigate plastic deformation of NiTi SMA at 400 °C. In this approach, the macroscale material behavior is modeled with a relatively coarse finite element mesh, and then the corresponding deformation history in some selected regions in this mesh is extracted by the sub-model technique of finite element code ABAQUS and subsequently used as boundary conditions for the microscale simulation by means of crystal plasticity finite element method (CPFEM). Simulation results show that NiTi SMA exhibits an inhomogeneous plastic deformation at the microscale. Moreover, regions that suffered canning compression sustain more homogeneous plastic deformation by comparison with the corresponding regions subjected to uniaxial compression. The mitigation of inhomogeneous plastic deformation contributes to reducing the statistically stored dislocation (SSD) density in polycrystalline aggregation and also to reducing the difference of stress level in various regions of deformed NiTi SMA sample, and therefore sustaining large plastic deformation in the canning compression process.

Quantitative analysis and feature recognition in 3-D microstructural data sets

NASA Astrophysics Data System (ADS)

Lewis, A. C.; Suh, C.; Stukowski, M.; Geltmacher, A. B.; Spanos, G.; Rajan, K.

2006-12-01

A three-dimensional (3-D) reconstruction of an austenitic stainless-steel microstructure was used as input for an image-based finite-element model to simulate the anisotropic elastic mechanical response of the microstructure. The quantitative data-mining and data-warehousing techniques used to correlate regions of high stress with critical microstructural features are discussed. Initial analysis of elastic stresses near grain boundaries due to mechanical loading revealed low overall correlation with their location in the microstructure. However, the use of data-mining and feature-tracking techniques to identify high-stress outliers revealed that many of these high-stress points are generated near grain boundaries and grain edges (triple junctions). These techniques also allowed for the differentiation between high stresses due to boundary conditions of the finite volume reconstructed, and those due to 3-D microstructural features.

High order Nyström method for elastodynamic scattering

NASA Astrophysics Data System (ADS)

Chen, Kun; Gurrala, Praveen; Song, Jiming; Roberts, Ron

2016-02-01

Elastic waves in solids find important applications in ultrasonic non-destructive evaluation. The scattering of elastic waves has been treated using many approaches like the finite element method, boundary element method and Kirchhoff approximation. In this work, we propose a novel accurate and efficient high order Nyström method to solve the boundary integral equations for elastodynamic scattering problems. This approach employs high order geometry description for the element, and high order interpolation for fields inside each element. Compared with the boundary element method, this approach makes the choice of the nodes for interpolation based on the Gaussian quadrature, which renders matrix elements for far field interaction free from integration, and also greatly simplifies the process for singularity and near singularity treatment. The proposed approach employs a novel efficient near singularity treatment that makes the solver able to handle extreme geometries like very thin penny-shaped crack. Numerical results are presented to validate the approach. By using the frequency domain response and performing the inverse Fourier transform, we also report the time domain response of flaw scattering.

International Symposium on Numerical Methods in Engineering, 5th, Ecole Polytechnique Federale de Lausanne, Switzerland, Sept. 11-15, 1989, Proceedings. Volumes 1 & 2

NASA Astrophysics Data System (ADS)

Gruber, Ralph; Periaux, Jaques; Shaw, Richard Paul

Recent advances in computational mechanics are discussed in reviews and reports. Topics addressed include spectral superpositions on finite elements for shear banding problems, strain-based finite plasticity, numerical simulation of hypersonic viscous continuum flow, constitutive laws in solid mechanics, dynamics problems, fracture mechanics and damage tolerance, composite plates and shells, contact and friction, metal forming and solidification, coupling problems, and adaptive FEMs. Consideration is given to chemical flows, convection problems, free boundaries and artificial boundary conditions, domain-decomposition and multigrid methods, combustion and thermal analysis, wave propagation, mixed and hybrid FEMs, integral-equation methods, optimization, software engineering, and vector and parallel computing.

High-order cyclo-difference techniques: An alternative to finite differences

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Otto, John C.

1993-01-01

The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.

Analysis of the sound field in finite length infinite baffled cylindrical ducts with vibrating walls of finite impedance.

PubMed

Shao, Wei; Mechefske, Chris K

2005-04-01

This paper describes an analytical model of finite cylindrical ducts with infinite flanges. This model is used to investigate the sound radiation characteristics of the gradient coil system of a magnetic resonance imaging (MRI) scanner. The sound field in the duct satisfies both the boundary conditions at the wall and at the open ends. The vibrating cylindrical wall of the duct is assumed to be the only sound source. Different acoustic conditions for the wall (rigid and absorptive) are used in the simulations. The wave reflection phenomenon at the open ends of the finite duct is described by general radiation impedance. The analytical model is validated by the comparison with its counterpart in a commercial code based on the boundary element method (BEM). The analytical model shows significant advantages over the BEM model with better numerical efficiency and a direct relation between the design parameters and the sound field inside the duct.

Grain Boundary Conformed Volumetric Mesh Generation from a Three-Dimensional Voxellated Polycrystalline Microstructure

NASA Astrophysics Data System (ADS)

Lee, Myeong-Jin; Jeon, Young-Ju; Son, Ga-Eun; Sung, Sihwa; Kim, Ju-Young; Han, Heung Nam; Cho, Soo Gyeong; Jung, Sang-Hyun; Lee, Sukbin

2018-07-01

We present a new comprehensive scheme for generating grain boundary conformed, volumetric mesh elements from a three-dimensional voxellated polycrystalline microstructure. From the voxellated image of a polycrystalline microstructure obtained from the Monte Carlo Potts model in the context of isotropic normal grain growth simulation, its grain boundary network is approximated as a curvature-maintained conformal triangular surface mesh using a set of in-house codes. In order to improve the surface mesh quality and to adjust mesh resolution, various re-meshing techniques in a commercial software are applied to the approximated grain boundary mesh. It is found that the aspect ratio, the minimum angle and the Jacobian value of the re-meshed surface triangular mesh are successfully improved. Using such an enhanced surface mesh, conformal volumetric tetrahedral elements of the polycrystalline microstructure are created using a commercial software, again. The resultant mesh seamlessly retains the short- and long-range curvature of grain boundaries and junctions as well as the realistic morphology of the grains inside the polycrystal. It is noted that the proposed scheme is the first to successfully generate three-dimensional mesh elements for polycrystals with high enough quality to be used for the microstructure-based finite element analysis, while the realistic characteristics of grain boundaries and grains are maintained from the corresponding voxellated microstructure image.

Grain Boundary Conformed Volumetric Mesh Generation from a Three-Dimensional Voxellated Polycrystalline Microstructure

NASA Astrophysics Data System (ADS)

Lee, Myeong-Jin; Jeon, Young-Ju; Son, Ga-Eun; Sung, Sihwa; Kim, Ju-Young; Han, Heung Nam; Cho, Soo Gyeong; Jung, Sang-Hyun; Lee, Sukbin

2018-03-01

We present a new comprehensive scheme for generating grain boundary conformed, volumetric mesh elements from a three-dimensional voxellated polycrystalline microstructure. From the voxellated image of a polycrystalline microstructure obtained from the Monte Carlo Potts model in the context of isotropic normal grain growth simulation, its grain boundary network is approximated as a curvature-maintained conformal triangular surface mesh using a set of in-house codes. In order to improve the surface mesh quality and to adjust mesh resolution, various re-meshing techniques in a commercial software are applied to the approximated grain boundary mesh. It is found that the aspect ratio, the minimum angle and the Jacobian value of the re-meshed surface triangular mesh are successfully improved. Using such an enhanced surface mesh, conformal volumetric tetrahedral elements of the polycrystalline microstructure are created using a commercial software, again. The resultant mesh seamlessly retains the short- and long-range curvature of grain boundaries and junctions as well as the realistic morphology of the grains inside the polycrystal. It is noted that the proposed scheme is the first to successfully generate three-dimensional mesh elements for polycrystals with high enough quality to be used for the microstructure-based finite element analysis, while the realistic characteristics of grain boundaries and grains are maintained from the corresponding voxellated microstructure image.

Particle-based simulation of charge transport in discrete-charge nano-scale systems: the electrostatic problem

PubMed Central

2012-01-01

The fast and accurate computation of the electric forces that drive the motion of charged particles at the nanometer scale represents a computational challenge. For this kind of system, where the discrete nature of the charges cannot be neglected, boundary element methods (BEM) represent a better approach than finite differences/finite elements methods. In this article, we compare two different BEM approaches to a canonical electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations: the iterative method proposed by Hoyles et al. and the Induced Charge Computation introduced by Boda et al. PMID:22338640

Particle-based simulation of charge transport in discrete-charge nano-scale systems: the electrostatic problem.

PubMed

Berti, Claudio; Gillespie, Dirk; Eisenberg, Robert S; Fiegna, Claudio

2012-02-16

The fast and accurate computation of the electric forces that drive the motion of charged particles at the nanometer scale represents a computational challenge. For this kind of system, where the discrete nature of the charges cannot be neglected, boundary element methods (BEM) represent a better approach than finite differences/finite elements methods. In this article, we compare two different BEM approaches to a canonical electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations: the iterative method proposed by Hoyles et al. and the Induced Charge Computation introduced by Boda et al.

Shape design sensitivity analysis and optimal design of structural systems

NASA Technical Reports Server (NTRS)

Choi, Kyung K.

1987-01-01

The material derivative concept of continuum mechanics and an adjoint variable method of design sensitivity analysis are used to relate variations in structural shape to measures of structural performance. A domain method of shape design sensitivity analysis is used to best utilize the basic character of the finite element method that gives accurate information not on the boundary but in the domain. Implementation of shape design sensitivty analysis using finite element computer codes is discussed. Recent numerical results are used to demonstrate the accuracy obtainable using the method. Result of design sensitivity analysis is used to carry out design optimization of a built-up structure.

Application of micropolar plasticity to post failure analysis in geomechanics

NASA Astrophysics Data System (ADS)

Manzari, Majid T.

2004-08-01

A micropolar elastoplastic model for soils is formulated and a series of finite element analyses are employed to demonstrate the use of a micropolar continuum in overcoming the numerical difficulties encountered in application of finite element method in standard Cauchy-Boltzmann continuum. Three examples of failure analysis involving a deep excavation, shallow foundation, and a retaining wall are presented. In all these cases, it is observed that the length scale introduced in the polar continuum regularizes the incremental boundary value problem and allows the numerical simulation to be continued until a clear collapse mechanism is achieved. The issue of grain size effect is also discussed. Copyright

Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure

NASA Astrophysics Data System (ADS)

Szafran, J.; Juszczyk, K.; Kamiński, M.

2017-12-01

The main goal of this paper is to present coupled Computational Fluid Dynamics and structural analysis for the precise determination of wind impact on internal forces and deformations of structural elements of a longspan roof structure. The Finite Volume Method (FVM) serves for a solution of the fluid flow problem to model the air flow around the structure, whose results are applied in turn as the boundary tractions in the Finite Element Method problem structural solution for the linear elastostatics with small deformations. The first part is carried out with the use of ANSYS 15.0 computer system, whereas the FEM system Robot supports stress analysis in particular roof members. A comparison of the wind pressure distribution throughout the roof surface shows some differences with respect to that available in the engineering designing codes like Eurocode, which deserves separate further numerical studies. Coupling of these two separate numerical techniques appears to be promising in view of future computational models of stochastic nature in large scale structural systems due to the stochastic perturbation method.

Multiscale Modeling of Grain-Boundary Fracture: Cohesive Zone Models Parameterized From Atomistic Simulations

NASA Technical Reports Server (NTRS)

Glaessgen, Edward H.; Saether, Erik; Phillips, Dawn R.; Yamakov, Vesselin

2006-01-01

A multiscale modeling strategy is developed to study grain boundary fracture in polycrystalline aluminum. Atomistic simulation is used to model fundamental nanoscale deformation and fracture mechanisms and to develop a constitutive relationship for separation along a grain boundary interface. The nanoscale constitutive relationship is then parameterized within a cohesive zone model to represent variations in grain boundary properties. These variations arise from the presence of vacancies, intersticies, and other defects in addition to deviations in grain boundary angle from the baseline configuration considered in the molecular dynamics simulation. The parameterized cohesive zone models are then used to model grain boundaries within finite element analyses of aluminum polycrystals.

A finite element procedure for radio-frequency sheath–plasma interactions based on a sheath impedance model

DOE PAGES

Kohno, H.; Myra, J. R.

2017-07-24

A finite element code that solves self-consistent radio-frequency (RF) sheath-plasma interaction problems is improved by incorporating a generalized sheath boundary condition in the macroscopic solution scheme. This sheath boundary condition makes use of a complex sheath impedance including both the sheath capacitance and resistance, which enables evaluation of not only the RF voltage across the sheath but also the power dissipation in the sheath. The newly developed finite element procedure is applied to cases where the background magnetic field is perpendicular to the sheath surface in one- and two-dimensional domains filled by uniform low- and high-density plasmas. The numerical resultsmore » are compared with those obtained by employing the previous capacitive sheath model at a typical frequency for ion cyclotron heating used in fusion experiments. It is shown that for sheaths on the order of 100 V in a high-density plasma, localized RF power deposition can reach a level which causes material damage. It is also shown that the sheath-plasma wave resonances predicted by the capacitive sheath model do not occur when parameters are such that the generalized sheath impedance model substantially modifies the capacitive character of the sheath. Here, possible explanations for the difference in the maximum RF sheath voltage depending on the plasma density are also discussed.« less

A finite element procedure for radio-frequency sheath–plasma interactions based on a sheath impedance model

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

Kohno, H.; Myra, J. R.

A finite element code that solves self-consistent radio-frequency (RF) sheath-plasma interaction problems is improved by incorporating a generalized sheath boundary condition in the macroscopic solution scheme. This sheath boundary condition makes use of a complex sheath impedance including both the sheath capacitance and resistance, which enables evaluation of not only the RF voltage across the sheath but also the power dissipation in the sheath. The newly developed finite element procedure is applied to cases where the background magnetic field is perpendicular to the sheath surface in one- and two-dimensional domains filled by uniform low- and high-density plasmas. The numerical resultsmore » are compared with those obtained by employing the previous capacitive sheath model at a typical frequency for ion cyclotron heating used in fusion experiments. It is shown that for sheaths on the order of 100 V in a high-density plasma, localized RF power deposition can reach a level which causes material damage. It is also shown that the sheath-plasma wave resonances predicted by the capacitive sheath model do not occur when parameters are such that the generalized sheath impedance model substantially modifies the capacitive character of the sheath. Here, possible explanations for the difference in the maximum RF sheath voltage depending on the plasma density are also discussed.« less

Finite Element Model Calibration Approach for Area I-X

NASA Technical Reports Server (NTRS)

Horta, Lucas G.; Reaves, Mercedes C.; Buehrle, Ralph D.; Templeton, Justin D.; Gaspar, James L.; Lazor, Daniel R.; Parks, Russell A.; Bartolotta, Paul A.

2010-01-01

Ares I-X is a pathfinder vehicle concept under development by NASA to demonstrate a new class of launch vehicles. Although this vehicle is essentially a shell of what the Ares I vehicle will be, efforts are underway to model and calibrate the analytical models before its maiden flight. Work reported in this document will summarize the model calibration approach used including uncertainty quantification of vehicle responses and the use of non-conventional boundary conditions during component testing. Since finite element modeling is the primary modeling tool, the calibration process uses these models, often developed by different groups, to assess model deficiencies and to update parameters to reconcile test with predictions. Data for two major component tests and the flight vehicle are presented along with the calibration results. For calibration, sensitivity analysis is conducted using Analysis of Variance (ANOVA). To reduce the computational burden associated with ANOVA calculations, response surface models are used in lieu of computationally intensive finite element solutions. From the sensitivity studies, parameter importance is assessed as a function of frequency. In addition, the work presents an approach to evaluate the probability that a parameter set exists to reconcile test with analysis. Comparisons of pretest predictions of frequency response uncertainty bounds with measured data, results from the variance-based sensitivity analysis, and results from component test models with calibrated boundary stiffness models are all presented.

Finite Element Model Calibration Approach for Ares I-X

NASA Technical Reports Server (NTRS)

Horta, Lucas G.; Reaves, Mercedes C.; Buehrle, Ralph D.; Templeton, Justin D.; Lazor, Daniel R.; Gaspar, James L.; Parks, Russel A.; Bartolotta, Paul A.

2010-01-01

Ares I-X is a pathfinder vehicle concept under development by NASA to demonstrate a new class of launch vehicles. Although this vehicle is essentially a shell of what the Ares I vehicle will be, efforts are underway to model and calibrate the analytical models before its maiden flight. Work reported in this document will summarize the model calibration approach used including uncertainty quantification of vehicle responses and the use of nonconventional boundary conditions during component testing. Since finite element modeling is the primary modeling tool, the calibration process uses these models, often developed by different groups, to assess model deficiencies and to update parameters to reconcile test with predictions. Data for two major component tests and the flight vehicle are presented along with the calibration results. For calibration, sensitivity analysis is conducted using Analysis of Variance (ANOVA). To reduce the computational burden associated with ANOVA calculations, response surface models are used in lieu of computationally intensive finite element solutions. From the sensitivity studies, parameter importance is assessed as a function of frequency. In addition, the work presents an approach to evaluate the probability that a parameter set exists to reconcile test with analysis. Comparisons of pre-test predictions of frequency response uncertainty bounds with measured data, results from the variance-based sensitivity analysis, and results from component test models with calibrated boundary stiffness models are all presented.

The Boundary Integral Equation Method for Porous Media Flow

NASA Astrophysics Data System (ADS)

Anderson, Mary P.

Just as groundwater hydrologists are breathing sighs of relief after the exertions of learning the finite element method, a new technique has reared its nodes—the boundary integral equation method (BIEM) or the boundary equation method (BEM), as it is sometimes called. As Liggett and Liu put it in the preface to The Boundary Integral Equation Method for Porous Media Flow, “Lately, the Boundary Integral Equation Method (BIEM) has emerged as a contender in the computation Derby.” In fact, in July 1984, the 6th International Conference on Boundary Element Methods in Engineering will be held aboard the Queen Elizabeth II, en route from Southampton to New York. These conferences are sponsored by the Department of Civil Engineering at Southampton College (UK), whose members are proponents of BIEM. The conferences have featured papers on applications of BIEM to all aspects of engineering, including flow through porous media. Published proceedings are available, as are textbooks on application of BIEM to engineering problems. There is even a 10-minute film on the subject.

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

Frolov, T.; Setyawan, W.; Kurtz, R. J.

We report a computational discovery of novel grain boundary structures and multiple grain boundary phases in elemental bcc tungsten. While grain boundary structures created by the - surface method as a union of two perfect half crystals have been studied extensively, it is known that the method has limitations and does not always predict the correct ground states. Here, we use a newly developed computational tool, based on evolutionary algorithms, to perform a grand-canonical search of high-angle symmetric tilt boundary in tungsten, and we find new ground states and multiple phases that cannot be described using the conventional structural unitmore » model. We use MD simulations to demonstrate that the new structures can coexist at finite temperature in a closed system, confirming these are examples of different GB phases. The new ground state is confirmed by first-principles calculations.Evolutionary grand-canonical search predicts novel grain boundary structures and multiple grain boundary phases in elemental body-centered cubic (bcc) metals represented by tungsten, tantalum and molybdenum.« less

Software For Three-Dimensional Stress And Thermal Analyses

NASA Technical Reports Server (NTRS)

Banerjee, P. K.; Wilson, R. B.; Hopkins, D. A.

1994-01-01

BEST3D is advanced engineering software system for three-dimensional thermal and stress analyses, particularly of components of hot sections of gas-turbine engines. Utilizes boundary element method, offering, in many situations, more accuracy, efficiency, and ease of use than finite element method. Performs engineering analyses of following types: elastic, heat transfer, plastic, forced vibration, free vibration, and transient elastodynamic. Written in FORTRAN 77.

Mass-conservative reconstruction of Galerkin velocity fields for transport simulations

NASA Astrophysics Data System (ADS)

Scudeler, C.; Putti, M.; Paniconi, C.

2016-08-01

Accurate calculation of mass-conservative velocity fields from numerical solutions of Richards' equation is central to reliable surface-subsurface flow and transport modeling, for example in long-term tracer simulations to determine catchment residence time distributions. In this study we assess the performance of a local Larson-Niklasson (LN) post-processing procedure for reconstructing mass-conservative velocities from a linear (P1) Galerkin finite element solution of Richards' equation. This approach, originally proposed for a-posteriori error estimation, modifies the standard finite element velocities by imposing local conservation on element patches. The resulting reconstructed flow field is characterized by continuous fluxes on element edges that can be efficiently used to drive a second order finite volume advective transport model. Through a series of tests of increasing complexity that compare results from the LN scheme to those using velocity fields derived directly from the P1 Galerkin solution, we show that a locally mass-conservative velocity field is necessary to obtain accurate transport results. We also show that the accuracy of the LN reconstruction procedure is comparable to that of the inherently conservative mixed finite element approach, taken as a reference solution, but that the LN scheme has much lower computational costs. The numerical tests examine steady and unsteady, saturated and variably saturated, and homogeneous and heterogeneous cases along with initial and boundary conditions that include dry soil infiltration, alternating solute and water injection, and seepage face outflow. Typical problems that arise with velocities derived from P1 Galerkin solutions include outgoing solute flux from no-flow boundaries, solute entrapment in zones of low hydraulic conductivity, and occurrences of anomalous sources and sinks. In addition to inducing significant mass balance errors, such manifestations often lead to oscillations in concentration values that can moreover cause the numerical solution to explode. These problems do not occur when using LN post-processed velocities.

