The GPRIME approach to finite element modeling
NASA Technical Reports Server (NTRS)
Wallace, D. R.; Mckee, J. H.; Hurwitz, M. M.
1983-01-01
GPRIME, an interactive modeling system, runs on the CDC 6000 computers and the DEC VAX 11/780 minicomputer. This system includes three components: (1) GPRIME, a user friendly geometric language and a processor to translate that language into geometric entities, (2) GGEN, an interactive data generator for 2-D models; and (3) SOLIDGEN, a 3-D solid modeling program. Each component has a computer user interface of an extensive command set. All of these programs make use of a comprehensive B-spline mathematics subroutine library, which can be used for a wide variety of interpolation problems and other geometric calculations. Many other user aids, such as automatic saving of the geometric and finite element data bases and hidden line removal, are available. This interactive finite element modeling capability can produce a complete finite element model, producing an output file of grid and element data.
Variational approach to probabilistic finite elements
NASA Technical Reports Server (NTRS)
Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.
1991-01-01
Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
Variational approach to probabilistic finite elements
NASA Technical Reports Server (NTRS)
Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.
1987-01-01
Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
Slave finite elements: The temporal element approach to nonlinear analysis
NASA Technical Reports Server (NTRS)
Gellin, S.
1984-01-01
A formulation method for finite elements in space and time incorporating nonlinear geometric and material behavior is presented. The method uses interpolation polynomials for approximating the behavior of various quantities over the element domain, and only explicit integration over space and time. While applications are general, the plate and shell elements that are currently being programmed are appropriate to model turbine blades, vanes, and combustor liners.
A finite element approach for prediction of aerothermal loads
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Vemaganti, G.
1986-01-01
A Taylor-Galerkin finite element approach is presented for analysis of high speed viscous flows with an emphasis on predicting heating rates. Five computational issues relevant to the computation of steady flows are examined. Numerical results for supersonic and hypersonic problems address the computational issues and demonstrate the validity for the approach for analysis of high speed flows.
Coupled finite-difference/finite-element approach for wing-body aeroelasticity
NASA Technical Reports Server (NTRS)
Guruswamy, Guru P.
1992-01-01
Computational methods using finite-difference approaches for fluids and finite-element approaches for structures have individually advanced to solve almost full-aircraft configurations. However, coupled approaches to solve fluid/structural interaction problems are still in their early stages of development, particularly for complex geometries using complete equations such as the Euler/Navier-Stokes equations. Earlier work demonstrated the success of coupling finite-difference and finite-element methods for simple wing configurations using the Euler/Navier-Stokes equations. In this paper, the same approach is extended for general wing-body configurations. The structural properties are represented by beam-type finite elements. The flow is modeled using the Euler/Navier-Stokes equations. A general procedure to fully couple structural finite-element boundary conditions with fluid finite-difference boundary conditions is developed for wing-body configurations. Computations are made using moving grids that adapt to wing-body structural deformations. Results are illustrated for a typical wing-body configuration.
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.
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.
Neutral solute transport across osteochondral interface: A finite element approach.
Arbabi, Vahid; Pouran, Behdad; Weinans, Harrie; Zadpoor, Amir A
2016-12-08
Investigation of the solute transfer across articular cartilage and subchondral bone plate could nurture the understanding of the mechanisms of osteoarthritis (OA) progression. In the current study, we approached the transport of neutral solutes in human (slight OA) and equine (healthy) samples using both computed tomography and biphasic-solute finite element modeling. We developed a multi-zone biphasic-solute finite element model (FEM) accounting for the inhomogeneity of articular cartilage (superficial, middle and deep zones) and subchondral bone plate. Fitting the FEM model to the concentration-time curves of the cartilage and the equilibrium concentration of the subchondral plate/calcified cartilage enabled determination of the diffusion coefficients in the superficial, middle and deep zones of cartilage and subchondral plate. We found slightly higher diffusion coefficients for all zones in the human samples as compared to the equine samples. Generally the diffusion coefficient in the superficial zone of human samples was about 3-fold higher than the middle zone, the diffusion coefficient of the middle zone was 1.5-fold higher than that of the deep zone, and the diffusion coefficient of the deep zone was 1.5-fold higher than that of the subchondral plate/calcified cartilage. Those ratios for equine samples were 9, 2 and 1.5, respectively. Regardless of the species considered, there is a gradual decrease of the diffusion coefficient as one approaches the subchondral plate, whereas the rate of decrease is dependent on the type of species. Copyright © 2016 Elsevier Ltd. All rights reserved.
A finite element approach to x-ray optics design
NASA Astrophysics Data System (ADS)
Honkanen, A. P.; Ferrero, C.; Guigay, J. P.; Mocella, V.
2017-05-01
Dynamical diffraction in a deformed (often bent) crystal is described by the Takagi equations 1 which, in general, have to be solved numerically on a regular 2-D grid of points representing a planar cross section of the crystal in which the diffraction of an incident X-ray wavefront occurs . Presently, the majority of numerical approaches are based on a finite difference solving scheme2-4 which can be easily implemented on a regular Cartesian grid but is not suitable for deformed meshes. In this case, the inner deformed crystal structure can be taken into account, but not the shape of the crystal surface if this differs substantially from a planar profile 5,6. Conversely, a finite element method (FEM) can be easily applied to a deformed mesh and serves very well to the purpose of modelling any incident wave on an arbitrarily shaped entrance surface 7 e.g. that of a bent crystal or a crystal submitted to a strong heat load 8-10. For instance, the cylindrical shape of the surface of a strongly bent crystal plate can easily be taken into account in a FEM calculation. Bent crystals are often used as focusing optical elements in Xray beamlines 11-13. In the following, we show the implementation of a general numerical framework for describing the propagation of X-rays inside a crystal based on the solution of the Takagi equations via the COMSOL Multiphysics FEM software package (www.comsol.com). A cylindrically bent crystal will be taken as an example to illustrate the capabilities of the new approach.
Finite element approach for transient analysis of multibody systems
NASA Technical Reports Server (NTRS)
Wu, Shih-Chin; Chang, Che-Wei; Housner, Jerrold M.
1992-01-01
A three-dimensional, finite element based formulation for the transient dynamics of constrained multibody systems with trusslike configurations is presented. A convected coordinate system is used to define the rigid-body motion of individual elements in the system. Deformation of each element is defined relative to its convected coordinate system. The formulation is oriented toward joint-dominated structures. Through a series of sequential transformations, the joint degree of freedom is built into the equations of motion of the element to reduce geometric constraints. Based on the derivation, a general-purpose code has been developed. Two examples are presented to illustrate the application of the code.
Galvanic coupling transmission in intrabody communication: a finite element approach.
Amparo Callejón, M; Reina-Tosina, Javier; Naranjo-Hernández, David; Roa, Laura M
2014-03-01
Galvanic coupling in intrabody communication (IBC) is a technique that couples low-power and low-frequency voltages and currents into the human body, which acts as a transmission medium, and thus constitutes a promising approach in the design of personal health devices. Despite important advances being made during recent years, the investigation of relevant galvanic IBC parameters, including the influence of human tissues and different electrode configurations, still requires further research efforts. The objective of this work is to disclose knowledge into IBC galvanic coupling transmission mechanisms by using a realistic 3-D finite element model of the human arm. Unlike other computational models for IBC, we have modeled the differential configuration of the galvanic coupling as a four-port network in order to analyze the electric field distribution and current density through different tissues. This has allowed us to provide an insight into signal transmission paths through the human body, showing them to be considerably dependent on variables such as frequency and inter-electrode distance. In addition, other important variables, for example bioimpedance and pathloss, have also been analyzed. Finally, experimental measurements were also carried out for the sake of validation, demonstrating the reliability of the model to emulate in general forms some of the behaviors observed in practice.
Biomechanical simulation of thorax deformation using finite element approach.
Zhang, Guangzhi; Chen, Xian; Ohgi, Junji; Miura, Toshiro; Nakamoto, Akira; Matsumura, Chikanori; Sugiura, Seiryo; Hisada, Toshiaki
2016-02-06
The biomechanical simulation of the human respiratory system is expected to be a useful tool for the diagnosis and treatment of respiratory diseases. Because the deformation of the thorax significantly influences airflow in the lungs, we focused on simulating the thorax deformation by introducing contraction of the intercostal muscles and diaphragm, which are the main muscles responsible for the thorax deformation during breathing. We constructed a finite element model of the thorax, including the rib cage, intercostal muscles, and diaphragm. To reproduce the muscle contractions, we introduced the Hill-type transversely isotropic hyperelastic continuum skeletal muscle model, which allows the intercostal muscles and diaphragm to contract along the direction of the fibres with clinically measurable muscle activation and active force-length relationship. The anatomical fibre orientations of the intercostal muscles and diaphragm were introduced. Thorax deformation consists of movements of the ribs and diaphragm. By activating muscles, we were able to reproduce the pump-handle and bucket-handle motions for the ribs and the clinically observed motion for the diaphragm. In order to confirm the effectiveness of this approach, we simulated the thorax deformation during normal quiet breathing and compared the results with four-dimensional computed tomography (4D-CT) images for verification. Thorax deformation can be simulated by modelling the respiratory muscles according to continuum mechanics and by introducing muscle contractions. The reproduction of representative motions of the ribs and diaphragm and the comparison of the thorax deformations during normal quiet breathing with 4D-CT images demonstrated the effectiveness of the proposed approach. This work may provide a platform for establishing a computational mechanics model of the human respiratory system.
Finite element meshing approached as a global minimization process
WITKOWSKI,WALTER R.; JUNG,JOSEPH; DOHRMANN,CLARK R.; LEUNG,VITUS J.
2000-03-01
The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within a charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested
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.
A nonlinear dynamic finite element approach for simulating muscular hydrostats.
Vavourakis, V; Kazakidi, A; Tsakiris, D P; Ekaterinaris, J A
2014-01-01
An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching.
A CAD Approach to Integrating NDE With Finite Element
NASA Technical Reports Server (NTRS)
Abdul-Aziz, Ali; Downey, James; Ghosn, Louis J.; Baaklini, George Y.
2004-01-01
Nondestructive evaluation (NDE) is one of several technologies applied at NASA Glenn Research Center to determine atypical deformities, cracks, and other anomalies experienced by structural components. NDE consists of applying high-quality imaging techniques (such as x-ray imaging and computed tomography (CT)) to discover hidden manufactured flaws in a structure. Efforts are in progress to integrate NDE with the finite element (FE) computational method to perform detailed structural analysis of a given component. This report presents the core outlines for an in-house technical procedure that incorporates this combined NDE-FE interrelation. An example is presented to demonstrate the applicability of this analytical procedure. FE analysis of a test specimen is performed, and the resulting von Mises stresses and the stress concentrations near the anomalies are observed, which indicates the fidelity of the procedure. Additional information elaborating on the steps needed to perform such an analysis is clearly presented in the form of mini step-by-step guidelines.
A new approach in cascade flow analysis using the finite element method
NASA Technical Reports Server (NTRS)
Baskharone, E.; Hamed, A.
1980-01-01
A new approach in analyzing the potential flow past cascades and single airfoils using the finite element method is developed. In this analysis the circulation around the airfoil is not externally imposed but is directly computed in the numerical solution. Different finite element discretization patterns, orders of piecewise approximation, and grid sizes are used in the solution. The results obtained are compared with existing experimental measurements and exact solutions in cascades and single airfoils.
NASA Astrophysics Data System (ADS)
Ballandras, S.; Lardat, R.; Wilm, M.; Pastureaud, Th.; Reinhardt, A.; Champavert, N.; Steichen, W.; Daniau, W.; Laude, V.; Armati, R.; Martin, G.
2009-01-01
The development of new surface acoustic wave devices exhibiting complicated electrode patterns or layered excitation transducers has been favored by an intense innovative activity in this area. For instance, devices exhibiting interdigital transducers covered by piezoelectric or dielectric layers have been fabricated and tested, but the design of such structures requires simulation tools capable to accurately take into account the actual shape of the wave guide elements. A modeling approach able to address complicated surface acoustic wave periodic structures (defined in the saggital plane) exhibiting any geometry then has been developed and implemented. It is based on the combination of a finite element analysis and a boundary element method. A first validation of the computation is reported by comparison with standard surface wave devices. Surface transverse wave resonators covered by amorphous silica have been built and consequently used for theory/experiment assessment. Also the case of recessed electrodes has been considered. The proposed model offers large opportunities for modeling any two-dimensional periodic elastic wave guide.
NASA Astrophysics Data System (ADS)
Arbatani, Siamak; Callejo, Alfonso; Kövecses, József; Kalantari, Masoud; Marchand, Nick R.; Dargahi, Javad
2016-06-01
Directional drilling is a popular technique for oil well drilling. Accurate prediction of the directional performance is critical in order to achieve the desired well profile. Simplified geometry methods are, to date, the industry standard for predicting directional performance. A comprehensive, high-fidelity method for the simulation of directional drilling is presented here. It consists of a detailed discretization of the actual geometry and a rigorous application of two modeling techniques: the finite element and the finite segment methods. By doing so, the dynamic problem is addressed from two different yet complementary perspectives: structural mechanics and rigid-body motion. Collision detection and contact dynamics algorithms are also presented. Results show that both methods agree in terms of the dynamic response, and that the build rate estimations are consistent with available experimental data. Owing to the framework efficiency and physics-based nature, the presented tools are very well-suited for design engineering and real-time simulation.
Brigham, John C.; Aquino, Wilkins; Aguilo, Miguel A.; Diamessis, Peter J.
2010-01-01
An approach for efficient and accurate finite element analysis of harmonically excited soft solids using high-order spectral finite elements is presented and evaluated. The Helmholtz-type equations used to model such systems suffer from additional numerical error known as pollution when excitation frequency becomes high relative to stiffness (i.e. high wave number), which is the case, for example, for soft tissues subject to ultrasound excitations. The use of high-order polynomial elements allows for a reduction in this pollution error, but requires additional consideration to counteract Runge's phenomenon and/or poor linear system conditioning, which has led to the use of spectral element approaches. This work examines in detail the computational benefits and practical applicability of high-order spectral elements for such problems. The spectral elements examined are tensor product elements (i.e. quad or brick elements) of high-order Lagrangian polynomials with non-uniformly distributed Gauss-Lobatto-Legendre nodal points. A shear plane wave example is presented to show the dependence of the accuracy and computational expense of high-order elements on wave number. Then, a convergence study for a viscoelastic acoustic-structure interaction finite element model of an actual ultrasound driven vibroacoustic experiment is shown. The number of degrees of freedom required for a given accuracy level was found to consistently decrease with increasing element order. However, the computationally optimal element order was found to strongly depend on the wave number. PMID:21461402
Brigham, John C; Aquino, Wilkins; Aguilo, Miguel A; Diamessis, Peter J
2011-01-15
An approach for efficient and accurate finite element analysis of harmonically excited soft solids using high-order spectral finite elements is presented and evaluated. The Helmholtz-type equations used to model such systems suffer from additional numerical error known as pollution when excitation frequency becomes high relative to stiffness (i.e. high wave number), which is the case, for example, for soft tissues subject to ultrasound excitations. The use of high-order polynomial elements allows for a reduction in this pollution error, but requires additional consideration to counteract Runge's phenomenon and/or poor linear system conditioning, which has led to the use of spectral element approaches. This work examines in detail the computational benefits and practical applicability of high-order spectral elements for such problems. The spectral elements examined are tensor product elements (i.e. quad or brick elements) of high-order Lagrangian polynomials with non-uniformly distributed Gauss-Lobatto-Legendre nodal points. A shear plane wave example is presented to show the dependence of the accuracy and computational expense of high-order elements on wave number. Then, a convergence study for a viscoelastic acoustic-structure interaction finite element model of an actual ultrasound driven vibroacoustic experiment is shown. The number of degrees of freedom required for a given accuracy level was found to consistently decrease with increasing element order. However, the computationally optimal element order was found to strongly depend on the wave number.
Coupled thermomechanical behavior of graphene using the spring-based finite element approach
Georgantzinos, S. K. Anifantis, N. K.; Giannopoulos, G. I.
2016-07-07
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 are 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.
NASA Technical Reports Server (NTRS)
Bey, K. S.; Thornton, E. A.; Dechaumphai, P.; Ramakrishnan, R.
1985-01-01
Recent progress in the development of finite element methodology for the prediction of aerothermal loads is described. Two dimensional, inviscid computations are presented, but emphasis is placed on development of an approach extendable to three dimensional viscous flows. Research progress is described for: (1) utilization of a commercially available program to construct flow solution domains and display computational results, (2) development of an explicit Taylor-Galerkin solution algorithm, (3) closed form evaluation of finite element matrices, (4) vector computer programming strategies, and (5) validation of solutions. Two test problems of interest to NASA Langley aerothermal research are studied. Comparisons of finite element solutions for Mach 6 flow with other solution methods and experimental data validate fundamental capabilities of the approach for analyzing high speed inviscid compressible flows.
NASA Technical Reports Server (NTRS)
Bey, K. S.; Thornton, E. A.; Dechaumphai, P.; Ramakrishnan, R.
1985-01-01
Recent progress in the development of finite element methodology for the prediction of aerothermal loads is described. Two dimensional, inviscid computations are presented, but emphasis is placed on development of an approach extendable to three dimensional viscous flows. Research progress is described for: (1) utilization of a commerically available program to construct flow solution domains and display computational results, (2) development of an explicit Taylor-Galerkin solution algorithm, (3) closed form evaluation of finite element matrices, (4) vector computer programming strategies, and (5) validation of solutions. Two test problems of interest to NASA Langley aerothermal research are studied. Comparisons of finite element solutions for Mach 6 flow with other solution methods and experimental data validate fundamental capabilities of the approach for analyzing high speed inviscid compressible flows.
Finite Element approach for Density Functional Theory calculations on locally refined meshes
Fattebert, J; Hornung, R D; Wissink, A M
2007-02-23
We present a quadratic Finite Element approach to discretize the Kohn-Sham equations on structured non-uniform meshes. A multigrid FAC preconditioner is proposed to iteratively solve the equations by an accelerated steepest descent scheme. The method was implemented using SAMRAI, a parallel software infrastructure for general AMR applications. Examples of applications to small nanoclusters calculations are presented.
Inversion of Robin coefficient by a spectral stochastic finite element approach
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.
An approach for verification of finite-element analysis in nonlinear elasticity under large strains
NASA Astrophysics Data System (ADS)
Zingerman, K. M.; Vershinin, A. V.; Levin, V. A.
2016-11-01
An approach to verification of finite-element calculations of stress-strain state of nonlinear elastic bodies under large deformations is suggested. The problems that may be reduced to one-dimensional ones using a semi-inverse method are taken as test problems. An example of such a test problem is the Lame problem for a cylinder. Generally, this problem for compressible hyperelastic materials has no exact analytical solution, but it can be reduced to a boundary value problem for an ordinary second-order nonlinear differential equation, and in some cases - to the Cauchy problem. A numerical solution of this problem can be used as a test one for finite element calculations carried out in three-dimensional statement. Some results of such verification (finite element calculations were performed using the Fidesys CAE-system) are presented.
NASA Astrophysics Data System (ADS)
Fan, Y.; Collet, M.; Ichchou, M.; Li, L.; Bareille, O.; Dimitrijevic, Z.
2016-01-01
This paper presents a rapid and accurate numerical tool for the energy flow evaluation in a periodic substructure from the near-field to the far-field domain. Here we suppose that the near-field part contains a point source characterized by the injected power in the structure. The near-field part is then modeled by Finite Element Method (FEM) while the periodic structure and the far-field part are regarded as waveguides and modeled by an enhanced Wave and Finite Element Method (WFEM). Enhancements are made on the eigenvalue scheme, the condensation of the unit cell and the consideration of a reduced wave basis. Efforts are made to adapt substructures modeled by different strategies in a multi-scale manner such that the final matrices dimensions of the built-up structure are largely reduced. The method is then validated numerically and theoretically. An application is presented, where a structural dynamical system coupled with periodic resistive piezoelectric shunts is discussed.
Approaches to the automatic generation and control of finite element meshes
NASA Technical Reports Server (NTRS)
Shephard, Mark S.
1987-01-01
The algorithmic approaches being taken to the development of finite element mesh generators capable of automatically discretizing general domains without the need for user intervention are discussed. It is demonstrated that because of the modeling demands placed on a automatic mesh generator, all the approaches taken to date produce unstructured meshes. Consideration is also given to both a priori and a posteriori mesh control devices for automatic mesh generators as well as their integration with geometric modeling and adaptive analysis procedures.
An Efficient Finite Element Approach for Modeling Fibrotic Clefts in the Heart
Costa, Caroline Mendonca; Campos, Fernando O.; Prassl, Anton J.; dos Santos, Rodrigo Weber; Sánchez-Quintana, Damián; Ahammer, Helmut; Hofer, Ernst; Plank, Gernot
2014-01-01
Advanced medical imaging technologies provide a wealth of information on cardiac anatomy and structure at a paracellular resolution, allowing to identify micro-structural discontinuities which disrupt the intracellular matrix. Current state-of-the-art computer models built upon such datasets account for increasingly finer anatomical details, however, structural discontinuities at the paracellular level are typically discarded in the model generation process, owing to the significant costs which incur when using high resolutions for explicit representation. In this study, a novel discontinuous finite element (dFE) approach for discretizing the bidomain equations is presented, which accounts for fine-scale structures in a computer model without the need to increase spatial resolution. In the dFE method this is achieved by imposing infinitely thin lines of electrical insulation along edges of finite elements which approximate the geometry of discontinuities in the intracellular matrix. Simulation results demonstrate that the dFE approach accounts for effects induced by microscopic size scale discontinuities, such as the formation of microscopic virtual electrodes, with vast computational savings as compared to high resolution continuous finite element models. Moreover, the method can be implemented in any standard continuous finite element code with minor effort. PMID:24557691
An efficient finite element approach for modeling fibrotic clefts in the heart.
Costa, Caroline Mendonca; Campos, Fernando O; Prassl, Anton J; dos Santos, Rodrigo Weber; Sánchez-Quintana, Damián; Ahammer, Helmut; Hofer, Ernst; Plank, Gernot
2014-03-01
Advanced medical imaging technologies provide a wealth of information on cardiac anatomy and structure at a paracellular resolution, allowing to identify microstructural discontinuities which disrupt the intracellular matrix. Current state-of-the-art computer models built upon such datasets account for increasingly finer anatomical details, however, structural discontinuities at the paracellular level are typically discarded in the model generation process, owing to the significant costs which incur when using high resolutions for explicit representation. In this study, a novel discontinuous finite element (dFE) approach for discretizing the bidomain equations is presented, which accounts for fine-scale structures in a computer model without the need to increase spatial resolution. In the dFE method, this is achieved by imposing infinitely thin lines of electrical insulation along edges of finite elements which approximate the geometry of discontinuities in the intracellular matrix. Simulation results demonstrate that the dFE approach accounts for effects induced by microscopic size scale discontinuities, such as the formation of microscopic virtual electrodes, with vast computational savings as compared to high resolution continuous finite element models. Moreover, the method can be implemented in any standard continuous finite element code with minor effort.
Variance analysis for model updating with a finite element based subspace fitting approach
NASA Astrophysics Data System (ADS)
Gautier, Guillaume; Mevel, Laurent; Mencik, Jean-Mathieu; Serra, Roger; Döhler, Michael
2017-07-01
Recently, a subspace fitting approach has been proposed for vibration-based finite element model updating. The approach makes use of subspace-based system identification, where the extended observability matrix is estimated from vibration measurements. Finite element model updating is performed by correlating the model-based observability matrix with the estimated one, by using a single set of experimental data. Hence, the updated finite element model only reflects this single test case. However, estimates from vibration measurements are inherently exposed to uncertainty due to unknown excitation, measurement noise and finite data length. In this paper, a covariance estimation procedure for the updated model parameters is proposed, which propagates the data-related covariance to the updated model parameters by considering a first-order sensitivity analysis. In particular, this propagation is performed through each iteration step of the updating minimization problem, by taking into account the covariance between the updated parameters and the data-related quantities. Simulated vibration signals are used to demonstrate the accuracy and practicability of the derived expressions. Furthermore, an application is shown on experimental data of a beam.
NASA Technical Reports Server (NTRS)
Oden, J. Tinsley; Fly, Gerald W.; Mahadevan, L.
1987-01-01
A hybrid stress finite element method is developed for accurate stress and vibration analysis of problems in linear anisotropic elasticity. A modified form of the Hellinger-Reissner principle is formulated for dynamic analysis and an algorithm for the determination of the anisotropic elastic and compliance constants from experimental data is developed. These schemes were implemented in a finite element program for static and dynamic analysis of linear anisotropic two dimensional elasticity problems. Specific numerical examples are considered to verify the accuracy of the hybrid stress approach and compare it with that of the standard displacement method, especially for highly anisotropic materials. It is that the hybrid stress approach gives much better results than the displacement method. Preliminary work on extensions of this method to three dimensional elasticity is discussed, and the stress shape functions necessary for this extension are included.
Calculation of positron observables using a finite-element-based approach
Klein, B. M.; Pask, J. E.; Sterne, P.
1998-11-04
We report the development of a new method for calculating positron observables using a finite-element approach for the solution of the Schrodinger equation. This method combines the advantages of both basis-set and real-space-grid approaches. The strict locality in real space of the finite element basis functions results in a method that is well suited for calculating large systems of a thousand or more atoms, as required for calculations of extended defects such as dislocations. In addition, the method is variational in nature and its convergence can be controlled systematically. The calculation of positron observables is straightforward due to the real-space nature of this method. We illustrate the power of this method with positron lifetime calculations on defects and defect-free materials, using overlapping atomic charge densities.
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.
Use of adjoint methods in the probabilistic finite element approach to fracture mechanics
NASA Technical Reports Server (NTRS)
Liu, Wing Kam; Besterfield, Glen; Lawrence, Mark; Belytschko, Ted
1988-01-01
The adjoint method approach to probabilistic finite element methods (PFEM) is presented. When the number of objective functions is small compared to the number of random variables, the adjoint method is far superior to the direct method in evaluating the objective function derivatives with respect to the random variables. The PFEM is extended to probabilistic fracture mechanics (PFM) using an element which has the near crack-tip singular strain field embedded. Since only two objective functions (i.e., mode I and II stress intensity factors) are needed for PFM, the adjoint method is well suited.
NASA Astrophysics Data System (ADS)
Römer, Ulrich; Schöps, Sebastian; De Gersem, Herbert
2017-04-01
In electromagnetic simulations of magnets and machines, one is often interested in a highly accurate and local evaluation of the magnetic field uniformity. Based on local post-processing of the solution, a defect correction scheme is proposed as an easy to realize alternative to higher order finite element or hybrid approaches. Radial basis functions (RBFs) are key for the generality of the method, which in particular can handle unstructured grids. Also, contrary to conventional finite element basis functions, higher derivatives of the solution can be evaluated, as required, e.g., for deflection magnets. Defect correction is applied to obtain a solution with improved accuracy and adjoint techniques are used to estimate the remaining error for a specific quantity of interest. Significantly improved (local) convergence orders are obtained. The scheme is also applied to the simulation of a Stern-Gerlach magnet currently in operation.
Determination of stress intensity factor with direct stress approach using finite element analysis
NASA Astrophysics Data System (ADS)
Ji, X.; Zhu, F.; He, P. F.
2017-03-01
In this article, a direct stress approach based on finite element analysis to determine the stress intensity factor is improved. Firstly, by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack, we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity factor, which is nearly equal to the stress intensity factor given by the asymptotic solution. Secondly, the crack problem is solved numerically by the finite element method. Depending on the modeling capability of the software, we designed an adaptive mesh model to simulate the stress singularity. Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corresponding crack problem. Therefore, the stress intensity factor may be calculated from the stress distribution in the appropriate interval, with a high accuracy.
NASA Astrophysics Data System (ADS)
Gupta, Swapnil Sheelkumar
Paper variants such as paper napkins, tissue paper are manufactured by a process called as creping during which a paper adhesively bonded to a rotating drum is continuously scraped off by a blade. Resulting low density paper provides critical attributes such as fluid absorbency, softness, and stretchiness to the final paper product. The macroscopic effect of creping is the formation of fine ridges called as " crepes". The quality of the final product is characterized by the length of the crepes. The process of creping has been hypothesized to be a periodic sequence of delamination, buckling and post-buckling compression of paper. A quasi-static comparison of a two dimensional finite element model implementing surface based cohesive zone theory and a critical stress criteria based fracture model is presented. The adhesive being a critical part of creping is represented by a zero thickness cohesive layer in the cohesive model . A comparison of a 1-D analytical model implementing an energy release rate approach and a Virtual Crack Closure Technique (VCCT) quasi-static finite element model is presented. An experimental investigation to quantitatively determine the adhesive fracture toughness during creping is conducted by an energy based approach. The influence of drum speed and adhesive concentration on the adhesive fracture energy is analyzed and comparison with a dynamic finite element model is obtained.
An approach to parameter estimation for breast tumor by finite element method
NASA Astrophysics Data System (ADS)
Xu, A.-qing; Yang, Hong-qin; Ye, Zhen; Su, Yi-ming; Xie, Shu-sen
2009-02-01
The temperature of human body on the surface of the skin depends on the metabolic activity, the blood flow, and the temperature of the surroundings. Any abnormality in the tissue, such as the presence of a tumor, alters the normal temperature on the skin surface due to increased metabolic activity of the tumor. Therefore, abnormal skin temperature profiles are an indication of diseases such as tumor or cancer. This study is to present an approach to detect the female breast tumor and its related parameter estimations by combination the finite element method with infrared thermography for the surface temperature profile. A 2D simplified breast embedded a tumor model based on the female breast anatomical structure and physiological characteristics was first established, and then finite element method was used to analyze the heat diffuse equation for the surface temperature profiles of the breast. The genetic optimization algorithm was used to estimate the tumor parameters such as depth, size and blood perfusion by minimizing a fitness function involving the temperature profiles simulated data by finite element method to the experimental data obtained by infrared thermography. This preliminary study shows it is possible to determine the depth and the heat generation rate of the breast tumor by using infrared thermography and the optimization analysis, which may play an important role in the female breast healthcare and diseases evaluation or early detection. In order to develop the proposed methodology to be used in clinical, more accurate anatomy 3D breast geometry should be considered in further investigations.
Microwave imaging using the finite-element method and a sensitivity analysis approach.
Rekanos, I T; Panas, S M; Tsiboukis, T D
1999-11-01
A method for reconstructing the constitutive parameters of two-dimensional (2-D) penetrable scatterers from scattered field measurements is presented. This method is based on the differential formulation of the forward scattering problem, which is solved by applying the finite-element method (FEM). Given a set of scattered field measurements, the objective is to minimize a cost function which consists of two terms. The first is the standard error term, which is related to the measurements and their estimates, while the second term, which is related to the Tikhonov regularization, is used to heal the ill posedness of the inverse problem. The iterative Polak-Ribière nonlinear conjugate gradient algorithm is applied to the minimization of the cost function. During each iteration of the algorithm, the direction of correction is computed by using a sensitivity analysis approach, which is carried out by an elaborate finite-element scheme. The adoption of the finite-element method results in sparse systems of equations, while the computational burden is further reduced by applying the adjoint state vector methodology. Finally, a microwave medical imaging application, which is related to the detection of proliferated bone marrow, is examined, while the robustness of the proposed technique in the presence of noise and for different regularization levels is investigated.
Electrical defibrillation optimization: An automated, iterative parallel finite-element approach
Hutchinson, S.A.; Shadid, J.N.; Ng, K.T.; Nadeem, A.
1997-04-01
To date, optimization of electrode systems for electrical defibrillation has been limited to hand-selected electrode configurations. In this paper we present an automated approach which combines detailed, three-dimensional (3-D) finite element torso models with optimization techniques to provide a flexible analysis and design tool for electrical defibrillation optimization. Specifically, a parallel direct search (PDS) optimization technique is used with a representative objective function to find an electrode configuration which corresponds to the satisfaction of a postulated defibrillation criterion with a minimum amount of power and a low possibility of myocardium damage. For adequate representation of the thoracic inhomogeneities, 3-D finite-element torso models are used in the objective function computations. The CPU-intensive finite-element calculations required for the objective function evaluation have been implemented on a message-passing parallel computer in order to complete the optimization calculations in a timely manner. To illustrate the optimization procedure, it has been applied to a representative electrode configuration for transmyocardial defibrillation, namely the subcutaneous patch-right ventricular catheter (SP-RVC) system. Sensitivity of the optimal solutions to various tissue conductivities has been studied. 39 refs., 9 figs., 2 tabs.
Balima, O.; Favennec, Y.; Rousse, D.
2013-10-15
Highlights: •New strategies to improve the accuracy of the reconstruction through mesh and finite element parameterization. •Use of gradient filtering through an alternative inner product within the adjoint method. •An integral form of the cost function is used to make the reconstruction compatible with all finite element formulations, continuous and discontinuous. •Gradient-based algorithm with the adjoint method is used for the reconstruction. -- Abstract: Optical tomography is mathematically treated as a non-linear inverse problem where the optical properties of the probed medium are recovered through the minimization of the errors between the experimental measurements and their predictions with a numerical model at the locations of the detectors. According to the ill-posed behavior of the inverse problem, some regularization tools must be performed and the Tikhonov penalization type is the most commonly used in optical tomography applications. This paper introduces an optimized approach for optical tomography reconstruction with the finite element method. An integral form of the cost function is used to take into account the surfaces of the detectors and make the reconstruction compatible with all finite element formulations, continuous and discontinuous. Through a gradient-based algorithm where the adjoint method is used to compute the gradient of the cost function, an alternative inner product is employed for preconditioning the reconstruction algorithm. Moreover, appropriate re-parameterization of the optical properties is performed. These regularization strategies are compared with the classical Tikhonov penalization one. It is shown that both the re-parameterization and the use of the Sobolev cost function gradient are efficient for solving such an ill-posed inverse problem.
Lehtovaara, Lauri; Havu, Ville; Puska, Martti
2011-10-21
We present an all-electron method for time-dependent density functional theory which employs hierarchical nonuniform finite-element bases and the time-propagation approach. The method is capable of treating linear and nonlinear response of valence and core electrons to an external field. We also introduce (i) a preconditioner for the propagation equation, (ii) a stable way to implement absorbing boundary conditions, and (iii) a new kind of absorbing boundary condition inspired by perfectly matched layers. © 2011 American Institute of Physics
Stress analysis of composite spur gear using the finite element approach
NASA Astrophysics Data System (ADS)
Vijayarangan, S.; Ganesan, N.
1993-03-01
Engineering components made of composite materials find increasing applications ranging from spacecraft to small instruments. Many types of gear pump use composite gears, however little literature is available on their use. In this paper results obtained by static stress analysis of composite gears using a three-dimensional finite element approach are presented. Performance of two orthotropic material gears are presented and compared with mild steel gear. From the results it is concluded that composite material such as graphite/epoxy can be thought of as a material for power transmission gears.
Finite element approaches for static and dynamic analysis of partially wrinkled membrane structures
NASA Astrophysics Data System (ADS)
Adler, Aaron Lee
In the past few years, there has been an increasing interest in the use of large and extremely lightweight tensioned membrane structures for spacecraft applications. Typical uses include sunshields, parabolic reflectors, concentrators, and solar sails. Due to complex and/or changing load and boundary conditions, these structures can experience situations for which localized buckling (wrinkling) occurs within the membrane. This behavior is not possible to analyze using conventional finite element codes. This thesis discusses the development of modeling techniques for the static and dynamic analysis of partially wrinkled membrane structures using a constitutive model that accounts for the "overcontraction" and change in load path within the membrane in an averaged sense. This constitutive model has been successfully used and verified in the past on several static membrane problems with regular boundary and loading conditions that were amenable to closed form solutions. In the present thesis, this constitutive model is introduced into two different commercially available finite element codes to enable the analysis of realistic membrane structures that involve complex shapes and loading conditions. The analysis method, which involves an iterative procedure to determine the extent and shape of the wrinkled region(s) and then modify the element material properties accordingly, is referred to as the Iterative Membrane Properties (IMP) method. In one case the IMP method was implemented external to the finite element code, while the in the other case the IMP method was implemented internally via a modifiable material property subroutine. In addition to the IMP approaches, an approximate Cable Network Modeling approach was studied to enable preliminary dynamic studies of partially wrinkled membrane structures. This approach was successfully applied to a realistic problem, NASA's NGST sunshield. The analysis was used in the design of a tenth scale test article, and its
Automatic finite element generators
NASA Technical Reports Server (NTRS)
Wang, P. S.
1984-01-01
The design and implementation of a software system for generating finite elements and related computations are described. Exact symbolic computational techniques are employed to derive strain-displacement matrices and element stiffness matrices. Methods for dealing with the excessive growth of symbolic expressions are discussed. Automatic FORTRAN code generation is described with emphasis on improving the efficiency of the resultant code.
Three dimensional stress analysis of diabetic insole: a finite element approach.
Barani, Zohreh; Haghpanahi, Mohammad; Katoozian, Hamid
2005-01-01
Current research in foot biomechanics includes studies on prevention of recurrence of neuropathic foot ulcers. This paper attempts to prescribe accommodative insoles, which reduce plantar pressure levels particularly under the hallux. There is little quantitative information available regarding the effects of insole materials on reduction of plantar pressure. The insole models available in the literature are mostly two-dimensional (2-D). Hence, there is a need to develop a 3-D model with actual geometry which includes sufficient details. In this study a three-dimensional (3-D) model of the insole was constructed. A linear and non-linear static analysis using finite element method (FEM) was performed. Results were compared for different materials such as Silicon Gel, Plastozot, Polyfoam, and Ethinil Vinyl Acetate (EVA). Our 3-D finite element model was constructed using 16170 ten-node tetrahedral, mixed U-P (displacement-pressure), hyperelastic, solid elements. Four different hyperelastic and foam materials were used and compared and the loading condition was based on the mid-stance phase of the gait. This research has shown that most of these materials are very effective in terms of reduction of plantar stress concentrations. The technique used in this research provides a promising approach to understanding of behavior of insole materials and suggests a design guideline for therapeutic footwear and orthoses.
Free and forced vibrations of a tyre using a wave/finite element approach
NASA Astrophysics Data System (ADS)
Waki, Y.; Mace, B. R.; Brennan, M. J.
2009-06-01
Free and forced vibrations of a tyre are predicted using a wave/finite element (WFE) approach. A short circumferential segment of the tyre is modelled using conventional finite element (FE) methods, a periodicity condition applied and the mass and stiffness matrices post-processed to yield wave properties. Since conventional FE methods are used, commercial FE packages and existing element libraries can be utilised. An eigenvalue problem is formulated in terms of the transfer matrix of the segment. Zhong's method is used to improve numerical conditioning. The eigenvalues and eigenvectors give the wavenumbers and wave mode shapes, which in turn define transformations between the physical and wave domains. A method is described by which the frequency dependent material properties of the rubber components of the tyre can be included without the need to remesh the structure. Expressions for the forced response are developed which are numerically well-conditioned. Numerical results for a smooth tyre are presented. Dispersion curves for real, imaginary and complex wavenumbers are shown. The propagating waves are associated with various forms of motion of the tread supported by the stiffness of the side wall. Various dispersion phenomena are observed, including curve veering, non-zero cut-off and waves for which the phase velocity and the group velocity have opposite signs. Results for the forced response are compared with experimental measurements and good agreement is seen. The forced response is numerically determined for both finite area and point excitations. It is seen that the size of area of the excitation is particularly important at high frequencies. When the size of the excitation area is small enough compared to the tread thickness, the response at high frequencies becomes stiffness-like (reactive) and the effect of shear stiffness becomes important.
NASA Astrophysics Data System (ADS)
Roirand, Q.; Missoum-Benziane, D.; Thionnet, A.; Laiarinandrasana, L.
2017-09-01
Textile composites are composed of 3D complex architecture. To assess the durability of such engineering structures, the failure mechanisms must be highlighted. Examinations of the degradation have been carried out thanks to tomography. The present work addresses a numerical damage model dedicated to the simulation of the crack initiation and propagation at the scale of the warp yarns. For the 3D woven composites under study, loadings in tension and combined tension and bending were considered. Based on an erosion procedure of broken elements, the failure mechanisms have been modelled on 3D periodic cells by finite element calculations. The breakage of one element was determined using a failure criterion at the mesoscopic scale based on the yarn stress at failure. The results were found to be in good agreement with the experimental data for the two kinds of macroscopic loadings. The deterministic approach assumed a homogeneously distributed stress at failure all over the integration points in the meshes of woven composites. A stochastic approach was applied to a simple representative elementary periodic cell. The distribution of the Weibull stress at failure was assigned to the integration points using a Monte Carlo simulation. It was shown that this stochastic approach allowed more realistic failure simulations avoiding the idealised symmetry due to the deterministic modelling. In particular, the stochastic simulations performed have shown several variations of the stress as well as strain at failure and the failure modes of the yarn.
NASA Astrophysics Data System (ADS)
Roirand, Q.; Missoum-Benziane, D.; Thionnet, A.; Laiarinandrasana, L.
2017-01-01
Textile composites are composed of 3D complex architecture. To assess the durability of such engineering structures, the failure mechanisms must be highlighted. Examinations of the degradation have been carried out thanks to tomography. The present work addresses a numerical damage model dedicated to the simulation of the crack initiation and propagation at the scale of the warp yarns. For the 3D woven composites under study, loadings in tension and combined tension and bending were considered. Based on an erosion procedure of broken elements, the failure mechanisms have been modelled on 3D periodic cells by finite element calculations. The breakage of one element was determined using a failure criterion at the mesoscopic scale based on the yarn stress at failure. The results were found to be in good agreement with the experimental data for the two kinds of macroscopic loadings. The deterministic approach assumed a homogeneously distributed stress at failure all over the integration points in the meshes of woven composites. A stochastic approach was applied to a simple representative elementary periodic cell. The distribution of the Weibull stress at failure was assigned to the integration points using a Monte Carlo simulation. It was shown that this stochastic approach allowed more realistic failure simulations avoiding the idealised symmetry due to the deterministic modelling. In particular, the stochastic simulations performed have shown several variations of the stress as well as strain at failure and the failure modes of the yarn.
Finite ElementModelingof FRP-Confined Concrete using Extended Damage-Plasticity Approach
NASA Astrophysics Data System (ADS)
Gholampour, Aliakbar; Ozbakkaloglu, Togay
2017-08-01
A study on finite element (FE) modelingof fiber-reinforced polymer (FRP)-confined normal-strength and high-strength concrete (NSC and HSC) based on an extended concrete damage-plasticity approach is presented. The study focuses on the extension ofLubliner’s model by accurately incorporating the effects of confinement level, concrete strength, and nonlinear dilation behavior of FRP-confined concrete. Failure surface and flow rule were established using an up-to-date database. In order to validate the extended damage-plasticity model, the predictions of the FE modeling are compared with the experimental results. These comparisons indicate that the extended approach accurately predicts the compressive behavior of FRP-confined NSC and HSC.
NASA Technical Reports Server (NTRS)
Krueger, Ronald
2008-01-01
An approach for assessing the delamination propagation simulation capabilities in commercial finite element codes is presented and demonstrated. For this investigation, the Double Cantilever Beam (DCB) specimen and the Single Leg Bending (SLB) specimen were chosen for full three-dimensional finite element simulations. First, benchmark results were created for both specimens. Second, starting from an initially straight front, the delamination was allowed to propagate. The load-displacement relationship and the total strain energy obtained from the propagation analysis results and the benchmark results were compared and good agreements could be achieved by selecting the appropriate input parameters. Selecting the appropriate input parameters, however, was not straightforward and often required an iterative procedure. Qualitatively, the delamination front computed for the DCB specimen did not take the shape of a curved front as expected. However, the analysis of the SLB specimen yielded a curved front as was expected from the distribution of the energy release rate and the failure index across the width of the specimen. Overall, the results are encouraging but further assessment on a structural level is required.
An Approach for Assessing Delamination Propagation Capabilities in Commercial Finite Element Codes
NASA Technical Reports Server (NTRS)
Krueger, Ronald
2007-01-01
An approach for assessing the delamination propagation capabilities in commercial finite element codes is presented and demonstrated for one code. For this investigation, the Double Cantilever Beam (DCB) specimen and the Single Leg Bending (SLB) specimen were chosen for full three-dimensional finite element simulations. First, benchmark results were created for both specimens. Second, starting from an initially straight front, the delamination was allowed to propagate. Good agreement between the load-displacement relationship obtained from the propagation analysis results and the benchmark results could be achieved by selecting the appropriate input parameters. Selecting the appropriate input parameters, however, was not straightforward and often required an iterative procedure. Qualitatively, the delamination front computed for the DCB specimen did not take the shape of a curved front as expected. However, the analysis of the SLB specimen yielded a curved front as may be expected from the distribution of the energy release rate and the failure index across the width of the specimen. Overall, the results are encouraging but further assessment on a structural level is required.
Rheological changes after stenting of a cerebral aneurysm: a finite element modeling approach.
Ohta, Makoto; Wetzel, Stephan G; Dantan, Philippe; Bachelet, Caroline; Lovblad, Karl O; Yilmaz, Hasan; Flaud, Patrice; Rüfenacht, Daniel A
2005-01-01
Hemodynamic changes in intracranial aneurysms after stent placement include the appearance of areas with stagnant flow and low shear rates. We investigated the influence of stent placement on blood flow velocity and wall shear stress of an intracranial aneurysm using a finite element modeling approach. To assess viscosity changes induced by stent placement, the rheology of blood as non-Newtonian fluid was taken into account in this model. A two-dimensional model with a parent artery, a smaller branching artery, and an aneurysm located at the bifurcation, before and after stent placement, was used for simulation. Flow velocity plots and wall shear stress before and after stent placement was calculated over the entire cardiac circle. Values for dynamic viscosity were calculated with a constitutive equation that was based on experimental studies and yielded a viscosity, which decreases as the shear rate increases. Stent placement lowered peak velocities in the main vortex of the aneurysm by a factor of at least 4 compared to peak velocities in the main artery, and it considerably decreased the wall shear stress of the aneurysm. Dynamic viscosity increases after stent placement persisted over a major part of the cardiac cycle, with a factor of up to 10, most pronounced near the dome of the aneurysm. Finite element modeling can offer insight into rheological changes induced by stent treatment of aneurysms and allows visualizing dynamic viscosity changes induced by stent placement.
Rheological Changes After Stenting of a Cerebral Aneurysm: A Finite Element Modeling Approach
Ohta, Makoto; Wetzel, Stephan G. Dantan, Philippe; Bachelet, Caroline; Lovblad, Karl O.; Yilmaz, Hasan; Flaud, Patrice; Ruefenacht, Daniel A.
2005-12-15
Hemodynamic changes in intracranial aneurysms after stent placement include the appearance of areas with stagnant flow and low shear rates. We investigated the influence of stent placement on blood flow velocity and wall shear stress of an intracranial aneurysm using a finite element modeling approach. To assess viscosity changes induced by stent placement, the rheology of blood as non-Newtonian fluid was taken into account in this model. A two-dimensional model with a parent artery, a smaller branching artery, and an aneurysm located at the bifurcation, before and after stent placement, was used for simulation. Flow velocity plots and wall shear stress before and after stent placement was calculated over the entire cardiac circle. Values for dynamic viscosity were calculated with a constitutive equation that was based on experimental studies and yielded a viscosity, which decreases as the shear rate increases. Stent placement lowered peak velocities in the main vortex of the aneurysm by a factor of at least 4 compared to peak velocities in the main artery, and it considerably decreased the wall shear stress of the aneurysm. Dynamic viscosity increases after stent placement persisted over a major part of the cardiac cycle, with a factor of up to 10, most pronounced near the dome of the aneurysm. Finite element modeling can offer insight into rheological changes induced by stent treatment of aneurysms and allows visualizing dynamic viscosity changes induced by stent placement.
An Approach for Assessing Delamination Propagation Capabilities in Commercial Finite Element Codes
NASA Technical Reports Server (NTRS)
Krueger, Ronald
2007-01-01
An approach to assessing the delamination propagation capabilities in commercial finite element codes is presented and demonstrated for one code. For this investigation, the Double Cantilever Beam (DCB) specimen and the Single Leg Bending (SLB) specimen were chosen for full three-dimensional finite element simulations. First, benchmark results were created for both specimens. Second, starting from an initially straight front, the delamination was allowed to propagate. Good agreement between the load-displacement relationship obtained from the propagation analysis results and the benchmark results could be achieved by selecting the appropriate input parameters. Selecting the appropriate input parameters, however, was not straightforward and often required an iterative procedure. Qualitatively, the delamination front computed for the DCB specimen did not take the shape of a curved front as expected. However, the analysis of the SLB specimen yielded a curved front as may be expected from the distribution of the energy release rate and the failure index across the width of the specimen. Overall, the results are encouraging but further assessment on a structural level is required.
A finite element approach to self-consistent field theory calculations of multiblock polymers
NASA Astrophysics Data System (ADS)
Ackerman, David M.; Delaney, Kris; Fredrickson, Glenn H.; Ganapathysubramanian, Baskar
2017-02-01
Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.
NASA Technical Reports Server (NTRS)
Adams, M. L.; Padovan, J.; Fertis, D. G.
1981-01-01
NASA-sponsored research on engine dynamic simulation using general finite element nonlinear time transient computer codes available on the open market is reviewed. The approach taken was to develop software packages to model engine components which are not typically found on dynamical structures and are therefore not already computer codes. The software package developed for squeeze-film bearing dampers is outlined, and the results of a parametric study of damper pressure for a variety of specified circular orbits are presented for both long-bearing and short-bearing solutions. The data from a four-degree-of-freedom rotor-damper-stator model under conditions of small rotor unbalance through large rotor unbalance are also given.
Permeswaran, Vijay N; Goetz, Jessica E; Rudert, M James; Hettrich, Carolyn M; Anderson, Donald D
2016-09-06
Cadaveric experiments were undertaken to validate a finite element (FE) modeling approach for studying impingement-related scapular notching in reverse shoulder arthroplasty (RSA). The specific focus of the validation was contact at the site of impingement between the humeral polyethylene component and the inferior aspect of the scapula during an adduction motion. Lateralization of the RSA center of rotation was varied because it has been advocated clinically to reduce impingement and presumably decrease the risk of scapular notching. Tekscan sensors were utilized to directly measure contact stress at the impingement site, and FE was used to compute contact stresses. Favorable agreement was seen between physically measured and FE-computed impingement site location (within one sensing element of the Tekscan sensor) and contact loads (mean absolute difference of 14.9%). Contact stresses and contact areas were difficult to compare directly due to the disparate spatial resolutions of the Tekscan sensor and the FE model. FE-computed contact at the impingement site was highly focal, with a total contact area comparable to the area of an individual Tekscan sensing element. The good agreement between the physically measured and FE-computed contact data (i.e., contact load and location) support the use of FE modeling as a tool for computationally testing the efficacy of changing various surgical variables associated with RSA.
Chen, G; Wu, F Y; Liu, Z C; Yang, K; Cui, F
2015-08-01
Subject-specific finite element (FE) models can be generated from computed tomography (CT) datasets of a bone. A key step is assigning material properties automatically onto finite element models, which remains a great challenge. This paper proposes a node-based assignment approach and also compares it with the element-based approach in the literature. Both approaches were implemented using ABAQUS. The assignment procedure is divided into two steps: generating the data file of the image intensity of a bone in a MATLAB program and reading the data file into ABAQUS via user subroutines. The node-based approach assigns the material properties to each node of the finite element mesh, while the element-based approach assigns the material properties directly to each integration point of an element. Both approaches are independent from the type of elements. A number of FE meshes are tested and both give accurate solutions; comparatively the node-based approach involves less programming effort. The node-based approach is also independent from the type of analyses; it has been tested on the nonlinear analysis of a Sawbone femur. The node-based approach substantially improves the level of automation of the assignment procedure of bone material properties. It is the simplest and most powerful approach that is applicable to many types of analyses and elements.
Finite elements: Theory and application
NASA Technical Reports Server (NTRS)
Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)
1988-01-01
Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.
Finite elements: Theory and application
NASA Technical Reports Server (NTRS)
Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)
1988-01-01
Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.
NASA Technical Reports Server (NTRS)
Robinson, J. C.
1979-01-01
Two methods for determining stresses and internal forces in geometrically nonlinear structural analysis are presented. The simplified approach uses the mid-deformed structural position to evaluate strains when rigid body rotation is present. The important feature of this approach is that it can easily be used with a general-purpose finite-element computer program. The refined approach uses element intrinsic or corotational coordinates and a geometric transformation to determine element strains from joint displacements. Results are presented which demonstrate the capabilities of these potentially useful approaches for geometrically nonlinear structural analysis.
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.
2017-08-01
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.
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.
NASA Astrophysics Data System (ADS)
Yang, Weizhu; Yue, Zhufeng; Li, Lei; Wang, Peiyan
2016-01-01
An optimization procedure combining an automated finite element modelling (AFEM) technique with a ground structure approach (GSA) is proposed for structural layout and sizing design of aircraft wings. The AFEM technique, based on CATIA VBA scripting and PCL programming, is used to generate models automatically considering the arrangement of inner systems. GSA is used for local structural topology optimization. The design procedure is applied to a high-aspect-ratio wing. The arrangement of the integral fuel tank, landing gear and control surfaces is considered. For the landing gear region, a non-conventional initial structural layout is adopted. The positions of components, the number of ribs and local topology in the wing box and landing gear region are optimized to obtain a minimum structural weight. Constraints include tank volume, strength, buckling and aeroelastic parameters. The results show that the combined approach leads to a greater weight saving, i.e. 26.5%, compared with three additional optimizations based on individual design approaches.
A new approach to finite element modeling, analysis and post-processing
NASA Technical Reports Server (NTRS)
White, Gil
1987-01-01
Recent advances in both hardware and software have opened the door to a new generation of finite element modeling systems. INTERGRAPH CORP has combined an innovative programming concept with a stand alone workstation hardware platform to produce a new standard in finite element modeling called I/FEM. The system offers the COSMIC NASTRAN user full integration between design and analysis. I/FEM not only addresses the needs of the NASTRAN user of today, it also provides for continued evolution of the COSMIC NASTRAN product.
Finite element analysis of an extended end-plate connection using the T-stub approach
Muresan, Ioana Cristina; Balc, Roxana
2015-03-10
Beam-to-column end-plate bolted connections are usually used as moment-resistant connections in steel framed structures. For this joint type, the deformability is governed by the deformation capacity of the column flange and end-plate under tension and elongation of the bolts. All these elements around the beam tension flange form the tension region of the joint, which can be modeled by means of equivalent T-stubs. In this paper a beam-to-column end-plate bolted connection is substituted with a T-stub of appropriate effective length and it is analyzed using the commercially available finite element software ABAQUS. The performance of the model is validated by comparing the behavior of the T-stub from the numerical simulation with the behavior of the connection as a whole. The moment-rotation curve of the T-stub obtained from the numerical simulation is compared with the behavior of the whole extended end-plate connection, obtained by numerical simulation, experimental tests and analytical approach.
A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling
NASA Astrophysics Data System (ADS)
Ren, Zhengyong; Kalscheuer, Thomas; Greenhalgh, Stewart; Maurer, Hansruedi
2013-08-01
We have developed a novel goal-oriented adaptive mesh refinement approach for finite-element methods to model plane wave electromagnetic (EM) fields in 3-D earth models based on the electric field differential equation. To handle complicated models of arbitrary conductivity, magnetic permeability and dielectric permittivity involving curved boundaries and surface topography, we employ an unstructured grid approach. The electric field is approximated by linear curl-conforming shape functions which guarantee the divergence-free condition of the electric field within each tetrahedron and continuity of the tangential component of the electric field across the interior boundaries. Based on the non-zero residuals of the approximated electric field and the yet to be satisfied boundary conditions of continuity of both the normal component of the total current density and the tangential component of the magnetic field strength across the interior interfaces, three a-posterior error estimators are proposed as a means to drive the goal-oriented adaptive refinement procedure. The first a-posterior error estimator relies on a combination of the residual of the electric field, the discontinuity of the normal component of the total current density and the discontinuity of the tangential component of the magnetic field strength across the interior faces shared by tetrahedra. The second a-posterior error estimator is expressed in terms of the discontinuity of the normal component of the total current density (conduction plus displacement current). The discontinuity of the tangential component of the magnetic field forms the third a-posterior error estimator. Analytical solutions for magnetotelluric (MT) and radiomagnetotelluric (RMT) fields impinging on a homogeneous half-space model are used to test the performances of the newly developed goal-oriented algorithms using the above three a-posterior error estimators. A trapezoidal topographical model, using normally incident EM waves
A unidirectional approach for d-dimensional finite element methods for higher order on sparse grids
Bungartz, H.J.
1996-12-31
In the last years, sparse grids have turned out to be a very interesting approach for the efficient iterative numerical solution of elliptic boundary value problems. In comparison to standard (full grid) discretization schemes, the number of grid points can be reduced significantly from O(N{sup d}) to O(N(log{sub 2}(N)){sup d-1}) in the d-dimensional case, whereas the accuracy of the approximation to the finite element solution is only slightly deteriorated: For piecewise d-linear basis functions, e. g., an accuracy of the order O(N{sup - 2}(log{sub 2}(N)){sup d-1}) with respect to the L{sub 2}-norm and of the order O(N{sup -1}) with respect to the energy norm has been shown. Furthermore, regular sparse grids can be extended in a very simple and natural manner to adaptive ones, which makes the hierarchical sparse grid concept applicable to problems that require adaptive grid refinement, too. An approach is presented for the Laplacian on a uinit domain in this paper.
A Stimulating Approach To Teaching, Learning and Assessing Finite Element Methods: A Case Study.
ERIC Educational Resources Information Center
Karadelis, J. N.
1998-01-01
Examines the benefits of introducing finite element methods into the curriculum of undergraduate courses. Analyzes the structure of the computer-assisted-design module and the extent to which it fulfills its main objectives. Discusses the efficiency of modern teaching and learning techniques used to develop skills for solving engineering problems;…
Gaston, L.; Glut, B.; Bellet, M.; Chenot, J.L.
1995-12-31
This paper presents a two-dimensional lagrangian-eulerian finite element approach of non-steady state Navier-Stokes fluid flows with free surfaces, like those occurring during the mould filling stage in casting processes. The proposed model is based on a mixed velocity-pressure finite element formulation, including an augmented Lagrangian technique and an iterative solver of Uzawa type. Mesh updating is carried out through an arbitrary lagrangian-eulerian method in order to describe properly the free surface evolution. Heat transfer through the fluid flow is solved by a convection-diffusion splitting technique. The efficiency of the method is illustrated on an example of gravity casting.
A finite element approach for large motion dynamic analysis of multibody structures in space
NASA Technical Reports Server (NTRS)
Chang, Che-Wei
1989-01-01
A three-dimensional finite element formulation for modeling the transient dynamics of constrained multibody space sructures with truss-like configurations is presented. Convected coordinate systems are used to define rigid-body motion of individual elements in the system. These systems are located at one end of each element and are oriented such that one axis passes through the other end of the element. Deformation of each element, relative to its convected coordinate system, is defined by cubic flexural shape functions as used in finite element methods of structural analysis. The formulation is oriented toward joint dominated structures and places the generalized coordinates at the joint. A transformation matrix is derived to integrate joint degree-of-freedom into the equations of motion of the element. Based on the derivation, a general-purpose code LATDYN (Large Angle Transient DYNamics) was developed. Two examples are presented to illustrate the application of the code. For the spin-up of a flexible beam, results are compared with existing solutions available in the literature. For the deployment of one bay of a deployable space truss (the Minimast), results are verified by the geometric knowledge of the system and converged solution of a successively refined model.
A finite element approach for the dynamic analysis of joint-dominated structures
NASA Technical Reports Server (NTRS)
Chang, Che-Wei; Wu, Shih-Chin
1991-01-01
A finite element method to model dynamic structural systems undergoing large rotations is presented. The dynamic systems are composed of rigid joint bodies and flexible beam elements. The configurations of these systems are subject to change due to the relative motion in the joints among interconnected elastic beams. A body fixed reference is defined for each joint body to describe the joint body's displacements. Using the finite element method and the kinematic relations between each flexible element and its corotational reference, the total displacement field of an element, which contains gross rigid as well as elastic effects, can be derived in terms of the translational and rotational displacements of the two end nodes. If one end of an element is hinged to a joint body, the joint body's displacements and the hinge degree of freedom at the end are used to represent the nodal displacements. This results in a highly coupled system of differential equations written in terms of hinge degrees of freedom as well as the rotational and translational displacements of joint bodies and element nodes.
A critical assessment of finite element modeling approach for protein dynamics
NASA Astrophysics Data System (ADS)
Yun, Giseok; Kim, Jaehoon; Kim, Do-Nyun
2017-07-01
Finite element (FE) modeling approach has emerged as an efficient way of calculating the dynamic properties of supramolecular protein structures and their complexes. Its efficiency mainly stems from the fact that the complexity of three-dimensional shape of a molecular surface dominates the computational cost rather than the molecular size or the number of atoms. However, no critical evaluation of the method has been made yet particularly for its sensitivity to the parameters used in model construction. Here, we make a close investigation on the effect of FE model parameters by analyzing 135 representative protein structures whose normal modes calculated using all-atom normal mode analysis are publicly accessible online. Results demonstrate that it is more beneficial to use a contour surface of electron densities as the molecular surface, in general, rather than to employ a solvent excluded surface, and that the solution accuracy is almost insensitive to the model parameters unless we avoid extreme values leading to an inaccurate depiction of the characteristic shapes.
Finite Element Analysis of the Cingulata Jaw: An Ecomorphological Approach to Armadillo's Diets.
Serrano-Fochs, Sílvia; De Esteban-Trivigno, Soledad; Marcé-Nogué, Jordi; Fortuny, Josep; Fariña, Richard A
2014-01-01
Finite element analyses (FEA) were applied to assess the lower jaw biomechanics of cingulate xenarthrans: 14 species of armadillos as well as one Pleistocene pampathere (11 extant taxa and the extinct forms Vassallia, Eutatus and Macroeuphractus). The principal goal of this work is to comparatively assess the biomechanical capabilities of the mandible based on FEA and to relate the obtained stress patterns with diet preferences and variability, in extant and extinct species through an ecomorphology approach. The results of FEA showed that omnivorous species have stronger mandibles than insectivorous species. Moreover, this latter group of species showed high variability, including some similar biomechanical features of the insectivorous Tolypeutes matacus and Chlamyphorus truncatus to those of omnivorous species, in agreement with reported diets that include items other than insects. It remains unclear the reasons behind the stronger than expected lower jaw of Dasypus kappleri. On the other hand, the very strong mandible of the fossil taxon Vassallia maxima agrees well with the proposed herbivorous diet. Moreover, Eutatus seguini yielded a stress pattern similar to Vassalia in the posterior part of the lower jaw, but resembling that of the stoutly built Macroeuphractus outesi in the anterior part. The results highlight the need for more detailed studies on the natural history of extant armadillos. FEA proved a powerful tool for biomechanical studies in a comparative framework.
Finite Element Analysis of the Cingulata Jaw: An Ecomorphological Approach to Armadillo’s Diets
Serrano-Fochs, Sílvia; De Esteban-Trivigno, Soledad; Marcé-Nogué, Jordi; Fortuny, Josep; Fariña, Richard A.
2015-01-01
Finite element analyses (FEA) were applied to assess the lower jaw biomechanics of cingulate xenarthrans: 14 species of armadillos as well as one Pleistocene pampathere (11 extant taxa and the extinct forms Vassallia, Eutatus and Macroeuphractus). The principal goal of this work is to comparatively assess the biomechanical capabilities of the mandible based on FEA and to relate the obtained stress patterns with diet preferences and variability, in extant and extinct species through an ecomorphology approach. The results of FEA showed that omnivorous species have stronger mandibles than insectivorous species. Moreover, this latter group of species showed high variability, including some similar biomechanical features of the insectivorous Tolypeutes matacus and Chlamyphorus truncatus to those of omnivorous species, in agreement with reported diets that include items other than insects. It remains unclear the reasons behind the stronger than expected lower jaw of Dasypus kappleri. On the other hand, the very strong mandible of the fossil taxon Vassallia maxima agrees well with the proposed herbivorous diet. Moreover, Eutatus seguini yielded a stress pattern similar to Vassalia in the posterior part of the lower jaw, but resembling that of the stoutly built Macroeuphractus outesi in the anterior part. The results highlight the need for more detailed studies on the natural history of extant armadillos. FEA proved a powerful tool for biomechanical studies in a comparative framework. PMID:25919313
Numerical computation of transonic flows by finite-element and finite-difference methods
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.
1978-01-01
Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.
An Integrated Magnetic Circuit Model and Finite Element Model Approach to Magnetic Bearing Design
NASA Technical Reports Server (NTRS)
Provenza, Andrew J.; Kenny, Andrew; Palazzolo, Alan B.