Accuracy of the domain method for the material derivative approach to shape design sensitivities

NASA Technical Reports Server (NTRS)

Yang, R. J.; Botkin, M. E.

1987-01-01

Numerical accuracy for the boundary and domain methods of the material derivative approach to shape design sensitivities is investigated through the use of mesh refinement. The results show that the domain method is generally more accurate than the boundary method, using the finite element technique. It is also shown that the domain method is equivalent, under certain assumptions, to the implicit differentiation approach not only theoretically but also numerically.

Boundary value problems with incremental plasticity in granular media

NASA Technical Reports Server (NTRS)

Chung, T. J.; Lee, J. K.; Costes, N. C.

1974-01-01

Discussion of the critical state concept in terms of an incremental theory of plasticity in granular (soil) media, and formulation of the governing equations which are convenient for a computational scheme using the finite element method. It is shown that the critical state concept with its representation by the classical incremental theory of plasticity can provide a powerful means for solving a wide variety of boundary value problems in soil media.

Transpiration and film cooling boundary layer computer program. Volume 2: Computer program and user's manual

NASA Technical Reports Server (NTRS)

Gloss, R. J.

1971-01-01

A finite difference turbulent boundary layer computer program which allows for mass transfer wall cooling and equilibrium chemistry effects is presented. The program is capable of calculating laminar or turbulent boundary layer solutions for an arbitrary ideal gas or an equilibrium hydrogen oxygen system. Either two dimensional or axisymmetric geometric configurations may be considered. The equations are solved, in nondimension-alized physical coordinates, using the implicit Crank-Nicolson technique. The finite difference forms of the conservation of mass, momentum, total enthalpy and elements equations are linearized and uncoupled, thereby generating easily solvable tridiagonal sets of algebraic equations. A detailed description of the computer program, as well as a program user's manual is provided. Detailed descriptions of all boundary layer subroutines are included, as well as a section defining all program symbols of principal importance. Instructions are then given for preparing card input to the program and for interpreting the printed output. Finally, two sample cases are included to illustrate the use of the program.

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

Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.

An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems.more » Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.« less

TranAir: A full-potential, solution-adaptive, rectangular grid code for predicting subsonic, transonic, and supersonic flows about arbitrary configurations. Theory document

NASA Technical Reports Server (NTRS)

Johnson, F. T.; Samant, S. S.; Bieterman, M. B.; Melvin, R. G.; Young, D. P.; Bussoletti, J. E.; Hilmes, C. L.

1992-01-01

A new computer program, called TranAir, for analyzing complex configurations in transonic flow (with subsonic or supersonic freestream) was developed. This program provides accurate and efficient simulations of nonlinear aerodynamic flows about arbitrary geometries with the ease and flexibility of a typical panel method program. The numerical method implemented in TranAir is described. The method solves the full potential equation subject to a set of general boundary conditions and can handle regions with differing total pressure and temperature. The boundary value problem is discretized using the finite element method on a locally refined rectangular grid. The grid is automatically constructed by the code and is superimposed on the boundary described by networks of panels; thus no surface fitted grid generation is required. The nonlinear discrete system arising from the finite element method is solved using a preconditioned Krylov subspace method embedded in an inexact Newton method. The solution is obtained on a sequence of successively refined grids which are either constructed adaptively based on estimated solution errors or are predetermined based on user inputs. Many results obtained by using TranAir to analyze aerodynamic configurations are presented.

Thermal properties of composite materials : effective conductivity tensor and edge effects

NASA Astrophysics Data System (ADS)

Matine, A.; Boyard, N.; Cartraud, P.; Legrain, G.; Jarny, Y.

2012-11-01

The homogenization theory is a powerful approach to determine the effective thermal conductivity tensor of heterogeneous materials such as composites, including thermoset matrix and fibres. Once the effective properties are calculated, they can be used to solve a heat conduction problem on the composite structure at the macroscopic scale. This approach leads to good approximations of both the heat flux and temperature in the interior zone of the structure, however edge effects occur in the vicinity of the domain boundaries. In this paper, following the approach proposed in [10] for elasticity, it is shown how these edge effects can be corrected. Thus an additional asymptotic expansion is introduced, which plays the role of a edge effect term. This expansion tends to zero far from the boundary, and is assumed to decrease exponentially. Moreover, the length of the edge effect region can be determined from the solution of an eigenvalue problem. Numerical examples are considered for a standard multilayered material. The homogenized solutions computed with a finite element software, and corrected with the edge effect terms, are compared to a heterogeneous finite element solution at the microscopic scale. The influences of the thermal contrast and scale factor are illustrated for different kind of boundary conditions.

LaRC design analysis report for National Transonic Facility for 304 stainless steel tunnel shell. Volume 1S: Finite difference analysis of cone/cylinder junction

NASA Technical Reports Server (NTRS)

Ramsey, J. W., Jr.; Taylor, J. T.; Wilson, J. F.; Gray, C. E., Jr.; Leatherman, A. D.; Rooker, J. R.; Allred, J. W.

1976-01-01

The results of extensive computer (finite element, finite difference and numerical integration), thermal, fatigue, and special analyses of critical portions of a large pressurized, cryogenic wind tunnel (National Transonic Facility) are presented. The computer models, loading and boundary conditions are described. Graphic capability was used to display model geometry, section properties, and stress results. A stress criteria is presented for evaluation of the results of the analyses. Thermal analyses were performed for major critical and typical areas. Fatigue analyses of the entire tunnel circuit are presented.

Axioms of adaptivity

PubMed Central

Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D.

2014-01-01

This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower bounds, inexact solvers, inhomogeneous boundary data, or the use of equivalent error estimators. Solely four axioms guarantee the optimality in terms of the error estimators. Compared to the state of the art in the temporary literature, the improvements of this article can be summarized as follows: First, a general framework is presented which covers the existing literature on optimality of adaptive schemes. The abstract analysis covers linear as well as nonlinear problems and is independent of the underlying finite element or boundary element method. Second, efficiency of the error estimator is neither needed to prove convergence nor quasi-optimal convergence behavior of the error estimator. In this paper, efficiency exclusively characterizes the approximation classes involved in terms of the best-approximation error and data resolution and so the upper bound on the optimal marking parameters does not depend on the efficiency constant. Third, some general quasi-Galerkin orthogonality is not only sufficient, but also necessary for the R-linear convergence of the error estimator, which is a fundamental ingredient in the current quasi-optimality analysis due to Stevenson 2007. Finally, the general analysis allows for equivalent error estimators and inexact solvers as well as different non-homogeneous and mixed boundary conditions. PMID:25983390

A parallel finite element simulator for ion transport through three-dimensional ion channel systems.

PubMed

Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Bob; Lu, Benzhuo

2013-09-15

A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can effectively lead to reduced current in the channel, and the results are closer to BD simulation results. Copyright © 2013 Wiley Periodicals, Inc.

Pre and post processing using the IBM 3277 display station graphics attachment (RPQ7H0284)

NASA Technical Reports Server (NTRS)

Burroughs, S. H.; Lawlor, M. B.; Miller, I. M.

1978-01-01

A graphical interactive procedure operating under TSO and utilizing two CRT display terminals is shown to be an effective means of accomplishing mesh generation, establishing boundary conditions, and reviewing graphic output for finite element analysis activity.

Computational aspects of helicopter trim analysis and damping levels from Floquet theory

NASA Technical Reports Server (NTRS)

Gaonkar, Gopal H.; Achar, N. S.

1992-01-01

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

A musculo-mechanical model of esophageal transport based on an immersed boundary-finite element approach

NASA Astrophysics Data System (ADS)

Kou, Wenjun; Griffith, Boyce E.; Pandolfino, John E.; Kahrilas, Peter J.; Patankar, Neelesh A.

2015-11-01

This work extends a fiber-based immersed boundary (IB) model of esophageal transport by incorporating a continuum model of the deformable esophageal wall. The continuum-based esophagus model adopts finite element approach that is capable of describing more complex and realistic material properties and geometries. The leakage from mismatch between Lagrangian and Eulerian meshes resulting from large deformations of the esophageal wall is avoided by careful choice of interaction points. The esophagus model, which is described as a multi-layered, fiber-reinforced nonlinear elastic material, is coupled to bolus and muscle-activation models using the IB approach to form the esophageal transport model. Cases of esophageal transport with different esophagus models are studied. Results on the transport characteristics, including pressure field and esophageal wall kinematics and stress, are analyzed and compared. Support from NIH grant R01 DK56033 and R01 DK079902 is gratefully acknowledged. BEG is supported by NSF award ACI 1460334.

[Stress analysis on the acetabular side of bipolar hemiarthroplasty by the two-dimensional finite element method incorporating the boundary friction layer].

PubMed

Ichihashi, K; Imura, S; Oomori, H; Gesso, H

1994-11-01

We compared the biomechanical characteristics of bipolar and unipolar hemiarthroplasty on the proximal migration of the outer head by determining the von Mises stress distribution and acetabular (outer head) displacement with clinical assessment of hemiarthroplasty in 75 patients. This analysis used the two-dimensional finite element method, which incorporated boundary friction layers on both the inner and outer bearings of the prosthesis. Acetabular reaming increased stress within the pelvic bone and migration of the outer head. A combination of the acetabular reaming and bone transplantation increased the stress within the pelvic bone and grafted bone, and caused outer head migration. These findings were supported by clinical results. Although the bipolar endoprosthesis was biomechanically superior to the unipolar endoprosthesis, migration of the outer head still occurred. The bipolar endoprosthesis appeared to be indicated in cases of a femoral neck fracture or of avascular necrosis in the femoral head, but its use in cases of osteoarthritis in the hip required caution.

Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 1

NASA Technical Reports Server (NTRS)

Felippa, Carlos A.; Farhat, Charbel; Park, K. C.; Militello, Carmelo; Schuler, James J.

1993-01-01

This research program has dealt with the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements; (2) finite element modeling of the electromagnetic problem; (3) coupling of thermal and mechanical effects; and (4) computer implementation and solution of the superconductivity transition problem. The research was carried out over the period September 1988 through March 1993. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles; (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements; and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects; and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The grant has fully supported the thesis work of one doctoral student (James Schuler, who started on January 1989 and completed on January 1993), and partly supported another thesis (Carmelo Militello, who started graduate work on January 1988 completing on August 1991). Twenty-three publications have acknowledged full or part support from this grant, with 16 having appeared in archival journals and 3 in edited books or proceedings.

SutraPlot, a graphical post-processor for SUTRA, a model for ground-water flow with solute or energy transport

USGS Publications Warehouse

Souza, W.R.

1999-01-01

This report documents a graphical display post-processor (SutraPlot) for the U.S. Geological Survey Saturated-Unsaturated flow and solute or energy TRAnsport simulation model SUTRA, Version 2D3D.1. This version of SutraPlot is an upgrade to SutraPlot for the 2D-only SUTRA model (Souza, 1987). It has been modified to add 3D functionality, a graphical user interface (GUI), and enhanced graphic output options. Graphical options for 2D SUTRA (2-dimension) simulations include: drawing the 2D finite-element mesh, mesh boundary, and velocity vectors; plots of contours for pressure, saturation, concentration, and temperature within the model region; 2D finite-element based gridding and interpolation; and 2D gridded data export files. Graphical options for 3D SUTRA (3-dimension) simulations include: drawing the 3D finite-element mesh; plots of contours for pressure, saturation, concentration, and temperature in 2D sections of the 3D model region; 3D finite-element based gridding and interpolation; drawing selected regions of velocity vectors (projected on principal coordinate planes); and 3D gridded data export files. Installation instructions and a description of all graphic options are presented. A sample SUTRA problem is described and three step-by-step SutraPlot applications are provided. In addition, the methodology and numerical algorithms for the 2D and 3D finite-element based gridding and interpolation, developed for SutraPlot, are described. 1

Development and validation of a weight-bearing finite element model for total knee replacement.

PubMed

Woiczinski, M; Steinbrück, A; Weber, P; Müller, P E; Jansson, V; Schröder, Ch

2016-01-01

Total knee arthroplasty (TKA) is a successful procedure for osteoarthritis. However, some patients (19%) do have pain after surgery. A finite element model was developed based on boundary conditions of a knee rig. A 3D-model of an anatomical full leg was generated from magnetic resonance image data and a total knee prosthesis was implanted without patella resurfacing. In the finite element model, a restarting procedure was programmed in order to hold the ground reaction force constant with an adapted quadriceps muscle force during a squat from 20° to 105° of flexion. Knee rig experimental data were used to validate the numerical model in the patellofemoral and femorotibial joint. Furthermore, sensitivity analyses of Young's modulus of the patella cartilage, posterior cruciate ligament (PCL) stiffness, and patella tendon origin were performed. Pearson's correlations for retropatellar contact area, pressure, patella flexion, and femorotibial ap-movement were near to 1. Lowest root mean square error for retropatellar pressure, patella flexion, and femorotibial ap-movement were found for the baseline model setup with Young's modulus of 5 MPa for patella cartilage, a downscaled PCL stiffness of 25% compared to the literature given value and an anatomical origin of the patella tendon. The results of the conducted finite element model are comparable with the experimental results. Therefore, the finite element model developed in this study can be used for further clinical investigations and will help to better understand the clinical aspects after TKA with an unresurfaced patella.

Construction and validation of a three-dimensional finite element model of degenerative scoliosis.

PubMed

Zheng, Jie; Yang, Yonghong; Lou, Shuliang; Zhang, Dongsheng; Liao, Shenghui

2015-12-24

With the aging of the population, degenerative scoliosis (DS) incidence rate is increasing. In recent years, increasing research on this topic has been carried out, yet biomechanical research on the subject is seldom seen and in vitro biomechanical model of DS nearly cannot be available. The objective of this study was to develop and validate a complete three-dimensional finite element model of DS in order to build the digital platform for further biomechanical study. A 55-year-old female DS patient (Suer Pan, ID number was P141986) was selected for this study. This study was performed in accordance with the ethical standards of Declaration of Helsinki and its amendments and was approved by the local ethics committee (117 hospital of PLA ethics committee). Spiral computed tomography (CT) scanning was conducted on the patient's lumbar spine from the T12 to S1. CT images were then imported into a finite element modeling system. A three-dimensional solid model was then formed from segmentation of the CT scan. The three-dimensional model of each vertebra was then meshed, and material properties were assigned to each element according to the pathological characteristics of DS. Loads and boundary conditions were then applied in such a manner as to simulate in vitro biomechanical experiments conducted on lumbar segments. The results of the model were then compared with experimental results in order to validate the model. An integral three-dimensional finite element model of DS was built successfully, consisting of 113,682 solid elements, 686 cable elements, 33,329 shell elements, 4968 target elements, 4968 contact elements, totaling 157,635 elements, and 197,374 nodes. The model accurately described the physical features of DS and was geometrically similar to the object of study. The results of analysis with the finite element model agreed closely with in vitro experiments, validating the accuracy of the model. The three-dimensional finite element model of DS built in this study is clear, reliable, and effective for further biomechanical simulation study of DS.

Implementation of Hybrid V-Cycle Multilevel Methods for Mixed Finite Element Systems with Penalty

NASA Technical Reports Server (NTRS)

Lai, Chen-Yao G.

1996-01-01

The goal of this paper is the implementation of hybrid V-cycle hierarchical multilevel methods for the indefinite discrete systems which arise when a mixed finite element approximation is used to solve elliptic boundary value problems. By introducing a penalty parameter, the perturbed indefinite system can be reduced to a symmetric positive definite system containing the small penalty parameter for the velocity unknown alone. We stabilize the hierarchical spatial decomposition approach proposed by Cai, Goldstein, and Pasciak for the reduced system. We demonstrate that the relative condition number of the preconditioner is bounded uniformly with respect to the penalty parameter, the number of levels and possible jumps of the coefficients as long as they occur only across the edges of the coarsest elements.

Aeroelastic analysis of circular cylindrical and truncated conical shells subjected to a supersonic flow

NASA Astrophysics Data System (ADS)

Sabri, Farhad

Shells of revolution, particularly cylindrical and conical shells, are one of the basic structural elements in the aerospace structures. With the advent of high speed aircrafts, these shells can show dynamic instabilities when they are exposed to a supersonic flow. Therefore, aeroelastic analysis of these elements is one of the primary design criteria which aeronautical engineers are dealing with. This analysis can be done with the help of finite element method (FEM) coupled with the computational fluid dynamic (CFD) or by experimental methods but it is time consuming and very expensive. The purpose of this dissertation is to develop such a numerical tool to do aeroelastic analysis in a fast and precise way. Meanwhile during the design stage, where the different configurations, loading and boundary conditions may need to be analyzed, this numerical method can be used very easily with the high order of reliability. In this study structural modeling is a combination of linear Sanders thin shell theory and classical finite element method. Based on this hybrid finite element method, the shell displacements are found from the exact solutions of shell theory rather than approximating by polynomial function done in traditional finite element method. This leads to a precise and fast convergence. Supersonic aerodynamic modeling is done based on the piston theory and modified piston theory with the shell curvature term. The stress stiffening due to lateral pressure and axial compression are also taken into accounts. Fluid-structure interaction in the presence of inside quiescent fluid is modeled based on the potential theory. In this method, fluid is considered as a velocity potential variable at each node of the shell element where its motion is expressed in terms of nodal elastic displacements at the fluid-structure interface. This proposed hybrid finite element has capabilities to do following analysis: (i) Buckling and vibration of an empty or partially fluid filled circular cylindrical shell or truncated conical shell subjected to internal/external pressure and axial compression loading. This is a typical example of external liquid propellant tanks of space shuttles and re-entry vehicles where they may experience this kind of loading during the flight. In the current work, different end boundary conditions of a circular cylindrical shell with different filling ratios were analyzed. To the best author' knowledge this is the first study where this kind of complex loading and boundary conditions are treated together during such an analysis. Only static instability, divergence, was observed where it showed that the fluid filling ratio does not have any effect on the critical buckling pressure and axial compression. It only reduces the vibration frequencies. It also revealed that the pressurized shell loses its stability at a higher critical axial load. (ii) Aeroelastic analysis of empty or partially liquid filled circular cylindrical and conical shells. Different boundary conditions with different geometries of shells subjected to supersonic air flow are studied here. In all of cases shell loses its stability though the coupled mode flutter. The results showed that internal pressure has a stabilizing effect and increases the critical flutter speed. It is seen that the value of critical dynamic pressure changes rapidly and widely as the filling ratio increases from a low value. In addition, by increasing the length ratio the decrement of flutter speed is decreased and vanishes. This rapid change in critical dynamic pressure at low filling ratios and its almost steady behaviour at large filling ratios indicate that the fluid near the bottom of the shell is largely influenced by elastic deformation when a shell is subjected to external subsonic flow. Based on comparison with the existing numerical, analytical and experimental data and the power of capabilities of this hybrid finite element method to model different boundary conditions and complex loadings, this FEM package can be used effectively for the design of advanced aerospace structures. It provides the results at less computational cost compare to the commercial FEM software, which imposes some restrictions when such an analysis is done.

Numerical simulation of a flow-like landslide using the particle finite element method

NASA Astrophysics Data System (ADS)

Zhang, Xue; Krabbenhoft, Kristian; Sheng, Daichao; Li, Weichao

2015-01-01

In this paper, an actual landslide process that occurred in Southern China is simulated by a continuum approach, the particle finite element method (PFEM). The PFEM attempts to solve the boundary-value problems in the framework of solid mechanics, satisfying the governing equations including momentum conservation, displacement-strain relation, constitutive relation as well as the frictional contact between the sliding mass and the slip surface. To warrant the convergence behaviour of solutions, the problem is formulated as a mathematical programming problem, while the particle finite element procedure is employed to tackle the issues of mesh distortion and free-surface evolution. The whole procedure of the landslide, from initiation, sliding to deposition, is successfully reproduced by the continuum approach. It is shown that the density of the mass has little influence on the sliding process in the current landslide, whereas both the geometry and the roughness of the slip surface play important roles. Comparative studies are also conducted where a satisfactory agreement is obtained.

Real-time adaptive finite element solution of time-dependent Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Bao, Gang; Hu, Guanghui; Liu, Di

2015-01-01

In our previous paper (Bao et al., 2012 [1]), a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

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

Delpassand, M.S.