2003-01-01
A code for designing magnetic bearings is described. The code generates curves from magnetic circuit equations relating important bearing performance parameters. Bearing parameters selected from the curves by a designer to meet the requirements of a particular application are input directly by the code into a three-dimensional finite element analysis preprocessor. This means that a three-dimensional computer model of the bearing being developed is immediately available for viewing. The finite element model solution can be used to show areas of magnetic saturation and make more accurate predictions of the bearing load capacity, current stiffness, position stiffness, and inductance than the magnetic circuit equations did at the start of the design process. In summary, the code combines one-dimensional and three-dimensional modeling methods for designing magnetic bearings.
MODELING OF HIGH SPEED FRICTION STIR SPOT WELDING USING A LAGRANGIAN FINITE ELEMENT APPROACH
Miles, Michael; Karki, U.; Woodward, C.; Hovanski, Yuri
2013-09-03
Friction stir spot welding (FSSW) has been shown to be capable of joining steels of very high strength, while also being very flexible in terms of controlling the heat of welding and the resulting microstructure of the joint. This makes FSSW a potential alternative to resistance spot welding (RSW) if tool life is sufficiently high, and if machine spindle loads are sufficiently low so that the process can be implemented on an industrial robot. Robots for spot welding can typically sustain vertical loads of about 8kN, but FSSW at tool speeds of less than 3000 rpm cause loads that are too high, in the range of 11-14 kN. Therefore, in the current work tool speeds of 3000 rpm and higher were employed, in order to generate heat more quickly and to reduce welding loads to acceptable levels. The FSSW process was modeled using a finite element approach with the Forge® software package. An updated Lagrangian scheme with explicit time integration was employed to model the flow of the sheet material, subjected to boundary conditions of a rotating tool and a fixed backing plate [3]. The modeling approach can be described as two-dimensional, axisymmetric, but with an aspect of three dimensions in terms of thermal boundary conditions. Material flow was calculated from a velocity field which was two dimensional, but heat generated by friction was computed using a virtual rotational velocity component from the tool surface. An isotropic, viscoplastic Norton-Hoff law was used to model the evolution of material flow stress as a function of strain, strain rate, and temperature. The model predicted welding temperatures and the movement of the joint interface with reasonable accuracy for the welding of a dual phase 980 steel.
Lin, Yi-Tsung; Wu, James Shih-Shyn; Chen, Jian-Horng
2016-07-01
An acetabular cup with larger abduction angles is able to affect the normal function of the cup seriously that may cause early failure of the total hip replacement (THR). Complexity of the finite element (FE) simulation in the wear analysis of the THR is usually concerned with the contact status, the computational effort, and the possible divergence of results, which become more difficult on THRs with larger cup abduction angles. In the study, we propose a FE approach with contact transformation that offers less computational effort. Related procedures, such as Lagrangian Multiplier, partitioned matrix inversion, detection of contact forces, continuity of contact surface, nodal area estimation, etc. are explained in this report. Through the transformed methodology, the computer round-off error is tremendously reduced and the embedded repetitive procedure can be processed precisely and quickly. Here, wear behaviors of THR with various abduction angles are investigated. The most commonly used combination, i.e., metal-on-polyethylene, is adopted in the current study where a cobalt-chromium femoral head is paired with an Ultra High Molecular Weight Polyethylene (UHMWPE) cup. In all illustrations, wear coefficients are estimated by self-averaging strategy with available experimental datum reported elsewhere. The results reveal that the THR with larger abduction angles may produce deeper depth of wear but the volume of wear presents an opposite tendency; these results are comparable with clinical and experimental reports. The current approach can be widely applied easily to fields such as the study of the wear behaviors on ante-version, impingement, and time-dependent behaviors of prostheses etc.
Li, H.; Li, G.
2014-08-28
An accelerated Finite Element Contact Block Reduction (FECBR) approach is presented for computational analysis of ballistic transport in nanoscale electronic devices with arbitrary geometry and unstructured mesh. Finite element formulation is developed for the theoretical CBR/Poisson model. The FECBR approach is accelerated through eigen-pair reduction, lead mode space projection, and component mode synthesis techniques. The accelerated FECBR is applied to perform quantum mechanical ballistic transport analysis of a DG-MOSFET with taper-shaped extensions and a DG-MOSFET with Si/SiO{sub 2} interface roughness. The computed electrical transport properties of the devices obtained from the accelerated FECBR approach and associated computational cost as a function of system degrees of freedom are compared with those obtained from the original CBR and direct inversion methods. The performance of the accelerated FECBR in both its accuracy and efficiency is demonstrated.
NASA Astrophysics Data System (ADS)
Li, H.; Li, G.
2014-08-01
An accelerated Finite Element Contact Block Reduction (FECBR) approach is presented for computational analysis of ballistic transport in nanoscale electronic devices with arbitrary geometry and unstructured mesh. Finite element formulation is developed for the theoretical CBR/Poisson model. The FECBR approach is accelerated through eigen-pair reduction, lead mode space projection, and component mode synthesis techniques. The accelerated FECBR is applied to perform quantum mechanical ballistic transport analysis of a DG-MOSFET with taper-shaped extensions and a DG-MOSFET with Si/SiO2 interface roughness. The computed electrical transport properties of the devices obtained from the accelerated FECBR approach and associated computational cost as a function of system degrees of freedom are compared with those obtained from the original CBR and direct inversion methods. The performance of the accelerated FECBR in both its accuracy and efficiency is demonstrated.
NASA Astrophysics Data System (ADS)
Ringwelski, S.; Gabbert, U.
2010-10-01
A recently developed approach for the simulation and design of a fluid-loaded lightweight structure with surface-mounted piezoelectric actuators and sensors capable of actively reducing the sound radiation and the vibration is presented. The objective of this paper is to describe the theoretical background of the approach in which the FEM is applied to model the actively controlled shell structure. The FEM is also employed to model finite fluid domains around the shell structure as well as fluid domains that are partially or totally bounded by the structure. Boundary elements are used to characterize the unbounded acoustic pressure fields. The approach presented is based on the coupling of piezoelectric and acoustic finite elements with boundary elements. A coupled finite element-boundary element model is derived by introducing coupling conditions at the fluid-fluid and fluid-structure interfaces. Because of the possibility of using piezoelectric patches as actuators and sensors, feedback control algorithms can be implemented directly into the multi-coupled structural-acoustic approach to provide a closed-loop model for the design of active noise and vibration control. In order to demonstrate the applicability of the approach developed, a number of test simulations are carried out and the results are compared with experimental data. As a test case, a box-shaped shell structure with surface-mounted piezoelectric actuators and four sensors and an open rearward end is considered. A comparison between the measured values and those predicted by the coupled finite element-boundary element model shows a good agreement.
Grosland, Nicole M.; Shivanna, Kiran H.; Magnotta, Vincent A.; Kallemeyn, Nicole A.; DeVries, Nicole A.; Tadepalli, Srinivas C.; Lisle, Curtis
2009-01-01
Finite element (FE) analysis is a valuable tool in musculoskeletal research. The demands associated with mesh development, however, often prove daunting. In an effort to facilitate anatomic FE model development we have developed an open source software toolkit (IA-FEMesh). IA-FEMesh employs a multiblock meshing scheme aimed at hexahedral mesh generation. An emphasis has been placed on making the tools interactive, in an effort to create a user friendly environment. The goal is to provide an efficient and reliable method for model development, visualization, and mesh quality evaluation. While these tools have been developed, initially, in the context of skeletal structures they can be applied to countless applications. PMID:19157630
A finite-element approach to evaluating the size effects of complex nanostructures
Lu, Dingjie; Xie, Yi Min; Li, Qing; Huang, Xiaodong; Li, Yang Fan
2016-01-01
The size effects that reveal the dramatic changes of mechanical behaviour at nanoscales have traditionally been analysed for regular beam systems. Here, the method of using finite-element analysis is explored with the intention of evaluating the size effects for complex nanostructures. The surface elasticity theory and generalized Young–Laplace equation are integrated into a beam element to account for the size effects in classical Euler–Bernoulli and Timoshenko beam theories. Computational results match well with the theoretical predictions on the size effect for a cantilever beam and a cubic unit cell containing 24 horizontal/vertical ligaments. For a simply supported nanowire, it is found that the results are very close to the experimental data. With the assumption that nanoporous gold is composed of many randomly connected beams, for the first time, the size effect of such a complex structure is numerically determined. PMID:28083106
A finite-element approach to evaluating the size effects of complex nanostructures
NASA Astrophysics Data System (ADS)
Lu, Dingjie; Xie, Yi Min; Li, Qing; Huang, Xiaodong; Li, Yang Fan; Zhou, Shiwei
2016-12-01
The size effects that reveal the dramatic changes of mechanical behaviour at nanoscales have traditionally been analysed for regular beam systems. Here, the method of using finite-element analysis is explored with the intention of evaluating the size effects for complex nanostructures. The surface elasticity theory and generalized Young-Laplace equation are integrated into a beam element to account for the size effects in classical Euler-Bernoulli and Timoshenko beam theories. Computational results match well with the theoretical predictions on the size effect for a cantilever beam and a cubic unit cell containing 24 horizontal/vertical ligaments. For a simply supported nanowire, it is found that the results are very close to the experimental data. With the assumption that nanoporous gold is composed of many randomly connected beams, for the first time, the size effect of such a complex structure is numerically determined.
Johannesson, G; Glaser, R E; Lee, C L; Nitao, J J; Hanley, W G
2005-02-07
Estimating unknown system configurations/parameters by combining system knowledge gained from a computer simulation model on one hand and from observed data on the other hand is challenging. An example of such inverse problem is detecting and localizing potential flaws or changes in a structure by using a finite-element model and measured vibration/displacement data. We propose a probabilistic approach based on Bayesian methodology. This approach does not only yield a single best-guess solution, but a posterior probability distribution over the parameter space. In addition, the Bayesian approach provides a natural framework to accommodate prior knowledge. A Markov chain Monte Carlo (MCMC) procedure is proposed to generate samples from the posterior distribution (an ensemble of likely system configurations given the data). The MCMC procedure proposed explores the parameter space at different resolutions (scales), resulting in a more robust and efficient procedure. The large-scale exploration steps are carried out using coarser-resolution finite-element models, yielding a considerable decrease in computational time, which can be a crucial for large finite-element models. An application is given using synthetic displacement data from a simple cantilever beam with MCMC exploration carried out at three different resolutions.
Wong, J.; Göktepe, S.; Kuhl, E.
2014-01-01
Summary Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, while the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of four days on a standard desktop computer. PMID:23798328
A goal-oriented adaptive finite-element approach for multi-electrode resistivity system
NASA Astrophysics Data System (ADS)
Ren, Zhengyong; Tang, Jingtian
2014-10-01
We present a novel accurate and efficient goal-oriented adaptive finite-element method solution for complex multi-electrodes resistivity system with arbitrary smooth surface topographies. A simple Green's function of a half-space model is adopted to eliminate the singularity. A unified boundary value problem for the regular potential is formulated for a multi-electrodes system so that it shares a common system matrix. In addition, a goal-oriented error estimation technique is developed to generate an optimal common grid so that highly accurate solutions are obtained with minimum computation cost. Synthetic models are used to verify our algorithm and excellent agreements are obtained by comparing with other methods.
A Finite-Element Approach for Modeling Inviscid and Viscous Compressible Flows using Prismatic Grids
NASA Technical Reports Server (NTRS)
Pandya, S. A.; Hefez, M.
2000-01-01
The Galerkin finite-element method is used to solve the Euler and Navier-Stokes equations on prismatic meshes. It is shown that the prismatic grid is advantageous for correctly and efficiently capturing the boundary layers in high Reynolds number flows. It can be captured accurately because of the ability to cluster grid points normal to the body. The efficiency derives from the implicit treatment of the normal direction. To treat the normal direction implicitly, a semi-implicit Runge-Kutta time stepping scheme is developed. The semi-implicit algorithm is validated on simple geometries for inviscid and viscous flows and its convergence history is compared to that of the explicit Runge-Kutta scheme. The semi-implicit scheme is shown to be a factor of 3 to 4 faster in terms of CPU time to convergence.
A Finite Element Method for Computation of Structural Intensity by the Normal Mode Approach
NASA Astrophysics Data System (ADS)
Gavrić, L.; Pavić, G.
1993-06-01
A method for numerical computation of structural intensity in thin-walled structures is presented. The method is based on structural finite elements (beam, plate and shell type) enabling computation of real eigenvalues and eigenvectors of the undamped structure which then serve in evaluation of complex response. The distributed structural damping is taken into account by using the modal damping concept, while any localized damping is treated as an external loading, determined by use of impedance matching conditions and eigenproperties of the structure. Emphasis is given to aspects of accuracy of the results and efficiency of the numerical procedures used. High requirements on accuracy of the structural response (displacements and stresses) needed in intensity applications are satisfied by employing the "swept static solution", which effectively takes into account the influence of higher modes otherwise inaccessible to numerical computation. A comparison is made between the results obtained by using analytical methods and the proposed numerical procedure to demonstrate the validity of the method presented.
Using a general purpose finite element approach to attain higher fidelity rotordynamic analyses
NASA Astrophysics Data System (ADS)
Gyekenyesi, Andrew L.; Wroblewski, Adam C.
2015-04-01
By utilizing a general purpose finite element (FE) code, the dynamic response of a rotor system was numerically studied in order to assess physical effects that are typically not taken into account using traditional rotordynamic codes. This included the allowance for disk flexibility as well as conducting a simultaneous heat transfer analysis that resulted in varying temperatures in the axial and radial directions. The numerical study utilized a generic, multi-disk model with a flexible hollow shaft. The Campbell diagrams and the mode shapes showed that neglecting any of the additional influences may cause errors regarding the predicted rotor dynamic response. By increasing the fidelity of the rotor model and accounting for the various effects, the slight signal modifications due to damage can be more easily recognized allowing for increased accuracy during rotor health monitoring.
Finite element approach analysis for characteristics of electromagnetic acoustic Lamb wave
NASA Astrophysics Data System (ADS)
Chen, Xiaoming; Li, Songsong
2016-04-01
The electromagnetic acoustic Lamb wave, with the advantages of quickly detecting the defect and sensitivity to the defects, is widely used in non-destructive testing of thin sheet. In this paper, the directivity of sound field, Phase velocity, group velocity and particle displacement amplitude of Lamb wave are study based on finite element analysis method. The results show that, for 1mm aluminum, when the excitation frequency 0.64MHz, the displacement amplitude of A0 mode is minimum, and the displacement amplitude S0 mode is largest. Appropriate to increase the displacement amplitude of a mode, while reducing displacement amplitude of another mode, to achieve the excitation of a single mode Lamb wave. It is helpful to the Optimization of transducer parameters, the choice of Lamb wave modes and providing optimal excitation frequency.
Macho, Gabriele A; Shimizu, Daisuke; Jiang, Yong; Spears, Iain R
2005-04-01
Australopithecus anamensis is the stem species of all later hominins and exhibits the suite of characters traditionally associated with hominins, i.e., bipedal locomotion when on the ground, canine reduction, and thick-enameled teeth. The functional consequences of its thick enamel are, however, unclear. Without appropriate structural reinforcement, these thick-enameled teeth may be prone to failure. This article investigates the mechanical behavior of A. anamensis enamel and represents the first in a series that will attempt to determine the functional adaptations of hominin teeth. First, the microstructural arrangement of enamel prisms in A. anamensis teeth was reconstructed using recently developed software and was compared with that of extant hominoids. Second, a finite-element model of a block of enamel containing one cycle of prism deviation was reconstructed for Homo, Pan, Gorilla, and A. anamensis and the behavior of these tissues under compressive stress was determined. Despite similarities in enamel microstructure between A. anamensis and the African great apes, the structural arrangement of prismatic enamel in A. anamensis appears to be more effective in load dissipation under these compressive loads. The findings may imply that this hominin species was well adapted to puncture crushing and are in some respects contrary to expectations based on macromorphology of teeth. Taking together, information obtained from both finite-element analyses and dental macroanatomy leads us to suggest that A. anamensis was probably adapted for habitually consuming a hard-tough diet. However, additional tests are needed to understand the functional adaptations of A. anamensis teeth fully.
A discontinuous finite element approach to cracking in coupled poro-elastic fluid flow models
NASA Astrophysics Data System (ADS)
Wilson, C. R.; Spiegelman, M. W.; Evans, O.; Ulven, O. I.; Sun, W.
2016-12-01
Reaction-driven cracking is a coupled process whereby fluid-induced reactions drive large volume changes in the host rock which produce stresses leading to crack propagation and failure. This in turn generates new surface area and fluid-flow pathways for subsequent reaction in a potentially self-sustaining system. This mechanism has has been proposed for the pervasive serpentinization and carbonation of peridotite, as well as applications to mineral carbon sequestration and hydrocarbon extraction. The key computational issue in this problem is implementing algorithms that adequately model the formation of discrete fractures. Here we present models using a discontinuous finite element method for modeling fracture formation (Radovitsky et al., 2011). Cracks are introduced along facets of the mesh by the relaxation of penalty parameters once a failure criterion is met. It is fully described in the weak form of the equations, requiring no modification of the underlying mesh structure and allowing fluid properties to be easily adjusted along cracked facets. To develop and test the method, we start by implementing the algorithm for the simplified Biot equations for poro-elasticity using the finite element model assembler TerraFERMA. We consider hydro-fracking around a borehole (Grassl et al., 2015), where elevated fluid pressure in the poro-elastic solid causes it to fail radially in tension. We investigate the effects of varying the Biot coefficient and adjusting the fluid transport properties in the vicinity of the crack and compare our results to related dual-graph models (Ulven & Sun, submitted). We discuss issues arising from this method, including the formation of null spaces and appropriate preconditioning and solution strategies. Initial results suggest that this method provides a promising way to incorporate cracking into our reactive fluid flow models and future work aims to integrate the mechanical and chemical aspects of this process.
Implant platform switching: biomechanical approach using two-dimensional finite element analysis.
Tabata, Lucas Fernando; Assunção, Wirley Gonçalves; Adelino Ricardo Barão, Valentim; de Sousa, Edson Antonio Capello; Gomes, Erica Alves; Delben, Juliana Aparecida
2010-01-01
In implant therapy, a peri-implant bone resorption has been noticed mainly in the first year after prosthesis insertion. This bone remodeling can sometimes jeopardize the outcome of the treatment, especially in areas in which short implants are used and also in aesthetic cases. To avoid this occurrence, the use of platform switching (PS) has been used. This study aimed to evaluate the biomechanical concept of PS with relation to stress distribution using two-dimensional finite element analysis. A regular matching diameter connection of abutment-implant (regular platform group [RPG]) and a PS connection (PS group [PSG]) were simulated by 2 two-dimensional finite element models that reproduced a 2-piece implant system with peri-implant bone tissue. A regular implant (prosthetic platform of 4.1 mm) and a wide implant (prosthetic platform of 5.0 mm) were used to represent the RPG and PSG, respectively, in which a regular prosthetic component of 4.1 mm was connected to represent the crown. A load of 100 N was applied on the models using ANSYS software. The RPG spreads the stress over a wider area in the peri-implant bone tissue (159 MPa) and the implant (1610 MPa), whereas the PSG seems to diminish the stress distribution on bone tissue (34 MPa) and implant (649 MPa). Within the limitation of the study, the PS presented better biomechanical behavior in relation to stress distribution on the implant but especially in the bone tissue (80% less). However, in the crown and retention screw, an increase in stress concentration was observed.
Pasquariello, Vito; Hammerl, Georg; Örley, Felix; Hickel, Stefan; Danowski, Caroline; Popp, Alexander; Wall, Wolfgang A.; Adams, Nikolaus A.
2016-02-15
We present a loosely coupled approach for the solution of fluid–structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet–Neumann partitioning. The interface motion in the Eulerian frame is accounted for by a conservative cut-cell Immersed Boundary method. The present approach enables sub-cell resolution by considering individual cut-elements within a single fluid cell, which guarantees an accurate representation of the time-varying solid interface. The cut-cell procedure inevitably leads to non-matching interfaces, demanding for a special treatment. A Mortar method is chosen in order to obtain a conservative and consistent load transfer. We validate our method by investigating two-dimensional test cases comprising a shock-loaded rigid cylinder and a deformable panel. Moreover, the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset. Finally, we propose a three-dimensional fluid–structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations.
NASA Astrophysics Data System (ADS)
Pasquariello, Vito; Hammerl, Georg; Örley, Felix; Hickel, Stefan; Danowski, Caroline; Popp, Alexander; Wall, Wolfgang A.; Adams, Nikolaus A.
2016-02-01
We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in the Eulerian frame is accounted for by a conservative cut-cell Immersed Boundary method. The present approach enables sub-cell resolution by considering individual cut-elements within a single fluid cell, which guarantees an accurate representation of the time-varying solid interface. The cut-cell procedure inevitably leads to non-matching interfaces, demanding for a special treatment. A Mortar method is chosen in order to obtain a conservative and consistent load transfer. We validate our method by investigating two-dimensional test cases comprising a shock-loaded rigid cylinder and a deformable panel. Moreover, the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset. Finally, we propose a three-dimensional fluid-structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations.
An asymmetric approach to modeling ion channels using finite element analysis.
Siksik, M; Krishnamurthy, V
2009-01-01
Biological ion channels are water filled pores in the cell membrane. They regulate the flow of ions in and out of the cell. Modeling the dynamics of these channels and relating their structure to functionality is crucial in understanding the mechanisms by which they conduct. This paper proposes a novel Finite Element Method (FEM) based simulation framework for modeling of ion channels that does not assume channel symmetry. This is the first framework that allows the use of multiple dielectric constants inside such channels without assuming geometrical symmetry thus providing a more realistic model of the channel. Due to the run-time complexity of the problem, lookup tables must be constructed in memory to store pre-calculated electric potential information. The large number of elements involved in FEM and channel resolution requirements can potentially result in very large lookup tables leading to a performance "bottleneck". This paper answers the following question: Does the accuracy introduced by using an asymmetric model outweigh the inaccuracy caused by having to reduce the size and resolution of electric-field look-up tables? This paper compares the memory footprint of an ion channel simulator that assumes a symmetric channel model versus an asymmetric model. We show that currently available personal computers are sufficient for attaining reasonable levels of accuracy for both. Our results show diminishing returns in accuracy with tables sized greater than 8.5 GB for the asymmetric model.
Finite element computational fluid mechanics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
Finite element computational fluid mechanics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
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.
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.
3D finite element model of the diabetic neuropathic foot: a gait analysis driven approach.
Guiotto, Annamaria; Sawacha, Zimi; Guarneri, Gabriella; Avogaro, Angelo; Cobelli, Claudio
2014-09-22
Diabetic foot is an invalidating complication of diabetes that can lead to foot ulcers. Three-dimensional (3D) finite element analysis (FEA) allows characterizing the loads developed in the different anatomical structures of the foot in dynamic conditions. The aim of this study was to develop a subject specific 3D foot FE model (FEM) of a diabetic neuropathic (DNS) and a healthy (HS) subject, whose subject specificity can be found in term of foot geometry and boundary conditions. Kinematics, kinetics and plantar pressure (PP) data were extracted from the gait analysis trials of the two subjects with this purpose. The FEM were developed segmenting bones, cartilage and skin from MRI and drawing a horizontal plate as ground support. Materials properties were adopted from previous literature. FE simulations were run with the kinematics and kinetics data of four different phases of the stance phase of gait (heel strike, loading response, midstance and push off). FEMs were then driven by group gait data of 10 neuropathic and 10 healthy subjects. Model validation focused on agreement between FEM-simulated and experimental PP. The peak values and the total distribution of the pressures were compared for this purpose. Results showed that the models were less robust when driven from group data and underestimated the PP in each foot subarea. In particular in the case of the neuropathic subject's model the mean errors between experimental and simulated data were around the 20% of the peak values. This knowledge is crucial in understanding the aetiology of diabetic foot.
An ALE Finite Element Approach for Two-Phase Flow with Phase Change
NASA Astrophysics Data System (ADS)
Gros, Erik; Anjos, Gustavo; Thome, John; Ltcm Team; Gesar Team
2016-11-01
In this work, two-phase flow with phase change is investigated through the Finite Element Method (FEM) in the Arbitrary Lagrangian-Eulerian (ALE) framework. The equations are discretized on an unstructured mesh where the interface between the phases is explicitly defined as a sub-set of the mesh. The two-phase interface position is described by a set of interconnected nodes which ensures a sharp representation of the boundary, including the role of the surface tension. The methodology proposed for computing the curvature leads to very accurate results with moderate programming effort and computational costs. Such a methodology can be employed to study accurately many two-phase flow and heat transfer problems in industry such as oil extraction and refinement, design of refrigeration systems, modelling of microfluidic and biological systems and efficient cooling of electronics for computational purposes. The latter is the principal aim of the present research. The numerical results are discussed and compared to analytical solutions and reference results, thereby revealing the capability of the proposed methodology as a platform for the study of two-phase flow with phase change.
Toward automatic finite element analysis
NASA Technical Reports Server (NTRS)
Kela, Ajay; Perucchio, Renato; Voelcker, Herbert
1987-01-01
Two problems must be solved if the finite element method is to become a reliable and affordable blackbox engineering tool. Finite element meshes must be generated automatically from computer aided design databases and mesh analysis must be made self-adaptive. The experimental system described solves both problems in 2-D through spatial and analytical substructuring techniques that are now being extended into 3-D.
Second order tensor finite element
NASA Technical Reports Server (NTRS)
Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.
1990-01-01
The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.
Fortuny, Josep; Marcé-Nogué, Jordi; Konietzko-Meier, Dorota
2017-03-29
The Late Triassic freshwater ecosystems were occupied by different tetrapod groups including large-sized anamniotes, such as metoposaurids. Most members of this group of temnospondyls acquired gigantic sizes (up to 5 m long) with a nearly worldwide distribution. The paleoecology of metoposaurids is controversial; they have been historically considered passive, bottom-dwelling animals, waiting for prey on the bottom of rivers and lakes, or they have been suggested to be active mid-water feeders. The present study aims to expand upon the paleoecological interpretations of these animals using 3D finite element analyses (FEA). Skulls from two taxa, Metoposaurus krasiejowensis, a gigantic taxon from Europe, and Apachesaurus gregorii, a non-gigantic taxon from North America, were analyzed under different biomechanical scenarios. Both 3D models of the skulls were scaled to allow comparisons between them and reveal that the general stress distribution pattern found in both taxa is clearly similar in all scenarios. In light of our results, both previous hypotheses about the paleoecology of these animals can be partly merged: metoposaurids probably were ambush and active predators, but not the top predators of these aquatic environments. The FEA results demonstrate that they were particularly efficient at bilateral biting, and together with their characteristically anteropositioned orbits, optimal for an ambush strategy. Nonetheless, the results also show that these animals were capable of lateral strikes of the head, suggesting active hunting of prey. Regarding the important skull size differences between the taxa analyzed, our results suggest that the size reduction in the North American taxon could be related to drastic environmental changes or the increase of competitors. The size reduction might have helped them expand into new ecological niches, but they likely remained fully aquatic, as are all other metoposaurids.
Maceri, Franco; Martignoni, Marco; Vairo, Giuseppe
2007-01-01
This paper investigates some mechanical aspects of a new endodontic restoration technique, based on the idea that the root cavity can be more efficiently filled if multiple prefabricated composite posts (PCP) are employed. Multi-post technique increases bearing capacity and durability of endodontically treated teeth, as shown by numerical simulations performed through three-dimensional elastic finite-element static analyses of a lower premolar, constrained by a non-linearly elastic spring system representing the periodontal ligament, under several parafunctional loads. The influence of PCPs' number, material and dimensions is investigated by comparison of the resulting stress fields with those obtained in cases of traditional restorations (cast metal post and cemented single-PCP) and natural tooth, highlighting the advantages of the proposed technique when standard restorative materials are considered. A risk-analysis of root-fracture and interface-failure shows that cast gold-alloy post produces high stress concentrations at post-dentin interface, whereas multi-post solution leads to a behaviour closer to the natural tooth's, exhibiting some advantages with respect to single-PCP restorations. As a matter of fact, whenever PCPs' overall cross-section area increases, multi-post solution induces a significant reduction of stress levels into the residual dentin (and therefore the root-fracture-risk decreases) as well as of the expected polymerization shrinkage effects. Moreover, interfacial stress values in multi-post restorations can be higher than the single-PCP ones when carbon-fibre posts are considered. Nevertheless, the interfacial adhesive/cohesive failure-risk is certainly acceptable if glass-fibre posts are employed.
Finite element shell instability analysis
NASA Technical Reports Server (NTRS)
1975-01-01
Formulation procedures and the associated computer program for finite element thin shell instability analysis are discussed. Data cover: (1) formulation of basic element relationships, (2) construction of solution algorithms on both the conceptual and algorithmic levels, and (3) conduction of numerical analyses to verify the accuracy and efficiency of the theory and related programs therein are described.
Chang, Yia-Chung; Li, Guangwei; Chu, Hanyou; Opsal, Jon
2006-03-01
We present an efficient method for calculating the reflectivity of three-dimensional gratings on multilayer films based on a finite-element, Green's function approach. Our method scales as NlogN, where N is the number of plane waves used in the expansion. Therefore, it is much more efficient than the commonly adopted rigorous-coupled-wave analysis (RCWA), which scales as N3. We demonstrate the effectiveness of this method by applying it to a two-dimensional periodic array of contact holes on a multilayer film. We find that our Green's function approach is about one order of magnitude faster than the RCWA approach when applied to typical contact holes considered in industry. For most cases, this method is efficient enough for application as a realtime, critical-dimension metrology tool.
NASA Technical Reports Server (NTRS)
Contreras, Michael T.; Peng, Chia-Yen; Wang, Dongdong; Chen, Jiun-Shyan
2012-01-01
A wheel experiencing sinkage and slippage events poses a high risk to rover missions as evidenced by recent mobility challenges on the Mars Exploration Rover (MER) project. Because several factors contribute to wheel sinkage and slippage conditions such as soil composition, large deformation soil behavior, wheel geometry, nonlinear contact forces, terrain irregularity, etc., there are significant benefits to modeling these events to a sufficient degree of complexity. For the purposes of modeling wheel sinkage and slippage at an engineering scale, meshfree finite element approaches enable simulations that capture sufficient detail of wheel-soil interaction while remaining computationally feasible. This study demonstrates some of the large deformation modeling capability of meshfree methods and the realistic solutions obtained by accounting for the soil material properties. A benchmark wheel-soil interaction problem is developed and analyzed using a specific class of meshfree methods called Reproducing Kernel Particle Method (RKPM). The benchmark problem is also analyzed using a commercially available finite element approach with Lagrangian meshing for comparison. RKPM results are comparable to classical pressure-sinkage terramechanics relationships proposed by Bekker-Wong. Pending experimental calibration by future work, the meshfree modeling technique will be a viable simulation tool for trade studies assisting rover wheel design.
NASA Technical Reports Server (NTRS)
Contreras, Michael T.; Peng, Chia-Yen; Wang, Dongdong; Chen, Jiun-Shyan
2012-01-01
A wheel experiencing sinkage and slippage events poses a high risk to rover missions as evidenced by recent mobility challenges on the Mars Exploration Rover (MER) project. Because several factors contribute to wheel sinkage and slippage conditions such as soil composition, large deformation soil behavior, wheel geometry, nonlinear contact forces, terrain irregularity, etc., there are significant benefits to modeling these events to a sufficient degree of complexity. For the purposes of modeling wheel sinkage and slippage at an engineering scale, meshfree finite element approaches enable simulations that capture sufficient detail of wheel-soil interaction while remaining computationally feasible. This study demonstrates some of the large deformation modeling capability of meshfree methods and the realistic solutions obtained by accounting for the soil material properties. A benchmark wheel-soil interaction problem is developed and analyzed using a specific class of meshfree methods called Reproducing Kernel Particle Method (RKPM). The benchmark problem is also analyzed using a commercially available finite element approach with Lagrangian meshing for comparison. RKPM results are comparable to classical pressure-sinkage terramechanics relationships proposed by Bekker-Wong. Pending experimental calibration by future work, the meshfree modeling technique will be a viable simulation tool for trade studies assisting rover wheel design.
Al-sukhun, Jehad; Penttilä, Heikki; Ashammakhi, Nureddin
2012-05-01
The progress in computer technology and the increased use of finite element analysis in the medical field by nonengineers and medical researchers lead us to believe that there is a need to develop a systematic approach to validate a finite element model (FEM), of a human orbit, that simulates part of the maxillofacial skeleton and to investigate the effects and the clinical significance of changing the geometry, boundary conditions, that is, muscle forces, and orthotropic material properties on the predictive outcome of an FEM of a human orbit. Forty-seven variables affecting the material properties, boundary conditions, and the geometry of an FEM of a human orbit including the globe were systematically changed, creating a number of FEMs of the orbit. The effects of the variations were quantified as differences in the principal strain magnitudes modeled by the original FEM (criterion standard), before the sensitivity analyses, and those generated by the changed FEMs. The material properties that had the biggest impact on the predicted principal strains were the shear moduli (up to 21%) and the absence of fatty tissue (up to 75%). The boundary condition properties that had the biggest impact on the predicted principal strains were the superior rectus muscle and canthal ligaments (up to 18% and 23%, respectively). Alterations to the geometry of the orbit, such as an increase in its volume, had the greatest effect on principal strain magnitudes (up to 52%). Changes in geometry, boundary conditions, and orthotropic material properties can induce significant changes in strain patterns. These values must therefore be chosen with care when using finite element modeling techniques. This study also highlights the importance of restoring the orbital fat and volume when reconstructing the orbital floor following a blunt injury. The possibility that the unrestored increase in the orbital volume and the resulting stresses may be a source of globe injuries, causing diplopia
Robust and scalable 3-D geo-electromagnetic modelling approach using the finite element method
NASA Astrophysics Data System (ADS)
Grayver, Alexander V.; Bürg, Markus
2014-07-01
We present a robust and scalable solver for time-harmonic Maxwell's equations for problems with large conductivity contrasts, wide range of frequencies, stretched grids and locally refined meshes. The solver is part of the fully distributed adaptive 3-D electromagnetic modelling scheme which employs the finite element method and unstructured non-conforming hexahedral meshes for spatial discretization using the open-source software deal.II. We use the complex-valued electric field formulation and split it into two real-valued equations for which we utilize an optimal block-diagonal pre-conditioner. Application of this pre-conditioner requires the solution of two smaller real-valued symmetric problems. We solve them by using either a direct solver or the conjugate gradient method pre-conditioned with the recently introduced auxiliary space technique. The auxiliary space pre-conditioner reformulates the original problem in form of several simpler ones, which are then solved using highly efficient algebraic multigrid methods. In this paper, we consider the magnetotelluric case and verify our numerical scheme by using COMMEMI 3-D models. Afterwards, we run a series of numerical experiments and demonstrate that the solver converges in a small number of iterations for a wide frequency range and variable problem sizes. The number of iterations is independent of the problem size, but exhibits a mild dependency on frequency. To test the stability of the method on locally refined meshes, we have implemented a residual-based a posteriori error estimator and compared it with uniform mesh refinement for problems up to 200 million unknowns. We test the scalability of the most time consuming parts of our code and show that they fulfill the strong scaling assumption as long as each MPI process possesses enough degrees of freedom to alleviate communication overburden. Finally, we refer back to a direct solver-based pre-conditioner and analyse its complexity in time. The results show
Ishak, Muhammad Ikman; Kadir, Mohammed Rafiq Abdul; Sulaiman, Eshamsul; Kasim, Noor Hayaty Abu
2013-01-01
To compare the extramaxillary approach with the widely used intrasinus approach via finite element method. A unilateral three-dimensional model of the craniofacial area surrounding the region of interest was developed using computed tomography image datasets. The zygomatic implants were modeled using three-dimensional computer-aided design software and virtually placed according to the described techniques together with one conventional implant and a prosthesis. The bone was assumed to be linear isotropic with a stiffness of 13.4 GPa, while the implants were of titanium alloy with a stiffness of 110 GPa. Masseter forces were applied at the zygomatic arch, and occlusal loads were applied to the surface of the prosthesis. The stresses and displacements generated on the surrounding bone and within the implant due to the simulated loading configuration were analyzed. The bone-implant interface and zygomatic implant body for the intrasinus approach produced 1.41- and 4.27-fold higher stress, respectively, compared with the extramaxillary approach under vertical loading. However, under lateral loading, the extramaxillary approach generated 2.48-fold higher stress than the intrasinus at the bone-implant interface. The zygomatic implant in the extramaxillary approach had twofold higher micromotion than those with intrasinus approach under lateral loading. No one technique was found to be superior; however, if lateral loading is used, the intrasinus approach is the most favorable for the rehabilitation of severely atrophic maxillae.
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.
NASA Astrophysics Data System (ADS)
Bhuiyan, Yeasin; Shen, Yanfeng; Giurgiutiu, Victor
2016-04-01
Ultrasonic inspection of multiple-rivet-hole lap joint cracks has been introduced using combined analytical and finite element approach (CAFA). Finite element analyses have been performed on local damage area in spite of the whole large structure and transfer function based analytical model is used to analyze the full structure. "Scattered cube" of complex valued wave damage interaction coefficient (WDIC) that involves scattering and mode conversion of Lamb waves around the damage is used as coupling between analytical and FEM simulation. WDIC is captured for multiple angles of incident Lamb mode (S0 and A0) over the frequency domain to analyze the cracks of multiple-rivet-hole lap joint. By analyzing the scattered cube of WDICs over the frequency domain and azimuthal angles the optimum parameters can be determined for each angle of incidence and the most sensitive signals are obtained using WaveformRevealer2D (WFR2D). These sensitive signals confirm the detection of the butterfly cracks in rivet holes through the installment of the transmitting and sensing PWASs in the proper locations and selecting the right frequency of excitation.
Parallel, Implicit, Finite Element Solver
NASA Astrophysics Data System (ADS)
Lowrie, Weston; Shumlak, Uri; Meier, Eric; Marklin, George
2007-11-01
A parallel, implicit, finite element solver is described for solutions to the ideal MHD equations and the Pseudo-1D Euler equations. The solver uses the conservative flux source form of the equations. This helps simplify the discretization of the finite element method by keeping the specification of the physics separate. An implicit time advance is used to allow sufficiently large time steps. The Portable Extensible Toolkit for Scientific Computation (PETSc) is implemented for parallel matrix solvers and parallel data structures. Results for several test cases are described as well as accuracy of the method.
Exact finite elements for conduction and convection
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.
Tang, C Y; Tsui, C P; Tang, Y M; Wei, L; Wong, C T; Lam, K W; Ip, W Y; Lu, W W J; Pang, M Y C
2014-01-01
With the development of micro-computed tomography (micro-CT) technology, it is possible to construct three-dimensional (3D) models of human bone without destruction of samples and predict mechanical behavior of bone using finite element analysis (FEA). However, due to large number of elements required for constructing the FE models of entire bone, this demands a substantial computational effort and the analysis usually needs a high level of computer. In this article, a voxel-based approach for generation of FE models of entire bone with microscopic architecture from micro-CT image data is proposed. To enable the FE analyses of entire bone to be run even on a general personal computer, grayscale intensity thresholds were adopted to reduce the amount of elements. Human metacarpal bone (MCP) bone was used as an example for demonstrating the applicability of the proposed method. The micro-CT images of the MCP bone were combined and converted into 3D array of pixels. Dual grayscale intensity threshold parameters were used to distinguish the pixels of bone tissues from those of surrounding soft tissues and improve predictive accuracy for the FE analyses with different sizes of elements. The method of selecting an appropriate value of the second grayscale intensity threshold was also suggested to minimize the area error for the reconstructed cross-sections of a FE structure. Experimental results showed that the entire FE MCP bone with microscopic architecture could be modeled and analyzed on a personal computer with reasonable accuracy.
On numerically accurate finite element
NASA Technical Reports Server (NTRS)
Nagtegaal, J. C.; Parks, D. M.; Rice, J. R.
1974-01-01
A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional element types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing finite element program, is presented. This allows accurate computations to be made even for element designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various element designs and of the new variational procedure are illustrated. Elastic-plastic computation at finite strain are discussed.
An adaptive finite element approach to modelling sediment laden density currents
NASA Astrophysics Data System (ADS)
Parkinson, S.; Hill, J.; Allison, P. A.; Piggott, M. D.
2012-04-01
Modelling sediment-laden density currents at real-world scales is a challenging task. Here we present Fluidity, which uses dynamic adaptive re-meshing to reduce computational costs whilst maintaining sufficient resolution where and when it is required. This allows small-scale processes to be captured in large scale simulations. Density currents, also known as gravity or buoyancy currents, occur wherever two fluids with different densities meet. They can occur at scales of up to hundred kilometres in the ocean when continental shelves collapse. This process releases large quantities of sediment into the ocean which increase the bulk density of the fluid to form a density current. These currents can carry sediment hundreds of kilometres, at speeds of up to a hundred kilometres per hour, over the sea bed. They can be tsunamigenic and they have the potential to cause significant damage to submarine infrastructure, such as submarine telecommunications cables or oil and gas infrastructure. They are also a key process for movement of organic material into the depths of the ocean. Due to this, they play an important role in the global carbon cycle on the Earth, forming a significant component of the stratigraphic record, and their deposits can form useful sources of important hydrocarbons. Modelling large scale sediment laden density currents is a very challenging problem. Particles within the current are suspended by turbulence that occurs at length scales that are several orders of magnitude smaller than the size of the current. Models that resolve the vertical structure of the flow require a very large, highly resolved mesh, and substantial computing power to solve. Here, we verify our adaptive model by comparison with a set of laboratory experiments by Gladstone et al. [1998] on the propagation and sediment deposition of bidisperse gravity currents. Comparisons are also made with fixed mesh solutions, and it is shown that accuracy can be maintained with fewer elements
Ural, Ani; Bruno, Peter; Zhou, Bin; Shi, X Tony; Guo, X Edward
2013-04-26
A new fracture assessment approach that combines HR-pQCT imaging with fracture mechanics-based finite element modeling was developed to evaluate distal radius fracture load. Twenty distal radius images obtained from postmenopausal women (fracture, n=10; nonfracture, n=10) were processed to obtain a cortical and a whole bone model for each subject. The geometrical properties of each model were evaluated and the corresponding fracture load was determined under realistic fall conditions using cohesive finite element modeling. The results showed that the whole bone fracture load can be estimated based on the cortical fracture load for nonfracture (R(2)=0.58, p=0.01) and pooled data (R(2)=0.48, p<0.001) but not for the fracture group. The portion of the whole bone fracture load carried by the cortical bone increased with increasing cortical fracture load (R(2)≥0.5, p<0.05) indicating that a more robust cortical bone carries a larger percentage of whole bone fracture load. Cortical thickness was found to be the best predictor of both cortical and whole bone fracture load for all groups (R(2) range: 0.49-0.96, p<0.02) with the exception of fracture group whole bone fracture load showing the predictive capability of cortical geometrical properties in determining whole bone fracture load. Fracture group whole bone fracture load was correlated with trabecular thickness (R(2)=0.4, p<0.05) whereas the nonfracture and the pooled group did not show any correlation with the trabecular parameters. In summary, this study introduced a new modeling approach that coupled HR-pQCT imaging with fracture mechanics-based finite element simulations, incorporated fracture toughness and realistic fall loading conditions in the models, and showed the significant contribution of the cortical compartment to the overall fracture load of bone. Our results provide more insight into the fracture process in bone and may lead to improved fracture load predictions. Copyright © 2013 Elsevier Ltd. All
Ural, Ani; Bruno, Peter; Zhou, Bin; Shi, X. Tony; Guo, X. Edward
2013-01-01
A new fracture assessment approach that combines HR-pQCT imaging with fracture mechanics-based finite element modeling was developed to evaluate distal radius fracture load. Twenty distal radius images obtained from postmenopausal women (fracture, n = 10; nonfracture, n = 10) were processed to obtain a cortical and a whole bone model for each subject. The geometrical properties of each model were evaluated and the corresponding fracture load was determined under realistic fall conditions using cohesive finite element modeling. The results showed that the whole bone fracture load can be estimated based on the cortical fracture load for nonfracture (R2 = 0.58, p = 0.01) and pooled data (R2 = 0.48, p < 0.001) but not for the fracture group. The portion of the whole bone fracture load carried by the cortical bone increased with increasing cortical fracture load (R2 ≥ 0.5, p < 0.05) indicating that a more robust cortical bone carries a larger percentage of whole bone fracture load. Cortical thickness was found to be the best predictor of both cortical and whole bone fracture load for all groups (R2 range: 0.49–0.96, p < 0.02) with the exception of fracture group whole bone fracture load showing the predictive capability of cortical geometrical properties in determining whole bone fracture load. Fracture group whole bone fracture load was correlated with trabecular thickness (R2 = 0.4, p < 0.05) whereas the nonfracture and the pooled group did not show any correlation with the trabecular parameters. In summary, this study introduced a new modeling approach that coupled HR-pQCT imaging with fracture mechanics-based finite element simulations, incorporated fracture toughness and realistic fall loading conditions in the models, and showed the significant contribution of the cortical compartment to the overall fracture load of bone. Our results provide more insight into the fracture process in bone and may lead to improved fracture load predictions. PMID:23497802
Sadeghi-Goughari, Moslem; Mojra, Afsaneh
2015-10-01
Intraoperative Thermal Imaging (ITI) is a novel neuroimaging method that can potentially locate tissue abnormalities and hence improves surgeon's diagnostic ability. In the present study, thermography technique coupled with artificial tactile sensing method called "haptic thermography" is utilized to investigate the presence of an abnormal object as a tumor with an elevated temperature relative to the normal tissue in the brain. The brain tissue is characterized as a hyper-viscoelastic material to be descriptive of mechanical behavior of the brain tissue during tactile palpation. Based on a finite element approach, Magnetic Resonance Imaging (MRI) data of a patient diagnosed to have a brain tumor is utilized to simulate and analyze the capability of haptic thermography in detection and localization of brain tumor. Steady-state thermal results prove that temperature distribution is an appropriate outcome of haptic thermography for the superficial tumors while heat flux distribution can be used as an extra thermal result for deeply located tumors.
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.
Improved finite element methodology for integrated thermal structural analysis
NASA Technical Reports Server (NTRS)
Dechaumphai, P.; Thornton, E. A.
1982-01-01
An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. New thermal finite elements which yield exact nodal and element temperatures for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.
Improved finite element methodology for integrated thermal structural analysis
NASA Technical Reports Server (NTRS)
Dechaumphai, P.; Thornton, E. A.
1982-01-01
An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analyses is presented. New thermal finite elements which yield exact nodal and element temperature for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal-structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.
Klöppel, Thomas; Wall, Wolfgang A
2011-07-01
A novel finite element approach is presented to simulate the mechanical behavior of human red blood cells (RBC, erythrocytes). As the RBC membrane comprises a phospholipid bilayer with an intervening protein network, we propose to model the membrane with two distinct layers. The fairly complex characteristics of the very thin lipid bilayer are represented by special incompressible solid shell elements and an anisotropic viscoelastic constitutive model. Properties of the protein network are modeled with an isotropic hyperelastic third-order material. The elastic behavior of the model is validated with existing optical tweezers studies with quasi-static deformations. Employing material parameters consistent with literature, simulation results are in excellent agreement with experimental data. Available models in literature neglect either the surface area conservation of the RBC membrane or realistic loading conditions of the optical tweezers experiments. The importance of these modeling assumptions, that are both included in this study, are discussed and their influence quantified. For the simulation of the dynamic motion of RBC, the model is extended to incorporate the cytoplasm. This is realized with a monolithic fully coupled fluid-structure interaction simulation, where the fluid is described by the incompressible Navier-Stokes equations in an arbitrary Lagrangian Eulerian framework. It is shown that both membrane viscosity and cytoplasm viscosity have significant influence on simulation results. Characteristic recovery times and energy dissipation for varying strain rates in dynamic laser trap experiments are calculated for the first time and are found to be comparable with experimental data.
NASA Astrophysics Data System (ADS)
Wroblewski, Adam C.; Gyekenyesi, Andrew L.
2014-04-01
With continual improvement in computing power and software codes that simulate multiple physical effects, complex analyses can be performed that allow for more accurate modeling of real world systems. Here, a general purpose finite element (FE) code was utilized to conduct a rotordynamic assessment of a rotor system containing a flexible disk. Typically, specialized rotordynamic software packages make numerous assumptions to simplify the various types of rotor response calculations. Disks, for example, are commonly assumed rigid and are represented by lumped masses or discrete beam elements. Such idealizations may cause inaccuracies when calculating critical speeds for rotor systems that involve a relatively flexible disk. By utilizing a general purpose FE approach, where multiple rotational effects are considered, a more accurate model can be developed that includes the dynamic contributions of a flexible disk. This paper illustrates the rotordynamic analysis of a generic, yet realistic, compressor with a shrouded impeller model, without extensive geometric simplification. Furthermore, through the utilization of the fully featured geometry, several dynamic effects are demonstrated to have a significant influence on the rotor system's Campbell diagram. The dynamic effects investigated include disk flexibility, stress stiffening, and spin softening. It is shown that neglecting any of these may cause significant errors regarding the rotordynamic analysis predictions.
A Computational Approach for Automated Posturing of a Human Finite Element Model
2016-07-01
simple terms like “hinges” and “ball and socket”, rarely move as perfect hinges or ball and socket joints. This can become an issue when 2 stiff...approach is flexible in that improvements to the joint functions can be made at any time. Thus, at first a model might assume a perfect hinge and then
Nonlinear, finite deformation, finite element analysis
NASA Astrophysics Data System (ADS)
Nguyen, Nhung; Waas, Anthony M.
2016-06-01
The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli ( C e ) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated
NASA Astrophysics Data System (ADS)
Arshadi, Amir
Image-based simulation of complex materials is a very important tool for understanding their mechanical behavior and an effective tool for successful design of composite materials. In this thesis an image-based multi-scale finite element approach is developed to predict the mechanical properties of asphalt mixtures. In this approach the "up-scaling" and homogenization of each scale to the next is critically designed to improve accuracy. In addition to this multi-scale efficiency, this study introduces an approach for consideration of particle contacts at each of the scales in which mineral particles exist. One of the most important pavement distresses which seriously affects the pavement performance is fatigue cracking. As this cracking generally takes place in the binder phase of the asphalt mixture, the binder fatigue behavior is assumed to be one of the main factors influencing the overall pavement fatigue performance. It is also known that aggregate gradation, mixture volumetric properties, and filler type and concentration can affect damage initiation and progression in the asphalt mixtures. This study was conducted to develop a tool to characterize the damage properties of the asphalt mixtures at all scales. In the present study the Viscoelastic continuum damage model is implemented into the well-known finite element software ABAQUS via the user material subroutine (UMAT) in order to simulate the state of damage in the binder phase under the repeated uniaxial sinusoidal loading. The inputs are based on the experimentally derived measurements for the binder properties. For the scales of mastic and mortar, the artificially 2-Dimensional images of mastic and mortar scales were generated and used to characterize the properties of those scales. Finally, the 2D scanned images of asphalt mixtures are used to study the asphalt mixture fatigue behavior under loading. In order to validate the proposed model, the experimental test results and the simulation results were
2001-06-01
fin during maneuvers at high angles of attack. in the IFOST Program test facility in Australia. The An initial approach to minimize the problem...controller countries within The Technical Co-operation Program , robustness under different excitation loads. (TTCP) that include the F/A-18 in their fleets...The TTCP is a program of technical collaboration and data exchange among five nations: Canada, the United NASTRAN Model States, Australia, United
ANSYS duplicate finite-element checker routine
NASA Technical Reports Server (NTRS)
Ortega, R.
1995-01-01
An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.
Su, Yukun; Kluess, Daniel; Mittelmeier, Wolfram; van Rienen, Ursula; Bader, Rainer
2016-09-01
The dielectric properties of human bone are one of the most essential inputs required by electromagnetic stimulation for improved bone regeneration. Measuring the electric properties of bone is a difficult task because of the complexity of the bone structure. Therefore, an automatic approach is presented to calibrate the electric properties of bone. The numerical method consists of three steps: generating input from experimental data, performing the numerical simulation, and calibrating the bone dielectric properties. As an example, the dielectric properties at 20 Hz of a rabbit distal femur were calibrated. The calibration process was considered as an optimization process with the aim of finding the optimum dielectric bone properties that match most of the numerically calculated simulation and experimentally measured data sets. The optimization was carried out automatically by the optimization software tool iSIGHT in combination with the finite-element solver COMSOL Multiphysics. As a result, the optimum conductivity and relative permittivity of the rabbit distal femur at 20 Hz were found to be 0.09615 S/m and 19522 for cortical bone and 0.14913 S/m and 1561507 for cancellous bone, respectively. The proposed method is a potential tool for the identification of realistic dielectric properties of the entire bone volume. The presented approach combining iSIGHT with COMSOL is applicable to, amongst others, designing implantable electro-stimulative devices or the optimization of electrical stimulation parameters for improved bone regeneration.
NASA Astrophysics Data System (ADS)
Mansur, Ali; Nganbe, Michel
2015-03-01
The ballistic impact was numerically modeled for AISI 450 steel struck by a 17.3 g ogive nose WC-Co projectile using Abaqus/Explicit. The model was validated using experimental results and data for different projectiles and metal targets. The Abaqus ductile-shear, local principal strain to fracture, and absorbed strain energy at failure criteria were investigated. Due to the highly dynamic nature of ballistic impacts, the absorbed strain energy approach posed serious challenges in estimating the effective deformation volume and yielded the largest critical plate thicknesses for through-thickness penetration (failure). In contrast, the principal strain criterion yielded the lowest critical thicknesses and provided the best agreement with experimental ballistic test data with errors between 0 and 30%. This better accuracy was due to early failure definition when the very first mesh at the target back side reached the strain to fracture, which compensated for the overall model overestimation. The ductile-shear criterion yielded intermediate results between those of the two comparative approaches. In contrast to the ductile-shear criterion, the principal strain criterion requires only basic data readily available for practically all materials. Therefore, it is a viable alternative for an initial assessment of the ballistic performance and pre-screening of a large number of new candidate materials as well as for supporting the development of novel armor systems.
Infinite Possibilities for the Finite Element.
ERIC Educational Resources Information Center
Finlayson, Bruce A.
1981-01-01
Describes the uses of finite element methods in solving problems of heat transfer, fluid flow, etc. Suggests that engineers should know the general concepts and be able to apply the principles of finite element methods. (Author/WB)
SUPG Finite Element Simulations of Compressible Flows
NASA Technical Reports Server (NTRS)
Kirk, Brnjamin, S.
2006-01-01
The Streamline-Upwind Petrov-Galerkin (SUPG) finite element simulations of compressible flows is presented. The topics include: 1) Introduction; 2) SUPG Galerkin Finite Element Methods; 3) Applications; and 4) Bibliography.
A distributed finite-element modeling and control approach for large flexible structures
NASA Technical Reports Server (NTRS)
Young, K. D.
1989-01-01
An unconventional framework is described for the design of decentralized controllers for large flexible structures. In contrast to conventional control system design practice which begins with a model of the open loop plant, the controlled plant is assembled from controlled components in which the modeling phase and the control design phase are integrated at the component level. The developed framework is called controlled component synthesis (CCS) to reflect that it is motivated by the well developed Component Mode Synthesis (CMS) methods which were demonstrated to be effective for solving large complex structural analysis problems for almost three decades. The design philosophy behind CCS is also closely related to that of the subsystem decomposition approach in decentralized control.
Validation of a Methodology to Predict Micro-Vibrations Based on Finite Element Model Approach
NASA Astrophysics Data System (ADS)
Soula, Laurent; Rathband, Ian; Laduree, Gregory
2014-06-01
This paper presents the second part of the ESA R&D study called "METhodology for Analysis of structure- borne MICro-vibrations" (METAMIC). After defining an integrated analysis and test methodology to help predicting micro-vibrations [1], a full-scale validation test campaign has been carried out. It is based on a bread-board representative of typical spacecraft (S/C) platform consisting in a versatile structure made of aluminium sandwich panels equipped with different disturbance sources and a dummy payload made of a silicon carbide (SiC) bench. The bread-board has been instrumented with a large set of sensitive accelerometers and tests have been performed including back-ground noise measurement, modal characterization and micro- vibration tests. The results provided responses to the perturbation coming from a reaction wheel or cryo-cooler compressors, operated independently then simultaneously with different operation modes. Using consistent modelling and associated experimental characterization techniques, a correlation status has been assessed by comparing test results with predictions based on FEM approach. Very good results have been achieved particularly for the case of a wheel in sweeping rate operation with test results over-predicted within a reasonable margin lower than two. Some limitations of the methodology have also been identified for sources operating at a fixed rate or coming with a small number of dominant harmonics and recommendations have been issued in order to deal with model uncertainties and stay conservative.
Peridynamic Multiscale Finite Element Methods
Costa, Timothy; Bond, Stephen D.; Littlewood, David John; Moore, Stan Gerald
2015-12-01
The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the
Finite element model and identification procedure
NASA Technical Reports Server (NTRS)
How, Jonathan P.; Blackwood, Gary; Anderson, Eric; Balmes, Etienne
1992-01-01
Viewgraphs on finite element model and identification procedure are presented. Topics covered include: interferometer finite element model; testbed mode shapes; finite element model update; identification procedure; shaker locations; data analysis; modal frequency and damping comparison; computational procedure; fit comparison; residue analysis; typical residues; identification/FEM residual comparison; and pathlength control using isolation mounts.
On Hybrid and mixed finite element methods
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1981-01-01
Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.
Finite element simulation of microindentation
NASA Astrophysics Data System (ADS)
Zhuk, D. I.; Isaenkova, M. G.; Perlovich, Yu. A.; Krymskaya, O. A.
2017-05-01
Finite element models are created to describe the testing of a material by a Berkovich indenter. The results of calculations by these models are compared to experimental data on indentation of the same material (grade 10 steel). The experimental and calculated data agree well with each other. The developed models for an indenter and the material to be tested are used to find the laws of behavior of a material during indentation. The state of stress in the material under an indenter is studied by various methods. The indentation results are plotted versus the mechanical properties of a material.
Du, Chengfei; Mo, Zhongjun; Tian, Shan; Wang, Lizhen; Fan, Jie; Liu, Songyang; Fan, Yubo
2014-11-01
The aim of this study is to investigate the dynamic response of a multi-segment model of the thoracolumbar spine and determine how the sitting posture affects the response under the impact of ejection. A nonlinear finite element model of the thoracolumbar-pelvis complex (T9-S1) was developed and validated. A multi-body dynamic model of a pilot was also constructed so an ejection seat restraint system could be incorporated into the finite element model. The distribution of trunk mass on each vertebra was also considered in the model. Dynamics analysis showed that ejection impact induced obvious axial compression and anterior flexion of the spine, which may contribute to spinal injuries. Compared with a normal posture, the relaxed posture led to an increase in stress on the cortical wall, endplate, and intradiscal pressure of 43%, 10%, 13%, respectively, and accordingly increased the risk of inducing spinal injuries.
Finite Element Output Bounds for Hyperbolic Problems
Machiels, L.
2000-03-27
We propose a Neumann-subproblem a posteriori finite element error bound technique for linear stationary scalar advection problems. The method is similar in many respects to the previous output bound technique developed for elliptic problems. In the new approach, however, the primal residual is enhanced with a streamline diffusion term. We first formulate the bound algorithm, with particular emphasis on the proof of the bounding properties; then, we provide numerical results for an illustrative example.
Finite Element Methods: Principles for Their Selection.
1983-02-01
the finite element methods. 39 Various statements in the literature that certain mixed methods work well inspite of the fact that the LBB (BB...method, displacement and mixed methods , various adaptive approaches, etc. The examples discussed in Sections 2 and 3 show that the same computational...performance and their relation to mixed methods , SIAM J. Num. Anal., to appear. 5. F. Brezzi, On the existence uniqueness and approximation of saddle-point
NASA Astrophysics Data System (ADS)
Xie, Zhihua; Pavlidis, Dimitrios; Percival, James; Gomes, Jefferson; Pain, Christopher; Matar, Omar
2013-11-01
Interfacial flows with surface tension are often found in industrial and practical engineering applications, including bubbles, droplets, liquid film and jets. Accurate modelling of such flows is challenging due to their highly complex dynamics, which often involve changes of interfacial topology. We present a balanced-force finite-element method with adaptive unstructured meshes for interfacial flows. The method uses a mixed control-volume and finite element formulation, which ensures the surface tension forces, and the resulting pressure gradients, are exactly balanced, minimising the spurious velocities often found in numerical simulations of such flows. A volume-of-fluid-type method is employed for interface capturing based on a compressive control-volume advection method, and second-order finite element methods. A distance function is reconstructed from the volume fraction on the unstructured meshes, which provides accurate estimation of the curvature. Numerical examples of an equilibrium drop and dynamics of bubbles (droplets) are presented to demonstrate the capability of this method.
NASA Technical Reports Server (NTRS)
Pindera, Marek-Jerzy; Dunn, Patrick
1995-01-01
A comparison is presented between the predictions of the finite-element analysis and a recently developed higher-order theory for functionally graded materials subjected to a thorough-thickness temperature gradient. In contrast to existing micromechanical theories that utilize classical (i.e., uncoupled) homogenization schemes to calculate micro-level and macro-level stress and displacement fields in materials with uniform or nonuniform fiber spacing (i.e., functionally graded materials), the new theory explicitly couples the microstructural details with the macrostructure of the composite. Previous thermo-elastic analysis has demonstrated that such coupling is necessary when: the temperature gradient is large with respect to the dimension of the reinforcement; the characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing fibers or inclusions is small. In these circumstances, the standard micromechanical analyses based on the concept of the representative volume element used to determine average composite properties produce questionable results. The comparison between the predictions of the finite-element method and the higher-order theory presented herein establish the theory's accuracy in predicting thermal and stress fields within composites with a finite number of fibers in the thickness direction subjected to a thorough-thickness thermal gradient.
NASA Astrophysics Data System (ADS)
Pietropaoli, Elisa; Riccio, Aniello
2011-04-01
This paper addresses the prediction of intralaminar and interlaminar damage onset and evolution in composite structures through the use of a finite element based procedure. This procedure joins methodologies whose credibility has been already assessed in literature such as the Virtual Crack Closure Technique (for delamination) and the ply discount approach (for matrix/fiber failures). In order to establish the reliability of the procedure developed, comparisons with literature experimental results on a stiffened panel with an embedded delamination are illustrated. The methodology proposed, implemented in ANSYS as post-processing routines, is combined with a finite element model of the panel, built by adopting both shell and solid elements within the frame of an embedded global/local approach to connect differently modelled substructures.
Transient finite element method using edge elements for moving conductor
Tani, Koji; Nishio, Takayuki; Yamada, Takashi ); Kawase, Yoshihiro . Dept. of Information Science)
1999-05-01
For the next generation of high speed railway systems and automobiles new braking systems are currently under development. These braking systems take into account the eddy currents, which are produced by the movement of the conductor in the magnetic field. For their optimum design, it is necessary to know the distribution of eddy currents in the moving conductor. The finite element method (FEM) is often used to simulate them. Here, transient finite element method using edge elements for moving conductor is presented. Here the magnetic vector potential is interpolated at the upwind position and the time derivative term is discretized by the backward difference method. As a result, the system matrix becomes symmetric and the ICCG method is applicable to solve the matrix. This method is used to solve an eddy current rail brake system. The results demonstrate that this approach is suitable to solve transient problems involving movement.
Aagaard, B.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.
Finite element modelling of SAW correlator
NASA Astrophysics Data System (ADS)
Tikka, Ajay C.; Al-Sarawi, Said F.; Abbott, Derek
2007-12-01
Numerical simulations of SAW correlators so far are limited to delta function and equivalent circuit models. These models are not accurate as they do not replicate the actual behaviour of the device. Manufacturing a correlator to specifically realise a different configuration is both expensive and time consuming. With the continuous improvement in computing capacity, switching to finite element modelling would be more appropriate. In this paper a novel way of modelling a SAW correlator using finite element analysis is presented. This modelling approach allows the consideration of different code implementation and device structures. This is demonstrated through simulation results for a 5×2-bit Barker sequence encoded SAW correlator. These results show the effect of both bulk and leaky modes on the device performance at various operating frequencies. Moreover, the ways in which the gain of the correlator can be optimised though variation of design parameters will also be outlined.