The power section of a mud driven progressing cavity drill motors consists of a steel rotor shaped with an external helix rotating within a stationary tube with a molded helical elastomeric lining (stator). Operating temperature of the elastomer lining is an important parameter that affects the stator life. Motor operating conditions such as down hole temperature, torque, differential pressure, and speed determine the elastomer temperature. This paper presents an analysis technique to predict stator elastomer temperature as a function of the motor`s operating parameters. A non-linear finite element analysis technique is used to predict the stator temperature. Physical and mechanicalmore » properties of the elastomer are measured, using laboratory equipment such as Monsanto`s RPA2000 dynamic analyzer and BFGoodrich model (II) flexometer. Boundary conditions of the finite element model are defined based on the down hole temperature, differential pressure, and the motor`s speed. Results of the finite element analysis are compared with laboratory test data to verify the accuracy of the analysis.« less

Three-dimensional finite element modelling of muscle forces during mastication.

PubMed

Röhrle, Oliver; Pullan, Andrew J

2007-01-01

This paper presents a three-dimensional finite element model of human mastication. Specifically, an anatomically realistic model of the masseter muscles and associated bones is used to investigate the dynamics of chewing. A motion capture system is used to track the jaw motion of a subject chewing standard foods. The three-dimensional nonlinear deformation of the masseter muscles are calculated via the finite element method, using the jaw motion data as boundary conditions. Motion-driven muscle activation patterns and a transversely isotropic material law, defined in a muscle-fibre coordinate system, are used in the calculations. Time-force relationships are presented and analysed with respect to different tasks during mastication, e.g. opening, closing, and biting, and are also compared to a more traditional one-dimensional model. The results strongly suggest that, due to the complex arrangement of muscle force directions, modelling skeletal muscles as conventional one-dimensional lines of action might introduce a significant source of error.

A high order accurate finite element algorithm for high Reynolds number flow prediction

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

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

Wannamaker, Philip E.

We have developed an algorithm for the inversion of magnetotelluric (MT) data to a 3D earth resistivity model based upon the finite element method. Hexahedral edge finite elements are implemented to accommodate discontinuities in the electric field across resistivity boundaries, and to accurately simulate topographic variations. All matrices are reduced and solved using direct solution modules which avoids ill-conditioning endemic to iterative solvers such as conjugate gradients, principally PARDISO for the finite element system and PLASMA for the parameter step estimate. Large model parameterizations can be handled by transforming the Gauss-Newton estimator to data-space form. Accuracy of the forward problemmore » and jacobians has been checked by comparison to integral equations results and by limiting asymptotes. Inverse accuracy and performance has been verified against the public Dublin Secret Test Model 2 and the well-known Mount St Helens 3D MT data set. This algorithm we believe is the most capable yet for forming 3D images of earth resistivity structure and their implications for geothermal fluids and pathways.« less

Intervertebral disc biomechanical analysis using the finite element modeling based on medical images.

PubMed

Li, Haiyun; Wang, Zheng

2006-01-01

In this paper, a 3D geometric model of the intervertebral and lumbar disks has been presented, which integrated the spine CT and MRI data-based anatomical structure. Based on the geometric model, a 3D finite element model of an L1-L2 segment was created. Loads, which simulate the pressure from above were applied to the FEM, while a boundary condition describing the relative L1-L2 displacement is imposed on the FEM to account for 3D physiological states. The simulation calculation illustrates the stress and strain distribution and deformation of the spine. The method has two characteristics compared to previous studies: first, the finite element model of the lumbar are based on the data directly derived from medical images such as CTs and MRIs. Second, the result of analysis will be more accurate than using the data of geometric parameters. The FEM provides a promising tool in clinical diagnosis and for optimizing individual therapy in the intervertebral disc herniation.

Dipole excitation of surface plasmon on a conducting sheet: Finite element approximation and validation

NASA Astrophysics Data System (ADS)

Maier, Matthias; Margetis, Dionisios; Luskin, Mitchell

2017-06-01

We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon-polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the tangential magnetic field across the hypersurface can be incorporated naturally into the variational formulation. We carry out numerical simulations for an infinite sheet with constant isotropic conductivity embedded in two spatial dimensions; and validate our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as an absorbing perfectly matched layer, as well as local refinement and a posteriori error control are discussed.

Shear-lag analysis about an internally-dropped ply

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

Vizzini, A.J.

1995-12-31

The region around a terminated ply is modeled as several elastic layers separated by shear regions. A shear-lag analysis is then performed allowing for the thickness of the elastic and shear layers to vary. Boundary conditions, away for the ply drop, are based on the deflections determined by a finite element model. The interlaminar stresses are compared against those generated by the finite element model for tapered laminates under pure extension, pure bending, and extension-bending coupling. The shear-lag analysis predicts the interlaminar shear at and near the ply drop for pure extension and in cases involving bending if the deflectionsmore » due to bending are removed. The interlaminar shear stress and force equilibrium are used to determine the interlaminar normal stress. The trends in the interlaminar normal stress shown by the finite element model are partially captured by the shear-lag analysis. This simple analysis indicates that the mechanism for load transfer about a ply drop is primarily due to shear transfer through the resin rich areas.« less

SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

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

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-08-01

This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. Themore » notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.« less

A study on thermal damage during hyperthermia treatment based on DPL model for multilayer tissues using finite element Legendre wavelet Galerkin approach.

PubMed

Kumar, Dinesh; Rai, K N

2016-12-01

Hyperthermia is a process that uses heat from the spatial heat source to kill cancerous cells without damaging the surrounding healthy tissues. Efficacy of hyperthermia technique is related to achieve temperature at the infected cells during the treatment process. A mathematical model on heat transfer in multilayer tissues in finite domain is proposed to predict the control temperature profile at hyperthermia position. The treatment technique uses dual-phase-lag model of heat transfer in multilayer tissues with modified Gaussian distribution heat source subjected to the most generalized boundary condition and interface at the adjacent layers. The complete dual-phase-lag model of bioheat transfer is solved using finite element Legendre wavelet Galerkin approach. The present solution has been verified with exact solution in a specific case and provides a good accuracy. The effect of the variability of different parameters such as lagging times, external heat source, metabolic heat source and the most generalized boundary condition on temperature profile in multilayer tissues is analyzed and also discussed the effective approach of hyperthermia treatment. Furthermore, we studied the modified thermal damage model with regeneration of healthy tissues as well. For viewpoint of thermal damage, the least thermal damage has been observed in boundary condition of second kind. The article concludes with a discussion of better opportunities for future clinical application of hyperthermia treatment. Copyright © 2016 Elsevier Ltd. All rights reserved.

Quality use of the computer: Computational mechanics, artificial intelligence, robotics, and acoustic sensing; Proceedings of the ASME/JSME Pressure Vessels and Piping Conference, Honolulu, HI, July 23-27, 1989

NASA Astrophysics Data System (ADS)

Cory, J. F., Jr.; Gordon, J. L.; Miyoshi, T.; Suzuki, K.

1989-06-01

Papers are presented on the use of microcomputers, supercomputers, and workstations in solid and structural mechanics. Artificial intelligence technology, the development and use of expert systems, and research in the area of robotics are discussed. Attention is also given to probabilistic finite element and boundary element methods and acoustic sensing.

Cross-sectional mapping for refined beam elements with applications to shell-like structures

NASA Astrophysics Data System (ADS)

Pagani, A.; de Miguel, A. G.; Carrera, E.

2017-06-01

This paper discusses the use of higher-order mapping functions for enhancing the physical representation of refined beam theories. Based on the Carrera unified formulation (CUF), advanced one-dimensional models are formulated by expressing the displacement field as a generic expansion of the generalized unknowns. According to CUF, a novel physically/geometrically consistent model is devised by employing Legendre-like polynomial sets to approximate the generalized unknowns at the cross-sectional level, whereas a local mapping technique based on the blending functions method is used to describe the exact physical boundaries of the cross-section domain. Classical and innovative finite element methods, including hierarchical p-elements and locking-free integration schemes, are utilized to solve the governing equations of the unified beam theory. Several numerical applications accounting for small displacements/rotations and strains are discussed, including beam structures with cross-sectional curved edges, cylindrical shells, and thin-walled aeronautical wing structures with reinforcements. The results from the proposed methodology are widely assessed by comparisons with solutions from the literature and commercial finite element software tools. The attention is focussed on the high computational efficiency and the marked capabilities of the present beam model, which can deal with a broad spectrum of structural problems with unveiled accuracy in terms of geometrical representation of the domain boundaries.

Validation of finite element and boundary element methods for predicting structural vibration and radiated noise

NASA Technical Reports Server (NTRS)

Seybert, A. F.; Wu, X. F.; Oswald, Fred B.

1992-01-01

Analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise radiated from the box. The FEM was used to predict the vibration, and the surface vibration was used as input to the BEM to predict the sound intensity and sound power. Vibration predicted by the FEM model was validated by experimental modal analysis. Noise predicted by the BEM was validated by sound intensity measurements. Three types of results are presented for the total radiated sound power: (1) sound power predicted by the BEM modeling using vibration data measured on the surface of the box; (2) sound power predicted by the FEM/BEM model; and (3) sound power measured by a sound intensity scan. The sound power predicted from the BEM model using measured vibration data yields an excellent prediction of radiated noise. The sound power predicted by the combined FEM/BEM model also gives a good prediction of radiated noise except for a shift of the natural frequencies that are due to limitations in the FEM model.

Passive interior noise reduction analysis of King Air 350 turboprop aircraft using boundary element method/finite element method (BEM/FEM)

NASA Astrophysics Data System (ADS)

Dandaroy, Indranil; Vondracek, Joseph; Hund, Ron; Hartley, Dayton

2005-09-01

The objective of this study was to develop a vibro-acoustic computational model of the Raytheon King Air 350 turboprop aircraft with an intent to reduce propfan noise in the cabin. To develop the baseline analysis, an acoustic cavity model of the aircraft interior and a structural dynamics model of the aircraft fuselage were created. The acoustic model was an indirect boundary element method representation using SYSNOISE, while the structural model was a finite-element method normal modes representation in NASTRAN and subsequently imported to SYSNOISE. In the acoustic model, the fan excitation sources were represented employing the Ffowcs Williams-Hawkings equation. The acoustic and the structural models were fully coupled in SYSNOISE and solved to yield the baseline response of acoustic pressure in the aircraft interior and vibration on the aircraft structure due to fan noise. Various vibration absorbers, tuned to fundamental blade passage tone (100 Hz) and its first harmonic (200 Hz), were applied to the structural model to study their effect on cabin noise reduction. Parametric studies were performed to optimize the number and location of these passive devices. Effects of synchrophasing and absorptive noise treatments applied to the aircraft interior were also investigated for noise reduction.

Numerical solution of acoustic scattering by finite perforated elastic plates

PubMed Central

2016-01-01

We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k0 based on the plate length. However, at low k0, finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k0. The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k0 for perforated elastic plates. PMID:27274685

Numerical solution of acoustic scattering by finite perforated elastic plates.

PubMed

Cavalieri, A V G; Wolf, W R; Jaworski, J W

2016-04-01

We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k 0 based on the plate length. However, at low k 0 , finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k 0 . The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k 0 for perforated elastic plates.

COMOC: Three dimensional boundary region variant, programmer's manual

NASA Technical Reports Server (NTRS)

Orzechowski, J. A.; Baker, A. J.

1974-01-01

The three-dimensional boundary region variant of the COMOC computer program system solves the partial differential equation system governing certain three-dimensional flows of a viscous, heat conducting, multiple-species, compressible fluid including combustion. The solution is established in physical variables, using a finite element algorithm for the boundary value portion of the problem description in combination with an explicit marching technique for the initial value character. The computational lattice may be arbitrarily nonregular, and boundary condition constraints are readily applied. The theoretical foundation of the algorithm, a detailed description on the construction and operation of the program, and instructions on utilization of the many features of the code are presented.

KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Abrashkevich, A. G.; Amaya-Tapia, A.; Kaschiev, M. S.; Larsen, S. Y.; Vinitsky, S. I.

2007-10-01

A FORTRAN 77 program is presented which calculates energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on the finite interval with homogeneous boundary conditions of the third type. The resulting system of radial equations which contains the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite-element method. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials. Program summaryProgram title: KANTBP Catalogue identifier: ADZH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4224 No. of bytes in distributed program, including test data, etc.: 31 232 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM: depends on (a) the number of differential equations; (b) the number and order of finite-elements; (c) the number of hyperradial points; and (d) the number of eigensolutions required. Test run requires 30 MB Classification: 2.1, 2.4 External routines: GAULEG and GAUSSJ [W.H. Press, B.F. Flanery, S.A. Teukolsky, W.T. Vetterley, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986] Nature of problem: In the hyperspherical adiabatic approach [J. Macek, J. Phys. B 1 (1968) 831-843; U. Fano, Rep. Progr. Phys. 46 (1983) 97-165; C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142], a multi-dimensional Schrödinger equation for a two-electron system [A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Comm. 90 (1995) 311-339] or a hydrogen atom in magnetic field [M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352] is reduced by separating the radial coordinate ρ from the angular variables to a system of second-order ordinary differential equations which contain potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite-element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions for such systems of coupled differential equations. Solution method: The boundary problems for coupled differential equations are solved by the finite-element method using high-order accuracy approximations [A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Comm. 85 (1995) 40-64]. The generalized algebraic eigenvalue problem AF=EBF with respect to pair unknowns ( E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. The generalized algebraic eigenvalue problem (A-EB)F=λDF with respect to pair unknowns (λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDL factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials described in [Yu. A. Kuperin, P.B. Kurasov, Yu.B. Melnikov, S.P. Merkuriev, Ann. Phys. 205 (1991) 330-361; O. Chuluunbaatar, A.A. Gusev, S.Y. Larsen, S.I. Vinitsky, J. Phys. A 35 (2002) L513-L525; N.P. Mehta, J.R. Shepard, Phys. Rev. A 72 (2005) 032728-1-11; O. Chuluunbaatar, A.A. Gusev, M.S. Kaschiev, V.A. Kaschieva, A. Amaya-Tapia, S.Y. Larsen, S.I. Vinitsky, J. Phys. B 39 (2006) 243-269]. For this benchmark model the needed analytical expressions for the potential matrix elements and first-derivative coupling terms, their asymptotics and asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system. Restrictions: The computer memory requirements depend on: (a) the number of differential equations; (b) the number and order of finite-elements; (c) the total number of hyperradial points; and (d) the number of eigensolutions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Long Write-Up and listing for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMSC (when solving the scattering problem) that evaluate the asymptotics of the radial wave functions at the right boundary point in case of a boundary condition of the third type, respectively. Running time: The running time depends critically upon: (a) the number of differential equations; (b) the number and order of finite-elements; (c) the total number of hyperradial points on interval [0,ρ]; and (d) the number of eigensolutions required. The test run which accompanies this paper took 28.48 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz.

KANTBP 2.0: New version of a program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Vinitsky, S. I.; Abrashkevich, A. G.

2008-11-01

A FORTRAN 77 program for calculating energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach is presented. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on a finite interval with homogeneous boundary conditions: (i) the Dirichlet, Neumann and third type at the left and right boundary points for continuous spectrum problem, (ii) the Dirichlet and Neumann type conditions at left boundary point and Dirichlet, Neumann and third type at the right boundary point for the discrete spectrum problem. The resulting system of radial equations containing the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite element method. As a test desk, the program is applied to the calculation of the reaction matrix and radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field. This version extends the previous version 1.0 of the KANTBP program [O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675]. Program summaryProgram title: KANTBP Catalogue identifier: ADZH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 20 403 No. of bytes in distributed program, including test data, etc.: 147 563 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM: This depends on the number of differential equations; the number and order of finite elements; the number of hyperradial points; and the number of eigensolutions required. The test run requires 2 MB Classification: 2.1, 2.4 External routines: GAULEG and GAUSSJ [2] Nature of problem: In the hyperspherical adiabatic approach [3-5], a multidimensional Schrödinger equation for a two-electron system [6] or a hydrogen atom in magnetic field [7-9] is reduced by separating radial coordinate ρ from the angular variables to a system of the second-order ordinary differential equations containing the potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions of the continuum spectrum for such systems of coupled differential equations on finite intervals of the radial variable ρ∈[ρ,ρ]. This approach can be used in the calculations of effects of electron screening on low-energy fusion cross sections [10-12]. Solution method: The boundary problems for the coupled second-order differential equations are solved by the finite element method using high-order accuracy approximations [13]. The generalized algebraic eigenvalue problem AF=EBF with respect to pair unknowns ( E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [14]. The generalized algebraic eigenvalue problem (A-EB)F=λDF with respect to pair unknowns ( λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDL factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [14]. As a test desk, the program is applied to the calculation of the reaction matrix and corresponding radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field described in [9] on finite intervals of the radial variable ρ∈[ρ,ρ]. For this benchmark model the required analytical expressions for asymptotics of the potential matrix elements and first-derivative coupling terms, and also asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system. Restrictions: The computer memory requirements depend on: the number of differential equations; the number and order of finite elements; the total number of hyperradial points; and the number of eigensolutions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Section 3 and [1] for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should also supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMS0 and ASYMSC (when solving the scattering problem) which evaluate asymptotics of the radial wave functions at left and right boundary points in case of a boundary condition of the third type for the above problems. Running time: The running time depends critically upon: the number of differential equations; the number and order of finite elements; the total number of hyperradial points on interval [ ρ,ρ]; and the number of eigensolutions required. The test run which accompanies this paper took 2 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz. References: [1] O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675; http://cpc.cs.qub.ac.uk/summaries/ADZHv10.html. [2] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986. [3] J. Macek, J. Phys. B 1 (1968) 831-843. [4] U. Fano, Rep. Progr. Phys. 46 (1983) 97-165. [5] C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142. [6] A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Commun. 90 (1995) 311-339. [7] M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352. [8] O. Chuluunbaatar, A.A. Gusev, V.L. Derbov, M.S. Kaschiev, L.A. Melnikov, V.V. Serov, S.I. Vinitsky, J. Phys. A 40 (2007) 11485-11524. [9] O. Chuluunbaatar, A.A. Gusev, V.P. Gerdt, V.A. Rostovtsev, S.I. Vinitsky, A.G. Abrashkevich, M.S. Kaschiev, V.V. Serov, Comput. Phys. Commun. 178 (2007) 301 330; http://cpc.cs.qub.ac.uk/summaries/AEAAv10.html. [10] H.J. Assenbaum, K. Langanke, C. Rolfs, Z. Phys. A 327 (1987) 461-468. [11] V. Melezhik, Nucl. Phys. A 550 (1992) 223-234. [12] L. Bracci, G. Fiorentini, V.S. Melezhik, G. Mezzorani, P. Pasini, Phys. Lett. A 153 (1991) 456-460. [13] A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Commun. 85 (1995) 40-64. [14] K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982.

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

On the Effects of Surface Roughness on Boundary Layer Transition

NASA Technical Reports Server (NTRS)

Choudhari, Meelan M.; Li, Fei; Chang, Chau-Lyan; Edwards, Jack

2009-01-01

Surface roughness can influence laminar-turbulent transition in many different ways. This paper outlines selected analyses performed at the NASA Langley Research Center, ranging in speed from subsonic to hypersonic Mach numbers and highlighting the beneficial as well as adverse roles of the surface roughness in technological applications. The first theme pertains to boundary-layer tripping on the forebody of a hypersonic airbreathing configuration via a spanwise periodic array of trip elements, with the goal of understanding the physical mechanisms underlying roughness-induced transition in a high-speed boundary layer. The effect of an isolated, finite amplitude roughness element on a supersonic boundary layer is considered next. The other set of flow configurations examined herein corresponds to roughness based laminar flow control in subsonic and supersonic swept wing boundary layers. A common theme to all of the above configurations is the need to apply higher fidelity, physics based techniques to develop reliable predictions of roughness effects on laminar-turbulent transition.

Three-dimensional finite element modeling of a maxillary premolar tooth based on the micro-CT scanning: a detailed description.

PubMed

Huang, Zheng; Chen, Zhi

2013-10-01

This study describes the details of how to construct a three-dimensional (3D) finite element model of a maxillary first premolar tooth based on micro-CT data acquisition technique, MIMICS software and ANSYS software. The tooth was scanned by micro-CT, in which 1295 slices were obtained and then 648 slices were selected for modeling. The 3D surface mesh models of enamel and dentin were created by MIMICS (STL file). The solid mesh model was constructed by ANSYS. After the material properties and boundary conditions were set, a loading analysis was performed to demonstrate the applicableness of the resulting model. The first and third principal stresses were then evaluated. The results showed that the number of nodes and elements of the finite element model were 56 618 and 311801, respectively. The geometric form of the model was highly consistent with that of the true tooth, and the deviation between them was -0.28%. The loading analysis revealed the typical stress patterns in the contour map. The maximum compressive stress existed in the contact points and the maximum tensile stress existed in the deep fissure between the two cusps. It is concluded that by using the micro-CT and highly integrated software, construction of the 3D finite element model with high quality will not be difficult for clinical researchers.

The Programming Language Python In Earth System Simulations

NASA Astrophysics Data System (ADS)

Gross, L.; Imranullah, A.; Mora, P.; Saez, E.; Smillie, J.; Wang, C.