Armas-Pérez, Julio C; Hernández-Ortiz, Juan P; de Pablo, Juan J
2015-12-28
A theoretically informed Monte Carlo method is proposed for Monte Carlo simulation of liquid crystals on the basis of theoretical representations in terms of coarse-grained free energy functionals. The free energy functional is described in the framework of the Landau-de Gennes formalism. A piecewise finite element discretization is used to approximate the alignment field, thereby providing an excellent geometrical representation of curved interfaces and accurate integration of the free energy. The method is suitable for situations where the free energy functional includes highly non-linear terms, including chirality or high-order deformation modes. The validity of the method is established by comparing the results of Monte Carlo simulations to traditional Ginzburg-Landau minimizations of the free energy using a finite difference scheme, and its usefulness is demonstrated in the context of simulations of chiral liquid crystal droplets with and without nanoparticle inclusions.
Analysis of finite deformations of elastic solids by the finite element method.
NASA Technical Reports Server (NTRS)
Oden, J. T.; Key, J. E.
1971-01-01
Finite element applications, particularly to analyses of finite deformations in elastic solids, are reviewed, along with the difficulties encountered in the formulation of certain problems and in their numerical solution. Various approaches are discussed for overcoming these and other difficulties. A computer program designed for finite elasticity problems is described, and several numerical examples are presented.
Thermal-structural finite element analysis using linear flux formulation
NASA Technical Reports Server (NTRS)
Pandey, Ajay K.; Dechaumphai, Pramote; Wieting, Allan R.
1990-01-01
A linear flux approach is developed for a finite element thermal-structural analysis of steady state thermal and structural problems. The element fluxes are assumed to vary linearly in the same form as the element unknown variables, and the finite element matrices are evaluated in closed form. Since numerical integration is avoided, significant computational time saving is achieved. Solution accuracy and computational speed improvements are demonstrated by solving several two and three dimensional thermal-structural examples.
Domain decomposition methods for mortar finite elements
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
Gautam, Pawan; Zhao, Linping; Patel, Pravin
2011-05-01
To evaluate the stress pattern in the craniofacial skeleton in a patient with unilateral cleft deformity of the secondary palate and alveolus in response to various techniques of surgically assisted rapid maxillary expansion (SARME). Three patient-specific composite skull models were developed for finite element model analysis. The details of the modeling procedure have been described in Part I of this series. The finite element analysis was performed on each model with a specified SARME technique in combination with RME using Abaqus (6.7). The ideal form of surgery in SARME for patients with unilateral cleft deformity of the secondary palate and alveolus would be complete unilateral LeFort I with pterygoid dysjunction in combination with midpalatal split, followed by isolated midpalatal split and zygomatic buttress osteotomies. A more invasive SARME technique can significantly reduce the resultant stresses. However, this benefit should be weighed against the risk of increasing complications associated with more extensive surgeries. When a more conservative surgical technique is selected, it would be preferable to perform a midpalatal split rather than zygomatic buttress osteotomies, as indicated by the stress-strain distribution and displacement pattern associated with different SARME techniques.
An efficient finite element solution for gear dynamics
NASA Astrophysics Data System (ADS)
Cooley, C. G.; Parker, R. G.; Vijayakar, S. M.
2010-06-01
A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static solution is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides accurate calculation of the static solution and average mesh stiffness that are used in the dynamic simulation. The frequency domain finite element calculation of dynamic response compares well with numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, housing structures, and other deformable components.
Finite element coiled cochlea model
NASA Astrophysics Data System (ADS)
Isailovic, Velibor; Nikolic, Milica; Milosevic, Zarko; Saveljic, Igor; Nikolic, Dalibor; Radovic, Milos; Filipović, Nenad
2015-12-01
Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers - scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experimental measurements. Future work is needed for more realistic geometry model. Coiled model of the cochlea was created and results are compared with initial simplified coiled model of the cochlea.
Finite elements and finite differences for transonic flow calculations
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Murman, E. M.; Wellford, L. C.
1978-01-01
The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.
Element-topology-independent preconditioners for parallel finite element computations
NASA Technical Reports Server (NTRS)
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
Element-topology-independent preconditioners for parallel finite element computations
NASA Technical Reports Server (NTRS)
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
Finite-Element Composite-Analysis Program
NASA Technical Reports Server (NTRS)
Bowles, David E.
1990-01-01
Finite Element Composite Analysis Program, FECAP, special-purpose finite-element program for analyzing behavior of composite material with microcomputer. Procedure leads to set of linear simultaneous equations relating unknown nodal displacement to applied loads. Written in HP BASIC 3.0.
Finite element analysis of helicopter structures
NASA Technical Reports Server (NTRS)
Rich, M. J.
1978-01-01
Application of the finite element analysis is now being expanded to three dimensional analysis of mechanical components. Examples are presented for airframe, mechanical components, and composite structure calculations. Data are detailed on the increase of model size, computer usage, and the effect on reducing stress analysis costs. Future applications for use of finite element analysis for helicopter structures are projected.
Nonlinear finite element modeling of corrugated board
A. C. Gilchrist; J. C. Suhling; T. J. Urbanik
1999-01-01
In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...
3-D Finite Element Code Postprocessor
1996-07-15
TAURUS is an interactive post-processing application supporting visualization of finite element analysis results on unstructured grids. TAURUS provides the ability to display deformed geometries and contours or fringes of a large number of derived results on meshes consisting of beam, plate, shell, and solid type finite elements. Time history plotting is also available.
NASA Technical Reports Server (NTRS)
Melis, Matthew E.
2003-01-01
Explicit finite element techniques employing an Arbitrary Lagrangian-Eulerian (ALE) methodology, within the transient dynamic code LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.
Thompson, M C; Field, C J; Swain, M V
2012-03-01
In a previous study, the authors used a finite element analysis (FEA) to evaluate the stresses developed during the loading of an all-ceramic, inlay supported fixed partial denture and compared it with the more traditional full crown supported prosthesis. To date there has been little research into correlating the responses of the numerical model against physical mechanical tests; such validation analysis is crucial if the results from the FEA are to be confidently relied upon. This study reports on the experimental methods used to compare with the FEA and thereby to validate the predictive fracture behaviour of the numerical model. This study also outlines the methods for manufacture and testing of the ceramic structure along with observations of the fracture tests. In addition the procedure used for developing the FEA model for the test system is outlined.
NASA Astrophysics Data System (ADS)
Melis, Matthew E.
2003-01-01
Explicit finite element techniques employing an Arbitrary Lagrangian-Eulerian (ALE) methodology, within the transient dynamic code LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.
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.
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.
NASA Astrophysics Data System (ADS)
Shaidurov, V.; Shchepanovskaya, G.; Yakubovich, M.
2014-11-01
The approach is proposed for the numerical solution of the Navier-Stokes equations for the two-dimensional motion of viscous heat-conducting gas. The discretization of equations is performed by a combination of a special semi-Lagrangian approximation for transport derivatives and the conforming finite element method with piecewise linear or bilinear basis functions for other terms. This approach gives a simpler structure of the discrete system of algebraic equations and does not involve the Courant-Friedrichs-Lewy restriction on the relation between temporal and spatial steps. Numerical results for a supersonic flow around an obstacle for some Mach and Reynolds numbers are presented.
Adaptive finite element methods in electrochemistry.
Gavaghan, David J; Gillow, Kathryn; Süli, Endre
2006-12-05
In this article, we review some of our previous work that considers the general problem of numerical simulation of the currents at microelectrodes using an adaptive finite element approach. Microelectrodes typically consist of an electrode embedded (or recessed) in an insulating material. For all such electrodes, numerical simulation is made difficult by the presence of a boundary singularity at the electrode edge (where the electrode meets the insulator), manifested by the large increase in the current density at this point, often referred to as the edge effect. Our approach to overcoming this problem has involved the derivation of an a posteriori bound on the error in the numerical approximation for the current that can be used to drive an adaptive mesh-generation algorithm, allowing calculation of the quantity of interest (the current) to within a prescribed tolerance. We illustrate the generic applicability of the approach by considering a broad range of steady-state applications of the technique.
Accurate finite element modeling of acoustic waves
NASA Astrophysics Data System (ADS)
Idesman, A.; Pham, D.
2014-07-01
In the paper we suggest an accurate finite element approach for the modeling of acoustic waves under a suddenly applied load. We consider the standard linear elements and the linear elements with reduced dispersion for the space discretization as well as the explicit central-difference method for time integration. The analytical study of the numerical dispersion shows that the most accurate results can be obtained with the time increments close to the stability limit. However, even in this case and the use of the linear elements with reduced dispersion, mesh refinement leads to divergent numerical results for acoustic waves under a suddenly applied load. This is explained by large spurious high-frequency oscillations. For the quantification and the suppression of spurious oscillations, we have modified and applied a two-stage time-integration technique that includes the stage of basic computations and the filtering stage. This technique allows accurate convergent results at mesh refinement as well as significantly reduces the numerical anisotropy of solutions. We should mention that the approach suggested is very general and can be equally applied to any loading as well as for any space-discretization technique and any explicit or implicit time-integration method.
NASA Astrophysics Data System (ADS)
Zeumann, Stefanie; Hampel, Andrea
2017-04-01
Subduction of aseismic oceanic ridges causes considerable uplift and deformation of the upper continental plate and may therefore ultimately affect also coastal drainage systems. To investigate the impact of a subducting ridge on the river network of the upper plate, we link a landscape evolution model with 3D finite-element models of ridge subduction. The landscape evolution model includes diffusive hillslope processes and fluvial erosion and deposition. The finite-element model represents a deformable forearc and a rigid oceanic plate, which carries the model ridge beneath the upper plate (cf. Zeumann and Hampel, 2015, 2016). Our model results show that as long as the forearc is unaffected by the ridge, rivers flow more or less straight toward the model coast. Once the ridge tip has arrived at a position beneath the coast, the uplift caused by the ridge changes the flow direction of the rivers. If the slope at the ridge tip exceeds the slope of the forearc wedge, the flow direction of rivers above the ridge crest is inversed, i.e. the rivers flow away from the coast. Once the main part of the ridge (with constant maximum elevation of the ridge crest) has arrived beneath the coast, the rivers inverse their flow direction once more and flow toward the coast again. At this stage, rivers flowing above the ridge flanks are deflected away from the ridge crest. This deflection gets more pronounced during further subduction of the ridge. In case of a stationary subducting ridge, no further drainage reorganization takes place after the ridge tip has passed and the main part of the ridge with its constant crest height has arrived beneath the forearc. For a migrating ridge, further reorganization of the drainage network takes place as the ridge moves along the margin. We compare the modelled deflection of rivers during stationary ridge subduction with the flow direction of rivers in Costa Rica and Panama, which are affected by the subduction of the approximately stationary
Assignment Of Finite Elements To Parallel Processors
NASA Technical Reports Server (NTRS)
Salama, Moktar A.; Flower, Jon W.; Otto, Steve W.
1990-01-01
Elements assigned approximately optimally to subdomains. Mapping algorithm based on simulated-annealing concept used to minimize approximate time required to perform finite-element computation on hypercube computer or other network of parallel data processors. Mapping algorithm needed when shape of domain complicated or otherwise not obvious what allocation of elements to subdomains minimizes cost of computation.
Assignment Of Finite Elements To Parallel Processors
NASA Technical Reports Server (NTRS)
Salama, Moktar A.; Flower, Jon W.; Otto, Steve W.
1990-01-01
Elements assigned approximately optimally to subdomains. Mapping algorithm based on simulated-annealing concept used to minimize approximate time required to perform finite-element computation on hypercube computer or other network of parallel data processors. Mapping algorithm needed when shape of domain complicated or otherwise not obvious what allocation of elements to subdomains minimizes cost of computation.
Quality assessment and control of finite element solutions
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Babuska, Ivo
1987-01-01
Status and some recent developments in the techniques for assessing the reliability of finite element solutions are summarized. Discussion focuses on a number of aspects including: the major types of errors in the finite element solutions; techniques used for a posteriori error estimation and the reliability of these estimators; the feedback and adaptive strategies for improving the finite element solutions; and postprocessing approaches used for improving the accuracy of stresses and other important engineering data. Also, future directions for research needed to make error estimation and adaptive movement practical are identified.
Gupta, Shikha; Lin, Jeremy; Ashby, Paul; Pruitt, Lisa
2009-08-01
Nanoindentation has shown promise as a mechanical characterization tool for orthopaedic biomaterials since it can probe the properties of small, heterogeneous, irregularly shaped tissue volumes in physiological environments. However, the majority of nanoindentation analyses have been limited to the determination of linear elastic and viscoelastic properties. Since biomaterials possess complex nonlinear, hydrated, time-dependent constitutive behavior, the objective of the present study is to explore the ability of nanoindentation to determine physiologically relevant material properties using a fibril reinforced poroelastic (FRPE) model. A further goal is to ascertain the sensitivity of nanoindentation load-displacement curves to different FRPE parameters, including the elastic properties of the nonfibrillar matrix, the composition and distribution of fibers, and nonlinearity in the fluid permeability. Porcine costal cartilage specimens are experimentally tested with nanoindentation load relaxation experiments at two different loading depths and loading rates. The FRPE material properties are extracted from comparisons to finite element simulations. The study demonstrates the behavior of the model in nanoindentation is distinct from bulk indentation; the static response of the nanoindentation is determined almost exclusively by the elastic properties of the nonfibrillar matrix and the volume fraction of fibers, while the transient response is dominated by the fluid permeability of the tissue. The FRPE model can accurately describe the time-dependent mechanical behavior of costal cartilage in nanoindentation, with good agreement between experimental and numerical curve fits (R(2)=0.98+/-0.01) at multiple indentation depths and indentation rates.
Nishio, C; Tanimoto, K; Hirose, M; Horiuchi, S; Kuroda, S; Tanne, K; Tanaka, E
2009-08-01
Parafunctional habits, such as bruxism and prolonged clenching, have been associated with functional overloading in the temporomandibular joint (TMJ), which may result in internal derangement and osteoarthrosis of the TMJ. In this study, the distributions of stress on the mandibular condylar surface during prolonged clenching were examined with TMJ mathematical models. Finite element models were developed on the basis of magnetic resonance images from two subjects with or without anterior disc displacement of the TMJ. Masticatory muscle forces were used as a loading condition for stress analysis during a 10 min clenching. In the asymptomatic model, the stress values in the anterior area (0.100 MPa) and lateral area (0.074 MPa) were relatively high among the five areas at 10 min. In the middle and posterior areas, stress relaxation occurred during the first 2 min. In contrast, the stress value in the lateral area was markedly lower (0.020 MPa) than in other areas in the symptomatic model at 10 min. The largest stress (0.050 MPa) was located in the posterior area. All except the anterior area revealed an increase in stress during the first 2 min. The present result indicates that the displacement of the disc could affect the stress distribution on the condylar articular surface during prolonged clenching, especially in the posterior area, probably leading to the cartilage breakdown on the condylar articular surface.
Optimizing header strength utilizing finite element analyses
NASA Astrophysics Data System (ADS)
Burchett, S. N.
Finite element techniques have been successfully applied as a design tool in the optimization of high strength headers for pyrotechnic-driven actuators. These techniques have been applied to three aspects of the design process of a high strength header. The design process was a joint effort of experts from several disciplines including design engineers, material scientists, test engineers, manufacturing engineers, and structural analysts. Following material selection, finite element techniques were applied to evaluate the residual stresses due to manufacturing which were developed in the high strength glass ceramic-to-metal seal headers. Results from these finite element analyses were used to identify header designs which were manufacturable and had a minimum residual stress state. Finite element techniques were than applied to obtain the response of the header due to pyrotechnic burn. The results provided realistic upper bounds on the pressure containment ability of various preliminary header designs and provided a quick and inexpensive method of strengthening and refining the designs. Since testing of the headers was difficult and sometimes destructive, results of the analyses were also used to interpret test results and identify failure modes. In this paper, details of the finite element element techniques including the models used, material properties, material failure models, and loading will be presented. Results from the analyses showing the header failure process will also be presented. This paper will show that significant gains in capability and understanding can result when finite element techniques are included as an integral part of the design process of complicated high strength headers.
Visualization of higher order finite elements.
Thompson, David C.; Pebay, Philippe Pierre; Crawford, Richard H.; Khardekar, Rahul Vinay
2004-04-01
Finite element meshes are used to approximate the solution to some differential equation when no exact solution exists. A finite element mesh consists of many small (but finite, not infinitesimal or differential) regions of space that partition the problem domain, {Omega}. Each region, or element, or cell has an associated polynomial map, {Phi}, that converts the coordinates of any point, x = ( x y z ), in the element into another value, f(x), that is an approximate solution to the differential equation, as in Figure 1(a). This representation works quite well for axis-aligned regions of space, but when there are curved boundaries on the problem domain, {Omega}, it becomes algorithmically much more difficult to define {Phi} in terms of x. Rather, we define an archetypal element in a new coordinate space, r = ( r s t ), which has a simple, axis-aligned boundary (see Figure 1(b)) and place two maps onto our archetypal element:
An adaptive discontinuous finite element method for the transport equation
Lang, J.; Walter, A.
1995-03-01
In this paper we introduce a discontinuous finite element method. In our approach, it is possible to combine the advantages of finite element and finite difference methods. The main ingredients are numerical flux approximation and local orthogonal basis functions. The scheme is defined on arbitrary triangulations and two different error indicators are derived. Especially the second one is closely connected to our approach and able to handle arbitrary varying flow directions. Numerical results are given for boundary value problems in two dimensions. They demonstrate the performance of the scheme, combined with the two error indicators.
A survey of mixed finite element methods
NASA Technical Reports Server (NTRS)
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
Finite element schemes for Fermi equation
NASA Astrophysics Data System (ADS)
Asadzadeh, M.; Beilina, L.; Naseer, M.; Standar, C.
2017-07-01
A priori error estimates are derived for the streamline diffusion (SD) finite element methods for the Fermi pencil-beam equation. Two-dimensional numerical examples confirm our theoretical investigations.
Finite element analysis of multilayer coextrusion.
Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A.; Mrozek, Randy A.; Lenhart, Joseph Ludlow; Rao, Rekha Ranjana; Collins, Robert; Mondy, Lisa Ann
2011-09-01
Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.
Finite element modeling of the human pelvis
Carlson, B.
1995-11-01
A finite element model of the human pelvis was created using a commercial wire frame image as a template. To test the final mesh, the model`s mechanical behavior was analyzed through finite element analysis and the results were displayed graphically as stress concentrations. In the future, this grid of the pelvis will be integrated with a full leg model and used in side-impact car collision simulations.
Integration of geometric modeling and advanced finite element preprocessing
NASA Technical Reports Server (NTRS)
Shephard, Mark S.; Finnigan, Peter M.
1987-01-01
The structure to a geometry based finite element preprocessing system is presented. The key features of the system are the use of geometric operators to support all geometric calculations required for analysis model generation, and the use of a hierarchic boundary based data structure for the major data sets within the system. The approach presented can support the finite element modeling procedures used today as well as the fully automated procedures under development.
Quadratic finite elements and incompressible viscous flows.
Dohrmann, Clark R.; Gartling, David K.
2005-01-01
Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.
Finite Element Analysis of a Floating Microstimulator
Sahin, Mesut; Ur-Rahman, Syed S.
2011-01-01
Analytical solutions for voltage fields in a volume conductor are available only for ideal electrodes with radially symmetric contacts and infinitely extending substrates. Practical electrodes for neural stimulation may have asymmetric contacts and finite substrate dimensions and hence deviate from the ideal geometries. For instance, it needs to be determined if the analytical solutions are adequate for simulations of narrow shank electrodes where the substrate width is comparable to the size of the contacts. As an extension to this problem, a “floating” stimulator can be envisioned where the substrate would be finite in all directions. The question then becomes how small this floating stimulator can be made before its stimulation strength is compromised by the decrease in the medium impedance between the contacts as the contacts are approaching each other. We used finite element modeling to solve the voltage and current profiles generated by these radially asymmetric electrode geometries in a volume conductor. The simulation results suggest that both the substrate size and the bipolar contact separation influence the voltage field when these parameters are as small as a few times the contact size. Both of these effects are larger for increasing elevations from the contact surface, and even stronger for floating electrodes (finite substrate in all directions) than the shank-type electrodes. Location of the contacts on the floating electrode also plays a role in determining the voltage field. The voltage field for any device size and current, and any specific resistance of the volume conductor can be predicted from these results so long as the aspect ratios are preserved. PMID:17601192
Finite element analysis of flexible, rotating blades
NASA Technical Reports Server (NTRS)
Mcgee, Oliver G.
1987-01-01
A reference guide that can be used when using the finite element method to approximate the static and dynamic behavior of flexible, rotating blades is given. Important parameters such as twist, sweep, camber, co-planar shell elements, centrifugal loads, and inertia properties are studied. Comparisons are made between NASTRAN elements through published benchmark tests. The main purpose is to summarize blade modeling strategies and to document capabilities and limitations (for flexible, rotating blades) of various NASTRAN elements.
Wai-Chi Wong, Duo; Wang, Yan; Zhang, Ming; Kam-Lun Leung, Aaron
2015-09-18
First metatarsocuneiform arthrodesis is one of the surgical interventions to correct hallux valgus, especially those with hypermobile first ray. There is lacking of biomechanical investigations to assess this operation. The objective of this study was to explore the functional restoration and the risk of non-union after the surgery via finite element analysis. A three-dimensional foot model was constructed from a female aged 28 via magnetic resonance imaging. Thirty bones and encapsulated bulk tissue were modeled. Walking stance was simulated by the gait analysis data of the same participant. Parts of the first metatarsal and cuneiform were resected and the bone graft was assigned with the same stiffness as adjacent bones to resemble the surgery of first metatarsocuneiform arthrodesis. The third principal stress of the first metatarsal at midstance (25% stance) and push off (60% stance) was increased by 76% and 139% respectively after the operation, while that of the second metatarsal was decreased by 14% and 66%. The operation reduced the medial deviation of the first metatarsal head by about 3.5mm during initial push off (60% stance). Besides, the bone graft could experience tensile stress inferiorly (26.51MPa). In conclusion, the increase of stress on the first metatarsal and the reduced medial excursion of the first metatarsal head after the simulated operation reflected that metatarsocuneiform arthrodesis could restore the load-bearing function of the first ray. However, inter-fragmentary compression could not be guaranteed. The appropriate course of hardware and non-weight-bearing protocol should be noted and further investigated.
de la Rosa Castolo, Guillermo; Guevara Perez, Sonia V; Arnoux, Pierre-Jean; Badih, Laurent; Bonnet, Franck; Behr, Michel
2017-07-15
Implant prosthodontics provides high-quality outcomes thanks to recent technological developments and certification procedures such as International Organization for Standardization (ISO) standard 14801. However, these certification tests are costly, and the result is highly uncertain as the influence of design variables (materials and structure) is still unknown. The design process could be significantly improved if the influence of design parameters were identified. The purpose of this in vitro study was to use finite element analysis (FEA) to assess the influence of design parameters on the mechanical performance of an implant in regard to testing conditions of ISO 14801 standard. An endosseous dental implant was loaded under ISO standard 14801 testing conditions by numerical simulation, with 4 parameters evaluated under the following conditions: conditions of the contact surface area between the implant and the loading tool, length of the fixation screw, implant embedding depth, and material used for implant stiffness. FEA was used to compare the force that needed to reach the implant's yield and fracture strength. A dental implant's fracture point can be increased by 41% by improving the contact surface area, by 20% depending on the type of material, by 4% depending on the length of the fixation screw, and by 1.4% by changing the implant embedding depth. FEA made it possible to evaluate 4 performance parameters of a dental implant under ISO standard 14801 conditions. Under these conditions, the contact surface area was found to be the major parameter influencing implant performance. This observation was validated experimentally in a fatigue test under ISO standard 14801 conditions. Copyright © 2017 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.
Teklemariam, A.; Hodson-Tole, E. F.; Reeves, N. D.; Costen, N. P.; Cooper, G.
2016-01-01
Introduction Surface electromyography (sEMG) is the measurement of the electrical activity of the skeletal muscle tissue detected at the skin’s surface. Typically, a bipolar electrode configuration is used. Most muscles have pennate and/or curved fibres, meaning it is not always feasible to align the bipolar electrodes along the fibres direction. Hence, there is a need to explore how different electrode designs can affect sEMG measurements. Method A three layer finite element (skin, fat, muscle) muscle model was used to explore different electrode designs. The implemented model used as source signal an experimentally recorded intramuscular EMG taken from the biceps brachii muscle of one healthy male. A wavelet based intensity analysis of the simulated sEMG signal was performed to analyze the power of the signal in the time and frequency domain. Results The model showed muscle tissue causing a bandwidth reduction (to 20-92- Hz). The inter-electrode distance (IED) and the electrode orientation relative to the fibres affected the total power but not the frequency filtering response. The effect of significant misalignment between the electrodes and the fibres (60°- 90°) could be reduced by increasing the IED (25–30 mm), which attenuates signal cancellation. When modelling pennated fibres, the muscle tissue started to act as a low pass filter. The effect of different IED seems to be enhanced in the pennated model, while the filtering response is changed considerably only when the electrodes are close to the signal termination within the model. For pennation angle greater than 20°, more than 50% of the source signal was attenuated, which can be compensated by increasing the IED to 25 mm. Conclusion Differences in tissue filtering properties, shown in our model, indicates that different electrode designs should be considered for muscle with different geometric properties (i.e. pennated muscles). PMID:26886908
Stabilized Finite Elements in FUN3D
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle; Newman, James C.; Karman, Steve L.
2017-01-01
A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.
Wave dispersion properties of compound finite elements
NASA Astrophysics Data System (ADS)
Melvin, Thomas; Thuburn, John
2017-06-01
Mixed finite elements use different approximation spaces for different dependent variables. Certain classes of mixed finite elements, called compatible finite elements, have been shown to exhibit a number of desirable properties for a numerical weather prediction model. In two-dimensions the lowest order element of the Raviart-Thomas based mixed element is the finite element equivalent of the widely used C-grid staggering, which is known to possess good wave dispersion properties, at least for quadrilateral grids. It has recently been proposed that building compound elements from a number of triangular Raviart-Thomas sub-elements, such that both the primal and (implied) dual grid are constructed from the same sub-elements, would allow greater flexibility in the use of different advection schemes along with the ability to build arbitrary polygonal elements. Although the wave dispersion properties of the triangular sub-elements are well understood, those of the compound elements are unknown. It would be useful to know how they compare with the non-compound elements and what properties of the triangular sub-grid elements are inherited? Here a numerical dispersion analysis is presented for the linear shallow water equations in two dimensions discretised using the lowest order compound Raviart-Thomas finite elements on regular quadrilateral and hexagonal grids. It is found that, in comparison with the well known C-grid scheme, the compound elements exhibit a more isotropic dispersion relation, with a small over estimation of the frequency for short waves compared with the relatively large underestimation for the C-grid. On a quadrilateral grid the compound elements are found to differ from the non-compound Raviart-Thomas quadrilateral elements even for uniform elements, exhibiting the influence of the underlying sub-elements. This is shown to lead to small improvements in the accuracy of the dispersion relation: the compound quadrilateral element is slightly better for
Finite Element Interface to Linear Solvers
Williams, Alan
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on the problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.
Model Reduction of Viscoelastic Finite Element Models
NASA Astrophysics Data System (ADS)
Park, C. H.; Inman, D. J.; Lam, M. J.
1999-01-01
This paper examines a method of adding viscoelastic properties to finite element models by using additional co-ordinates to account for the frequency dependence usually associated with such damping materials. Several such methods exist and all suffer from an increase in order of the final finite model which is undesirable in many applications. Here we propose to combine one of these methods, the GHM (Golla-Hughes-McTavish) method, with model reduction techniques to remove the objection of increased model order. The result of combining several methods is an ability to add the effects of visoelastic components to finite element or other analytical models without increasing the order of the system. The procedure is illustrated by a numerical example. The method proposed here results in a viscoelastic finite element of a structure without increasing the order of the original model.
NASA Technical Reports Server (NTRS)
1976-01-01
The development of two new shell finite elements for applications to large deflection problems is considered. The elements in question are doubly curved and of triangular and quadrilateral planform. They are restricted to small strains of elastic materials, and can accommodate large rotations. The elements described, which are based on relatively simple linear elements, make use of a new displacement function approach specifically designed for strongly nonlinear problems. The displacement function development for nonlinear applications is based on certain beam element formulations, and the strain-displacement equations are of a shallow shell type. Additional terms were included in these equations in an attempt to avoid the large errors characteristic of shallow shell elements in certain types of problems. An incremental nonlinear solution procedure specifically adopted to the element formulation was developed. The solution procedure is of combined incremental and total Lagrangian type, and uses a new updating scheme. A computer program was written to evaluate the developed formulations. This program can accommodate small element groups in arbitrary arrangements. Two simple programs were successfully solved. The results indicate that this new type of element has definite promise and should be a fruitful area for further research.
Finite element analysis enhancement of cryogenic testing
NASA Astrophysics Data System (ADS)
Thiem, Clare D.; Norton, Douglas A.
1991-12-01
Finite element analysis (FEA) of large space optics enhances cryogenic testing by providing an analytical method by which to ensure that a test article survives proposed testing. The analyses presented in this paper were concerned with determining the reliability of a half meter mirror in an environment where the exact environmental profile was unknown. FEA allows the interaction between the test object and the environment to be simulated to detect potential problems prior to actual testing. These analyses examined worse case scenerios related to cooling the mirror, its structural integrity for the proposed test environment, and deformation of the reflective surface. The FEA was conducted in-house on the System's Reliability Division's VAX 11-750 and Decstation 3100 using Engineering Mechanics Research Corporation's numerically integrated elements for systems analysis finite element software. The results of the analyses showed that it would take at least 48 hours to cool the mirror to its desired testing temperature. It was also determined that the proposed mirror mount would not cause critical concentrated thermal stresses that would fracture the mirror. FEA and actual measurements of the front reflective face were compared and good agreement between computer simulation and physical tests were seen. Space deployment of large optics requires lightweight mirrors which can perform under the harsh conditions of space. The physical characteristics of these mirrors must be well understood in order that their deployment and operation are successful. Evaluating design approaches by analytical simulation, like FEA, verifies the reliability and structural integrity of a space optic during design prior to prototyping and testing. Eliminating an optic's poor design early in its life saves money, materials, and human resources while ensuring performance.
Finite-element models of continental extension
NASA Technical Reports Server (NTRS)
Lynch, H. David; Morgan, Paul
1990-01-01
Numerical models of the initial deformation of extending continental lithosphere, computed to investigate the control of preexisting thermal and mechanical heterogeneities on the style of deformation, are presented. The finite element method is used to calculate deformation with a viscoelastic-plastic model for the lithosphere. Comparisons of the results of analytic models and finite-element models using this method show that good results may be obtained by the numerical technique, even with elements containing both brittle and viscoelastic sampling points. It is shown that the gross style of initial extensional deformation is controlled by the depth and width of the initial heterogeneity which localizes deformation.
Quadrilateral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Benzley, Steven E
2012-10-16
Techniques for coarsening a quadrilateral mesh are described. These techniques include identifying a coarsening region within the quadrilateral mesh to be coarsened. Quadrilateral elements along a path through the coarsening region are removed. Node pairs along opposite sides of the path are identified. The node pairs along the path are then merged to collapse the path.
Waveguide finite elements for curved structures
NASA Astrophysics Data System (ADS)
Finnveden, Svante; Fraggstedt, Martin
2008-05-01
A waveguide finite element formulation for the analysis of curved structures is introduced. The formulation is valid for structures that along one axis have constant properties. It is based on a modified Hamilton's principle valid for general linear viscoelastic motion, which is derived here. Using this principle, material properties such as losses may be distributed in the system and may vary with frequency. Element formulations for isoparametric solid elements and deep shell elements are presented for curved waveguides as well as for straight waveguides. In earlier works, the curved elements have successfully been used to model a passenger car tyre. Here a simple validation example and convergence study is presented, which considers a finite length circular cylinder and all four elements presented are used, in turn, to model this structure. Calculated results compare favourably to those in the literature.
Exact finite elements for conduction and convection
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507
Exact finite elements for conduction and convection
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507
Higher-Order Finite Elements for Computing Thermal Radiation
NASA Technical Reports Server (NTRS)
Gould, Dana C.
2004-01-01
Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higher-order finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times. One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications. In the basic form of the RSE method, each finite element selected for use in computing radiative heat transfer is considered to be a parent element and is divided into sub-elements for the purpose of solving the surface-to-surface radiation-exchange problem. The sub-elements are then treated as classical finite elements; that is, they are assumed to be isothermal, and their view factors and absorbed heat fluxes are calculated accordingly. The heat fluxes absorbed by the sub-elements are then transferred back to the parent element to obtain a radiative heat flux that varies spatially across the parent element. Variants of the RSE method involve the use of polynomials to interpolate and/or extrapolate to approximate spatial variations of physical quantities. The other variant of the finite-element method is termed the integration method (IM). Unlike in the RSE methods, the parent finite elements are not subdivided into smaller elements, and neither isothermality nor other
An iterative algorithm for finite element analysis
NASA Astrophysics Data System (ADS)
Laouafa, F.; Royis, P.