2004-12-01

Mathematical models in earth sciences base on the solution of systems of coupled, non-linear, time-dependent partial differential equations (PDEs). The spatial and time-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

Spherical Viscoelastic Finite Element Model for Cascadia Interseismic Deformation

NASA Astrophysics Data System (ADS)

He, J.; Wang, K.; Dragert, H.; Miller, M. M.

2003-12-01

We have developed a 3-D spherical viscoelastic finite element model for the Cascadia subduction zone to study temporal and spatial variations of interseismic deformation. Previous 3-D viscoelastic finite element models of subduction zone earthquake cycles all use the Cartesian system, with the surface of the earth map-projected on to a horizontal plane. For earthquakes that rupture very long plate-boundary segments, such as the 1700 Cascadia, 1960 Chile, and 1964 Alaska great earthquakes, the Cartesian approach is inconvenient and less accurate. 3-D analytical solutions take into account the spherical geometry of the earth but have difficulty dealing with realistic plate boundary structure. For the new spherical finite element model, we use 27-node tri-quadratic isoparametric element. The resultant large sparse matrix system is solved by the stabilized bi-conjugate gradient method with ILUT preconditioning of fill-in level 6. Our experience suggests that lower order elements in the spherical system would result in unacceptable numerical errors unless one set of mesh lines is strictly radial. For the great Cascadia earthquake, we employ a smooth coseismic rupture model inferred from thermal data and results of tsunami models of the 1700 event, but we test different slip distances. For interseismic deformation, we use the conventional backslip approach. The contemporary deformation of the Cascadia margin consists of interseismic strain accumulation and a geological secular motion that can be described by a rotation of the forearc relative to North America. To isolate the interseismic deformation, we remove the secular motion from both the model formulation and geodetic data. The model predicts decreasing margin-normal shortening rates throughout the interseismic period as a result of stress relaxation in the viscoelastic mantle. The rate of decrease depends on the assumed mantle viscosity. With a viscosity of 1019 Pa s, model surface deformation at 300 years after the great earthquake agrees with geodetically observed contemporary deformation very well. The model also confirms the previous finding based on a Cartesian model that an inland region continues to move seaward several decades after the great earthquake.

An arbitrary boundary with ghost particles incorporated in coupled FEM-SPH model for FSI problems

NASA Astrophysics Data System (ADS)

Long, Ting; Hu, Dean; Wan, Detao; Zhuang, Chen; Yang, Gang

2017-12-01

It is important to treat the arbitrary boundary of Fluid-Structure Interaction (FSI) problems in computational mechanics. In order to ensure complete support condition and restore the first-order consistency near the boundary of Smoothed Particle Hydrodynamics (SPH) method for coupling Finite Element Method (FEM) with SPH model, a new ghost particle method is proposed by dividing the interceptive area of kernel support domain into subareas corresponding to boundary segments of structure. The ghost particles are produced automatically for every fluid particle at each time step, and the properties of ghost particles, such as density, mass and velocity, are defined by using the subareas to satisfy the boundary condition. In the coupled FEM-SPH model, the normal and shear forces from a boundary segment of structure to a fluid particle are calculated through the corresponding ghost particles, and its opposite forces are exerted on the corresponding boundary segment, then the momentum of the present method is conservation and there is no matching requirements between the size of elements and the size of particles. The performance of the present method is discussed and validated by several FSI problems with complex geometry boundary and moving boundary.

A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore

PubMed Central

Chaudhry, Jehanzeb Hameed; Comer, Jeffrey; Aksimentiev, Aleksei; Olson, Luke N.

2013-01-01

The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current. PMID:24363784

A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins

PubMed Central

Xu, Jingjie; Lu, Benzhuo

2018-01-01

Membrane channel proteins control the diffusion of ions across biological membranes. They are closely related to the processes of various organizational mechanisms, such as: cardiac impulse, muscle contraction and hormone secretion. Introducing a membrane region into implicit solvation models extends the ability of the Poisson–Boltzmann (PB) equation to handle membrane proteins. The use of lateral periodic boundary conditions can properly simulate the discrete distribution of membrane proteins on the membrane plane and avoid boundary effects, which are caused by the finite box size in the traditional PB calculations. In this work, we: (1) develop a first finite element solver (FEPB) to solve the PB equation with a two-dimensional periodicity for membrane channel proteins, with different numerical treatments of the singular charges distributions in the channel protein; (2) add the membrane as a dielectric slab in the PB model, and use an improved mesh construction method to automatically identify the membrane channel/pore region even with a tilt angle relative to the z-axis; and (3) add a non-polar solvation energy term to complete the estimation of the total solvation energy of a membrane protein. A mesh resolution of about 0.25 Å (cubic grid space)/0.36 Å (tetrahedron edge length) is found to be most accurate in linear finite element calculation of the PB solvation energy. Computational studies are performed on a few exemplary molecules. The results indicate that all factors, the membrane thickness, the length of periodic box, membrane dielectric constant, pore region dielectric constant, and ionic strength, have individually considerable influence on the solvation energy of a channel protein. This demonstrates the necessity to treat all of those effects in the PB model for membrane protein simulations. PMID:29495644

A Finite Element Solution of Lateral Periodic Poisson-Boltzmann Model for Membrane Channel Proteins.

PubMed

Ji, Nan; Liu, Tiantian; Xu, Jingjie; Shen, Longzhu Q; Lu, Benzhuo

2018-02-28

Membrane channel proteins control the diffusion of ions across biological membranes. They are closely related to the processes of various organizational mechanisms, such as: cardiac impulse, muscle contraction and hormone secretion. Introducing a membrane region into implicit solvation models extends the ability of the Poisson-Boltzmann (PB) equation to handle membrane proteins. The use of lateral periodic boundary conditions can properly simulate the discrete distribution of membrane proteins on the membrane plane and avoid boundary effects, which are caused by the finite box size in the traditional PB calculations. In this work, we: (1) develop a first finite element solver (FEPB) to solve the PB equation with a two-dimensional periodicity for membrane channel proteins, with different numerical treatments of the singular charges distributions in the channel protein; (2) add the membrane as a dielectric slab in the PB model, and use an improved mesh construction method to automatically identify the membrane channel/pore region even with a tilt angle relative to the z -axis; and (3) add a non-polar solvation energy term to complete the estimation of the total solvation energy of a membrane protein. A mesh resolution of about 0.25 Å (cubic grid space)/0.36 Å (tetrahedron edge length) is found to be most accurate in linear finite element calculation of the PB solvation energy. Computational studies are performed on a few exemplary molecules. The results indicate that all factors, the membrane thickness, the length of periodic box, membrane dielectric constant, pore region dielectric constant, and ionic strength, have individually considerable influence on the solvation energy of a channel protein. This demonstrates the necessity to treat all of those effects in the PB model for membrane protein simulations.

Finite Element Analysis of Free-Edge Delamination in Laminated Composite Specimens

DTIC Science & Technology

1991-06-18

for the degree of Doctor of Philosophy at the Ohio State University. Revision by H. R. Chu corrected some errors and added further studies on...Galerkin’s approach, in which interlaminar stresses and displacements of each layer satisfying geometrica ’ boundary conditions were represented as -series

Scattering of Acoustic Waves from Ocean Boundaries

DTIC Science & Technology

2014-09-30

of buried mines and improve SONAR performance in shallow water. OBJECTIVES 1) Determination of the correct physical model of acoustic propagation...Nicholas Chotiros, particularly for theoretical development of bulk acoustic /sediment modeling and laser roughness measurements. REFERENCES C...PUBLICATIONS 1. M. Isakson, and N. Chotiros. Finite Element Modeling of Acoustic

Modeling of nanostructured porous thermoelastic composites with surface effects

NASA Astrophysics Data System (ADS)

Nasedkin, A. V.; Nasedkina, A. A.; Kornievsky, A. S.

2017-01-01

The paper presents an integrated approach for determination of effective properties of anisotropic porous thermoelastic materials with a nanoscale stochastic porosity structure. This approach includes the effective moduli method for composite me-chanics, the simulation of representative volumes and the finite element method. In order to take into account nanoscale sizes of pores, the Gurtin-Murdoch model of surface stresses and the highly conducting interface model are used at the borders between material and pores. The general methodology for determination of effective properties of porous composites is demonstrated for a two-phase composite with special conditions for stresses and heat flux discontinuities at the phase interfaces. The mathematical statements of boundary value problems and the resulting formulas to determine the complete set of effective constants of the two-phase composites with arbitrary anisotropy and with surface properties are described; the generalized statements are formulated and the finite element approximations are given. It is shown that the homogenization procedures for porous composites with surface effects can be considered as special cases of the corresponding procedures for the two-phase composites with interphase stresses and heat fluxes if the moduli of nanoinclusions are negligibly small. These approaches have been implemented in the finite element package ANSYS for a model of porous material with cubic crystal system for various values of surface moduli, porosity and number of pores. It has been noted that the magnitude of the area of the interphase boundaries has influence on the effective moduli of the porous materials with nanosized structure.

The effect of the wind tunnel wall boundary layer on the acoustic testing of propellers

NASA Technical Reports Server (NTRS)

Eversman, Walter

1989-01-01

An approximation based on the representation of the boundary layer by lamina of uniform flow with suitable interlayer boundary conditions is shown to be accurate, efficient, and compatible with finite element formulations. The approximation has been implemented using existing codes to produce a model for assessing the suitability of the acoustic environment in a wind tunnel for the acoustic testing of propellers. It is found that, with suitable acoustic treatment and with measurements made near the propeller and well removed from the walls, the free field directivity and level can be reproduced with good fidelity.

Meshless method for solving fixed boundary problem of plasma equilibrium

NASA Astrophysics Data System (ADS)

Imazawa, Ryota; Kawano, Yasunori; Itami, Kiyoshi

2015-07-01

This study solves the Grad-Shafranov equation with a fixed plasma boundary by utilizing a meshless method for the first time. Previous studies have utilized a finite element method (FEM) to solve an equilibrium inside the fixed separatrix. In order to avoid difficulties of FEM (such as mesh problem, difficulty of coding, expensive calculation cost), this study focuses on the meshless methods, especially RBF-MFS and KANSA's method to solve the fixed boundary problem. The results showed that CPU time of the meshless methods was ten to one hundred times shorter than that of FEM to obtain the same accuracy.

Reentry heat transfer analysis of the space shuttle orbiter

NASA Technical Reports Server (NTRS)

Ko, W. L.; Quinn, R. D.; Gong, L.

1982-01-01

A structural performance and resizing finite element thermal analysis computer program was used in the reentry heat transfer analysis of the space shuttle. Two typical wing cross sections and a midfuselage cross section were selected for the analysis. The surface heat inputs to the thermal models were obtained from aerodynamic heating analyses, which assumed a purely turbulent boundary layer, a purely laminar boundary layer, separated flow, and transition from laminar to turbulent flow. The effect of internal radiation was found to be quite significant. With the effect of the internal radiation considered, the wing lower skin temperature became about 39 C (70 F) lower. The results were compared with fight data for space transportation system, trajectory 1. The calculated and measured temperatures compared well for the wing if laminar flow was assumed for the lower surface and bay one upper surface and if separated flow was assumed for the upper surfaces of bays other than bay one. For the fuselage, good agreement between the calculated and measured data was obtained if laminar flow was assumed for the bottom surface. The structural temperatures were found to reach their peak values shortly before touchdown. In addition, the finite element solutions were compared with those obtained from the conventional finite difference solutions.

Slip Continuity in Explicit Crystal Plasticity Simulations Using Nonlocal Continuum and Semi-discrete Approaches

DTIC Science & Technology

2013-01-01

Based Micropolar Single Crystal Plasticity: Comparison of Multi - and Single Criterion Theories. J. Mech. Phys. Solids 2011, 59, 398–422. ALE3D ...element boundaries in a multi -step constitutive evaluation (Becker, 2011). The results showed the desired effects of smoothing the deformation field...Implementation The model was implemented in the large-scale parallel, explicit finite element code ALE3D (2012). The crystal plasticity

Study of hypervelocity meteoroid impact on orbital space stations

NASA Technical Reports Server (NTRS)

Leimbach, K. R.; Prozan, R. J.

1973-01-01

Structural damage resulting in hypervelocity impact of a meteorite on a spacecraft is discussed. Of particular interest is the backside spallation caused by such a collision. To treat this phenomenon two numerical schemes were developed in the course of this study to compute the elastic-plastic flow fracture of a solid. The numerical schemes are a five-point finite difference scheme and a four-node finite element scheme. The four-node finite element scheme proved to be less sensitive to the type of boundary conditions and loadings. Although further development work is needed to improve the program versatility (generalization of the network topology, secondary storage for large systems, improving of the coding to reduce the run time, etc.), the basic framework is provided for a utilitarian computer program which may be used in a wide variety of situations. Analytic results showing the program output are given for several test cases.

A design pathfinder with material correlation points for inflatable systems

NASA Astrophysics Data System (ADS)

Fulcher, Jared Terrell

The incorporation of inflatable structures into aerospace systems can produce significant advantages in stowed volume to mechanical effectiveness and overall weight. Many applications of these ultra-lightweight systems are designed to precisely control internal or external surfaces, or both, to achieve desired performance. The modeling of these structures becomes complex due to the material nonlinearities inherent to the majority of construction materials used in inflatable structures. Furthermore, accurately modeling the response and behavior of the interfacing boundaries that are common to many inflatable systems will lead to better understanding of the entire class of structures. The research presented involved using nonlinear finite element simulations correlated with photogrammetry testing to develop a procedure for defining material properties for commercially available polyurethane-coated woven nylon fabric, which is representative of coated materials that have been proven materials for use in many inflatable systems. Further, the new material model was used to design and develop an inflatable pathfinder system which employs only internal pressure to control an assembly of internal membranes. This canonical inflatable system will be used for exploration and development of general understanding of efficient design methodology and analysis of future systems. Canonical structures are incorporated into the design of the phased pathfinder system to allow for more universal insight. Nonlinear finite element simulations were performed to evaluate the effect of various boundary conditions, loading configurations, and material orientations on the geometric precision of geometries representing typical internal/external surfaces commonly incorporated into inflatable pathfinder system. The response of the inflatable system to possible damage was also studied using nonlinear finite element simulations. Development of a correlated material model for analysis of the inflatable pathfinder system has improved the efficiency of design and analysis techniques of future inflatable structures. KEYWORDS: Nonlinear Finite Element, Inflatable Structures, Gossamer Space Systems, Photogrammetry Measurements, Coated Woven Fabric.

Copper Tube Compression in Z-Current Geometry, Numerical Simulations and Comparison with Cyclope Experiments

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

Lefrancois, A.; L'Eplattenier, P.; Burger, M.

2006-02-13

Metallic tubes compressions in Z-current geometry were performed at the Cyclope facility from Gramat Research Center in order to study the behavior of metals under large strain at high strain rate. 3D configurations of cylinder compressions have been calculated here to benchmark the new beta version of the electromagnetism package coupled with the dynamics in Ls-Dyna and compared with the Cyclope experiments. The electromagnetism module is being developed in the general-purpose explicit and implicit finite element program LS-DYNA{reg_sign} in order to perform coupled mechanical/thermal/electromagnetism simulations. The Maxwell equations are solved using a Finite Element Method (FEM) for the solid conductorsmore » coupled with a Boundary Element Method (BEM) for the surrounding air (or vacuum). More details can be read in the references.« less

ICANT, a code for the self-consistent computation of ICRH antenna coupling

NASA Astrophysics Data System (ADS)

Pécoul, S.; Heuraux, S.; Koch, R.; Leclert, G.

1996-02-01

The code deals with 3D antenna structures (finite length antennae) that are used to launch electromagnetic waves into tokamak plasmas. The antenna radiation problem is solved using a finite boundary element technique combined with a spectral solution of the interior problem. The slab approximation is used, and periodicity in y and z directions is introduced to account for toroidal geometry. We present results for various types of antennae radiating in vacuum: antenna with a finite Faraday screen and ideal Faraday screen, antenna with side limiters and phased antenna arrays. The results (radiated power, current profile) obtained are very close to analytical solutions when available.

Accurate traveltime computation in complex anisotropic media with discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Le Bouteiller, P.; Benjemaa, M.; Métivier, L.; Virieux, J.

2017-12-01

Travel time computation is of major interest for a large range of geophysical applications, among which source localization and characterization, phase identification, data windowing and tomography, from decametric scale up to global Earth scale.Ray-tracing tools, being essentially 1D Lagrangian integration along a path, have been used for their efficiency but present some drawbacks, such as a rather difficult control of the medium sampling. Moreover, they do not provide answers in shadow zones. Eikonal solvers, based on an Eulerian approach, have attracted attention in seismology with the pioneering work of Vidale (1988), while such approach has been proposed earlier by Riznichenko (1946). They have been used now for first-arrival travel-time tomography at various scales (Podvin & Lecomte (1991). The framework for solving this non-linear partial differential equation is now well understood and various finite-difference approaches have been proposed, essentially for smooth media. We propose a novel finite element approach which builds a precise solution for strongly heterogeneous anisotropic medium (still in the limit of Eikonal validity). The discontinuous Galerkin method we have developed allows local refinement of the mesh and local high orders of interpolation inside elements. High precision of the travel times and its spatial derivatives is obtained through this formulation. This finite element method also honors boundary conditions, such as complex topographies and absorbing boundaries for mimicking an infinite medium. Applications from travel-time tomography, slope tomography are expected, but also for migration and take-off angles estimation, thanks to the accuracy obtained when computing first-arrival times.References:Podvin, P. and Lecomte, I., 1991. Finite difference computation of traveltimes in very contrasted velocity model: a massively parallel approach and its associated tools, Geophys. J. Int., 105, 271-284.Riznichenko, Y., 1946. Geometrical seismics of layered media, Trudy Inst. Theor. Geophysics, Vol II, Moscow (in Russian).Vidale, J., 1988. Finite-difference calculation of travel times, Bull. seism. Soc. Am., 78, 2062-2076.

A tire contact solution technique

NASA Technical Reports Server (NTRS)

Tielking, J. T.

1983-01-01

An efficient method for calculating the contact boundary and interfacial pressure distribution was developed. This solution technique utilizes the discrete Fourier transform to establish an influence coefficient matrix for the portion of the pressurized tire surface that may be in the contact region. This matrix is used in a linear algebra algorithm to determine the contact boundary and the array of forces within the boundary that are necessary to hold the tire in equilibrium against a specified contact surface. The algorithm also determines the normal and tangential displacements of those points on the tire surface that are included in the influence coefficient matrix. Displacements within and outside the contact region are calculated. The solution technique is implemented with a finite-element tire model that is based on orthotropic, nonlinear shell of revolution elements which can respond to nonaxisymmetric loads. A sample contact solution is presented.

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time: application to non-rigid neuroimage registration.

PubMed

Wittek, Adam; Joldes, Grand; Couton, Mathieu; Warfield, Simon K; Miller, Karol

2010-12-01

Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer. Copyright © 2010 Elsevier Ltd. All rights reserved.

Selection of finite-element mesh parameters in modeling the growth of hydraulic fracturing cracks

NASA Astrophysics Data System (ADS)

Kurguzov, V. D.

2016-12-01

The effect of the mesh geometry on the accuracy of solutions obtained by the finite-element method for problems of linear fracture mechanics is investigated. The guidelines have been formulated for constructing an optimum mesh for several routine problems involving elements with linear and quadratic approximation of displacements. The accuracy of finite-element solutions is estimated based on the degree of the difference between the calculated stress-intensity factor (SIF) and its value obtained analytically. In problems of hydrofracturing of oil-bearing formation, the pump-in pressure of injected water produces a distributed load on crack flanks as opposed to standard fracture mechanics problems that have analytical solutions, where a load is applied to the external boundaries of the computational region and the cracks themselves are kept free from stresses. Some model pressure profiles, as well as pressure profiles taken from real hydrodynamic computations, have been considered. Computer models of cracks with allowance for the pre-stressed state, fracture toughness, and elastic properties of materials are developed in the MSC.Marc 2012 finite-element analysis software. The Irwin force criterion is used as a criterion of brittle fracture and the SIFs are computed using the Cherepanov-Rice invariant J-integral. The process of crack propagation in a linearly elastic isotropic body is described in terms of the elastic energy release rate G and modeled using the VCCT (Virtual Crack Closure Technique) approach. It has been found that the solution accuracy is sensitive to the mesh configuration. Several parameters that are decisive in constructing effective finite-element meshes, namely, the minimum element size, the distance between mesh nodes in the vicinity of a crack tip, and the ratio of the height of an element to its length, have been established. It has been shown that a mesh that consists of only small elements does not improve the accuracy of the solution.

Analytical approach to peel stresses in bonded composite stiffened panels

NASA Technical Reports Server (NTRS)

Barkey, Derek A.; Madan, Ram C.; Sutton, Jason O.

1987-01-01

A closed-form solution was obtained for the stresses and displacements of two bonded beams. A system of two fourth-order and two second-order differential equations with the associated boundary equations was determined using a variational work approach. A FORTRAN computer program was devised to solve for the eigenvalues and eigenvectors of this system and to calculate the coefficients from the boundary conditions. The results were then compared with NASTRAN finite-element solutions and shown to agree closely.

Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part 1. Boundary Value Problems for Linear Ellilptic Equation of Second Order.

DTIC Science & Technology

1986-05-01

neighborhood of the Program PROBE of Noetic Technologies, St. Louis. corners of the domain, place where the type of the boundary condition changes, etc...is studied . , r ° -. o. - *- . ,. .- -*. ... - - . . . ’ , ..- , .- *- , . --s,." . ",-:, "j’ . ], k i-, j!3 ,, :,’ - .A L...Manual. Noetic Technologies Corp., St. Louis, Missouri (1985). 318] Szab’, B. A.: Implementation of a Finite Element Software System with h and p

Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

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

Xia, Yidong, E-mail: yidong.xia@inl.gov; Wang, Chuanjin; Luo, Hong

Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, some form of solution verification has been attempted to identify sensitivities in the solution methods, and suggest best practices when using the Hydra-TH code. -- Highlights: •We performed a comprehensive study to verify and validate the turbulence models in Hydra-TH. •Hydra-TH delivers 2nd-order grid convergence for the incompressible Navier–Stokes equations. •Hydra-TH can accurately simulate the laminar boundary layers. •Hydra-TH can accurately simulate the turbulent boundary layers with RANS turbulence models. •Hydra-TH delivers high-fidelity LES capability for simulating turbulent flows in confined space.« less

Modeling of stresses at grain boundaries with respect to occurrence of stress corrosion cracking

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

Kozaczek, K.J.; Sinharoy, A.; Ruud, C.O.

The distributions of elastic stresses/strains in the grain boundary regions were studied by the analytical and the finite element models. The grain boundaries represent the sites where stress concentration occurs as a result of discontinuity of elastic properties across the grain boundary and the presence of second phase particles elastically different from the surrounding matrix grains. A quantitative analysis of those stresses for steels and nickel based alloys showed that the stress concentrations in the grain boundary regions are high enough to cause a local microplastic deformation even when the material is in the macroscopic elastic regime. The stress redistributionmore » as a result of such a plastic deformation was discussed.« less

Interface and permittivity simultaneous reconstruction in electrical capacitance tomography based on boundary and finite-elements coupling method

PubMed Central

Ren, Shangjie; Dong, Feng

2016-01-01

Electrical capacitance tomography (ECT) is a non-destructive detection technique for imaging the permittivity distributions inside an observed domain from the capacitances measurements on its boundary. Owing to its advantages of non-contact, non-radiation, high speed and low cost, ECT is promising in the measurements of many industrial or biological processes. However, in the practical industrial or biological systems, a deposit is normally seen in the inner wall of its pipe or vessel. As the actual region of interest (ROI) of ECT is surrounded by the deposit layer, the capacitance measurements become weakly sensitive to the permittivity perturbation occurring at the ROI. When there is a major permittivity difference between the deposit and the ROI, this kind of shielding effect is significant, and the permittivity reconstruction becomes challenging. To deal with the issue, an interface and permittivity simultaneous reconstruction approach is proposed. Both the permittivity at the ROI and the geometry of the deposit layer are recovered using the block coordinate descent method. The boundary and finite-elements coupling method is employed to improve the computational efficiency. The performance of the proposed method is evaluated with the simulation tests. This article is part of the themed issue ‘Supersensing through industrial process tomography’. PMID:27185960

A time-domain finite element boundary integral approach for elastic wave scattering

NASA Astrophysics Data System (ADS)

Shi, F.; Lowe, M. J. S.; Skelton, E. A.; Craster, R. V.

2018-04-01

The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.

Acoustic-Modal Testing of the Ares I Launch Abort System Attitude Control Motor Valve

NASA Technical Reports Server (NTRS)

Davis, R. Benjamin; Fischbach, Sean R.

2010-01-01

The Attitude Control Motor (ACM) is being developed for use in the Launch Abort System (LAS) of NASA's Ares I launch vehicle. The ACM consists of a small solid rocket motor and eight actuated pintle valves that directionally allocate.thrust_- 1t.has-been- predicted-that significant unsteady. pressure.fluctuations.will.exist. inside the-valves during operation. The dominant frequencies of these oscillations correspond to the lowest several acoustic natural frequencies of the individual valves. An acoustic finite element model of the fluid volume inside the valve has been critical to the prediction of these frequencies and their associated mode shapes. This work describes an effort to experimentally validate the acoustic finite model of the valve with an acoustic modal test. The modal test involved instrumenting a flight-like valve with six microphones and then exciting the enclosed air with a loudspeaker. The loudspeaker was configured to deliver broadband noise at relatively high sound pressure levels. The aquired microphone signals were post-processed and compared to results generated from the acoustic finite element model. Initial comparisons between the test data and the model results revealed that additional model refinement was necessary. Specifically, the model was updated to implement a complex impedance boundary condition at the entrance to the valve supply tube. This boundary condition models the frequency-dependent impedance that an acoustic wave will encounter as it reaches the end of the supply tube. Upon invoking this boundary condition, significantly improved agreement between the test data and the model was realized.

Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent

2018-05-01

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.

Numerical algorithms for computations of feedback laws arising in control of flexible systems

NASA Technical Reports Server (NTRS)

Lasiecka, Irena

1989-01-01

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Mixed models and reduction method for dynamic analysis of anisotropic shells

NASA Technical Reports Server (NTRS)

Noor, A. K.; Peters, J. M.

1985-01-01

A time-domain computational procedure is presented for predicting the dynamic response of laminated anisotropic shells. The two key elements of the procedure are: (1) use of mixed finite element models having independent interpolation (shape) functions for stress resultants and generalized displacements for the spatial discretization of the shell, with the stress resultants allowed to be discontinuous at interelement boundaries; and (2) use of a dynamic reduction method, with the global approximation vectors consisting of the static solution and an orthogonal set of Lanczos vectors. The dynamic reduction is accomplished by means of successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate the global approximation vectors. Then the Rayleigh-Ritz technique is used to generate a reduced system of ordinary differential equations in the amplitudes of these modes. The temporal integration of the reduced differential equations is performed by using an explicit half-station central difference scheme (Leap-frog method). The effectiveness of the proposed procedure is demonstrated by means of a numerical example and its advantages over reduction methods used with the displacement formulation are discussed.

Evaluation of a Kinematically-Driven Finite Element Footstrike Model.

PubMed

Hannah, Iain; Harland, Andy; Price, Dan; Schlarb, Heiko; Lucas, Tim

2016-06-01

A dynamic finite element model of a shod running footstrike was developed and driven with 6 degree of freedom foot segment kinematics determined from a motion capture running trial. Quadratic tetrahedral elements were used to mesh the footwear components with material models determined from appropriate mechanical tests. Model outputs were compared with experimental high-speed video (HSV) footage, vertical ground reaction force (GRF), and center of pressure (COP) excursion to determine whether such an approach is appropriate for the development of athletic footwear. Although unquantified, good visual agreement to the HSV footage was observed but significant discrepancies were found between the model and experimental GRF and COP readings (9% and 61% of model readings outside of the mean experimental reading ± 2 standard deviations, respectively). Model output was also found to be highly sensitive to input kinematics with a 120% increase in maximum GRF observed when translating the force platform 2 mm vertically. While representing an alternative approach to existing dynamic finite element footstrike models, loading highly representative of an experimental trial was not found to be achievable when employing exclusively kinematic boundary conditions. This significantly limits the usefulness of employing such an approach in the footwear development process.

Finite Element Solution of Unsteady Mixed Convection Flow of Micropolar Fluid over a Porous Shrinking Sheet

PubMed Central

Gupta, Diksha; Singh, Bani

2014-01-01

The objective of this investigation is to analyze the effect of unsteadiness on the mixed convection boundary layer flow of micropolar fluid over a permeable shrinking sheet in the presence of viscous dissipation. At the sheet a variable distribution of suction is assumed. The unsteadiness in the flow and temperature fields is caused by the time dependence of the shrinking velocity and surface temperature. With the aid of similarity transformations, the governing partial differential equations are transformed into a set of nonlinear ordinary differential equations, which are solved numerically, using variational finite element method. The influence of important physical parameters, namely, suction parameter, unsteadiness parameter, buoyancy parameter and Eckert number on the velocity, microrotation, and temperature functions is investigated and analyzed with the help of their graphical representations. Additionally skin friction and the rate of heat transfer have also been computed. Under special conditions, an exact solution for the flow velocity is compared with the numerical results obtained by finite element method. An excellent agreement is observed for the two sets of solutions. Furthermore, to verify the convergence of numerical results, calculations are conducted with increasing number of elements. PMID:24672310

Thermal Transport Model for Heat Sink Design

NASA Technical Reports Server (NTRS)

Chervenak, James A.; Kelley, Richard L.; Brown, Ari D.; Smith, Stephen J.; Kilbourne, Caroline a.

2009-01-01

A document discusses the development of a finite element model for describing thermal transport through microcalorimeter arrays in order to assist in heat-sinking design. A fabricated multi-absorber transition edge sensor (PoST) was designed in order to reduce device wiring density by a factor of four. The finite element model consists of breaking the microcalorimeter array into separate elements, including the transition edge sensor (TES) and the silicon substrate on which the sensor is deposited. Each element is then broken up into subelements, whose surface area subtends 10 10 microns. The heat capacity per unit temperature, thermal conductance, and thermal diffusivity of each subelement are the model inputs, as are the temperatures of each subelement. Numerical integration using the Finite in Time Centered in Space algorithm of the thermal diffusion equation is then performed in order to obtain a temporal evolution of the subelement temperature. Thermal transport across interfaces is modeled using a thermal boundary resistance obtained using the acoustic mismatch model. The document concludes with a discussion of the PoST fabrication. PoSTs are novel because they enable incident x-ray position sensitivity with good energy resolution and low wiring density.

Finite element analyses of a linear-accelerator electron gun

NASA Astrophysics Data System (ADS)

Iqbal, M.; Wasy, A.; Islam, G. U.; Zhou, Z.

2014-02-01

Thermo-structural analyses of the Beijing Electron-Positron Collider (BEPCII) linear-accelerator, electron gun, were performed for the gun operating with the cathode at 1000 °C. The gun was modeled in computer aided three-dimensional interactive application for finite element analyses through ANSYS workbench. This was followed by simulations using the SLAC electron beam trajectory program EGUN for beam optics analyses. The simulations were compared with experimental results of the assembly to verify its beam parameters under the same boundary conditions. Simulation and test results were found to be in good agreement and hence confirmed the design parameters under the defined operating temperature. The gun is operating continuously since commissioning without any thermal induced failures for the BEPCII linear accelerator.

Finite element analyses of a linear-accelerator electron gun.

PubMed

Iqbal, M; Wasy, A; Islam, G U; Zhou, Z

2014-02-01

Thermo-structural analyses of the Beijing Electron-Positron Collider (BEPCII) linear-accelerator, electron gun, were performed for the gun operating with the cathode at 1000 °C. The gun was modeled in computer aided three-dimensional interactive application for finite element analyses through ANSYS workbench. This was followed by simulations using the SLAC electron beam trajectory program EGUN for beam optics analyses. The simulations were compared with experimental results of the assembly to verify its beam parameters under the same boundary conditions. Simulation and test results were found to be in good agreement and hence confirmed the design parameters under the defined operating temperature. The gun is operating continuously since commissioning without any thermal induced failures for the BEPCII linear accelerator.

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.

Finite element stress analysis of idealized composite damage zones

NASA Technical Reports Server (NTRS)

Obrien, D.; Herakovich, C. T.

1978-01-01

A quasi three dimensional finite element stress analysis of idealized damage zones in composite laminates is presented. The damage zones consist of a long centered groove or cutout extending one or two layers in depth from both top and bottom surfaces of a thin composite laminate. Elastic results are presented for compressive loading of four and eight layer laminates. It is shown that a boundary layer exists near the cutout edge similar to that previously shown to exist along free edges. The cutout is shown to produce significant interlaminar stresses in the interior of the laminate away from free cutout edges. The interlaminar stresses are also shown to contribute to failure which is defined using the Tsai-Wu failure criteria.

Solution of the 2-D steady-state radiative transfer equation in participating media with specular reflections using SUPG and DG finite elements

NASA Astrophysics Data System (ADS)

Le Hardy, D.; Favennec, Y.; Rousseau, B.

2016-08-01

The 2D radiative transfer equation coupled with specular reflection boundary conditions is solved using finite element schemes. Both Discontinuous Galerkin and Streamline-Upwind Petrov-Galerkin variational formulations are fully developed. These two schemes are validated step-by-step for all involved operators (transport, scattering, reflection) using analytical formulations. Numerical comparisons of the two schemes, in terms of convergence rate, reveal that the quadratic SUPG scheme proves efficient for solving such problems. This comparison constitutes the main issue of the paper. Moreover, the solution process is accelerated using block SOR-type iterative methods, for which the determination of the optimal parameter is found in a very cheap way.

Active earth pressure model tests versus finite element analysis

NASA Astrophysics Data System (ADS)

Pietrzak, Magdalena

2017-06-01

The purpose of the paper is to compare failure mechanisms observed in small scale model tests on granular sample in active state, and simulated by finite element method (FEM) using Plaxis 2D software. Small scale model tests were performed on rectangular granular sample retained by a rigid wall. Deformation of the sample resulted from simple wall translation in the direction `from the soil" (active earth pressure state. Simple Coulomb-Mohr model for soil can be helpful in interpreting experimental findings in case of granular materials. It was found that the general alignment of strain localization pattern (failure mechanism) may belong to macro scale features and be dominated by a test boundary conditions rather than the nature of the granular sample.

An h-p Taylor-Galerkin finite element method for compressible Euler equations

NASA Technical Reports Server (NTRS)

Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O.

1991-01-01

An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.

Determination of the Shear Stress Distribution in a Laminate from the Applied Shear Resultant--A Simplified Shear Solution

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Aboudi, Jacob; Yarrington, Phillip W.

2007-01-01

The simplified shear solution method is presented for approximating the through-thickness shear stress distribution within a composite laminate based on laminated beam theory. The method does not consider the solution of a particular boundary value problem, rather it requires only knowledge of the global shear loading, geometry, and material properties of the laminate or panel. It is thus analogous to lamination theory in that ply level stresses can be efficiently determined from global load resultants (as determined, for instance, by finite element analysis) at a given location in a structure and used to evaluate the margin of safety on a ply by ply basis. The simplified shear solution stress distribution is zero at free surfaces, continuous at ply boundaries, and integrates to the applied shear load. Comparisons to existing theories are made for a variety of laminates, and design examples are provided illustrating the use of the method for determining through-thickness shear stress margins in several types of composite panels and in the context of a finite element structural analysis.

Finite-element modelling of thermal micracking in fresh and consolidated marbles

NASA Astrophysics Data System (ADS)

Weiss, T.; Fuller, E.; Siegesmund, S.

2003-04-01

The initial stage of marble weathering is supposed to be controlled by thermal microcracking. Due to the anisotropy of the thermal expansion coefficients of calcite, the main rock forming mineral in marble, stresses are caused which lead to thermally-induced microcracking, especially along the grain boundaries. The so-called "granular disintegration" is a frequent weathering phenomenon observed for marbles. The controlling parameters are the grain size, grain shape and grain orientation. We use a finite-element approach to constrain magnitude and directional dependence of thermal degradation. Therefore, different assumptions are validated including the fracture toughness of the grain boundaries, the effects of the grain-to-grain orientation and bulk lattice preferred orientation (here referred to as texture). The resulting thermal microcracking and bulk rock thermal expansion anisotropy are validated. It is evident that thermal degradation depends on the texture. Strongly textured marbles exhibit a clear directional dependence of thermal degradation and a smaller bulk thermal degradation than randomly oriented ones. The effect of different stone consolidants in the pore space of degraded marble is simulated and its influence on mechanical properties such as tensile strength are evaluated.

A finite element model development for simulation of the impact of slab thickness, joints, and membranes on indoor radon concentration.

PubMed

Muñoz, E; Frutos, B; Olaya, M; Sánchez, J

2017-10-01

The focus of this study is broadly to define the physics involved in radon generation and transport through the soil and other materials using different parameter-estimation tools from the literature. The effect of moisture in the soil and radon transport via water in the pore space was accounted for with the application of a porosity correction coefficient. A 2D finite element model is created, which reproduces the diffusion and advection mechanisms resulting from specified boundary conditions. A comparison between the model and several analytical and numerical solutions obtained from the literature and field studies validates the model. Finally, the results demonstrate that the model can predict radon entry through different building boundary conditions, such as concrete slabs with or without joints, variable slab thicknesses and diffusion coefficients, and the use of several radon barrier membranes. Cracks in the concrete or the radon barrier membrane have been studied to understand how indoor concentration is affected by these issues. Copyright © 2017 Elsevier Ltd. All rights reserved.

Finite-element simulation of ground-water flow in the vicinity of Yucca Mountain, Nevada-California

USGS Publications Warehouse

Czarnecki, J.B.; Waddell, R.K.

1984-01-01

A finite-element model of the groundwater flow system in the vicinity of Yucca Mountain at the Nevada Test Site was developed using parameter estimation techniques. The model simulated steady-state ground-water flow occurring in tuffaceous, volcanic , and carbonate rocks, and alluvial aquifers. Hydraulic gradients in the modeled area range from 0.00001 for carbonate aquifers to 0.19 for barriers in tuffaceous rocks. Three model parameters were used in estimating transmissivity in six zones. Simulated hydraulic-head values range from about 1,200 m near Timber Mountain to about 300 m near Furnace Creek Ranch. Model residuals for simulated versus measured hydraulic heads range from -28.6 to 21.4 m; most are less than +/-7 m, indicating an acceptable representation of the hydrologic system by the model. Sensitivity analyses of the model 's flux boundary condition variables were performed to assess the effect of varying boundary fluxes on the calculation of estimated model transmissivities. Varying the flux variables representing discharge at Franklin Lake and Furnace Creek Ranch has greater effect than varying other flux variables. (Author 's abstract)

Study on Material Parameters Identification of Brain Tissue Considering Uncertainty of Friction Coefficient

NASA Astrophysics Data System (ADS)

Guan, Fengjiao; Zhang, Guanjun; Liu, Jie; Wang, Shujing; Luo, Xu; Zhu, Feng

2017-10-01

Accurate material parameters are critical to construct the high biofidelity finite element (FE) models. However, it is hard to obtain the brain tissue parameters accurately because of the effects of irregular geometry and uncertain boundary conditions. Considering the complexity of material test and the uncertainty of friction coefficient, a computational inverse method for viscoelastic material parameters identification of brain tissue is presented based on the interval analysis method. Firstly, the intervals are used to quantify the friction coefficient in the boundary condition. And then the inverse problem of material parameters identification under uncertain friction coefficient is transformed into two types of deterministic inverse problem. Finally the intelligent optimization algorithm is used to solve the two types of deterministic inverse problems quickly and accurately, and the range of material parameters can be easily acquired with no need of a variety of samples. The efficiency and convergence of this method are demonstrated by the material parameters identification of thalamus. The proposed method provides a potential effective tool for building high biofidelity human finite element model in the study of traffic accident injury.

Fluid-structure interaction and aerodynamics damping; Proceedings of the Tenth Biennial Conference on Mechanical Vibration and Noise, Cincinnati, OH, September 10-13, 1985

NASA Astrophysics Data System (ADS)

Dowell, E. H.; Au-Yang, M. K.

1985-09-01

The response of a two-layer elastic coating to pressure disturbances from a turbulent boundary layer is considered along with the application of the finite element method in the calculation of transmission loss of flat and curved panels, the application of various solution techniques to the calculation of transonic flutter boundaries, and noise transmission of double wall composite shells. Other topics explored are related to chaotic behavior of a simple single-degree-of-freedom system, the entrainment of self-sustained flow oscillations, the effects of strong shock loading on coupled bending-torssion flutter of tuned and mistuned cascades, and turbulent buffeting of a multispan tube bundle. Attention is given to the dynamics of heat exchangers U-bend tubes with flat bar supports, a review of flow induced vibration of two circular cylinders in crossflow, the avoidance of leakage flow-induced vibration by a tube-in-tube slip joint, random load from multiple sources and its assessment, and wake-induced vibration of a conductor in the wake of another via a 3-D finite element method.

Finite element analysis of heat load of tungsten relevant to ITER conditions

NASA Astrophysics Data System (ADS)

Zinovev, A.; Terentyev, D.; Delannay, L.

2017-12-01

A computational procedure is proposed in order to predict the initiation of intergranular cracks in tungsten with ITER specification microstructure (i.e. characterised by elongated micrometre-sized grains). Damage is caused by a cyclic heat load, which emerges from plasma instabilities during operation of thermonuclear devices. First, a macroscopic thermo-mechanical simulation is performed in order to obtain temperature- and strain field in the material. The strain path is recorded at a selected point of interest of the macroscopic specimen, and is then applied at the microscopic level to a finite element mesh of a polycrystal. In the microscopic simulation, the stress state at the grain boundaries serves as the marker of cracking initiation. The simulated heat load cycle is a representative of edge-localized modes, which are anticipated during normal operations of ITER. Normal stresses at the grain boundary interfaces were shown to strongly depend on the direction of grain orientation with respect to the heat flux direction and to attain higher values if the flux is perpendicular to the elongated grains, where it apparently promotes crack initiation.

Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index

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

Lehtikangas, O., E-mail: Ossi.Lehtikangas@uef.fi; Tarvainen, T.; Department of Computer Science, University College London, Gower Street, London WC1E 6BT

2015-02-01

The radiative transport equation can be used as a light transport model in a medium with scattering particles, such as biological tissues. In the radiative transport equation, the refractive index is assumed to be constant within the medium. However, in biomedical media, changes in the refractive index can occur between different tissue types. In this work, light propagation in a medium with piece-wise constant refractive index is considered. Light propagation in each sub-domain with a constant refractive index is modeled using the radiative transport equation and the equations are coupled using boundary conditions describing Fresnel reflection and refraction phenomena onmore » the interfaces between the sub-domains. The resulting coupled system of radiative transport equations is numerically solved using a finite element method. The approach is tested with simulations. The results show that this coupled system describes light propagation accurately through comparison with the Monte Carlo method. It is also shown that neglecting the internal changes of the refractive index can lead to erroneous boundary measurements of scattered light.« less

Fully three-dimensional analysis of high-speed train-track-soil-structure dynamic interaction

NASA Astrophysics Data System (ADS)

Galvín, P.; Romero, A.; Domínguez, J.

2010-11-01

In this paper, a general and fully three dimensional multi-body-finite element-boundary element model, formulated in the time domain to predict vibrations due to train passage at the vehicle, the track and the free field, is presented. The vehicle is modelled as a multi-body system and, therefore, the quasi-static and the dynamic excitation mechanisms due to train passage can be considered. The track is modelled using finite elements. The soil is considered as a homogeneous half-space by the boundary element method. This methodology could be used to take into account local soil discontinuities, underground constructions such as underpasses, and coupling with nearby structures that break the uniformity of the geometry along the track line. The nonlinear behaviour of the structures could be also considered. In the present paper, in order to test the model, vibrations induced by high-speed train passage are evaluated for a ballasted track. The quasi-static and dynamic load components are studied and the influence of the suspended mass on the vertical loads is analyzed. The numerical model is validated by comparison with experimental records from two HST lines. Finally, the dynamic behaviour of a transition zone between a ballast track and a slab track is analyzed and the obtained results from the proposed model are compared with those obtained from a model with invariant geometry with respect to the track direction.

A Finite Element Method for Simulation of Compressible Cavitating Flows

NASA Astrophysics Data System (ADS)

Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad

2016-11-01

This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.

Numerical simulation of temperature field in K9 glass irradiated by ultraviolet pulse laser

NASA Astrophysics Data System (ADS)

Wang, Xi; Fang, Xiaodong

2015-10-01

The optical component of photoelectric system was easy to be damaged by irradiation of high power pulse laser, so the effect of high power pulse laser irradiation on K9 glass was researched. A thermodynamic model of K9 glass irradiated by ultraviolet pulse laser was established using the finite element software ANSYS. The article analyzed some key problems in simulation process of ultraviolet pulse laser damage of K9 glass based on ANSYS from the finite element models foundation, meshing, loading of pulse laser, setting initial conditions and boundary conditions and setting the thermal physical parameters of material. The finite element method (FEM) model was established and a numerical analysis was performed to calculate temperature field in K9 glass irradiated by ultraviolet pulse laser. The simulation results showed that the temperature of irradiation area exceeded the melting point of K9 glass, while the incident laser energy was low. The thermal damage dominated in the damage mechanism of K9 glass, the melting phenomenon should be much more distinct.

Adaptive Finite Element Methods for Continuum Damage Modeling

NASA Technical Reports Server (NTRS)

Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.

1995-01-01

The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.

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

NASA Technical Reports Server (NTRS)

1991-01-01

The fourth year of technical developments on the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) system for Probabilistic Structural Analysis Methods is summarized. The effort focused on the continued expansion of the Probabilistic Finite Element Method (PFEM) code, the implementation of the Probabilistic Boundary Element Method (PBEM), and the implementation of the Probabilistic Approximate Methods (PAppM) code. The principal focus for the PFEM code is the addition of a multilevel structural dynamics capability. The strategy includes probabilistic loads, treatment of material, geometry uncertainty, and full probabilistic variables. Enhancements are included for the Fast Probability Integration (FPI) algorithms and the addition of Monte Carlo simulation as an alternate. Work on the expert system and boundary element developments continues. The enhanced capability in the computer codes is validated by applications to a turbine blade and to an oxidizer duct.

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

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

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Transactions of the Army Conference on Applied Mathematics and Computing (10th) Held at West Point, New York on 16-19 Jun 92

DTIC Science & Technology

1993-03-01

1600 Break 1600 - 1700 General Session IV - Thayer Hall, Room 342 Chairperson: David W. Hislop , U.S. Army Research Office, Research Triangle Park...dynamics studies conducted in the 1950’s and 1960’% using finite difference and finite element methods, and in the 1970’s and 1980 ’s using Green’s...1966. [13] L. C. Young. Lectures on the Calculus of Variations and Optimal Control. Chelsa, 1980 . 68 Kinetically Driven Elastic Phase Boundary Motion

Influence of two-dimensional hygrothermal gradients on interlaminar stresses near free edges

NASA Technical Reports Server (NTRS)

Farley, G. L.; Herakovich, C. T.

1977-01-01

Interlaminar stresses are determined for mechanical loading, uniform hygrothermal loading, and gradient moisture loading through implementation of a finite element computer code. Nonuniform two-dimensional hygroscopic gradients are obtained from a finite difference solution of the diffusion equation. It is shown that hygroscopic induced stresses can be larger than those resulting from mechanical and thermal loading, and that the distribution of the interlaminar normal stress may be changed significantly in the presence of a two-dimensional moisture gradient in the boundary layer of a composite laminate.

Study of flow control by localized volume heating in hypersonic boundary layers

NASA Astrophysics Data System (ADS)

Keller, M. A.; Kloker, M. J.; Kirilovskiy, S. V.; Polivanov, P. A.; Sidorenko, A. A.; Maslov, A. A.

2014-12-01

Boundary-layer flow control is a prerequisite for a safe and efficient operation of future hypersonic transport systems. Here, the influence of an electric discharge—modeled by a heat-source term in the energy equation—on laminar boundary-layer flows over a flat plate with zero pressure gradient at Mach 3, 5, and 7 is investigated numerically. The aim was to appraise the potential of electro-gasdynamic devices for an application as turbulence generators in the super- and hypersonic flow regime. The results with localized heat-source elements in boundary layers are compared to cases with roughness elements serving as classical passive trips. The numerical simulations are performed using the commercial code ANSYS FLUENT (by ITAM) and the high-order finite-difference DNS code NS3D (by IAG), the latter allowing for the detailed analysis of laminar flow instability. For the investigated setups with steady heating, transition to turbulence is not observed, due to the Reynolds-number lowering effect of heating.

Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min-max optimal control problems with uncertainty

NASA Astrophysics Data System (ADS)

Nikooeinejad, Z.; Delavarkhalafi, A.; Heydari, M.

2018-03-01

The difficulty of solving the min-max optimal control problems (M-MOCPs) with uncertainty using generalised Euler-Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler-Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

Heat transfer at microscopic level in a MHD fractional inertial flow confined between non-isothermal boundaries

NASA Astrophysics Data System (ADS)

Shoaib Anwar, Muhammad; Rasheed, Amer

2017-07-01

Heat transfer through a Forchheimer medium in an unsteady magnetohydrodynamic (MHD) developed differential-type fluid flow is analyzed numerically in this study. The boundary layer flow is modeled with the help of the fractional calculus approach. The fluid is confined between infinite parallel plates and flows by motion of the plates in their own plane. Both the plates have variable surface temperature. Governing partial differential equations with appropriate initial and boundary conditions are solved by employing a finite-difference scheme to discretize the fractional time derivative and finite-element discretization for spatial variables. Coefficients of skin friction and local Nusselt numbers are computed for the fractional model. The flow behavior is presented for various values of the involved parameters. The influence of different dimensionless numbers on skin friction and Nusselt number is discussed by tabular results. Forchheimer medium flows that involve catalytic converters and gas turbines can be modeled in a similar manner.

Fictitious Domain Methods for Fracture Models in Elasticity.

NASA Astrophysics Data System (ADS)

Court, S.; Bodart, O.; Cayol, V.; Koko, J.

2014-12-01

As surface displacements depend non linearly on sources location and shape, simplifying assumptions are generally required to reduce computation time when inverting geodetic data. We present a generic Finite Element Method designed for pressurized or sheared cracks inside a linear elastic medium. A fictitious domain method is used to take the crack into account independently of the mesh. Besides the possibility of considering heterogeneous media, the approach permits the evolution of the crack through time or more generally through iterations: The goal is to change the less things we need when the crack geometry is modified; In particular no re-meshing is required (the boundary conditions at the level of the crack are imposed by Lagrange multipliers), leading to a gain of computation time and resources with respect to classic finite element methods. This method is also robust with respect to the geometry, since we expect to observe the same behavior whatever the shape and the position of the crack. We present numerical experiments which highlight the accuracy of our method (using convergence curves), the optimality of errors, and the robustness with respect to the geometry (with computation of errors on some quantities for all kind of geometric configurations). We will also provide 2D benchmark tests. The method is then applied to Piton de la Fournaise volcano, considering a pressurized crack - inside a 3-dimensional domain - and the corresponding computation time and accuracy are compared with results from a mixed Boundary element method. In order to determine the crack geometrical characteristics, and pressure, inversions are performed combining fictitious domain computations with a near neighborhood algorithm. Performances are compared with those obtained combining a mixed boundary element method with the same inversion algorithm.

A Statistical Approach for the Concurrent Coupling of Molecular Dynamics and Finite Element Methods

NASA Technical Reports Server (NTRS)

Saether, E.; Yamakov, V.; Glaessgen, E.

2007-01-01

Molecular dynamics (MD) methods are opening new opportunities for simulating the fundamental processes of material behavior at the atomistic level. However, increasing the size of the MD domain quickly presents intractable computational demands. A robust approach to surmount this computational limitation has been to unite continuum modeling procedures such as the finite element method (FEM) with MD analyses thereby reducing the region of atomic scale refinement. The challenging problem is to seamlessly connect the two inherently different simulation techniques at their interface. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the typical boundary value problem used to define a coupled domain. The method uses statistical averaging of the atomistic MD domain to provide displacement interface boundary conditions to the surrounding continuum FEM region, which, in return, generates interface reaction forces applied as piecewise constant traction boundary conditions to the MD domain. The two systems are computationally disconnected and communicate only through a continuous update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM) as opposed to a direct coupling method where interface atoms and FEM nodes are individually related. The methodology is inherently applicable to three-dimensional domains, avoids discretization of the continuum model down to atomic scales, and permits arbitrary temperatures to be applied.

Global Dynamic Modeling of Space-Geodetic Data

NASA Technical Reports Server (NTRS)

Bird, Peter

1995-01-01

The proposal had outlined a year for program conversion, a year for testing and debugging, and two years for numerical experiments. We kept to that schedule. In first (partial) year, author designed a finite element for isostatic thin-shell deformation on a sphere, derived all of its algebraic and stiffness properties, and embedded it in a new finite element code which derives its basic solution strategy (and some critical subroutines) from earlier flat-Earth codes. Also designed and programmed a new fault element to represent faults along plate boundaries. Wrote a preliminary version of a spherical graphics program for the display of output. Tested this new code for accuracy on individual model plates. Made estimates of the computer-time/cost efficiency of the code for whole-earth grids, which were reasonable. Finally, converted an interactive graphical grid-designer program from Cartesian to spherical geometry to permit the beginning of serious modeling. For reasons of cost efficiency, models are isostatic, and do not consider the local effects of unsupported loads or bending stresses. The requirements are: (1) ability to represent rigid rotation on a sphere; (2) ability to represent a spatially uniform strain-rate tensor in the limit of small elements; and (3) continuity of velocity across all element boundaries. Author designed a 3-node triangle shell element which has two different sets of basis functions to represent (vector) velocity and all other (scalar) variables. Such elements can be shown to converge to the formulas for plane triangles in the limit of small size, but can also applied to cover any area smaller than a hemisphere. The difficult volume integrals involved in computing the stiffness of such elements are performed numerically using 7 Gauss integration points on the surface of the sphere, beneath each of which a vertical integral is performed using about 100 points.

Cortical bone fracture analysis using XFEM - case study.

PubMed

Idkaidek, Ashraf; Jasiuk, Iwona

2017-04-01

We aim to achieve an accurate simulation of human cortical bone fracture using the extended finite element method within a commercial finite element software abaqus. A two-dimensional unit cell model of cortical bone is built based on a microscopy image of the mid-diaphysis of tibia of a 70-year-old human male donor. Each phase of this model, an interstitial bone, a cement line, and an osteon, are considered linear elastic and isotropic with material properties obtained by nanoindentation, taken from literature. The effect of using fracture analysis methods (cohesive segment approach versus linear elastic fracture mechanics approach), finite element type, and boundary conditions (traction, displacement, and mixed) on cortical bone crack initiation and propagation are studied. In this study cohesive segment damage evolution for a traction separation law based on energy and displacement is used. In addition, effects of the increment size and mesh density on analysis results are investigated. We find that both cohesive segment and linear elastic fracture mechanics approaches within the extended finite element method can effectively simulate cortical bone fracture. Mesh density and simulation increment size can influence analysis results when employing either approach, and using finer mesh and/or smaller increment size does not always provide more accurate results. Both approaches provide close but not identical results, and crack propagation speed is found to be slower when using the cohesive segment approach. Also, using reduced integration elements along with the cohesive segment approach decreases crack propagation speed compared with using full integration elements. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Thermal behavior spiral bevel gears. Ph.D. Thesis - Case Western Univ., Aug. 1993

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1995-01-01

An experimental and analytical study of the thermal behavior of spiral bevel gears is presented. Experimental data were taken using thermocoupled test hardware and an infrared microscope. Many operational parameters were varied to investigate their effects on the thermal behavior. The data taken were also used to validate the boundary conditions applied to the analytical model. A finite element-based solution sequence was developed. The three-dimensional model was developed based on the manufacturing process for these gears. Contact between the meshing gears was found using tooth contact analysis to describe the location, curvatures, orientations, and surface velocities. This information was then used in a three-dimensional Hertzian contact analysis to predict contact ellipse size and maximum pressure. From these results, an estimate of the heat flux magnitude and the location on the finite element model was made. The finite element model used time-averaged boundary conditions to permit the solution to attain steady state in a computationally efficient manner.Then time- and position-varying boundary conditions were applied to the model to analyze the cyclic heating and cooling due to the gears meshing and transferring heat to the surroundings, respectively. The model was run in this mode until the temperature behavior stabilized. The transient flash temperature on the surface was therefore described. The analysis can be used to predict the overall expected thermal behavior of spiral bevel gears. The experimental and analytical results were compared for this study and also with a limited number of other studies. The experimental and analytical results attained in the current study were basically within 10% of each other for the cases compared. The experimental comparison was for bulk thermocouple locations and data taken with an infrared microscope. The results of a limited number of other studies were compared with those obtained herein and predicted the same basic behavior.

Probabilistic finite elements for fatigue and fracture analysis

NASA Astrophysics Data System (ADS)

Belytschko, Ted; Liu, Wing Kam

1993-04-01

An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.

Computational plasticity algorithm for particle dynamics simulations

NASA Astrophysics Data System (ADS)

Krabbenhoft, K.; Lyamin, A. V.; Vignes, C.

2018-01-01

The problem of particle dynamics simulation is interpreted in the framework of computational plasticity leading to an algorithm which is mathematically indistinguishable from the common implicit scheme widely used in the finite element analysis of elastoplastic boundary value problems. This algorithm provides somewhat of a unification of two particle methods, the discrete element method and the contact dynamics method, which usually are thought of as being quite disparate. In particular, it is shown that the former appears as the special case where the time stepping is explicit while the use of implicit time stepping leads to the kind of schemes usually labelled contact dynamics methods. The framing of particle dynamics simulation within computational plasticity paves the way for new approaches similar (or identical) to those frequently employed in nonlinear finite element analysis. These include mixed implicit-explicit time stepping, dynamic relaxation and domain decomposition schemes.

Probabilistic finite elements for fatigue and fracture analysis

NASA Technical Reports Server (NTRS)

Belytschko, Ted; Liu, Wing Kam

1993-01-01

An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.

Three-dimensional Finite Element Modelling of Composite Slabs for High Speed Rails

NASA Astrophysics Data System (ADS)

Mlilo, Nhlanganiso; Kaewunruen, Sakdirat

2017-12-01

Currently precast steel-concrete composite slabs are being considered on railway bridges as a viable alternative replacement for timber sleepers. However, due to their nature and the loading conditions, their behaviour is often complex. Present knowledge of the behaviour of precast steel-concrete composite slabs subjected to rail loading is limited. FEA is an important tool used to simulate real life behaviour and is widely accepted in many disciples of engineering as an alternative to experimental test methods, which are often costly and time consuming. This paper seeks to detail FEM of precast steel-concrete slabs subjected to standard in-service loading in high-speed rail with focus on the importance of accurately defining material properties, element type, mesh size, contacts, interactions and boundary conditions that will give results representative of real life behaviour. Initial finite element model show very good results, confirming the accuracy of the modelling procedure

On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations

NASA Astrophysics Data System (ADS)

Schröder, Jörg; Viebahn, Nils; Wriggers, Peter; Auricchio, Ferdinando; Steeger, Karl

2017-09-01

In this work we investigate different mixed finite element formulations for the detection of critical loads for the possible occurrence of bifurcation and limit points. In detail, three- and two-field formulations for incompressible and quasi-incompressible materials are analyzed. In order to apply various penalty functions for the volume dilatation in displacement/pressure mixed elements we propose a new consistent scheme capturing the non linearities of the penalty constraints. It is shown that for all mixed formulations, which can be reduced to a generalized displacement scheme, a straight forward stability analysis is possible. However, problems based on the classical saddle-point structure require a different analyses based on the change of the signature of the underlying matrix system. The basis of these investigations is the work from Auricchio et al. (Comput Methods Appl Mech Eng 194:1075-1092, 2005, Comput Mech 52:1153-1167, 2013).

Isentropic Compression with a Rectangular Configuration for Tungstene and Tantalum, Computations and Comparison with Experiments

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

Lefrancois, A.; Reisman, D. B.; Bastea, M.

2006-02-13

Isentropic compression experiments and numerical simulations on metals are performed at Z accelerator facility from Sandia National Laboratory and at Lawrence Livermore National Laboratory in order to study the isentrope, associated Hugoniot and phase changes of these metals. 3D configurations have been calculated here to benchmark the new beta version of the electromagnetism package coupled with the dynamics in Ls-Dyna and compared with the ICE Z shots 1511 and 1555. The electromagnetism module is being developed in the general-purpose explicit and implicit finite element program LS-DYNA{reg_sign} in order to perform coupled mechanical/thermal/electromagnetism simulations. The Maxwell equations are solved using amore » Finite Element Method (FEM) for the solid conductors coupled with a Boundary Element Method (BEM) for the surrounding air (or vacuum). More details can be read in the references.« less

Isentropic Compression up to 200 KBars for LX 04, Numerical Simulations and Comparison with Experiments

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

Lefrancois, A.; Hare, D.; L'Eplattenier, P.

2006-02-13

Isentropic compression experiments and numerical simulations on LX-04 (HMX / Viton 85/15) were performed respectively at Z accelerator facility from Sandia National Laboratory and at Lawrence Livermore National Laboratory in order to study the isentrope and associated Hugoniot of this HE. 2D and 3D configurations have been calculated here to test the new beta version of the electromagnetism package coupled with the dynamics in Ls-Dyna and compared with the ICE Z shot 1067 on LX 04. The electromagnetism module is being developed in the general-purpose explicit and implicit finite element program LS-DYNA{reg_sign} in order to perform coupled mechanical/thermal/electromagnetism simulations. Themore » Maxwell equations are solved using a Finite Element Method (FEM) for the solid conductors coupled with a Boundary Element Method (BEM) for the surrounding air (or vacuum). More details can be read in the references.« less

Development of 3D electromagnetic modeling tools for airborne vehicles

NASA Technical Reports Server (NTRS)

Volakis, John L.