2004-03-01
In this paper, we state in a new form the algebraic problem arising from the one-field displacement finite element method (FEM). The displacement approach, in this discrete form, can be considered as the dual approach (force or equilibrium) with subsidiary constraints. This approach dissociates the nonlinear operator to the linear ones and their sizes are linear functions of integration rule which is of interest in the case of reduced integration. This new form of the problem leads to an inexpensive improvement of FEM computations, which acts at local, elementary and global levels. We demonstrate the numerical performances of this approach which is independent of the mesh structure. Using the GMRES algorithm we build, for nonsymmetric problems, a new algorithm based upon the discretized field of strain. The new algorithms proposed are more closer to the mechanical problem than the classical ones because all fields appear during the resolution process. The sizes of the different operators arising in these new forms are linear functions of integration rule, which is of great interest in the case of reduced integration.
NASA Astrophysics Data System (ADS)
Pearce, G. M. K.; Johnson, A. F.; Hellier, A. K.; Thomson, R. S.
2013-12-01
This paper presents the results of a study into a novel application of the "stacked-shell" laminate modelling approach to dynamically loaded bolted composite joints using the explicit finite element code PAM-CRASH. The stacked-shell approach provides medium-high fidelity resolution of the key joint failure modes, but is computationally much more efficient than full 3D modelling. For this work, a countersunk bolt in a composite laminate under in-plane bearing loading was considered. The models were able to predict the onset of damage, failure modes and the ultimate load of the joint. It was determined that improved debris models are required in order to accurately capture the progressive bearing damage after the onset of joint failure.
Least-squares finite element methods for compressible Euler equations
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Carey, G. F.
1990-01-01
A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.
Finite element modeling and analysis of tires
NASA Technical Reports Server (NTRS)
Noor, A. K.; Andersen, C. M.
1983-01-01
Predicting the response of tires under various loading conditions using finite element technology is addressed. Some of the recent advances in finite element technology which have high potential for application to tire modeling problems are reviewed. The analysis and modeling needs for tires are identified. Reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment of combined loads, displacement-dependent and nonconservative loadings; development of simple and efficient mixed finite element models for shell analysis, identification of equivalent mixed and purely displacement models, and determination of the advantages of using mixed models; and effective computational models for large-rotation nonlinear problems, based on a total Lagrangian description of the deformation are included.
Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; Rossi, Simone
2015-11-12
Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.
Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...
2015-11-12
Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less
Visualizing higher order finite elements. Final report
Thompson, David C; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elements into regions appropriate for isosurfacing and proves the conditions under which the algorithm will terminate. Finite elements are used to create piecewise polynomial approximants to the solution of partial differential equations for which no analytical solution exists. These polynomials represent fields such as pressure, stress, and momentum. In the past, these polynomials have been linear in each parametric coordinate. Each polynomial coefficient must be uniquely determined by a simulation, and these coefficients are called degrees of freedom. When there are not enough degrees of freedom, simulations will typically fail to produce a valid approximation to the solution. Recent work has shown that increasing the number of degrees of freedom by increasing the order of the polynomial approximation (instead of increasing the number of finite elements, each of which has its own set of coefficients) can allow some types of simulations to produce a valid approximation with many fewer degrees of freedom than increasing the number of finite elements alone. However, once the simulation has determined the values of all the coefficients in a higher-order approximant, tools do not exist for visual inspection of the solution. This report focuses on a technique for the visual inspection of higher-order finite element simulation results based on decomposing each finite element into simplicial regions where existing visualization algorithms such as isosurfacing will work. The requirements of the isosurfacing algorithm are enumerated and related to the places where the partial derivatives of the polynomial become zero. The original isosurfacing algorithm is then applied to each of these regions in turn.
NASA Astrophysics Data System (ADS)
Sassi, R.; Marcuzzi, F.; Mazzoli, C.
2008-12-01
One of the main goals of metamorphic petrology is to obtain information on the variations of metamorphic P-T conditions during orogenesis (P-T-t paths). For this purpose petrologists are aware of the potentiality of studying reaction microstructures, although results are not always satisfactory as in most cases qualitative approaches, failing on the real meaning of specific microstructral relationships, are often adopted. Thus, the present research aimed to study the petrogenetic meaning of reaction microstructure in metamorphic rocks through the formulation of a new true three-dimensional finite-element model. For this purpose, different petrologically well studied metamorphic microstructural situations have been selected, in order to identify information, variables and constraints fundamental for the development of the model. A generalised finite-elements model (FEM) has been developed, applicable to any microstructural situation, independently on grain-size and distribution of minerals in the matrix, and able to also consider growth anisotropies, intracrystalline diffusion, pressure solution, and possibly anisotropy of the strain field. This model is based on a combination of the usual diffusion linear equations used in current irreversible thermodynamic models, providing constraints on absolute values of diffusion coefficients of chemical components, chemical potential gradients and time of reactions during metamorphism, starting from information on textural anisotropies observed in metamorphic rocks. In the model, parameterization is given by diffusion, convection and reaction coefficients of each chemical species within each finite element, which dimension is equal to the spatial resolution of the experimentally measured input data (i.e. SEM elemental maps). Thus, parameterization is able to describe locally heterogeneous reaction phenomena although based on a basically linear partial derivative differential model. Such a discretization of the continuum model
NASA Astrophysics Data System (ADS)
Baqersad, Javad
Health monitoring of rotating structures such as wind turbines and helicopter rotors is generally performed using conventional sensors that provide a limited set of data at discrete locations near or on the hub. These sensors usually provide no data on the blades or interior locations where failures may occur. Within this work, an unique expansion algorithm was extended and combined with finite element (FE) modeling and an optical measurement technique to identify the dynamic strain in rotating structures. The merit of the approach is shown by using the approach to predict the dynamic strain on a small non-rotating and rotating wind turbine. A three-bladed wind turbine having 2.3-meter long blades was placed in a semi-built-in boundary condition using a hub, a machining chuck, and a steel block. A finite element model of the three wind turbine blades assembled to the hub was created and used to extract resonant frequencies and mode shapes. The FE model was validated and updated using experimental modal tests. For the non-rotating optical test, the turbine was excited using a sinusoidal excitation, a pluck test, arbitrary impacts on three blades, and random force excitations with a mechanical shaker. The response of the structure to the excitations was measured using three-dimensional point tracking. A pair of high-speed cameras was used to measure the displacement of optical targets on the structure when the blades were vibrating. The measured displacements at discrete locations were expanded and applied to the finite element model of the structure to extract the full-field dynamic strain. The results of the work show an excellent correlation between the strain predicted using the proposed approach and the strain measured with strain-gages for all of the three loading conditions. Similar to the non-rotating case, optical measurements were also preformed on a rotating wind turbine. The point tracking technique measured both rigid body displacement and flexible
Finite Element Analysis of Pipe Elbows.
1980-02-01
AD-AO81 077 DAVD TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CE--ETC F/B 13/11 FINITE ELEMENT ANALYSIS OF PIPE ELBOWS .(U) FE SO M S MARCUS, B C...TAYLOR NAVAL SHIP i RESEARCH AND DEVELOPMENT CENTER Bethesda, Md. 20084 4 FINITE ELEMENT ANALYSIS OF PIPE ELBOWS by 0 Melvyn S. Marcus and Gordon C...a 90-degree pipe elbow to determine principal stresses due to internal pressure, inplane bending, out-of-plane bending, and torsion moment loadings
Finite element methods for high speed flows
NASA Technical Reports Server (NTRS)
Loehner, R.; Morgan, K.; Peraire, J.; Zienkiewicz, O. C.
1985-01-01
An explicit finite element based solution procedure for solving the equations of compressible viscous high speed flow is presented. The method uses domain splitting to advance the solution with different timesteps on different portions of the mesh. For steady inviscid flows, adaptive mesh refinement procedures are successfully employed to enhance the definition of discontinuities. Preliminary ideas on the application of adaptive mesh refinement to the solution of problems involving steady viscous flow are presented. Sample timings are given for the performance of the finite element code on modern supercomputers.
Studies of finite element analysis of composite material structures
NASA Technical Reports Server (NTRS)
Douglas, D. O.; Holzmacher, D. E.; Lane, Z. C.; Thornton, E. A.
1975-01-01
Research in the area of finite element analysis is summarized. Topics discussed include finite element analysis of a picture frame shear test, BANSAP (a bandwidth reduction program for SAP IV), FEMESH (a finite element mesh generation program based on isoparametric zones), and finite element analysis of a composite bolted joint specimens.
Spectral finite-element methods for parametric constrained optimization problems.
Anitescu, M.; Mathematics and Computer Science
2009-01-01
We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem is solvable because it is feasible for a sufficiently large degree of the polynomial approximation and has an objective function with bounded level sets. In addition, the solutions of the finite-dimensional problems converge for an increasing degree of the polynomials considered, provided that the solutions exhibit a sufficiently large and uniform degree of smoothness. Our approach solves, in the case of optimization problems with uncertain parameters, the most computationally intensive part of stochastic finite-element approaches. We demonstrate that our framework is applicable to parametric eigenvalue problems.
Finite element modelling of buried structures
NASA Technical Reports Server (NTRS)
Playdon, D. K.; Simmonds, S. H.
1984-01-01
In many structures the final stress states are dependent on the sequence of construction or the stress states at various stages of construction are of interest. Such problems can be analyzed using finite element programs that have the capability of adding (birthing) elements to simulate the progress of construction. However, the usual procedure of assembling elements may lead to numerical instabilities or stress states that are unrealistic. Both problems are demonstrated in the analysis of a structure using the program ADINA. A technique which combines application of a preload with element birthing to overcome these problems is described and illustrated.
Finite element wavelets with improved quantitative properties
NASA Astrophysics Data System (ADS)
Nguyen, Hoang; Stevenson, Rob
2009-08-01
In [W. Dahmen, R. Stevenson, Element-by-element construction of wavelets satisfying stability and moment conditions, SIAM J. Numer. Anal. 37 (1) (1999) 319-352 (electronic)], finite element wavelets were constructed on polygonal domains or Lipschitz manifolds that are piecewise parametrized by mappings with constant Jacobian determinants. The wavelets could be arranged to have any desired order of cancellation properties, and they generated stable bases for the Sobolev spaces Hs for (or s<=1 on manifolds). Unfortunately, it appears that the quantitative properties of these wavelets are rather disappointing. In this paper, we modify the construction from the above-mentioned work to obtain finite element wavelets which are much better conditioned.
Finite element modeling of the deformation of magnetoelastic film
Barham, Matthew I.; White, Daniel A.; Steigmann, David J.
2010-09-01
Recently a new class of biocompatible elastic polymers loaded with small ferrous particles, a magnetoelastic polymer, has been developed. This engineered material is formed into a thin film using spin casting. An applied magnetic field will deform the film. The magnetic deformation of this film has many possible applications, particularly in microfluidic pumps and pressure regulators. In this paper a finite element method suitable for the transient simulation of arbitrarily shaped three-dimensional magnetoelastic polymers subjected to time-varying magnetic fields is developed. The approach is similar to that employed in finite elment magnetohydrodynamic simulations, the key difference is a more complex hyperelastic material model. In order to confirm the validity of the approach, finite element solutions for an axially symmetric thin film are compared to an analytical solution based on the membrane (infinitely thin) approximation. For this particular problem the two approaches give qualitatively similar results and converge as the film thickness approaches zero.
Finite Element Simulation of Smart Structures
NASA Technical Reports Server (NTRS)
Cui, Y. Lawrence; Panahandeh, M.
1996-01-01
Finite element equations representing the behavior of piezoelectric materials when bounded to a typical structure and used as sensors and actuators were developed. Emphasis was placed on generating sensor output equations of piezoelectric sensors and responses of a typical structure bonded with piezoelectric sensors and actuators on the basis of finite element formulation. The model can predict not only structural responses due to both mechanical and electrical loading but also electrical potential due to mechanical or thermal effects. The resulted finite element equations were then used for simple control design and performance evaluation. In the control algorithm, voltages coming out from piezoelectric sensors, which are proportional to strains at sensing locations, are taken as input. The voltages applied to the piezoelectric actuators are used as output. The feasibility of integrating control algorithm with the element routine developed herein and FEAP was demonstrated. In particular, optimal independent modal space control was implemented in a software package on the basis of finite element formulation. A rudimentary finite element-control algorithm package was also developed to evaluate the performance of candidate control laws. A few numerical simulations using the software package developed herein were given. The integrated software package will provide a design tool to address issues such as how adaptive smart systems will scale to a full size aircraft, the amount of piezoelectric materials and the powers needed to actuate it for desired performance. It will also provide a viable new structural control design concept for practical applications in large flexible structures such as aerospace vehicles and aircraft.
A multidimensional finite element method for CFD
NASA Technical Reports Server (NTRS)
Pepper, Darrell W.; Humphrey, Joseph W.
1991-01-01
A finite element method is used to solve the equations of motion for 2- and 3-D fluid flow. The time-dependent equations are solved explicitly using quadrilateral (2-D) and hexahedral (3-D) elements, mass lumping, and reduced integration. A Petrov-Galerkin technique is applied to the advection terms. The method requires a minimum of computational storage, executes quickly, and is scalable for execution on computer systems ranging from PCs to supercomputers.
Quadrilateral/hexahedral finite element mesh coarsening
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.
Adaptive finite element strategies for shell structures
NASA Technical Reports Server (NTRS)
Stanley, G.; Levit, I.; Stehlin, B.; Hurlbut, B.
1992-01-01
The present paper extends existing finite element adaptive refinement (AR) techniques to shell structures, which have heretofore been neglected in the AR literature. Specific challenges in applying AR to shell structures include: (1) physical discontinuities (e.g., stiffener intersections); (2) boundary layers; (3) sensitivity to geometric imperfections; (4) the sensitivity of most shell elements to mesh distortion, constraint definition and/or thinness; and (5) intrinsic geometric nonlinearity. All of these challenges but (5) are addressed here.
Finite element modeling of nonisothermal polymer flows
NASA Technical Reports Server (NTRS)
Roylance, D.
1981-01-01
A finite element formulation designed to simulate polymer melt flows in which both conductive and convective heat transfer are important is described, and the numerical model is illustrated by means of computer experiments using extruder drag flow and entry flow as trial problems. Fluid incompressibility is enforced by a penalty treatment of the element pressures, and the thermal convective transport is modeled by conventional Galerkin and optimal upwind treatments.
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.
Finite element analysis applied to cornea reshaping.
Cabrera Fernández, Delia; Niazy, A M; Kurtz, R M; Djotyan, G P; Juhasz, T
2005-01-01
A 2-D finite element model of the cornea is developed to simulate corneal reshaping and the resulting deformation induced by refractive surgery. In the numerical simulations, linear and nonlinear elastic models are applied when stiffness inhomogeneities varying with depth are considered. Multiple simulations are created that employ different geometric configurations for the removal of the corneal tissue. Side-by-side comparisons of the different constitutive laws are also performed. To facilitate the comparison, the material property constants are identified from the same experimental data, which are obtained from mechanical tests on corneal strips and membrane inflation experiments. We then validate the resulting models by comparing computed refractive power changes with clinical results. Tissue deformations created by simulated corneal tissue removal using finite elements are consistent with clinically observed postsurgical results. The model developed provides a much more predictable refractive outcome when the stiffness inhomogeneities of the cornea and nonlinearities of the deformations are included in the simulations. Finite element analysis is a useful tool for modeling surgical effects on the cornea and developing a better understanding of the biomechanics of the cornea. The creation of patient-specific simulations would allow surgical outcomes to be predicted based on individualized finite element models.
Finite element displacement analysis of a lung.
NASA Technical Reports Server (NTRS)
Matthews, F. L.; West, J. B.
1972-01-01
A method is given based on the technique of finite elements which determines theoretically the mechanical behavior of a lung-shaped body loaded by its own weight. The results of this theoretical analysis have been compared with actual measurements of alveolar size and pleural pressures in animal lungs.
Finite element modelling of acoustic emission sensor
NASA Astrophysics Data System (ADS)
Gerasimov, S. I.; Sych, T. V.
2017-08-01
With a validated finite element system COSMOS/M, the out-of-plane displacements corresponding to model sources of acoustic emission (AE) were calculated in three-dimensional samples. The displacement signals were calculated for positions of the receiver on the top plate surface at several different distances (in the far-field) from the source’s epicenter.
Bitter, Thom; Khan, Imran; Marriott, Tim; Lovelady, Elaine; Verdonschot, Nico; Janssen, Dennis
2017-09-01
Fretting corrosion at the taper interface of modular hip implants has been implicated as a possible cause of implant failure. This study was set up to gain more insight in the taper mechanics that lead to fretting corrosion. The objectives of this study therefore were (1) to select experimental loading conditions to reproduce clinically relevant fretting corrosion features observed in retrieved components, (2) to develop a finite element model consistent with the fretting experiments and (3) to apply more complicated loading conditions of activities of daily living to the finite element model to study the taper mechanics. The experiments showed similar wear patterns on the taper surface as observed in retrievals. The finite element wear score based on Archard's law did not correlate well with the amount of material loss measured in the experiments. However, similar patterns were observed between the simulated micromotions and the experimental wear measurements. Although the finite element model could not be validated, the loading conditions based on activities of daily living demonstrate the importance of assembly load on the wear potential. These findings suggest that finite element models that do not incorporate geometry updates to account for wear loss may not be appropriate to predict wear volumes of taper connections.
Revolution in Orthodontics: Finite element analysis
Singh, Johar Rajvinder; Kambalyal, Prabhuraj; Jain, Megha; Khandelwal, Piyush
2016-01-01
Engineering has not only developed in the field of medicine but has also become quite established in the field of dentistry, especially Orthodontics. Finite element analysis (FEA) is a computational procedure to calculate the stress in an element, which performs a model solution. This structural analysis allows the determination of stress resulting from external force, pressure, thermal change, and other factors. This method is extremely useful for indicating mechanical aspects of biomaterials and human tissues that can hardly be measured in vivo. The results obtained can then be studied using visualization software within the finite element method (FEM) to view a variety of parameters, and to fully identify implications of the analysis. This is a review to show the applications of FEM in Orthodontics. It is extremely important to verify what the purpose of the study is in order to correctly apply FEM. PMID:27114948
Large deformations of reconfigurable active membranes: a finite element model
NASA Astrophysics Data System (ADS)
Son, Seyul; Goulbourne, N. C.
2010-04-01
In this paper, a finite element model is used to describe the inhomogeneous deformations of dielectric elastomers (DE). In our previous work, inhomogeneous deformations of the DE with simple boundary conditions represented by a system of highly nonlinear coupled differential equations (ordinary and partial) were solved using numerical approaches [1-3]. To solve for the electromechanical response for complex shapes (asymmetric), nonuniform loading, and complex boundary conditions a finite element scheme is required. This paper describes a finite element implementation of the DE material model proposed in our previous work in a commercial FE code (ABAQUS 6.8-1, PAWTUCKET, R.I, USA). The total stress is postulated as the summation of the elastic stress tensor and the Maxwell stress tensor, or more generally the electrostatic stress tensor. The finite element model is verified by analytical solutions and experimental results for planar membrane extensions subject to mechanical loads and an electric field: (i) equibiaxial extension and (ii) generalized biaxial extension. Specifically, the analytical solutions for equibiaxial extension of the DE is obtained by combining a modified large deformation membrane theory that accounts for the electromechanical coupling effect in actuation commonly referred to as the Maxwell stress [4]. A Mooney-Rivlin strain energy function is employed to describe the constitutive stress strain behavior of the DE. For the finite element implementation, the constitutive relationships from our previously proposed mathematical model [4] are implemented into the finite element code. Experimentally, a 250% equibiaxially prestretched DE sample is attached to a rigid joint frame and inhomogeneous deformations of the reconfigurable DE are observed with respect to mechanical loads and an applied electric field. The computational result for the reconfigurable DE is compared with the test result to validate the accuracy and robustness of the finite
Finite Element Analysis of Piping Tees.
1980-06-01
Combustion Engineering, Inc., performed an experimental stress analysis3 on an ANSI B16.9 carbon steelt tee designated T-12. Pipe extensions were welded to...AD-ASS? 353 DAVID If TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CE--ETC F/S 13/11 FINITE ELEENT ANALYSIS OF PIPING TEES.(U) JUN 8 A J QUEZON. S C...DAVID W. TAYLOR NAVAL SHIP SRESEARCH AND DEVELOPMENT CENTER Bethesa Md. 20084 FINITE ELEMENT ANALYSIS OF PIPING TEES by Antonio J. Quezon, Gordon C
Finite Element Heat & Mass Transfer Code
Trease, Lynn
1996-10-10
FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; and double porosity and double porosity/double permeability capabilities.
FEHM. Finite Element Heat & Mass Transfer Code
Zyvoloski, G.A.
1996-10-10
FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; and double porosity and double porosity/double permeability capabilities.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2015-12-21
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying a series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2015-12-21
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less
Finite Element Modeling of the Buckling Response of Sandwich Panels
NASA Technical Reports Server (NTRS)
Rose, Cheryl A.; Moore, David F.; Knight, Norman F., Jr.; Rankin, Charles C.
2002-01-01
A comparative study of different modeling approaches for predicting sandwich panel buckling response is described. The study considers sandwich panels with anisotropic face sheets and a very thick core. Results from conventional analytical solutions for sandwich panel overall buckling and face-sheet-wrinkling type modes are compared with solutions obtained using different finite element modeling approaches. Finite element solutions are obtained using layered shell element models, with and without transverse shear flexibility, layered shell/solid element models, with shell elements for the face sheets and solid elements for the core, and sandwich models using a recently developed specialty sandwich element. Convergence characteristics of the shell/solid and sandwich element modeling approaches with respect to in-plane and through-the-thickness discretization, are demonstrated. Results of the study indicate that the specialty sandwich element provides an accurate and effective modeling approach for predicting both overall and localized sandwich panel buckling response. Furthermore, results indicate that anisotropy of the face sheets, along with the ratio of principle elastic moduli, affect the buckling response and these effects may not be represented accurately by analytical solutions. Modeling recommendations are also provided.
A composite nodal finite element for hexagons
Hennart, J.P.; Mund, E.H. |; Valle, E. Del
1997-10-01
A nodal algorithm for the solution of the multigroup diffusion equations in hexagonal arrays is analyzed. Basically, the method consists of dividing each hexagon into four quarters and mapping the hexagon quarters onto squares. The resulting boundary value problem on a quadrangular domain is solved in primal weak formulation. Nodal finite element methods like the Raviart-Thomas RTk schemes provide accurate analytical expansions of the solution in the hexagons. Transverse integration cannot be performed on the equations in the quadrangular domain as simply as it is usually done on squares because these equations have essentially variable coefficients. However, by considering an auxiliary problem with constant coefficients (on the same quadrangular domain) and by using a preconditioning approach, transverse integration can be performed as for rectangular geometry. A description of the algorithm is given for a one-group diffusion equation. Numerical results are presented for a simple model problem with a known analytical solution and for k{sub eff} evaluations of some benchmark problems proposed in the literature. For the analytical problem, the results indicate that the theoretical convergence orders of RTk schemes (k = 0,1) are obtained, yielding accurate solutions at the expense of a few preconditioning iterations.
Intra Plate Stresses Using Finite Element Modelling
NASA Astrophysics Data System (ADS)
Jayalakshmi, S.; Raghukanth, S. T. G.
2016-10-01
One of the most challenging problems in the estimation of seismic hazard is the ability to quantify seismic activity. Empirical models based on the available earthquake catalogue are often used to obtain activity of source regions. The major limitation with this approach is the lack of sufficient data near a specified source. The non-availability of data poses difficulties in obtaining distribution of earthquakes with large return periods. Such events recur over geological time scales during which tectonic processes, including mantle convection, formation of faults and new plate boundaries, are likely to take place. The availability of geometries of plate boundaries, plate driving forces, lithospheric stress field and GPS measurements has provided numerous insights on the mechanics of tectonic plates. In this article, a 2D finite element model of Indo-Australian plate is developed with the focus of representing seismic activity in India. The effect of large scale geological features including sedimentary basins, fold belts and cratons on the stress field in India is explored in this study. In order to address long term behaviour, the orientation of stress field and tectonic faults of the present Indo- Australian plate are compared with a reconstructed stress field from the early Miocene (20 Ma).
Convergence of finite element approximations of large eddy motion.
Iliescu, T.; John, V.; Layton, W. J.; Mathematics and Computer Science; Otto-von-Guericke Univ.; Univ. of Pittsburgh
2002-11-01
This report considers 'numerical errors' in LES. Specifically, for one family of space filtered flow models, we show convergence of the finite element approximation of the model and give an estimate of the error. Keywords: Navier Stokes equations, large eddy simulation, finite element method I. INTRODUCTION Consider the (turbulent) flow of an incompressible fluid. One promising and common approach to the simulation of the motion of the large fluid structures is Large Eddy Simulation (LES). Various models are used in LES; a common one is to find (w, q), where w : {Omega}
Finite element simulations of stacked crystal filters
NASA Astrophysics Data System (ADS)
Lee, Jiunn-Horng; Tzeng, Kung-Yu; Cheng, Chih-Wei; Shih, Yu-Ching; Yao, Chih-Min
2004-03-01
Wireless networks are growing rapidly. Their applications include cellular phone, satellite communication and wireless local area networks. In order to avoid interference between all these applications, high selectivity RF filters are essential. The stacked crystal filter (SCF) is a useful configuration when low insertion loss is desired and the near-in skirt selectivity requirement is not as high as that produced by ladder filters. A SCF is an acoustically coupled resonator filter which includes a pair of thickness mode piezoelectric plates attached to each other. Mounted between adjacent sides of the two plates is a shared electrode. The common ways to model the SCF are mason model and lumped element equivalent circuit method. To accommodate complicated geometries, we need to use the other kinds of numerical analysis techniques. Finite element methods have been applied to the modeling of thin film bulk acoustic wave resonator in recent years. Advanced FEM software has the capability to do a coupled piezoelectric-circuit analysis that can connect electrical circuits directly to the piezoelectric finite element models. In this work, we integrate the SCF two-dimensional piezoelectric finite element models and electrical circuits together to simulate the performance of SCF. The influences of electrode property and acoustic loss to the performance of filter are also investigated. The results of simulation are verified by mason model. This methodology can be applied to more complicated geometry models and other types of filters simulation such as coupled resonator filters (CRF) and ladder filters.
NASA Astrophysics Data System (ADS)
Kluczyk, K.; Jacak, W.
2016-01-01
We investigate metal nano-particle size influence on plasmon resonance within theoretical and numerical approaches and compare results with available experimental data in order to improve resolution of optical identification of metallic nano-particle size and shape. The developed microscopic approach is the quantum random phase approximation model of plasmons in metallic nano-particles including plasmon damping by electron scattering and by radiative losses (i.e., by the so-called Lorentz friction). The numerical approach is by the finite element method solution of Maxwell equations for incident planar wave in spherical (also nano-rod, spheroid) geometry upon the system COMSOL and Mie treatment, supplemented with phenomenologically modeled dielectric function of metallic nano-particle. Comparison with experimental data for light extinction in Au and Ag nano-particle colloidal solutions with different particle sizes is presented. The crucial role of the Lorentz friction in the size effect of plasmon resonance in large (e.g., 20-60 nm for Au in vacuum) metallic nanoparticles is evidenced.
NASA Technical Reports Server (NTRS)
Reddy, C. J.; Deshpande, Manohar D.; Cockrell, C. R.; Beck, F. B.
1995-01-01
A combined finite element method/method of moments (FEM/MoM) approach is used to analyze the electromagnetic scattering properties of a three-dimensional-cavity-backed aperture in an infinite ground plane. The FEM is used to formulate the fields inside the cavity, and the MoM (with subdomain bases) in both spectral and spatial domains is used to formulate the fields above the ground plane. Fields in the aperture and the cavity are solved using a system of equations resulting from the combination of the FEM and the MoM. By virtue of the FEM, this combined approach is applicable to all arbitrarily shaped cavities with inhomogeneous material fillings, and because of the subdomain bases used in the MoM, the apertures can be of any arbitrary shape. This approach leads to a partly sparse and partly full symmetric matrix, which is efficiently solved using a biconjugate gradient algorithm. Numerical results are presented to validate the analysis.
Kleban, Alexander
2015-01-01
Study Design Retrospective controlled cohort study comparing the in-brace correction of two samples of scoliosis patients with braces of different computer aided design (CAD). Purpose In-brace correction and compliance correlate with outcome. The more standardized CAD braces that are available should enable improved in-brace correction and outcome. This study compared recent CAD brace developments with respect to in-brace corrections. Overview of Literature A 2013 randomized controlled trial demonstrated that 72% of a population complying to Scoliosis Research Society inclusion criteria on bracing did not progress using braces (mainly Boston braces) used in the United States and Canada with moderate corrective effect. Methods In-brace corrections achieved in a sample of patients fulfilling the inclusion criteria for studies on bracing using the classification based approach (CBA) were compared to the recent individual CAD/computer aided manufacturing bracing based on finite element modelling approach (FEMA). Results In-brace corrections using the different approaches differed widely. CBA in-brace corrections were 66% of the initial value. FEMA in-brace correction was 42% of the initial value. Conclusions Considering the fact that in-brace correction (and compliance) determines the end result of bracing in the treatment of scoliosis, scoliosis braces based on CBA are superior to the FEMA and the standard plaster based brace applications. PMID:26435781
Weiss, Hans-Rudolf; Kleban, Alexander
2015-10-01
Retrospective controlled cohort study comparing the in-brace correction of two samples of scoliosis patients with braces of different computer aided design (CAD). In-brace correction and compliance correlate with outcome. The more standardized CAD braces that are available should enable improved in-brace correction and outcome. This study compared recent CAD brace developments with respect to in-brace corrections. A 2013 randomized controlled trial demonstrated that 72% of a population complying to Scoliosis Research Society inclusion criteria on bracing did not progress using braces (mainly Boston braces) used in the United States and Canada with moderate corrective effect. In-brace corrections achieved in a sample of patients fulfilling the inclusion criteria for studies on bracing using the classification based approach (CBA) were compared to the recent individual CAD/computer aided manufacturing bracing based on finite element modelling approach (FEMA). In-brace corrections using the different approaches differed widely. CBA in-brace corrections were 66% of the initial value. FEMA in-brace correction was 42% of the initial value. Considering the fact that in-brace correction (and compliance) determines the end result of bracing in the treatment of scoliosis, scoliosis braces based on CBA are superior to the FEMA and the standard plaster based brace applications.
Finite element method for eigenvalue problems in electromagnetics
NASA Technical Reports Server (NTRS)
Reddy, C. J.; Deshpande, Manohar D.; Cockrell, C. R.; Beck, Fred B.
1994-01-01
Finite element method (FEM) has been a very powerful tool to solve many complex problems in electromagnetics. The goal of the current research at the Langley Research Center is to develop a combined FEM/method of moments approach to three-dimensional scattering/radiation problem for objects with arbitrary shape and filled with complex materials. As a first step toward that goal, an exercise is taken to establish the power of FEM, through closed boundary problems. This paper demonstrates the developed of FEM tools for two- and three-dimensional eigenvalue problems in electromagnetics. In section 2, both the scalar and vector finite elements have been used for various waveguide problems to demonstrate the flexibility of FEM. In section 3, vector finite element method has been extended to three-dimensional eigenvalue problems.
EC Vacuum Vessel Finite Element Analysis
Rudland, D.; Luther, R.; /Fermilab
1992-02-04
This Note contains a summary of the results of the finite element analysis of the EC Cryostat vacuum vessel performed by Dave Rudland in 1987. The results are used in the structural evaluation of the EC cryostats presented in Engineering Note 194. It should also be noted that the adequacy of the design of the vacuum vessels was reviewed and verified by the Battelle Memorial Institute. Battelle used a shell of revolution program to essentially duplicate the FEA analysis with similar results. It should be noted that no plots of the finite element mesh were retained from the analysis, and these can not be easily reproduced due to a change in the version of the ANSYS computer program shortly after the analysis was completed.
Finite element substructuring methods for composite mechanics
NASA Technical Reports Server (NTRS)
Murthy, Pappu L. N.; Chamis, Christos C.
1988-01-01
Finite element substructuring strategies are presented to obtain numerical solutions for three typical problems of interest to the composites community: (1) impact and toughness characterization of composites using Charpy's impact test specimen; (2) free-edge stress analysis of composite laminates; and (3) fracture toughness predictions of composites for individual and combined fracture of modes I, II, and III. The key issue common to these problems is the presence of singular or near singular stress fields. The regions prone to see steep stress gradients are substructured with progressively refined meshes to study the local response simultaneously with the global response. The results from the select examples indicate that finite element substructuring methods are computationally effective for composite singularity mechanics.
Finite element modeling of permanent magnet devices
NASA Astrophysics Data System (ADS)
Brauer, J. R.; Larkin, L. A.; Overbye, V. D.
1984-03-01
New techniques are presented for finite element modeling of permanent magnets in magnetic devices such as motors and generators. These techniques extend a previous sheet-current permanent magnet model that applies only for straight line B-H loops and rectangular-shaped magnets. Here Maxwell's equations are used to derive the model of a permanent magnet having a general curved B-H loop and any geometric shape. The model enables a nonlinear magnetic finite element program to use Newton-Raphson iteration to solve for saturable magnetic fields in a wide variety of devices containing permanent magnets and steels. The techniques are applied to a brushless dc motor with irregular-shaped permanent magnets. The calculated motor torque agrees well with measured torque.
2-d Finite Element Code Postprocessor
Sanford, L. A.; Hallquist, J. O.
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forces along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.
Finite element analysis of human joints
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.
Finite element concepts in computational aerodynamics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1978-01-01
Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.
Finite-size scaling for quantum criticality using the finite-element method.
Antillon, Edwin; Wehefritz-Kaufmann, Birgit; Kais, Sabre
2012-03-01
Finite size scaling for the Schrödinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite-element method was shown to be a powerful numerical method for ab initio electronic-structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite-element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, local density approximation, and an "exact" formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.
Finite element analysis of wrinkling membranes
NASA Technical Reports Server (NTRS)
Miller, R. K.; Hedgepeth, J. M.; Weingarten, V. I.; Das, P.; Kahyai, S.
1984-01-01
The development of a nonlinear numerical algorithm for the analysis of stresses and displacements in partly wrinkled flat membranes, and its implementation on the SAP VII finite-element code are described. A comparison of numerical results with exact solutions of two benchmark problems reveals excellent agreement, with good convergence of the required iterative procedure. An exact solution of a problem involving axisymmetric deformations of a partly wrinkled shallow curved membrane is also reported.
Finite element methods in fracture mechanics
NASA Technical Reports Server (NTRS)
Liebowitz, H.; Moyer, E. T., Jr.
1989-01-01
Finite-element methodology specific to the analysis of fracture mechanics problems is reviewed. Primary emphasis is on the important algorithmic developments which have enhanced the numerical modeling of fracture processes. Methodologies to address elastostatic problems in two and three dimensions, elastodynamic problems, elastoplastic problems, special considerations for three-dimensional nonlinear problems, and the modeling of stable crack growth are reviewed. In addition, the future needs of the fracture community are discussed and open questions are identified.
EXODUS II: A finite element data model
Schoof, L.A.; Yarberry, V.R.
1994-09-01
EXODUS II is a model developed to store and retrieve data for finite element analyses. It is used for preprocessing (problem definition), postprocessing (results visualization), as well as code to code data transfer. An EXODUS II data file is a random access, machine independent, binary file that is written and read via C, C++, or Fortran library routines which comprise the Application Programming Interface (API).
Finite Element Analysis of Reverberation Chambers
NASA Technical Reports Server (NTRS)
Bunting, Charles F.; Nguyen, Duc T.
2000-01-01
The primary motivating factor behind the initiation of this work was to provide a deterministic means of establishing the validity of the statistical methods that are recommended for the determination of fields that interact in -an avionics system. The application of finite element analysis to reverberation chambers is the initial step required to establish a reasonable course of inquiry in this particularly data-intensive study. The use of computational electromagnetics provides a high degree of control of the "experimental" parameters that can be utilized in a simulation of reverberating structures. As the work evolved there were four primary focus areas they are: 1. The eigenvalue problem for the source free problem. 2. The development of a complex efficient eigensolver. 3. The application of a source for the TE and TM fields for statistical characterization. 4. The examination of shielding effectiveness in a reverberating environment. One early purpose of this work was to establish the utility of finite element techniques in the development of an extended low frequency statistical model for reverberation phenomena. By employing finite element techniques, structures of arbitrary complexity can be analyzed due to the use of triangular shape functions in the spatial discretization. The effects of both frequency stirring and mechanical stirring are presented. It is suggested that for the low frequency operation the typical tuner size is inadequate to provide a sufficiently random field and that frequency stirring should be used. The results of the finite element analysis of the reverberation chamber illustrate io-W the potential utility of a 2D representation for enhancing the basic statistical characteristics of the chamber when operating in a low frequency regime. The basic field statistics are verified for frequency stirring over a wide range of frequencies. Mechanical stirring is shown to provide an effective frequency deviation.
Finite element based electric motor design optimization
NASA Technical Reports Server (NTRS)
Campbell, C. Warren
1993-01-01
The purpose of this effort was to develop a finite element code for the analysis and design of permanent magnet electric motors. These motors would drive electromechanical actuators in advanced rocket engines. The actuators would control fuel valves and thrust vector control systems. Refurbishing the hydraulic systems of the Space Shuttle after each flight is costly and time consuming. Electromechanical actuators could replace hydraulics, improve system reliability, and reduce down time.
Finite Element Results Visualization for Unstructured Grids
Speck, Douglas E.; Dovey, Donald J.
1996-07-15
GRIZ is a general-purpose post-processing application supporting interactive visualization of finite element analysis results on unstructured grids. In addition to basic pseudocolor renderings of state variables over the mesh surface, GRIZ provides modern visualization techniques such as isocontours and isosurfaces, cutting planes, vector field display, and particle traces. GRIZ accepts both command-line and mouse-driven input, and is portable to virtually any UNIX platform which provides Motif and OpenGl libraries.
TAURUS. 3-D Finite Element Code Postprocessor
Whirley, R.G.
1984-05-01
TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D, DYNA3D, TACO3D, TOPAZ3D, and GEMINI and plots contours, time histories,and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing.
TAURUS. 3-D Finite Element Code Postprocessor
Kennedy, T.
1992-03-03
TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D, DYNA3D, TACO3D, TOPAZ3D, and GEMINI and plots contours, time histories, and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing.
TAURUS. 3-D Finite Element Code Postprocessor
Whirley, R.G.
1993-11-30
TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D, DYNA3D, TACO3D, TOPAZ3D, and GEMINI and plots contours, time histories,and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing.
TAURUS. 3-d Finite Element Code Postprocessor
Whirley, R.G.
1991-05-01
TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D (ESTSC 139), DYNA3D (ESTSC 138), TACO3D (ESTSC 287), TOPAZ3D (ESTSC 231), and GEMINI (ESTSC 455) and plots contours, time histories,and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing.
TAURUS. 3-d Finite Element Code Postprocessor
Whirley, R.G.
1992-03-03
TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D (ESTSC 139), DYNA3D (ESTSC 138), TACO3D (ESTSC 287), TOPAZ3D (ESTSC 231), and GEMINI (ESTSC 455) and plots contours, time histories,and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing.
TAURUS. 3-D Finite Element Code Postprocessor
Whirley, R.G.
1992-03-03
TAURUS reads the binary plot files generated by the LLNL three-dimensional finite element analysis codes, NIKE3D, DYNA3D, TACO3D, TOPAZ3D, and GEMINI and plots contours, time histories,and deformed shapes. Contours of a large number of quantities may be plotted on meshes consisting of plate, shell, and solid type elements. TAURUS can compute a variety of strain measures, reaction forces along constrained boundaries, and momentum. TAURUS has three phases: initialization, geometry display with contouring, and time history processing.
Finite element modeling of lipid bilayer membranes
NASA Astrophysics Data System (ADS)
Feng, Feng; Klug, William S.
2006-12-01
A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic model for these membranes employs a two-dimensional-fluid-like elastic constitutive law which is sensitive to curvature, and subjects vesicles to physically imposed constraints on surface area and volume. This model is implemented numerically via the use of C1-conforming triangular Loop subdivision finite elements. The validity of the framework is tested by computing equilibrium shapes from previously-determined axisymmetric shape-phase diagram of lipid bilayer vesicles with homogeneous material properties. Some of the benefits and challenges of finite element modeling of lipid bilayer systems are discussed, and it is indicated how this framework is natural for future investigation of biologically realistic bilayer structures involving nonaxisymmetric geometries, binding and adhesive interactions, heterogeneous mechanical properties, cytoskeletal interactions, and complex loading arrangements. These biologically relevant features have important consequences for the shape mechanics of nonidealized vesicles and cells, and their study requires not simply advances in theory, but also advances in numerical simulation techniques, such as those presented here.
Gauge finite element method for incompressible flows
NASA Astrophysics Data System (ADS)
E, Weinan; Liu, Jian-Guo
2000-12-01
A finite element method for computing viscous incompressible flows based on the gauge formulation introduced in [Weinan E, Liu J-G. Gauge method for viscous incompressible flows. Journal of Computational Physics (submitted)] is presented. This formulation replaces the pressure by a gauge variable. This new gauge variable is a numerical tool and differs from the standard gauge variable that arises from decomposing a compressible velocity field. It has the advantage that an additional boundary condition can be assigned to the gauge variable, thus eliminating the issue of a pressure boundary condition associated with the original primitive variable formulation. The computational task is then reduced to solving standard heat and Poisson equations, which are approximated by straightforward, piecewise linear (or higher-order) finite elements. This method can achieve high-order accuracy at a cost comparable with that of solving standard heat and Poisson equations. It is naturally adapted to complex geometry and it is much simpler than traditional finite element methods for incompressible flows. Several numerical examples on both structured and unstructured grids are presented. Copyright
FESDIF -- Finite Element Scalar Diffraction theory code
Kraus, H.G.
1992-09-01
This document describes the theory and use of a powerful scalar diffraction theory based computer code for calculation of intensity fields due to diffraction of optical waves by two-dimensional planar apertures and lenses. This code is called FESDIF (Finite Element Scalar Diffraction). It is based upon both Fraunhofer and Kirchhoff scalar diffraction theories. Simplified routines for circular apertures are included. However, the real power of the code comes from its basis in finite element methods. These methods allow the diffracting aperture to be virtually any geometric shape, including the various secondary aperture obstructions present in telescope systems. Aperture functions, with virtually any phase and amplitude variations, are allowed in the aperture openings. Step change aperture functions are accommodated. The incident waves are considered to be monochromatic. Plane waves, spherical waves, or Gaussian laser beams may be incident upon the apertures. Both area and line integral transformations were developed for the finite element based diffraction transformations. There is some loss of aperture function generality in the line integral transformations which are typically many times more computationally efficient than the area integral transformations when applicable to a particular problem.
NASA Astrophysics Data System (ADS)
Nawa, S.; Tamagaki, R.; Tatsumi, T.; Yoro, S.
1990-12-01
Static interaction between two spherical chiral bags is studied in a numerical way. In order to get the solutions of the confined quark states and the outside chiral-field which should satisfy the boundary conditions at both bag surfaces in the chiral bag model, the finite element method is utilized as numerical procedure. We extract the static interaction by calculating the energy change as the two bags approach from large separation to contact distance. Results obtained for three typical configurations indicate that such an approach is workable: We can see that the asymptotic behavior gives the OPEP-tail, and some nonperturbative effects are noticeable in the intermediate region. Although the deviation of the interaction energy from the OPEP value is not so remarkable beyond the pion Compton wavelength due to the cancellation between the energy change of the quark system and that of the chiral field, there arises a significant deviation of the quark wave function and the chiral field from those of the hedgehog solution in the single-baryon case. The procedure in numerical calculations adopted in this paper is explained in detail.
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.
Traction free finite elements with the assumed stress hybrid model. M.S. Thesis, 1981
NASA Technical Reports Server (NTRS)
Kafie, Kurosh
1991-01-01
An effective approach in the finite element analysis of the stress field at the traction free boundary of a solid continuum was studied. Conventional displacement and assumed stress finite elements were used in the determination of stress concentrations around circular and elliptical holes. Specialized hybrid elements were then developed to improve the satisfaction of prescribed traction boundary conditions. Results of the stress analysis indicated that finite elements which exactly satisfy the free stress boundary conditions are the most accurate and efficient in such problems. A general approach for hybrid finite elements which incorporate traction free boundaries of arbitrary geometry was formulated.
NASA Astrophysics Data System (ADS)
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
Harrison, Noel M; McDonnell, Pat; Mullins, Liam; Wilson, Niall; O'Mahoney, Denis; McHugh, Peter E
2013-04-01
Trabecular bone tissue failure can be considered as consisting of two stages: damage and fracture; however, most failure analyses of 3D high-resolution trabecular bone samples are confined to damage mechanisms only, that is, without fracture. This study aims to develop a computational model of trabecular bone consisting of an explicit representation of complete failure, incorporating damage criteria, fracture criteria, cohesive forces, asymmetry and large deformation capabilities. Following parameter studies on a test specimen, and experimental testing of bone sample to complete failure, the asymmetric critical tissue damage and fracture strains of ovine vertebral trabecular bone were calibrated and validated to be compression damage -1.16 %, tension damage 0.69 %, compression fracture -2.91 % and tension fracture 1.98 %. Ultimate strength and post-ultimate strength softening were captured by the computational model, and the failure of individual struts in bending and shear was also predicted. This modelling approach incorporated a cohesive parameter that provided a facility to calibrate ductile-brittle behaviour of bone tissue in this non-linear geometric and non-linear constitutive property analyses tool. Finally, the full accumulation of tissue damage and tissue fracture has been monitored from range of small magnitude (normal daily loading) through to specimen yielding, ultimate strength and post-ultimate strength softening.
Krittian, Sebastian B.S.; Lamata, Pablo; Michler, Christian; Nordsletten, David A.; Bock, Jelena; Bradley, Chris P.; Pitcher, Alex; Kilner, Philip J.; Markl, Michael; Smith, Nic P.
2012-01-01
The evaluation of cardiovascular velocities, their changes through the cardiac cycle and the consequent pressure gradients has the capacity to improve understanding of subject-specific blood flow in relation to adjacent soft tissue movements. Magnetic resonance time-resolved 3D phase contrast velocity acquisitions (4D flow) represent an emerging technology capable of measuring the cyclic changes of large scale, multi-directional, subject-specific blood flow. A subsequent evaluation of pressure differences in enclosed vascular compartments is a further step which is currently not directly available from such data. The focus of this work is to address this deficiency through the development of a novel simulation workflow for the direct computation of relative cardiovascular pressure fields. Input information is provided by enhanced 4D flow data and derived MR domain masking. The underlying methodology shows numerical advantages in terms of robustness, global domain composition, the isolation of local fluid compartments and a treatment of boundary conditions. This approach is demonstrated across a range of validation examples which are compared with analytic solutions. Four subject-specific test cases are subsequently run, showing good agreement with previously published calculations of intra-vascular pressure differences. The computational engine presented in this work contributes to non-invasive access to relative pressure fields, incorporates the effects of both blood flow acceleration and viscous dissipation, and enables enhanced evaluation of cardiovascular blood flow. PMID:22626833
Krittian, Sebastian B S; Lamata, Pablo; Michler, Christian; Nordsletten, David A; Bock, Jelena; Bradley, Chris P; Pitcher, Alex; Kilner, Philip J; Markl, Michael; Smith, Nic P
2012-07-01
The evaluation of cardiovascular velocities, their changes through the cardiac cycle and the consequent pressure gradients has the capacity to improve understanding of subject-specific blood flow in relation to adjacent soft tissue movements. Magnetic resonance time-resolved 3D phase contrast velocity acquisitions (4D flow) represent an emerging technology capable of measuring the cyclic changes of large scale, multi-directional, subject-specific blood flow. A subsequent evaluation of pressure differences in enclosed vascular compartments is a further step which is currently not directly available from such data. The focus of this work is to address this deficiency through the development of a novel simulation workflow for the direct computation of relative cardiovascular pressure fields. Input information is provided by enhanced 4D flow data and derived MR domain masking. The underlying methodology shows numerical advantages in terms of robustness, global domain composition, the isolation of local fluid compartments and a treatment of boundary conditions. This approach is demonstrated across a range of validation examples which are compared with analytic solutions. Four subject-specific test cases are subsequently run, showing good agreement with previously published calculations of intra-vascular pressure differences. The computational engine presented in this work contributes to non-invasive access to relative pressure fields, incorporates the effects of both blood flow acceleration and viscous dissipation, and enables enhanced evaluation of cardiovascular blood flow. Copyright © 2012 Elsevier B.V. All rights reserved.
Lew, S.; Wolters, C.H.; Dierkes, T.; Röer, C.; MacLeod, R.S.
2009-01-01
Accuracy and run-time play an important role in medical diagnostics and research as well as in the field of neuroscience. In Electroencephalography (EEG) source reconstruction, a current distribution in the human brain is reconstructed noninvasively from measured potentials at the head surface (the EEG inverse problem). Numerical modeling techniques are used to simulate head surface potentials for dipolar current sources in the human cortex, the so-called EEG forward problem. In this paper, the efficiency of algebraic multigrid (AMG), incomplete Cholesky (IC) and Jacobi preconditioners for the conjugate gradient (CG) method are compared for iteratively solving the finite element (FE) method based EEG forward problem. The interplay of the three solvers with a full subtraction approach and two direct potential approaches, the Venant and the partial integration method for the treatment of the dipole singularity is examined. The examination is performed in a four-compartment sphere model with anisotropic skull layer, where quasi-analytical solutions allow for an exact quantification of computational speed versus numerical error. Specifically-tuned constrained Delaunay tetrahedralization (CDT) FE meshes lead to high accuracies for both the full subtraction and the direct potential approaches. Best accuracies are achieved by the full subtraction approach if the homogeneity condition is fulfilled. It is shown that the AMG-CG achieves an order of magnitude higher computational speed than the CG with the standard preconditioners with an increasing gain factor when decreasing mesh size. Our results should broaden the application of accurate and fast high-resolution FE volume conductor modeling in source analysis routine. PMID:20161462
Nondestructive Evaluation Correlated with Finite Element Analysis
NASA Technical Reports Server (NTRS)
Abdul-Azid, Ali; Baaklini, George Y.
1999-01-01
Advanced materials are being developed for use in high-temperature gas turbine applications. For these new materials to be fully utilized, their deformation properties, their nondestructive evaluation (NDE) quality and material durability, and their creep and fatigue fracture characteristics need to be determined by suitable experiments. The experimental findings must be analyzed, characterized, modeled and translated into constitutive equations for stress analysis and life prediction. Only when these ingredients - together with the appropriate computational tools - are available, can durability analysis be performed in the design stage, long before the component is built. One of the many structural components being evaluated by the NDE group at the NASA Lewis Research Center is the flywheel system. It is being considered as an energy storage device for advanced space vehicles. Such devices offer advantages over electrochemical batteries in situations demanding high power delivery and high energy storage per unit weight. In addition, flywheels have potentially higher efficiency and longer lifetimes with proper motor-generator and rotor design. Flywheels made of fiber-reinforced polymer composite material show great promise for energy applications because of the high energy and power densities that they can achieve along with a burst failure mode that is relatively benign in comparison to those of flywheels made of metallic materials Therefore, to help improve durability and reduce structural uncertainties, we are developing a comprehensive analytical approach to predict the reliability and life of these components under these harsh loading conditions. The combination of NDE and two- and three-dimensional finite element analyses (e.g., stress analyses and fracture mechanics) is expected to set a standardized procedure to accurately assess the applicability of using various composite materials to design a suitable rotor/flywheel assembly.
Finite Element analyses of soil bioengineered slopes
NASA Astrophysics Data System (ADS)
Tamagnini, Roberto; Switala, Barbara Maria; Sudan Acharya, Madhu; Wu, Wei; Graf, Frank; Auer, Michael; te Kamp, Lothar
2014-05-01
Soil Bioengineering methods are not only effective from an economical point of view, but they are also interesting as fully ecological solutions. The presented project is aimed to define a numerical model which includes the impact of vegetation on slope stability, considering both mechanical and hydrological effects. In this project, a constitutive model has been developed that accounts for the multi-phase nature of the soil, namely the partly saturated condition and it also includes the effects of a biological component. The constitutive equation is implemented in the Finite Element (FE) software Comes-Geo with an implicit integration scheme that accounts for the collapse of the soils structure due to wetting. The mathematical formulation of the constitutive equations is introduced by means of thermodynamics and it simulates the growth of the biological system during the time. The numerical code is then applied in the analysis of an ideal rainfall induced landslide. The slope is analyzed for vegetated and non-vegetated conditions. The final results allow to quantitatively assessing the impact of vegetation on slope stability. This allows drawing conclusions and choosing whenever it is worthful to use soil bioengineering methods in slope stabilization instead of traditional approaches. The application of the FE methods show some advantages with respect to the commonly used limit equilibrium analyses, because it can account for the real coupled strain-diffusion nature of the problem. The mechanical strength of roots is in fact influenced by the stress evolution into the slope. Moreover, FE method does not need a pre-definition of any failure surface. FE method can also be used in monitoring the progressive failure of the soil bio-engineered system as it calculates the amount of displacements and strains of the model slope. The preliminary study results show that the formulated equations can be useful for analysis and evaluation of different soil bio
Rapid mesh generation for finite element analysis of investment castings
Lober, R.R.; Bohnhoff, W.J.; Meyers, R.J.
1992-11-01
FASTCAST is a Sandia National Laboratories program to produce investment cast prototypical hardware faster by integrating experimental and computational technologies into the casting process. FASTCAST uses the finite element method to characterize the metal flow and solidification processes to reduce uncertainty in the mold design. For the casting process to benefit from finite element analysis, analysis results must be available in a very short time frame. By focusing on the bottleneck of finite element model creation, automated mesh generation can drastically reduce the time span between geometry definition (design) and accurate analysis results. The increased availability of analysis results will diminish the need for trial and error approaches to acquiring production worthy mold and gating systems for investment casting. The CUBIT meshing tool kit is being developed to address the need for rapid mesh generation. CUBIT is being designed to effectively automate the generation of quadrilateral and hexahedral elements. It is a solid-modeler based, two- and three-dimensional preprocessor that prepares solid models for finite element analysis. CUBIT contains several meshing algorithms including two- and three-dimensional mapping, two- and three-dimensional paving (patented), and a general two and one-half dimensional sweeper based upon the plastering algorithm. This paper describes progress in the development of the CUBIT meshing toolkit.
Rapid mesh generation for finite element analysis of investment castings
Lober, R.R.; Bohnhoff, W.J.; Meyers, R.J.
1992-01-01
FASTCAST is a Sandia National Laboratories program to produce investment cast prototypical hardware faster by integrating experimental and computational technologies into the casting process. FASTCAST uses the finite element method to characterize the metal flow and solidification processes to reduce uncertainty in the mold design. For the casting process to benefit from finite element analysis, analysis results must be available in a very short time frame. By focusing on the bottleneck of finite element model creation, automated mesh generation can drastically reduce the time span between geometry definition (design) and accurate analysis results. The increased availability of analysis results will diminish the need for trial and error approaches to acquiring production worthy mold and gating systems for investment casting. The CUBIT meshing tool kit is being developed to address the need for rapid mesh generation. CUBIT is being designed to effectively automate the generation of quadrilateral and hexahedral elements. It is a solid-modeler based, two- and three-dimensional preprocessor that prepares solid models for finite element analysis. CUBIT contains several meshing algorithms including two- and three-dimensional mapping, two- and three-dimensional paving (patented), and a general two and one-half dimensional sweeper based upon the plastering algorithm. This paper describes progress in the development of the CUBIT meshing toolkit.
Mixed Finite Element Method for Melt Migration
NASA Astrophysics Data System (ADS)
Taicher, A. L.; Hesse, M. A.; Arbogast, T.
2012-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium. Therefore, a numerical method must also carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. The finite element framework provides support for additional analysis of error and convergence. Moreover, both mesh refinement and anisotropy are naturally incorporated into finite elements. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. Mixed methods also produce discretely conservative fluxes that are required for the transport problem to remains stable without violating conservation of mass. Based preliminary investigations in 1D and derived energy estimates, we present a mixed formulation for the Darcy-Stokes system. Next, using novel elements of lowest order and
Modelling bucket excavation by finite element
NASA Astrophysics Data System (ADS)
Pecingina, O. M.
2015-11-01
Changes in geological components of the layers from lignite pits have an impact on the sustainability of the cup path elements and under the action of excavation force appear efforts leading to deformation of the entire assembly. Application of finite element method in the optimization of components leads to economic growth, to increase the reliability and durability of the studied machine parts thus the machine. It is obvious usefulness of knowledge the state of mechanical tensions that the designed piece or the assembly not to break under the action of tensions that must cope during operation. In the course of excavation work on all bucket cutting force components, the first coming into contact with the material being excavated cutting edge. Therefore in the study with finite element analysis is retained only cutting edge. To study the field of stress and strain on the cutting edge will be created geometric patterns for each type of cup this will be subject to static analysis. The geometric design retains the cutting edge shape and on this on the tooth cassette location will apply an areal force on the abutment tooth. The cutting edge real pattern is subjected to finite element study for the worst case of rock cutting by symmetrical and asymmetrical cups whose profile is different. The purpose of this paper is to determine the displacement and tensions field for both profiles considering the maximum force applied on the cutting edge and the depth of the cutting is equal with the width of the cutting edge of the tooth. It will consider the worst case when on the structure will act both the tangential force and radial force on the bucket profile. For determination of stress and strain field on the form design of cutting edge profile will apply maximum force assuming uniform distribution and on the edge surface force will apply a radial force. After geometric patterns discretization on the cutting knives and determining stress field, can be seen that at the
NASA Technical Reports Server (NTRS)
Aberson, J. A.; Anderson, J. M.
1973-01-01
The recent introduction of special crack-tip singularity elements, usually referred to as cracked elements, has brought the power and flexibility of the finite-element method to bear much more effectively on fracture mechanics problems. This paper recalls the development of two cracked elements and presents the results of some applications proving their accuracy and economy. Judging from the available literature on numerical methods in fracture mechanics, it seems clear that the elements described have been used more extensively than any others in practical fracture mechanics applications.
NASA Astrophysics Data System (ADS)
Tanaka, Y.; Hasegawa, T.; Tsuruoka, H.; Klemann, V.; Martinec, Z.
2015-01-01
Global navigation satellite systems (GNSSs) have revealed that a mega-thrust earthquake that occurs in an island-arc trench system causes post-seismic crustal deformation. Such crustal deformation data have been interpreted by combining three mechanisms: afterslip, poroelastic rebound and viscoelastic relaxation. It is seismologically important to determine the contribution of each mechanism because it provides frictional properties between the plate boundaries and viscosity estimates in the asthenosphere which are necessary to evaluate the stress behaviour during earthquake cycles. However, the observation sites of GNSS are mostly deployed over land and can detect only a small part of the large-scale deformation, which precludes a clear separation of the mechanisms. To extend the spatial coverage of the deformation area, recent studies started to use satellite gravity data that can detect long-wavelength deformations over the ocean. To date, compared with theoretical models for calculating the post-seismic crustal deformation, a few models have been proposed to interpret the corresponding gravity variations. Previous approaches have adopted approximations for the effects of compressibility, sphericity and self-gravitation when computing gravity changes. In this study, a new spectral-finite element approach is presented to consider the effects of material compressibility for Burgers viscoelastic earth model with a laterally heterogeneous viscosity distribution. After the basic principles are explained, it is applied to the 2004 Sumatra-Andaman earthquake. For this event, post-seismic deformation mechanisms are still a controversial topic. Using the developed approach, it is shown that the spatial patterns of gravity change generated by the above three mechanisms clearly differ from one another. A comparison of the theoretical simulation results with the satellite gravity data obtained from the Gravity Recovery and Climate Experiment reveals that both afterslip and
Visualization of transient finite element analyses on large unstructured grids
Dovey, D.
1995-03-22
Three-dimensional transient finite element analysis is performed on unstructured grids. A trend toward running larger analysis problems, combined with a desire for interactive animation of analysis results, demands efficient visualization techniques. This paper discusses a set of data structures and algorithms for visualizing transient analysis results on unstructured grids and introduces some modifications in order to better support large grids. In particular, an element grouping approach is used to reduce the amount of memory needed for external surface determination and to speed up ``point in element`` tests. The techniques described lend themselves to visualization of analyses carried out in parallel on a massively parallel computer (MPC).
System software for the finite element machine
NASA Technical Reports Server (NTRS)
Crockett, T. W.; Knott, J. D.
1985-01-01
The Finite Element Machine is an experimental parallel computer developed at Langley Research Center to investigate the application of concurrent processing to structural engineering analysis. This report describes system-level software which has been developed to facilitate use of the machine by applications researchers. The overall software design is outlined, and several important parallel processing issues are discussed in detail, including processor management, communication, synchronization, and input/output. Based on experience using the system, the hardware architecture and software design are critiqued, and areas for further work are suggested.
Iterative methods for mixed finite element equations
NASA Technical Reports Server (NTRS)
Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.
1985-01-01
Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.
A finite element model of ultrasonic extrusion
NASA Astrophysics Data System (ADS)
Lucas, M.; Daud, Y.
2009-08-01
Since the 1950's researchers have carried out investigations into the effects of applying ultrasonic excitation to metals undergoing elastic and plastic deformation. Experiments have been conducted where ultrasonic excitation is superimposed in complex metalworking operations such as wire drawing and extrusion, to identify the benefits of ultrasonic vibrations. This study presents a finite element analysis of ultrasonic excitation applied to the extrusion of a cylindrical aluminium bar. The effects of friction on the extrusion load are reported for the two excitation configurations of radially and axially applied ultrasonic vibrations and the results are compared with experimental data reported in the literature.
Finite Element Modeling of Mitral Valve Repair
Morgan, Ashley E.; Pantoja, Joe Luis; Weinsaft, Jonathan; Grossi, Eugene; Guccione, Julius M.; Ge, Liang; Ratcliffe, Mark
2016-01-01
The mitral valve is a complex structure regulating forward flow of blood between the left atrium and left ventricle (LV). Multiple disease processes can affect its proper function, and when these diseases cause severe mitral regurgitation (MR), optimal treatment is repair of the native valve. The mitral valve (MV) is a dynamic structure with multiple components that have complex interactions. Computational modeling through finite element (FE) analysis is a valuable tool to delineate the biomechanical properties of the mitral valve and understand its diseases and their repairs. In this review, we present an overview of relevant mitral valve diseases, and describe the evolution of FE models of surgical valve repair techniques. PMID:26632260
Algebraic surface design and finite element meshes
NASA Technical Reports Server (NTRS)
Bajaj, Chandrajit L.
1992-01-01
Some of the techniques are summarized which are used in constructing C sup 0 and C sup 1 continuous meshes of low degree, implicitly defined, algebraic surface patches in three dimensional space. These meshes of low degree algebraic surface patches are used to construct accurate computer models of physical objects. These meshes are also used in the finite element simulation of physical phenomena (e.g., heat dissipation, stress/strain distributions, fluid flow characteristics) required in the computer prototyping of both the manufacturability and functionality of the geometric design.
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.
NASA Astrophysics Data System (ADS)
Xue, Cheng; Tang, Fuk-Hay
2014-03-01
A patient specific registration model based on finite element method was investigated in this study. Image registration of Positron Emission Tomography (PET) and Magnetic Resonance imaging (MRI) has been studied a lot. Surface-based registration is extensively applied in medical imaging. We develop and evaluate a registration method combine surface-based registration with biomechanical modeling. .Four sample cases of patients with PET and MRI breast scans performed within 30 days were collected from hospital. K-means clustering algorithm was used to segment images into two parts, which is fat tissue and neoplasm [2]. Instead of placing extrinsic landmarks on patients' body which may be invasive, we proposed a new boundary condition to simulate breast deformation during two screening. Then a three dimensional model with meshes was built. Material properties were assigned to this model according to previous studies. The whole registration was based on a biomechanical finite element model, which could simulate deformation of breast under pressure.
Weis, Jared A.; Granero-Moltó, Froilán; Myers, Timothy J.; Longobardi, Lara; Spagnoli, Anna; Miga, Michael I.