1992-01-01

The main goal of this project is to develop methodologies for scattering by airborne composite vehicles. Although our primary focus continues to be the development of a general purpose code for analyzing the entire structure as a single unit, a number of other tasks are also pursued in parallel with this effort. These tasks are important in testing the overall approach and in developing suitable models for materials coatings, junctions and, more generally, in assessing the effectiveness of the various parts comprising the final code. Here, we briefly discuss our progress on the five different tasks which were pursued during this period. Our progress on each of these tasks is described in the detailed reports (listed at the end of this report) and the memoranda included. The first task described below is, of course, the core of this project and deals with the development of the overall code. Undoubtedly, it is the outcome of the research which was funded by NASA-Ames and the Navy over the past three years. During this year we developed the first finite element code for scattering by structures of arbitrary shape and composition. The code employs a new absorbing boundary condition which allows termination of the finite element mesh only 0.3 lambda from the outer surface of the target. This leads to a remarkable reduction of the mesh size and is a unique feature of the code. Other unique features of this code include capabilities to model resistive sheets, impedance sheets and anisotropic materials. This last capability is the latest feature of the code and is still under development. The code has been extensively validated for a number of composite geometries and some examples are given. The validation of the code is still in progress for anisotropic and larger non-metallic geometries and cavities. The developed finite element code is based on a Galerkin's formulation and employs edge-based tetrahedral elements for discretizing the dielectric sections and the region between the target and the outer mesh termination boundary (ATB). This boundary is placed in conformity with the target's outer surface, thus resulting in additional reduction of the unknown count.

Elastic critical moment for bisymmetric steel profiles and its sensitivity by the finite difference method

NASA Astrophysics Data System (ADS)

Kamiński, M.; Supeł, Ł.

2016-02-01

It is widely known that lateral-torsional buckling of a member under bending and warping restraints of its cross-sections in the steel structures are crucial for estimation of their safety and durability. Although engineering codes for steel and aluminum structures support the designer with the additional analytical expressions depending even on the boundary conditions and internal forces diagrams, one may apply alternatively the traditional Finite Element or Finite Difference Methods (FEM, FDM) to determine the so-called critical moment representing this phenomenon. The principal purpose of this work is to compare three different ways of determination of critical moment, also in the context of structural sensitivity analysis with respect to the structural element length. Sensitivity gradients are determined by the use of both analytical and the central finite difference scheme here and contrasted also for analytical, FEM as well as FDM approaches. Computational study is provided for the entire family of the steel I- and H - beams available for the practitioners in this area, and is a basis for further stochastic reliability analysis as well as durability prediction including possible corrosion progress.

An integral wall model for Large Eddy Simulation (iWMLES) and applications to developing boundary layers over smooth and rough plates

NASA Astrophysics Data System (ADS)

Yang, Xiang; Sadique, Jasim; Mittal, Rajat; Meneveau, Charles

2014-11-01

A new wall model for Large-Eddy-Simulations is proposed. It is based on an integral boundary layer method that assumes a functional form for the local mean velocity profile. The method, iWMLES, evaluates required unsteady and advective terms in the vertically integrated boundary layer equations analytically. The assumed profile contains a viscous or roughness sublayer, and a logarithmic layer with an additional linear term accounting for inertial and pressure gradient effects. The iWMLES method is tested in the context of a finite difference LES code. Test cases include developing turbulent boundary layers on a smooth flat plate at various Reynolds numbers, over flat plates with unresolved roughness, and a sample application to boundary layer flow over a plate that includes resolved roughness elements. The elements are truncated cones acting as idealized barnacle-like roughness elements that often occur in biofouling of marine surfaces. Comparisons with data show that iWMLES provides accurate predictions of near-wall velocity profiles in LES while, similarly to equilibrium wall models, its cost remains independent of Reynolds number and is thus significantly lower compared to standard zonal or hybrid wall models. This work is funded by ONR Grant N00014-12-1-0582 (Dr. R. Joslin, program manager).

A methodology for constraining power in finite element modeling of radiofrequency ablation.

PubMed

Jiang, Yansheng; Possebon, Ricardo; Mulier, Stefaan; Wang, Chong; Chen, Feng; Feng, Yuanbo; Xia, Qian; Liu, Yewei; Yin, Ting; Oyen, Raymond; Ni, Yicheng

2017-07-01

Radiofrequency ablation (RFA) is a minimally invasive thermal therapy for the treatment of cancer, hyperopia, and cardiac tachyarrhythmia. In RFA, the power delivered to the tissue is a key parameter. The objective of this study was to establish a methodology for the finite element modeling of RFA with constant power. Because of changes in the electric conductivity of tissue with temperature, a nonconventional boundary value problem arises in the mathematic modeling of RFA: neither the voltage (Dirichlet condition) nor the current (Neumann condition), but the power, that is, the product of voltage and current was prescribed on part of boundary. We solved the problem using Lagrange multiplier: the product of the voltage and current on the electrode surface is constrained to be equal to the Joule heating. We theoretically proved the equality between the product of the voltage and current on the surface of the electrode and the Joule heating in the domain. We also proved the well-posedness of the problem of solving the Laplace equation for the electric potential under a constant power constraint prescribed on the electrode surface. The Pennes bioheat transfer equation and the Laplace equation for electric potential augmented with the constraint of constant power were solved simultaneously using the Newton-Raphson algorithm. Three problems for validation were solved. Numerical results were compared either with an analytical solution deduced in this study or with results obtained by ANSYS or experiments. This work provides the finite element modeling of constant power RFA with a firm mathematical basis and opens pathway for achieving the optimal RFA power. Copyright © 2016 John Wiley & Sons, Ltd.

A Dynamic Finite Element Method for Simulating the Physics of Faults Systems

NASA Astrophysics Data System (ADS)

Saez, E.; Mora, P.; Gross, L.; Weatherley, D.

2004-12-01

We introduce a dynamic Finite Element method using a novel high level scripting language to describe the physical equations, boundary conditions and time integration scheme. The library we use is the parallel Finley library: a finite element kernel library, designed for solving large-scale problems. It is incorporated as a differential equation solver into a more general library called escript, based on the scripting language Python. This library has been developed to facilitate the rapid development of 3D parallel codes, and is optimised for the Australian Computational Earth Systems Simulator Major National Research Facility (ACcESS MNRF) supercomputer, a 208 processor SGI Altix with a peak performance of 1.1 TFlops. Using the scripting approach we obtain a parallel FE code able to take advantage of the computational efficiency of the Altix 3700. We consider faults as material discontinuities (the displacement, velocity, and acceleration fields are discontinuous at the fault), with elastic behavior. The stress continuity at the fault is achieved naturally through the expression of the fault interactions in the weak formulation. The elasticity problem is solved explicitly in time, using the Saint Verlat scheme. Finally, we specify a suitable frictional constitutive relation and numerical scheme to simulate fault behaviour. Our model is based on previous work on modelling fault friction and multi-fault systems using lattice solid-like models. We adapt the 2D model for simulating the dynamics of parallel fault systems described to the Finite-Element method. The approach uses a frictional relation along faults that is slip and slip-rate dependent, and the numerical integration approach introduced by Mora and Place in the lattice solid model. In order to illustrate the new Finite Element model, single and multi-fault simulation examples are presented.

Connectivity-based, all-hexahedral mesh generation method and apparatus

DOEpatents

Tautges, T.J.; Mitchell, S.A.; Blacker, T.D.; Murdoch, P.

1998-06-16

The present invention is a computer-based method and apparatus for constructing all-hexahedral finite element meshes for finite element analysis. The present invention begins with a three-dimensional geometry and an all-quadrilateral surface mesh, then constructs hexahedral element connectivity from the outer boundary inward, and then resolves invalid connectivity. The result of the present invention is a complete representation of hex mesh connectivity only; actual mesh node locations are determined later. The basic method of the present invention comprises the step of forming hexahedral elements by making crossings of entities referred to as ``whisker chords.`` This step, combined with a seaming operation in space, is shown to be sufficient for meshing simple block problems. Entities that appear when meshing more complex geometries, namely blind chords, merged sheets, and self-intersecting chords, are described. A method for detecting invalid connectivity in space, based on repeated edges, is also described, along with its application to various cases of invalid connectivity introduced and resolved by the method. 79 figs.

Connectivity-based, all-hexahedral mesh generation method and apparatus

DOEpatents

Tautges, Timothy James; Mitchell, Scott A.; Blacker, Ted D.; Murdoch, Peter

1998-01-01

The present invention is a computer-based method and apparatus for constructing all-hexahedral finite element meshes for finite element analysis. The present invention begins with a three-dimensional geometry and an all-quadrilateral surface mesh, then constructs hexahedral element connectivity from the outer boundary inward, and then resolves invalid connectivity. The result of the present invention is a complete representation of hex mesh connectivity only; actual mesh node locations are determined later. The basic method of the present invention comprises the step of forming hexahedral elements by making crossings of entities referred to as "whisker chords." This step, combined with a seaming operation in space, is shown to be sufficient for meshing simple block problems. Entities that appear when meshing more complex geometries, namely blind chords, merged sheets, and self-intersecting chords, are described. A method for detecting invalid connectivity in space, based on repeated edges, is also described, along with its application to various cases of invalid connectivity introduced and resolved by the method.

Three-dimensional piezoelectric boundary elements

NASA Astrophysics Data System (ADS)

Hill, Lisa Renee

The strong coupling between mechanical and electrical fields in piezoelectric ceramics makes them appropriate for use as actuation devices; as a result, they are an important part of the emerging technologies of smart materials and structures. These piezoceramics are very brittle and susceptible to fracture, especially under the severe loading conditions which may occur in service. A significant portion of the applications under investigation involve dynamic loading conditions. Once a crack is initiated in the piezoelectric medium, the mechanical and electrical fields can act to drive the crack growth. Failure of the actuator can result from a catastrophic fracture event or from the cumulative effects of cyclic fatigue. The presence of these cracks, or other types of material defects, alter the mechanical and electrical fields inside the body. Specifically, concentrations of stress and electric field are present near a flaw and can lead to material yielding or localized depoling, which in turn can affect the sensor/actuator performance or cause failure. Understanding these effects is critical to the success of these smart structures. The complex coupling behavior and the anisotropy of the material makes the use of numerical methods necessary for all but the simplest problems. To this end, a three-dimensional boundary element method program is developed to evaluate the effect of flaws on these piezoelectric materials. The program is based on the linear governing equations of piezoelectricity and relies on a numerically evaluated Green's function for solution. The boundary element method was selected as the evaluation tool due to its ability to model the interior domain exactly. Thus, for piezoelectric materials the coupling between mechanical and electrical fields is not approximated inside the body. Holes in infinite and finite piezoceramics are investigated, with the localized stresses and electric fields clearly developed. The accuracy of the piezoelectric boundary element method is demonstrated with two problems: a two-dimensional circular void and a three-dimensional spherical cavity, both inside infinite solids. Application of the program to a finite body with a centered, spherical void illustrates the complex nature of the mechanical and electrical coupling. Mode I fracture is also examined, combining the linear boundary element solution with the modified crack closure integral to determine strain energy release rates. Experimental research has shown that the strain, rather than the total, energy release rate is a better predictor of crack growth in piezoelectric materials. Solutions for a two-dimensional slit-like crack and for three-dimensional penny and elliptical cracks are presented. These solutions are developed using the insulated crack face electrical boundary condition. Although this boundary condition is used by most researchers, recent discussion indicates that it may not be an accurate model for the slender crack geometry. The boundary element method is used with the penny crack problem to investigate the effect of different electrical boundary conditions on the strain energy release rate. Use of a conductive crack face boundary condition, rather than an insulated one, acts to increase the strain energy release rate for the penny crack. These conductive strain energies are closer to the values determined using a permeable electrical boundary condition than to the original conductive boundary condition ones. It is shown that conclusions about structural integrity are strongly dependent on the choice of boundary conditions.

Studies of Sound Absorption by and Transmission Through Layers of Elastic Noise Control Foams: Finite Element Modeling and Effects of Anisotropy

NASA Astrophysics Data System (ADS)

Kang, Yeon June

In this thesis an elastic-absorption finite element model of isotropic elastic porous noise control materials is first presented as a means of investigating the effects of finite dimension and edge constraints on the sound absorption by, and transmission through, layers of acoustical foams. Methods for coupling foam finite elements with conventional acoustic and structural finite elements are also described. The foam finite element model based on the Biot theory allows for the simultaneous propagation of the three types of waves known to exist in an elastic porous material. Various sets of boundary conditions appropriate for modeling open, membrane-sealed and panel-bonded foam surfaces are formulated and described. Good agreement was achieved when finite element predictions were compared with previously established analytical results for the plane wave absorption coefficient and transmission loss in the case of wave propagation both in foam-filled waveguides and through foam-lined double panel structures of infinite lateral extent. The primary effect of the edge constraints of a foam layer was found to be an acoustical stiffening of the foam. Constraining the ends of the facing panels in foam-lined double panel systems was also found to increase the sound transmission loss significantly in the low frequency range. In addition, a theoretical multi-dimensional model for wave propagation in anisotropic elastic porous materials was developed to study the effect of anisotropy on the sound transmission of foam-lined noise control treatments. The predictions of the theoretical anisotropic model have been compared with experimental measurements for the random incidence sound transmission through double panel structure lined with polyimide foam. The predictions were made by using the measured and estimated macroscopic physical parameters of polyimide foam samples which were known to be anisotropic. It has been found that the macroscopic physical parameters in the direction normal to the face of foam layer play the principal role in determining the acoustical behavior of polyimide foam layers, although more satisfactory agreement between experimental measurements and theoretical predictions of transmission loss is obtained when the anisotropic properties are allowed in the model.

Geometric and boundary element method simulations of acoustic reflections from rough, finite, or non-planar surfaces

NASA Astrophysics Data System (ADS)

Rathsam, Jonathan

This dissertation seeks to advance the current state of computer-based sound field simulations for room acoustics. The first part of the dissertation assesses the reliability of geometric sound-field simulations, which are approximate in nature. The second part of the dissertation uses the rigorous boundary element method (BEM) to learn more about reflections from finite reflectors: planar and non-planar. Acoustical designers commonly use geometric simulations to predict sound fields quickly. Geometric simulation of reflections from rough surfaces is still under refinement. The first project in this dissertation investigates the scattering coefficient, which quantifies the degree of diffuse reflection from rough surfaces. The main result is that predicted reverberation time varies inversely with scattering coefficient if the sound field is nondiffuse. Additional results include a flow chart that enables acoustical designers to gauge how sensitive predicted results are to their choice of scattering coefficient. Geometric acoustics is a high-frequency approximation to wave acoustics. At low frequencies, more pronounced wave phenomena cause deviations between real-world values and geometric predictions. Acoustical designers encounter the limits of geometric acoustics in particular when simulating the low frequency response from finite suspended reflector panels. This dissertation uses the rigorous BEM to develop an improved low-frequency radiation model for smooth, finite reflectors. The improved low frequency model is suggested in two forms for implementation in geometric models. Although BEM simulations require more computation time than geometric simulations, BEM results are highly accurate. The final section of this dissertation uses the BEM to investigate the sound field around non-planar reflectors. The author has added convex edges rounded away from the source side of finite, smooth reflectors to minimize coloration of reflections caused by interference from boundary waves. Although the coloration could not be fully eliminated, the convex edge increases the sound energy reflected into previously nonspecular zones. This excess reflected energy is marginally audible using a standard of 20 dB below direct sound energy. The convex-edged panel is recommended for use when designers want to extend reflected energy spatially beyond the specular reflection zone of a planar panel.

Sound transmission analysis of partially treated MR fluid-based sandwich panels using finite element method

NASA Astrophysics Data System (ADS)

Hemmatian, M.; Sedaghati, R.

2017-04-01

This study aims at developing a finite element model to predict the sound transmission loss (STL) of a multilayer panel partially treated with a Magnetorheological (MR) fluid core layer. MR fluids are smart materials with promising controllable rheological characteristics in which the application of an external magnetic field instantly changes their rheological properties. Partial treatment of sandwich panels with MR fluid core layer provides an opportunity to change stiffness and damping of the structure without significantly increasing the mass. The STL of a finite sandwich panel partially treated with MR fluid is modeled using the finite element (FE) method. Circular sandwich panels with clamped boundary condition and elastic face sheets in which the core layer is segmented circumferentially is considered. The MR fluid core layer is considered as a viscoelastic material with complex shear modulus with the magnetic field and frequency dependent storage and loss moduli. Neglecting the effect of the panel's vibration on the pressure forcing function, the work done by the acoustic pressure is expressed as a function of the blocked pressure in order to calculate the force vector in the equation of the motion of the panel. The governing finite element equation of motion of the MR sandwich panel is then developed to predict the transverse vibration of the panel which can then be utilized to obtain the radiated sound using Green's function. The developed model is used to conduct a systematic parametric study on the effect of different locations of MR fluid treatment on the natural frequencies and the STL.

Quasi-static image-based immersed boundary-finite element model of left ventricle under diastolic loading

PubMed Central

Gao, Hao; Wang, Huiming; Berry, Colin; Luo, Xiaoyu; Griffith, Boyce E

2014-01-01

Finite stress and strain analyses of the heart provide insight into the biomechanics of myocardial function and dysfunction. Herein, we describe progress toward dynamic patient-specific models of the left ventricle using an immersed boundary (IB) method with a finite element (FE) structural mechanics model. We use a structure-based hyperelastic strain-energy function to describe the passive mechanics of the ventricular myocardium, a realistic anatomical geometry reconstructed from clinical magnetic resonance images of a healthy human heart, and a rule-based fiber architecture. Numerical predictions of this IB/FE model are compared with results obtained by a commercial FE solver. We demonstrate that the IB/FE model yields results that are in good agreement with those of the conventional FE model under diastolic loading conditions, and the predictions of the LV model using either numerical method are shown to be consistent with previous computational and experimental data. These results are among the first to analyze the stress and strain predictions of IB models of ventricular mechanics, and they serve both to verify the IB/FE simulation framework and to validate the IB/FE model. Moreover, this work represents an important step toward using such models for fully dynamic fluid–structure interaction simulations of the heart. © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons, Ltd. PMID:24799090

Multiscale Modeling of Grain Boundaries in ZrB2: Structure, Energetics, and Thermal Resistance

NASA Technical Reports Server (NTRS)

Lawson, John W.; Daw, Murray S.; Squire, Thomas H.; Bauschlicher, Charles W., Jr.

2012-01-01

A combination of ab initio, atomistic and finite element methods (FEM) were used to investigate the structures, energetics and lattice thermal conductance of grain boundaries for the ultra high temperature ceramic ZrB2. Atomic models of idealized boundaries were relaxed using density functional theory. Information about bonding across the interfaces was determined from the electron localization function. The Kapitza conductance of larger scale versions of the boundary models were computed using non-equilibrium molecular dynamics. The interfacial thermal parameters together with single crystal thermal conductivities were used as parameters in microstructural computations. FEM meshes were constructed on top of microstructural images. From these computations, the effective thermal conductivity of the polycrystalline structure was determined.

Local Modelling of Groundwater Flow Using Analytic Element Method Three-dimensional Transient Unconfined Groundwater Flow With Partially Penetrating Wells and Ellipsoidal Inhomogeneites

NASA Astrophysics Data System (ADS)

Jankovic, I.; Barnes, R. J.; Soule, R.

2001-12-01

The analytic element method is used to model local three-dimensional flow in the vicinity of partially penetrating wells. The flow domain is bounded by an impermeable horizontal base, a phreatic surface with recharge and a cylindrical lateral boundary. The analytic element solution for this problem contains (1) a fictitious source technique to satisfy the head and the discharge conditions along the phreatic surface, (2) a fictitious source technique to satisfy specified head conditions along the cylindrical boundary, (3) a method of imaging to satisfy the no-flow condition across the impermeable base, (4) the classical analytic solution for a well and (5) spheroidal harmonics to account for the influence of the inhomogeneities in hydraulic conductivity. Temporal variations of the flow system due to time-dependent recharge and pumping are represented by combining the analytic element method with a finite difference method: analytic element method is used to represent spatial changes in head and discharge, while the finite difference method represents temporal variations. The solution provides a very detailed description of local groundwater flow with an arbitrary number of wells of any orientation and an arbitrary number of ellipsoidal inhomogeneities of any size and conductivity. These inhomogeneities may be used to model local hydrogeologic features (such as gravel packs and clay lenses) that significantly influence the flow in the vicinity of partially penetrating wells. Several options for specifying head values along the lateral domain boundary are available. These options allow for inclusion of the model into steady and transient regional groundwater models. The head values along the lateral domain boundary may be specified directly (as time series). The head values along the lateral boundary may also be assigned by specifying the water-table gradient and a head value at a single point (as time series). A case study is included to demonstrate the application of the model in local modeling of the groundwater flow. Transient three-dimensional capture zones are delineated for a site on Prairie Island, MN. Prairie Island is located on the Mississippi River 40 miles south of the Twin Cities metropolitan area. The case study focuses on a well that has been known to contain viral DNA. The objective of the study was to assess the potential for pathogen migration toward the well.

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.

Specialty functions singularity mechanics problems

NASA Technical Reports Server (NTRS)

Sarigul, Nesrin

1989-01-01

The focus is in the development of more accurate and efficient advanced methods for solution of singular problems encountered in mechanics. At present, finite element methods in conjunction with special functions, boolean sum and blending interpolations are being considered. In dealing with systems which contain a singularity, special finite elements are being formulated to be used in singular regions. Further, special transition elements are being formulated to couple the special element to the mesh that models the rest of the system, and to be used in conjunction with 1-D, 2-D and 3-D elements within the same mesh. Computational simulation with a least squares fit is being utilized to construct special elements, if there is an unknown singularity in the system. A novel approach is taken in formulation of the elements in that: (1) the material properties are modified to include time, temperature, coordinate and stress dependant behavior within the element; (2) material properties vary at nodal points of the elements; (3) a hidden-symbolic computation scheme is developed and utilized in formulating the elements; and (4) special functions and boolean sum are utilized in order to interpolate the field variables and their derivatives along the boundary of the elements. It may be noted that the proposed methods are also applicable to fluids and coupled problems.

Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2018-03-01

A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

Elastic properties of rigid fiber-reinforced composites

NASA Astrophysics Data System (ADS)

Chen, J.; Thorpe, M. F.; Davis, L. C.

1995-05-01

We study the elastic properties of rigid fiber-reinforced composites with perfect bonding between fibers and matrix, and also with sliding boundary conditions. In the dilute region, there exists an exact analytical solution. Around the rigidity threshold we find the elastic moduli and Poisson's ratio by decomposing the deformation into a compression mode and a rotation mode. For perfect bonding, both modes are important, whereas only the compression mode is operative for sliding boundary conditions. We employ the digital-image-based method and a finite element analysis to perform computer simulations which confirm our analytical predictions.

Effect of Boundary Conditions on the Axial Compression Buckling of Homogeneous Orthotropic Composite Cylinders in the Long Column Range

NASA Technical Reports Server (NTRS)

Mikulas, Martin M., Jr.; Nemeth, Michael P.; Oremont, Leonard; Jegley, Dawn C.

2011-01-01

Buckling loads for long isotropic and laminated cylinders are calculated based on Euler, Fluegge and Donnell's equations. Results from these methods are presented using simple parameters useful for fundamental design work. Buckling loads for two types of simply supported boundary conditions are calculated using finite element methods for comparison to select cases of the closed form solution. Results indicate that relying on Donnell theory can result in an over-prediction of buckling loads by as much as 40% in isotropic materials.

Thermo-viscoelastic analysis of composite materials

NASA Technical Reports Server (NTRS)

Lin, Kuen Y.; Hwang, I. H.

1989-01-01

The thermo-viscoelastic boundary value problem for anisotropic materials is formulated and a numerical procedure is developed for the efficient analysis of stress and deformation histories in composites. The procedure is based on the finite element method and therefore it is applicable to composite laminates containing geometric discontinuities and complicated boundary conditions. Using the present formulation, the time-dependent stress and strain distributions in both notched and unnotched graphite/epoxy composites have been obtained. The effect of temperature and ply orientation on the creep and relaxation response is also studied.

Finite element analyses of a linear-accelerator electron gun

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

Iqbal, M., E-mail: muniqbal.chep@pu.edu.pk, E-mail: muniqbal@ihep.ac.cn; Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049; Wasy, A.

Thermo-structural analyses of the Beijing Electron-Positron Collider (BEPCII) linear-accelerator, electron gun, were performed for the gun operating with the cathode at 1000 °C. The gun was modeled in computer aided three-dimensional interactive application for finite element analyses through ANSYS workbench. This was followed by simulations using the SLAC electron beam trajectory program EGUN for beam optics analyses. The simulations were compared with experimental results of the assembly to verify its beam parameters under the same boundary conditions. Simulation and test results were found to be in good agreement and hence confirmed the design parameters under the defined operating temperature. The gunmore » is operating continuously since commissioning without any thermal induced failures for the BEPCII linear accelerator.« less

Multi-level adaptive finite element methods. 1: Variation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1979-01-01

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

CHAP-2 heat-transfer analysis of the Fort St. Vrain reactor core

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

Kotas, J.F.; Stroh, K.R.

1983-01-01

The Los Alamos National Laboratory is developing the Composite High-Temperature Gas-Cooled Reactor Analysis Program (CHAP) to provide advanced best-estimate predictions of postulated accidents in gas-cooled reactor plants. The CHAP-2 reactor-core model uses the finite-element method to initialize a two-dimensional temperature map of the Fort St. Vrain (FSV) core and its top and bottom reflectors. The code generates a finite-element mesh, initializes noding and boundary conditions, and solves the nonlinear Laplace heat equation using temperature-dependent thermal conductivities, variable coolant-channel-convection heat-transfer coefficients, and specified internal fuel and moderator heat-generation rates. This paper discusses this method and analyzes an FSV reactor-core accident thatmore » simulates a control-rod withdrawal at full power.« less

Proceedings of the 14th International Conference on the Numerical Simulation of Plasmas

NASA Astrophysics Data System (ADS)

Partial Contents are as follows: Numerical Simulations of the Vlasov-Maxwell Equations by Coupled Particle-Finite Element Methods on Unstructured Meshes; Electromagnetic PIC Simulations Using Finite Elements on Unstructured Grids; Modelling Travelling Wave Output Structures with the Particle-in-Cell Code CONDOR; SST--A Single-Slice Particle Simulation Code; Graphical Display and Animation of Data Produced by Electromagnetic, Particle-in-Cell Codes; A Post-Processor for the PEST Code; Gray Scale Rendering of Beam Profile Data; A 2D Electromagnetic PIC Code for Distributed Memory Parallel Computers; 3-D Electromagnetic PIC Simulation on the NRL Connection Machine; Plasma PIC Simulations on MIMD Computers; Vlasov-Maxwell Algorithm for Electromagnetic Plasma Simulation on Distributed Architectures; MHD Boundary Layer Calculation Using the Vortex Method; and Eulerian Codes for Plasma Simulations.

A globally well-posed finite element algorithm for aerodynamics applications

NASA Technical Reports Server (NTRS)

Iannelli, G. S.; Baker, A. J.

1991-01-01

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

Theoretical prediction on corrugated sandwich panels under bending loads

NASA Astrophysics Data System (ADS)

Shu, Chengfu; Hou, Shujuan

2018-05-01

In this paper, an aluminum corrugated sandwich panel with triangular core under bending loads was investigated. Firstly, the equivalent material parameters of the triangular corrugated core layer, which could be considered as an orthotropic panel, were obtained by using Castigliano's theorem and equivalent homogeneous model. Secondly, contributions of the corrugated core layer and two face panels were both considered to compute the equivalent material parameters of the whole structure through the classical lamination theory, and these equivalent material parameters were compared with finite element analysis solutions. Then, based on the Mindlin orthotropic plate theory, this study obtain the closed-form solutions of the displacement for a corrugated sandwich panel under bending loads in specified boundary conditions, and parameters study and comparison by the finite element method were executed simultaneously.

Numerical calculations of velocity and pressure distribution around oscillating airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.; Kobiske, M.

1974-01-01

An analytical procedure based on the Navier-Stokes equations was developed for analyzing and representing properties of unsteady viscous flow around oscillating obstacles. A variational formulation of the vorticity transport equation was discretized in finite element form and integrated numerically. At each time step of the numerical integration, the velocity field around the obstacle was determined for the instantaneous vorticity distribution from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints, using the Lagrangian Multiplier Technique, at each time step of the numerical integration. The procedure was then applied for determining pressures around obstacles oscillating in unsteady flow. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

An accurate and efficient acoustic eigensolver based on a fast multipole BEM and a contour integral method

NASA Astrophysics Data System (ADS)

Zheng, Chang-Jun; Gao, Hai-Feng; Du, Lei; Chen, Hai-Bo; Zhang, Chuanzeng

2016-01-01

An accurate numerical solver is developed in this paper for eigenproblems governed by the Helmholtz equation and formulated through the boundary element method. A contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem, so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations. In order to accelerate the solution procedure, the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared. Moreover, a wideband fast multipole method is implemented with a block IDR (s) solver to reduce the overall solution cost of the boundary element systems of equations with multiple right-hand sides. The Burton-Miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains. The actual effect of the Burton-Miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as α = i / k is confirmed through exterior sphere examples. Furthermore, the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method.

3-D inelastic analysis methods for hot section components (base program). [turbine blades, turbine vanes, and combustor liners

NASA Technical Reports Server (NTRS)

Wilson, R. B.; Bak, M. J.; Nakazawa, S.; Banerjee, P. K.

1984-01-01

A 3-D inelastic analysis methods program consists of a series of computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of combustor liners, turbine blades, and turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain) and global (dynamics, buckling) structural behavior of the three selected components. These models are used to solve 3-D inelastic problems using linear approximations in the sense that stresses/strains and temperatures in generic modeling regions are linear functions of the spatial coordinates, and solution increments for load, temperature and/or time are extrapolated linearly from previous information. Three linear formulation computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (MARC-Hot Section Technology), and BEST (Boundary Element Stress Technology), were developed and are described.

Continuum and crystal strain gradient plasticity with energetic and dissipative length scales

NASA Astrophysics Data System (ADS)

Faghihi, Danial

This work, standing as an attempt to understand and mathematically model the small scale materials thermal and mechanical responses by the aid of Materials Science fundamentals, Continuum Solid Mechanics, Misro-scale experimental observations, and Numerical methods. Since conventional continuum plasticity and heat transfer theories, based on the local thermodynamic equilibrium, do not account for the microstructural characteristics of materials, they cannot be used to adequately address the observed mechanical and thermal response of the micro-scale metallic structures. Some of these cases, which are considered in this dissertation, include the dependency of thin films strength on the width of the sample and diffusive-ballistic response of temperature in the course of heat transfer. A thermodynamic-based higher order gradient framework is developed in order to characterize the mechanical and thermal behavior of metals in small volume and on the fast transient time. The concept of the thermal activation energy, the dislocations interaction mechanisms, nonlocal energy exchange between energy carriers and phonon-electrons interactions are taken into consideration in proposing the thermodynamic potentials such as Helmholtz free energy and rate of dissipation. The same approach is also adopted to incorporate the effect of the material microstructural interface between two materials (e.g. grain boundary in crystals) into the formulation. The developed grain boundary flow rule accounts for the energy storage at the grain boundary due to the dislocation pile up as well as energy dissipation caused by the dislocation transfer through the grain boundary. Some of the abovementioned responses of small scale metallic compounds are addressed by means of the numerical implementation of the developed framework within the finite element context. In this regard, both displacement and plastic strain fields are independently discretized and the numerical implementation is performed in the finite element program ABAQUS/standard via the user element subroutine UEL. Using this numerical capability, an extensive study is conducted on the major characteristics of the proposed theories for bulk and interface such as size effect on yield and kinematic hardening, features of boundary layer formation, thermal softening and grain boundary weakening, and the effect of soft and stiff interfaces.

The effect of boundary constraints on finite element modelling of the human pelvis.

PubMed

Watson, Peter J; Dostanpor, Ali; Fagan, Michael J; Dobson, Catherine A

2017-05-01

The use of finite element analysis (FEA) to investigate the biomechanics of anatomical systems critically relies on the specification of physiologically representative boundary conditions. The biomechanics of the pelvis has been the specific focus of a number of FEA studies previously, but it is also a key aspect in other investigations of, for example, the hip joint or new design of hip prostheses. In those studies, the pelvis has been modelled in a number of ways with a variety of boundary conditions, ranging from a model of the whole pelvic girdle including soft tissue attachments to a model of an isolated hemi-pelvis. The current study constructed a series of FEA models of the same human pelvis to investigate the sensitivity of the predicted stress distributions to the type of boundary conditions applied, in particular to represent the sacro-iliac joint and pubic symphysis. Varying the method of modelling the sacro-iliac joint did not produce significant variations in the stress distribution, however changes to the modelling of the pubic symphysis were observed to have a greater effect on the results. Over-constraint of the symphysis prevented the bending of the pelvis about the greater sciatic notch, and underestimated high stresses within the ilium. However, permitting medio-lateral translation to mimic widening of the pelvis addressed this problem. These findings underline the importance of applying the appropriate boundary conditions to FEA models, and provide guidance on suitable methods of constraining the pelvis when, for example, scan data has not captured the full pelvic girdle. The results also suggest a valid method for performing hemi-pelvic modelling of cadaveric or archaeological remains which are either damaged or incomplete. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

Incompressible Navier-Stokes and parabolized Navier-Stokes solution procedures and computational techniques

NASA Technical Reports Server (NTRS)

Rubin, S. G.

1982-01-01

Recent developments with finite-difference techniques are emphasized. The quotation marks reflect the fact that any finite discretization procedure can be included in this category. Many so-called finite element collocation and galerkin methods can be reproduced by appropriate forms of the differential equations and discretization formulas. Many of the difficulties encountered in early Navier-Stokes calculations were inherent not only in the choice of the different equations (accuracy), but also in the method of solution or choice of algorithm (convergence and stability, in the manner in which the dependent variables or discretized equations are related (coupling), in the manner that boundary conditions are applied, in the manner that the coordinate mesh is specified (grid generation), and finally, in recognizing that for many high Reynolds number flows not all contributions to the Navier-Stokes equations are necessarily of equal importance (parabolization, preferred direction, pressure interaction, asymptotic and mathematical character). It is these elements that are reviewed. Several Navier-Stokes and parabolized Navier-Stokes formulations are also presented.

Tectonic stressing in California modeled from GPS observations

USGS Publications Warehouse

Parsons, T.

2006-01-01

What happens in the crust as a result of geodetically observed secular motions? In this paper we find out by distorting a finite element model of California using GPS-derived displacements. A complex model was constructed using spatially varying crustal thickness, geothermal gradient, topography, and creeping faults. GPS velocity observations were interpolated and extrapolated across the model and boundary condition areas, and the model was loaded according to 5-year displacements. Results map highest differential stressing rates in a 200-km-wide band along the Pacific-North American plate boundary, coinciding with regions of greatest seismic energy release. Away from the plate boundary, GPS-derived crustal strain reduces modeled differential stress in some places, suggesting that some crustal motions are related to topographic collapse. Calculated stressing rates can be resolved onto fault planes: useful for addressing fault interactions and necessary for calculating earthquake advances or delays. As an example, I examine seismic quiescence on the Garlock fault despite a calculated minimum 0.1-0.4 MPa static stress increase from the 1857 M???7.8 Fort Tejon earthquake. Results from finite element modeling show very low to negative secular Coulomb stress growth on the Garlock fault, suggesting that the stress state may have been too low for large earthquake triggering. Thus the Garlock fault may only be stressed by San Andreas fault slip, a loading pattern that could explain its erratic rupture history.

Influence of parafunctional loading and prosthetic connection on stress distribution: a 3D finite element analysis.

PubMed

Torcato, Leonardo Bueno; Pellizzer, Eduardo Piza; Verri, Fellippo Ramos; Falcón-Antenucci, Rosse Mary; Santiago Júnior, Joel Ferreira; de Faria Almeida, Daniel Augusto

2015-11-01

Clinicians should consider parafunctional occlusal load when planning treatment. Prosthetic connections can reduce the stress distribution on an implant-supported prosthesis. The purpose of this 3-dimensional finite element study was to assess the influence of parafunctional loading and prosthetic connections on stress distribution. Computer-aided design software was used to construct 3 models. Each model was composed of a bone and an implant (external hexagon, internal hexagon, or Morse taper) with a crown. Finite element analysis software was used to generate the finite element mesh and establish the loading and boundary conditions. A normal force (200-N axial load and 100-N oblique load) and parafunctional force (1000-N axial and 500-N oblique load) were applied. Results were visualized as the maximum principal stress. Three-way analysis of variance and Tukey test were performed, and the percentage of contribution of each variable to the stress concentration was calculated from sum-of squares-analysis. Stress was concentrated around the implant at the cortical bone, and models with the external hexagonal implant showed the highest stresses (P<.001). Oblique loads produced high tensile stress concentrations on the site opposite the load direction. Internal connection implants presented the most favorable biomechanical situation, whereas the least favorable situation was the biomechanical behavior of external connection implants. Parafunctional loading increased the magnitude of stress by 3 to 4 times. Copyright © 2015 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.

A Semi-Analytical Method for Determining the Energy Release Rate of Cracks in Adhesively-Bonded Single-Lap Composite Joints

NASA Technical Reports Server (NTRS)

Yang, Charles; Sun, Wenjun; Tomblin, John S.; Smeltzer, Stanley S., III

2007-01-01

A semi-analytical method for determining the strain energy release rate due to a prescribed interface crack in an adhesively-bonded, single-lap composite joint subjected to axial tension is presented. The field equations in terms of displacements within the joint are formulated by using first-order shear deformable, laminated plate theory together with kinematic relations and force equilibrium conditions. The stress distributions for the adherends and adhesive are determined after the appropriate boundary and loading conditions are applied and the equations for the field displacements are solved. Based on the adhesive stress distributions, the forces at the crack tip are obtained and the strain energy release rate of the crack is determined by using the virtual crack closure technique (VCCT). Additionally, the test specimen geometry from both the ASTM D3165 and D1002 test standards are utilized during the derivation of the field equations in order to correlate analytical models with future test results. The system of second-order differential field equations is solved to provide the adherend and adhesive stress response using the symbolic computation tool, Maple 9. Finite element analyses using J-integral as well as VCCT were performed to verify the developed analytical model. The finite element analyses were conducted using the commercial finite element analysis software ABAQUS. The results determined using the analytical method correlated well with the results from the finite element analyses.

2.5D Finite/infinite Element Approach for Simulating Train-Induced Ground Vibrations

NASA Astrophysics Data System (ADS)

Yang, Y. B.; Hung, H. H.; Kao, J. C.

2010-05-01

The 2.5D finite/infinite element approach for simulating the ground vibrations by surface or underground moving trains will be briefly summarized in this paper. By assuming the soils to be uniform along the direction of the railway, only a two-dimensional profile of the soil perpendicular to the railway need be considered in the modeling. Besides the two in-plane degrees of freedom (DOFs) per node conventionally used for plane strain elements, an extra DOF is introduced to account for the out-of-plane wave transmission. The profile of the half-space is divided into a near field and a semi-infinite far field. The near field containing the train loads and irregular structures is simulated by the finite elements, while the far field covering the soils with infinite boundary by the infinite elements, by which due account is taken of the radiation effects for the moving loads. Enhanced by the automated mesh expansion procedure proposed previously by the writers, the far field impedances for all the lower frequencies are generated repetitively from the mesh created for the highest frequency considered. Finally, incorporated with a proposed load generation mechanism that takes the rail irregularity and dynamic properties of trains into account, an illustrative case study was performed. This paper investigates the vibration isolation effect of the elastic foundation that separates the concrete slab track from the underlying soil or tunnel structure. In addition, the advantage of the 2.5D approach was clearly demonstrated in that the three-dimensional wave propagation effect can be virtually captured using a two-dimensional finite/infinite element mesh. Compared with the conventional 3D approach, the present approach appears to be simple, efficient and generally accurate.

Neurosurgery simulation using non-linear finite element modeling and haptic interaction

NASA Astrophysics Data System (ADS)

Lee, Huai-Ping; Audette, Michel; Joldes, Grand R.; Enquobahrie, Andinet

2012-02-01

Real-time surgical simulation is becoming an important component of surgical training. To meet the realtime requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.

Boundary states at reflective moving boundaries

NASA Astrophysics Data System (ADS)

Acosta Minoli, Cesar A.; Kopriva, David A.

2012-06-01

We derive and evaluate boundary states for Maxwell's equations, the linear, and the nonlinear Euler gas-dynamics equations to compute wave reflection from moving boundaries. In this study we use a Discontinuous Galerkin Spectral Element method (DGSEM) with Arbitrary Lagrangian-Eulerian (ALE) mapping for the spatial approximation, but the boundary states can be used with other methods, like finite volume schemes. We present four studies using Maxwell's equations, one for the linear Euler equations, and one more for the nonlinear Euler equations. These are: reflection of light from a plane mirror moving at constant velocity, reflection of light from a moving cylinder, reflection of light from a vibrating mirror, reflection of sound from a plane wall and dipole sound generation by an oscillating cylinder in an inviscid flow. The studies show that the boundary states preserve spectral convergence in the solution and in derived quantities like divergence and vorticity.

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

On Raviart-Thomas and VMS formulations for flow in heterogeneous materials.

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

Turner, Daniel Zack

It is well known that the continuous Galerkin method (in its standard form) is not locally conservative, yet many stabilized methods are constructed by augmenting the standard Galerkin weak form. In particular, the Variational Multiscale (VMS) method has achieved popularity for combating numerical instabilities that arise for mixed formulations that do not otherwise satisfy the LBB condition. Among alternative methods that satisfy local and global conservation, many employ Raviart-Thomas function spaces. The lowest order Raviart-Thomas finite element formulation (RT0) consists of evaluating fluxes over the midpoint of element edges and constant pressures within the element. Although the RT0 element posesmore » many advantages, it has only been shown viable for triangular or tetrahedral elements (quadrilateral variants of this method do not pass the patch test). In the context of heterogenous materials, both of these methods have been used to model the mixed form of the Darcy equation. This work aims, in a comparative fashion, to evaluate the strengths and weaknesses of either approach for modeling Darcy flow for problems with highly varying material permeabilities and predominantly open flow boundary conditions. Such problems include carbon sequestration and enhanced oil recovery simulations for which the far-field boundary is typically described with some type of pressure boundary condition. We intend to show the degree to which the VMS formulation violates local mass conservation for these types of problems and compare the performance of the VMS and RT0 methods at boundaries between disparate permeabilities.« less

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.