2013-01-01
An important concern in the study of fracture healing is the ability to assess mechanical integrity in response to candidate therapeutics in small-animal systems. In recent reports, it has been proposed that microCT image-derived densitometric parameters could be used as a surrogate for mechanical property assessment. Recently, we have proposed an inverse methodology that iteratively reconstructs the modulus of elasticity of the lumped soft callus/hard callus region by integrating both intrinsic mechanical property (from biomechanical testing) and geometrical information (from microCT) within an inverse finite element analysis (FEA) to define a callus quality measure. In this paper, data from a therapeutic system involving mesenchymal stem cells is analyzed within the context of comparing traditional microCT densitometric and mechanical property metrics. In addition, a novel multi-parameter regression microCT parameter is analyzed as well as our inverse FEA metric. The results demonstrate that the inverse FEA approach was the only metric to successfully detect both longitudinal and therapeutic responses. While the most promising microCT-based metrics were adequate at early healing states, they failed to track late-stage mechanical integrity. In addition, our analysis added insight to the role of MSCs by demonstrating accelerated healing and was the only metric to demonstrate therapeutic benefits at late-stage healing. In conclusion, the work presented here indicates that microCT densitometric parameters are an incomplete surrogate for mechanical integrity. Additionally, our inverse FEA approach is shown to be very sensitive and may provide a first-step towards normalizing the often challenging process of assessing mechanical integrity of healing fractures. PMID:22766379
1994-02-01
LOO estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials, RAIRO Anal...Superconvergence of the gradient of finite element solutions, RAIRO Anal. Numir., 13 (1979), pp. 139-166. 11. R.Z. DAUTOV, A.V. LAPIN AND A.D...PDEs, 3 (1987), pp. 65-82. 15. M.T. NAKAo, Superconvergence of the gradient of Galerkin approzimations for elliptic problems, RAIRO Math. Model
NASA Technical Reports Server (NTRS)
Mei, Chuh; Pates, Carl S., III
1994-01-01
A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.
An algorithm for domain decomposition in finite element analysis
NASA Technical Reports Server (NTRS)
Al-Nasra, M.; Nguyen, D. T.
1991-01-01
A simple and efficient algorithm is described for automatic decomposition of an arbitrary finite element domain into a specified number of subdomains for finite element and substructuring analysis in a multiprocessor computer environment. The algorithm is designed to balance the work loads, to minimize the communication among processors and to minimize the bandwidths of the resulting system of equations. Small- to large-scale finite element models, which have two-node elements (truss, beam element), three-node elements (triangular element) and four-node elements (quadrilateral element), are solved on the Convex computer to illustrate the effectiveness of the proposed algorithm. A FORTRAN computer program is also included.
Impeller deflection and modal finite element analysis.
Spencer, Nathan A.
2013-10-01
Deflections of an impeller due to centripetal forces are calculated using finite element analysis. The lateral, or out of plane, deflections are an important design consideration for this particular impeller because it incorporates an air bearing with critical gap tolerances. The target gap distance is approximately 10 microns at a rotational velocity of 2500 rpm. The centripetal forces acting on the impeller cause it deflect in a concave fashion, decreasing the initial gap distance as a function of radial position. This deflection is characterized for a previous and updated impeller design for comparative purposes. The impact of design options such as material selection, geometry dimensions, and operating rotational velocity are also explored, followed by a sensitivity study with these parameters bounded by specific design values. A modal analysis is also performed to calculate the impeller's natural frequencies which are desired to be avoided during operation. The finite element modeling techniques continue to be exercised by the impeller design team to address specific questions and evaluate conceptual designs, some of which are included in the Appendix.
Finite element analysis of bolted flange connections
NASA Astrophysics Data System (ADS)
Hwang, D. Y.; Stallings, J. M.
1994-06-01
A 2-D axisymmetric finite element model and a 3-D solid finite element model of a high pressure bolted flange joint were generated to investigate the stress behaviors. This investigation includes comparisons for axisymmetric loading of both the 2-D and 3-D models, the effects of non-axisymmetric bolt pretensions in the 3-D models, and the differences between 2-D and 3-D models subjected to non-axisymmetric loading. Comparisons indicated differences in von Mises stress up to 12% at various points due to the non-axisymmetric bolt pretensions. Applied bending moments were converted to equivalent axial forces for use in the 2-D model. It was found that the largest von Mises stresses in 3-D model did not occur on the side of the connection where the bending stresses and applied axial stresses were additive. Hence, in the 2-D model where the equivalent axial force (for bending moment) and applied axial forces were added, the 2-D model under estimated the maximum von Mises stress obtained from the 3-D model by 30%.
A multigrid solution method for mixed hybrid finite elements
Schmid, W.
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
Total quality management of forged products through finite element simulation
NASA Astrophysics Data System (ADS)
Chandra, U.; Rachakonda, S.; Chandrasekharan, S.
The paper reviews the entire thermo-mechanical history experienced by a complex shaped, high strength forged part during all stages of its manufacturing process, i.e. forging, heat treatment, and machining. It examines the current practice of selecting the process parameters using finite element simulation of forging and quenching operations on an individual basis. Some recent work related to the simulation of aging and machining operations is summarized. The capabilities of several well-known finite element codes for these individual simulations are compared. Then, an integrated simulation approach is presented which will permit the optimization of process parameters for all operations, as opposed to a single operation. This approach will ensure a total quality management of forged products by avoiding costly problems which, under the current practice, are detected only at the end of the manufacturing cycle, i.e. after final machining.
Cyclic creep analysis from elastic finite-element solutions
NASA Technical Reports Server (NTRS)
Kaufman, A.; Hwang, S. Y.
1986-01-01
A uniaxial approach was developed for calculating cyclic creep and stress relaxation at the critical location of a structure subjected to cyclic thermomechanical loading. This approach was incorporated into a simplified analytical procedure for predicting the stress-strain history at a crack initiation site for life prediction purposes. An elastic finite-element solution for the problem was used as input for the simplified procedure. The creep analysis includes a self-adaptive time incrementing scheme. Cumulative creep is the sum of the initial creep, the recovery from the stress relaxation and the incremental creep. The simplified analysis was exercised for four cases involving a benchmark notched plate problem. Comparisons were made with elastic-plastic-creep solutions for these cases using the MARC nonlinear finite-element computer code.
Finite element solution of transient fluid-structure interaction problems
NASA Technical Reports Server (NTRS)
Everstine, Gordon C.; Cheng, Raymond S.; Hambric, Stephen A.
1991-01-01
A finite element approach using NASTRAN is developed for solving time-dependent fluid-structure interaction problems, with emphasis on the transient scattering of acoustic waves from submerged elastic structures. Finite elements are used for modeling both structure and fluid domains to facilitate the graphical display of the wave motion through both media. For the liquid, the use of velocity potential as the fundamental unknown results in a symmetric matrix equation. The approach is illustrated for the problem of transient scattering from a submerged elastic spherical shell subjected to an incident tone burst. The use of an analogy between the equations of elasticity and the wave equation of acoustics, a necessary ingredient to the procedure, is summarized.
Parallel finite element simulation of large ram-air parachutes
NASA Astrophysics Data System (ADS)
Kalro, V.; Aliabadi, S.; Garrard, W.; Tezduyar, T.; Mittal, S.; Stein, K.
1997-06-01
In the near future, large ram-air parachutes are expected to provide the capability of delivering 21 ton payloads from altitudes as high as 25,000 ft. In development and test and evaluation of these parachutes the size of the parachute needed and the deployment stages involved make high-performance computing (HPC) simulations a desirable alternative to costly airdrop tests. Although computational simulations based on realistic, 3D, time-dependent models will continue to be a major computational challenge, advanced finite element simulation techniques recently developed for this purpose and the execution of these techniques on HPC platforms are significant steps in the direction to meet this challenge. In this paper, two approaches for analysis of the inflation and gliding of ram-air parachutes are presented. In one of the approaches the point mass flight mechanics equations are solved with the time-varying drag and lift areas obtained from empirical data. This approach is limited to parachutes with similar configurations to those for which data are available. The other approach is 3D finite element computations based on the Navier-Stokes equations governing the airflow around the parachute canopy and Newtons law of motion governing the 3D dynamics of the canopy, with the forces acting on the canopy calculated from the simulated flow field. At the earlier stages of canopy inflation the parachute is modelled as an expanding box, whereas at the later stages, as it expands, the box transforms to a parafoil and glides. These finite element computations are carried out on the massively parallel supercomputers CRAY T3D and Thinking Machines CM-5, typically with millions of coupled, non-linear finite element equations solved simultaneously at every time step or pseudo-time step of the simulation.
Nonlinear finite element analysis: An alternative formulation
NASA Technical Reports Server (NTRS)
Merazzi, S.; Stehlin, P.
1980-01-01
A geometrical nonlinear analysis based on an alternative definition of strain is presented. Expressions for strain are obtained by computing the change in length of the base vectors in the curvilinear element coordinate system. The isoparametric element formulation is assumed in the global Cartesian coordinate system. The approach is based on the minimization of the strain energy, and the resulting nonlinear equations are solved by the modified Newton method. Integration of the first and second variation of the strain energy is performed numerically in the case of two and three dimensional elements. Application is made to a simple long cantilever beam.
An hybrid finite volume finite element method for variable density incompressible flows
NASA Astrophysics Data System (ADS)
Calgaro, Caterina; Creusé, Emmanuel; Goudon, Thierry
2008-04-01
This paper is devoted to the numerical simulation of variable density incompressible flows, modeled by the Navier-Stokes system. We introduce an hybrid scheme which combines a finite volume approach for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint. The breakthrough relies on the definition of a suitable footbridge between the two methods, through the design of compatibility condition. In turn, the method is very flexible and allows to deal with unstructured meshes. Several numerical tests are performed to show the scheme capabilities. In particular, the viscous Rayleigh-Taylor instability evolution is carefully investigated.
Mixed Finite Element Methods for Melt Migration
NASA Astrophysics Data System (ADS)
Taicher, A. L.
2013-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium so must carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. We present a mixed formulation for the Darcy-Stokes system. Next, we present novel elements of lowest order and compatible with both Darcy and Stokes flow Finally, we present our 2D mixed FEM code result for solving Stokes and Darcy flow as well as the coupled Darcy-Stokes system the mid-ocean ridge or corner flow problem.
Finite element models and feedback control of flexible aerospace structures
NASA Technical Reports Server (NTRS)
Balas, M. J.
1980-01-01
Large flexible aerospace structures, such as the solar power satellite, are distributed parameter systems with very complex continuum descriptions. This paper investigates the use of finite element methods to produce reduced-order models and finite dimensional feedback controllers for these structures. The main results give conditions under which stable control of the finite element model will produce stable control of the actual structure.
Kang, Kyoung-Tak; Kim, Sung-Hwan; Son, Juhyun; Lee, Young Han; Chun, Heoung-Jae
2015-12-01
The material properties of in vivo meniscal attachments were evaluated using a probabilistic finite element (FE) model and magnetic resonance imaging (MRI). MRI scans of five subjects were collected at full extension and 30°, 60°, and 90° flexion. One subject with radiographic evidence of no knee injury and four subjects with Kellgren-Lawrence score of 1 or 2 (two each) were recruited. Isovoxel sagittal three-dimensional cube sequences of the knee were acquired in extension and flexion. Menisci movement in flexion was investigated using sensitivity analysis based on the Monte Carlo method in order to generate a subject-specific FE model to evaluate significant factors. The material properties of horn attachment in the five-subject FE model were optimized to minimize the differences between meniscal movements in the FE model and MR images in flexion. We found no significant difference between normal and patient knees in flexion with regard to movement of anterior, posterior, medial, and lateral menisci or changes in height morphology. At 90° flexion, menisci movement was primarily influenced by posterior horn stiffness, followed by anterior horn stiffness, the transverse ligament, and posterior cruciate ligament. The optimized material properties model predictions for menisci motion were more accurate than the initial material properties model. The results of this approach suggest that the material properties of horn attachment, which affects the mobile characteristics of menisci, could be determined in vivo. Thus, this study establishes a basis for a future design method of attachment for tissue-engineered replacement menisci.
Assessing performance and validating finite element simulations using probabilistic knowledge
Dolin, Ronald M.; Rodriguez, E. A.
2002-01-01
Two probabilistic approaches for assessing performance are presented. The first approach assesses probability of failure by simultaneously modeling all likely events. The probability each event causes failure along with the event's likelihood of occurrence contribute to the overall probability of failure. The second assessment method is based on stochastic sampling using an influence diagram. Latin-hypercube sampling is used to stochastically assess events. The overall probability of failure is taken as the maximum probability of failure of all the events. The Likelihood of Occurrence simulation suggests failure does not occur while the Stochastic Sampling approach predicts failure. The Likelihood of Occurrence results are used to validate finite element predictions.
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Decahaumphai, P.; Wieting, A. R.
1980-01-01
An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. An integrated thermal-structural rod element is developed and used in four thermal-structural applications; the accuracy of this integrated approach is illustrated by comparisons with the customary approach of finite difference thermal-finite element structural analyses. Results show that integrated thermal-structural analysis of structures modeled with rod elements is more accurate than conventional analysis, and that its further development promises significant results.
Patient-specific finite element modeling of bones.
Poelert, Sander; Valstar, Edward; Weinans, Harrie; Zadpoor, Amir A
2013-04-01
Finite element modeling is an engineering tool for structural analysis that has been used for many years to assess the relationship between load transfer and bone morphology and to optimize the design and fixation of orthopedic implants. Due to recent developments in finite element model generation, for example, improved computed tomography imaging quality, improved segmentation algorithms, and faster computers, the accuracy of finite element modeling has increased vastly and finite element models simulating the anatomy and properties of an individual patient can be constructed. Such so-called patient-specific finite element models are potentially valuable tools for orthopedic surgeons in fracture risk assessment or pre- and intraoperative planning of implant placement. The aim of this article is to provide a critical overview of current themes in patient-specific finite element modeling of bones. In addition, the state-of-the-art in patient-specific modeling of bones is compared with the requirements for a clinically applicable patient-specific finite element method, and judgment is passed on the feasibility of application of patient-specific finite element modeling as a part of clinical orthopedic routine. It is concluded that further development in certain aspects of patient-specific finite element modeling are needed before finite element modeling can be used as a routine clinical tool.
Recent advances in hybrid/mixed finite elements
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1985-01-01
In formulations of Hybrid/Mixed finite element methods respectively by the Hellinger-Reissner principle and the Hu-Washizu principle, the stress equilibrium equations are brought in as conditions of constraint through the introduction of additional internal displacement parameters. These two approaches are more flexible and have better computing efficiencies. A procedure for the choice of assumed stress terms for 3-D solids is suggested. Example solutions are given for plates and shells using the present formulations and the idea of semiloof elements.
North Atlantic Finite Element Ocean Modeling
NASA Astrophysics Data System (ADS)
Veluthedathekuzhiyil, Praveen
This thesis presents a modified version of the Finite Element Ocean Model (FEOM) developed at Alfred Wegener Institute for Polar and Marine Research (AWI) for the North Atlantic Ocean. A reasonable North Atlantic Ocean simulation is obtained against the observational data sets in a Control simulation (CS) where the surface boundary conditions are relaxed to a climatology. The vertical mixing in the model was tuned to represent convection in the model, also the horizontal mixing and diffusion coefficients to represent the changes in the resolution of the model’s unstructured grid. In addition, the open boundaries in the model are treated with a sponge layer where tracers are relaxed to climatology. The model is then further modified to accept the atmospheric flux forcing at the surface boundary with an added net heat flux correction and freshwater forcing from major rivers that are flowing into the North Atlantic Ocean. The impact of this boundary condition on the simulation results is then analyzed and shows many improvements albeit the drift in tracer properties around the Gulf Stream region remains as that of the CS case. However a comparison of the vertical sections at Cape Desolation and Cape Farewell with the available observational data sets shows many improvements in this simulation compared to that of the CS case. But the freshwater content in the Labrador Sea interior shows a continued drift as that of the CS case with an improvement towards the 10th model year. A detailed analysis of the boundary currents around the Labrador Sea shows the weak offshore transport of freshwater from the West Greenland Current (WGC) as one of the causes. To further improve the model and reasonably represent the boundary currents and associated sub-grid scale eddies in the model, a modified sub-grid scale parameterization based on Gent and McWilliams, (1990) is adopted. The sensitivity of using various approaches in the thickness diffusion parameter ( Kgm) for this
Efficient finite element modeling of elastodynamic scattering
NASA Astrophysics Data System (ADS)
Wilcox, Paul D.; Velichko, Alexander
2009-03-01
The scattering of elastic waves by defects is the physical basis of ultrasonic NDE. Although analytical models exist for some canonical problems, the general case of scattering from an arbitrarily-shaped defect requires numerical methods such as finite elements (FE). In this paper, a robust and efficient FE technique is presented that is based on the premise of meshing a relatively small domain sufficient to enclose the scatterer. Plane waves are then excited from a particular direction by a numerical implementation of the Helmholtz-Kirchhoff integral that uses an encircling array of uni-modal point sources. The scattered field displacements are recorded at the same points and the field decomposed into plane waves of different modes at different angles. By repeating this procedure for different incident angles it is possible to generate the scattering- or S-matrix for the scatterer. For a given size of scatterer, all the information in an S-matrix can be represented in the Fourier domain by a limited number of complex coefficients. Thus the complete scattering behavior of an arbitrary-shaped scatterer can be characterized by a finite number of complex coefficients, that can be obtained from a relatively small number of FE model executions.
Immersed molecular electrokinetic finite element method
NASA Astrophysics Data System (ADS)
Kopacz, Adrian M.; Liu, Wing K.
2013-07-01
A unique simulation technique has been developed capable of modeling electric field induced detection of biomolecules such as viruses, at room temperatures where thermal fluctuations must be considered. The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a suspending medium under an applied electric field. The force induced on an arbitrary object due to an electric field is calculated based on the continuum electromechanics and the Maxwell stress tensor. The thermal fluctuations are included in the Navier-Stokes fluid equations via the stochastic stress tensor. Dielectrophoretic and fluctuating forces acting on the particle are coupled through the fluid-structure interaction force calculated within the surrounding environment. This method was used to perform concentration and retention efficacy analysis of nanoscale biosensors using gold particles of various sizes. The analysis was also applied to a human papillomavirus.
Quality management of finite element analysis
NASA Astrophysics Data System (ADS)
Barlow, John
1991-09-01
A quality management system covering the use of finite element analysis is described. The main topics are as follows: acquisition, development and verification of software (including the software suppliers software quality control system), support, documentation, error control, internal software, software acceptance and release; development and qualification of analysis methods, including software evaluation, analysis procedure qualification and documentation, procedure quality checks, control of analysis procedure errors; product design and integrity analysis, including project quality assurance and analysis planning, task specification and allocation, analysis, execution, results checking and analysis records. Other issues include the commercial and business advantages of quality systems, project and technical management and the training and experience of personnel. The items are correlated with the requirements of International Standard Organization 9001.
Finite element or Galerkin type semidiscrete schemes
NASA Technical Reports Server (NTRS)
Durgun, K.
1983-01-01
A finite element of Galerkin type semidiscrete method is proposed for numerical solution of a linear hyperbolic partial differential equation. The question of stability is reduced to the stability of a system of ordinary differential equations for which Dahlquist theory applied. Results of separating the part of numerical solution which causes the spurious oscillation near shock-like response of semidiscrete scheme to a step function initial condition are presented. In general all methods produce such oscillatory overshoots on either side of shocks. This overshoot pathology, which displays a behavior similar to Gibb's phenomena of Fourier series, is explained on the basis of dispersion of separated Fourier components which relies on linearized theory to be satisfactory. Expository results represented.
Finite-element solutions for geothermal systems
NASA Technical Reports Server (NTRS)
Chen, J. C.; Conel, J. E.
1977-01-01
Vector potential and scalar potential are used to formulate the governing equations for a single-component and single-phase geothermal system. By assuming an initial temperature field, the fluid velocity can be determined which, in turn, is used to calculate the convective heat transfer. The energy equation is then solved by considering convected heat as a distributed source. Using the resulting temperature to compute new source terms, the final results are obtained by iterations of the procedure. Finite-element methods are proposed for modeling of realistic geothermal systems; the advantages of such methods are discussed. The developed methodology is then applied to a sample problem. Favorable agreement is obtained by comparisons with a previous study.
Finite-element solutions for geothermal systems
NASA Technical Reports Server (NTRS)
Chen, J. C.; Conel, J. E.
1977-01-01
Vector potential and scalar potential are used to formulate the governing equations for a single-component and single-phase geothermal system. By assuming an initial temperature field, the fluid velocity can be determined which, in turn, is used to calculate the convective heat transfer. The energy equation is then solved by considering convected heat as a distributed source. Using the resulting temperature to compute new source terms, the final results are obtained by iterations of the procedure. Finite-element methods are proposed for modeling of realistic geothermal systems; the advantages of such methods are discussed. The developed methodology is then applied to a sample problem. Favorable agreement is obtained by comparisons with a previous study.
A finite element model with nonviscous damping
NASA Technical Reports Server (NTRS)
Roussos, L. A.; Hyer, M. W.; Thornton, E. A.
1981-01-01
A constitutive law by which structural damping is modeled as a relationship between stress, strain, and strain rate in a material is used in conjunction with the finite element method to develop general integral expressions for viscous and nonviscous damping matrices. To solve the set of nonlinear equations resulting from the presence of nonviscous damping, a solution technique is developed by modifying the Newmark method to accommodate an iterative solution and treat the nonviscous damping as a pseudo-force. The technique is then checked for accuracy and convergence in single- and multi-degree-of-freedom problems, and is found to be accurate and efficient for initial-condition problems with small nonviscous damping.
Massively parallel finite element computation of three dimensional flow problems
NASA Astrophysics Data System (ADS)
Tezduyar, T.; Aliabadi, S.; Behr, M.; Johnson, A.; Mittal, S.
1992-12-01
The parallel finite element computation of three-dimensional compressible, and incompressible flows, with emphasis on the space-time formulations, mesh moving schemes and implementations on the Connection Machines CM-200 and CM-5 are presented. For computation of unsteady compressible and incompressible flows involving moving boundaries and interfaces, the Deformable-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation that previously developed are employed. In this approach, the stabilized finite element formulations of the governing equations are written over the space-time domain of the problem; therefore, the deformation of the spatial domain with respect to time is taken into account automatically. This approach gives the capability to solve a large class of problems involving free surfaces, moving interfaces, and fluid-structure and fluid-particle interactions. By using special mesh moving schemes, the frequency of remeshing is minimized to reduce the projection errors involved in remeshing and also to increase the parallelization ease of the computations. The implicit equation systems arising from the finite element discretizations are solved iteratively by using the GMRES update technique with the diagonal and nodal-block-diagonal preconditioners. These formulations have all been implemented on the CM-200 and CM-5, and have been applied to several large-scale problems. The three-dimensional problems in this report were all computed on the CM-200 and CM-5.
Crystal level simulations using Eulerian finite element methods
Becker, R; Barton, N R; Benson, D J
2004-02-06
Over the last several years, significant progress has been made in the use of crystal level material models in simulations of forming operations. However, in Lagrangian finite element approaches simulation capabilities are limited in many cases by mesh distortion associated with deformation heterogeneity. Contexts in which such large distortions arise include: bulk deformation to strains approaching or exceeding unity, especially in highly anisotropic or multiphase materials; shear band formation and intersection of shear bands; and indentation with sharp indenters. Investigators have in the past used Eulerian finite element methods with material response determined from crystal aggregates to study steady state forming processes. However, Eulerian and Arbitrary Lagrangian-Eulerian (ALE) finite element methods have not been widely utilized for simulation of transient deformation processes at the crystal level. The advection schemes used in Eulerian and ALE codes control mesh distortion and allow for simulation of much larger total deformations. We will discuss material state representation issues related to advection and will present results from ALE simulations.
Finite element structural redesign by large admissible perturbations
NASA Technical Reports Server (NTRS)
Bernitsas, Michael M.; Beyko, E.; Rim, C. W.; Alzahabi, B.
1991-01-01
In structural redesign, two structural states are involved; the baseline (known) State S1 with unacceptable performance, and the objective (unknown) State S2 with given performance specifications. The difference between the two states in performance and design variables may be as high as 100 percent or more depending on the scale of the structure. A Perturbation Approach to Redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model and represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads, and buckling modes of the objective S2 in terms of its performance specifications, and S1 data and Finite Element Analysis (FEA) results. Large Admissible Perturbation (LEAP) algorithms are implemented in code RESTRUCT to define the objective S2 incrementally without trial and error by postprocessing FEA results of S1 with no additional FEAs. Systematic numerical applications in redesign of a 10 element 48 degree of freedom (dof) beam, a 104 element 192 dof offshore tower, a 64 element 216 dof plate, and a 144 element 896 dof cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100 percent from the baseline design.
Generalization of mixed multiscale finite element methods with applications
Lee, C S
2016-08-01
Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii
A Decoupled Finite Element Heterogeneous Coarse Mesh Transport Method.
Mosher, S. W.; Rahnema, Farzad
2005-01-01
In a recent paper, an original finite element (FE) method was presented for solving eigenvalue transport problems on a coarse spatial mesh. The method employed a surface Green's function expansion of the angular flux trial functions, so that heterogeneous coarse-meshes could be treated with relative ease. Numerical problems were solved using the multigroup discrete ordinates approximation in one-dimensional (1-D) slab geometry. Unfortunately, difficulties were encountered in finding solutions to the algebraic finite element equations, which led to sizeable angular flux discontinuities at coarse-mesh interfaces and significant errors. For this reason, a nonvariational iterative technique was ultimately favored for converging the angular flux distribution, and was used in conjunction with a Rayleigh quotient for converging the eigenvalue. In this paper, a new derivation of finite element equations is presented, which seems to offer a remedy for at least some of the numerical ills that plagued the previous work. First, the equations are derived in terms of a generalized response function expansion. This allows a more efficient response basis to be employed and vastly reduces the overall computational effort without a substantial loss of accuracy. Second, the tight coupling between coarse-meshes in the original equations is effectively broken by assuming that an accurate estimate of the flux distribution entering a given coarse-mesh is known. With an additional assumption that an accurate eigenvalue estimate is known, an iterative approach to solving these decoupled finite element (DFE) equations is developed. The DFE method has been applied to both 1- and 2-D heterogeneous coarse-mesh problems with a far greater degree of success than the original FE method. However, some numerical difficulties remain to be overcome before the new approach can be considered robust.
Finite-element time evolution operator for the anharmonic oscillator
NASA Technical Reports Server (NTRS)
Milton, Kimball A.
1995-01-01
The finite-element approach to lattice field theory is both highly accurate (relative errors approximately 1/N(exp 2), where N is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is H = p(exp 2)/2 + lambda q(exp 4)/4. Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a results for the anharmonic oscillator ground state energy accurate to better than 1 percent, while a two-state approximation reduces the error to less than 0.1 percent.
Improved finite-element methods for rotorcraft structures
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1991-01-01
An overview of the research directed at improving finite-element methods for rotorcraft airframes is presented. The development of a modification to the finite element method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick finite element program.
Impact of new computing systems on finite element computations
NASA Technical Reports Server (NTRS)
Noor, A. K.; Storassili, O. O.; Fulton, R. E.
1983-01-01
Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified.
NASA Technical Reports Server (NTRS)
Fix, G. J.; Rose, M. E.
1983-01-01
A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.
NASA Technical Reports Server (NTRS)
Namburu, Raju R.; Tamma, Kumar K.
1993-01-01
An integrated finite element approach is presented for interdisciplinary thermal-structural problems. Of the various numerical approaches, finite element methods with direct time integration procedures are most widely used for these nonlinear problems. Traditionally, combined thermal-structural analysis is performed sequentially by transferring data between thermal and structural analysis. This approach is generally effective and routinely used. However, to solve the combined thermal-structural problems, this approach results in cumbersome data transfer, incompatible algorithmic representations, and different discretized element formulations. The integrated approach discussed in this paper effectively combines thermal and structural fields, thus overcoming the above major shortcomings. The approach follows Lax-Wendroff type finite element formulations with flux and stress based representations. As a consequence, this integrated approach uses common algorithmic representations and element formulations. Illustrative test examples show that the approach is effective for integrated thermal-structural problems.
Finite element modeling of bending failure at HPFRC plates using 2-dimensional isoparametric element
NASA Astrophysics Data System (ADS)
Krisnamurti, Soehardjono, Agoes; Zacoeb, Achfas; Wibowo, Ari
2017-03-01
This paper presents finite element modeling of the bending failure on High-Performance Fiber-Reinforced Concrete (HPFRC) plate subjected to monotonic loading. Plate analysis is commonly used approach to plate bending theory. The results are sometimes less in accordance with laboratory tests. The aim of this study is to analyze the behavior of bending until failure which occurred at HPFRC plate, and load-displacement relation caused by variations of plate depth. Analysis carried out by 2-D isoparametric finite element method, with the approach of plane strain condition. The analysis was done by decreasing the stiffness of plate elements layer gradually in accordance with the development of maximum stress in the element due to workload. The rigidity of plate elements layer will be close to zero when maximum stress reaches a maximum tensile strength of HPFRC. Validation testing program conducted on plate specimen with a span length of 600 mm, width 300 mm and thickness variation of 40 mm, 50 mm and 60 mm. HPFRC compressive strength is 93.045 MPa, and splitting tensile strength is 6.018 MPa. Test performed with four points bending pattern at a distance of 1/3 span length. Comparison between the calculation by the finite element method and laboratory testing showed very consistent results.
Ablative Thermal Response Analysis Using the Finite Element Method
NASA Technical Reports Server (NTRS)
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
Leapfrog/Finite Element Method for Fractional Diffusion Equation
Zhao, Zhengang; Zheng, Yunying
2014-01-01
We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an L 2-error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis. PMID:24955431
NASA Astrophysics Data System (ADS)
Goyal, Sunil; Laha, K.; Chandravathi, K. S.; Parameswaran, P.; Mathew, M. D.
2011-08-01
Creep studies were carried out on 2.25Cr-1Mo steel base metal and its fusion-welded weldments at 823 K over the stress range 100-240 MPa. The weldment possessed lower creep rupture strength than the base metal due to type IV failure at the outer edge of the heat-affected zone (HAZ). Premature failure of the weldment was associated with pronounced creep cavitation accompanied with localized creep deformation in the soft intercritical region of the HAZ that was sandwiched between relatively higher creep deformation-resistant microstructural regions. The cavitation was associated with coarse intergranular precipitates in the intercritical region of the HAZ. The type IV cracking in the intercritical region of the HAZ was found to initiate deep inside the weldment and propagate towards the specimen surface. Finite element analysis of stress and strain distributions across the weldment was carried out considering the micro-mechanical strength inhomogeneity across it to explain the observed features of type IV cracking. The estimated higher von-Mises and principal stresses deep inside the intercritical region of the HAZ of the weldment led to the localized creep deformation and preferential cavity nucleation and growth, resulting in type IV failure of the weldment. The role of intergranular precipitate particles in the intercritical region of the HAZ in facilitating creep cavity nucleation by the exhaustion of creep ductility of the material close to the precipitate was corroborated from finite element analysis of stress and strain distribution around the precipitates.
Global/local analysis of laminated composite plates using variable kinematic finite elements
NASA Technical Reports Server (NTRS)
Robbins, D. H., Jr.; Reddy, J. N.
1992-01-01
A finite element modeling methodology is developed for the hierarchical, global/local analysis of laminated composite plates. The method incorporates a new variable kinematics, displacement-based, finite element that is developed using a multiple assumed displacement field approach. The variable kinematic elements provide a great degree of flexibility in defining the transverse (through thickness) variation of the assumed displacement field. The resulting finite element model permits different subregions of the computational domain to be described by different mathematical models. Enforcing displacement continuity along subregion boundaries requires only the specification of certain homogeneous essential boundary conditions, thus avoiding the inconvenience of multi-point constraints, penalty function methods, or special transition elements.
Kim, S.
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Tadepalli, Srinivas C; Erdemir, Ahmet; Cavanagh, Peter R
2011-08-11
Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation. Copyright © 2011. Published by Elsevier Ltd.
Finite element solver for 3-D compressible viscous flows
NASA Technical Reports Server (NTRS)
Reddy, K. C.; Reddy, J. N.
1986-01-01
The space shuttle main engine (SSME) has extremely complex internal flow structure. The geometry of the flow domain is three-dimensional with complicated topology. The flow is compressible, viscous, and turbulent with large gradients in flow quantities and regions of recirculations. The analysis of the flow field in SSME involves several tedious steps. One is the geometrical modeling of the particular zone of the SSME being studied. Accessing the geometry definition, digitalizing it, and developing surface interpolations suitable for an interior grid generator require considerable amount of manual labor. There are several types of grid generators available with some general-purpose finite element programs. An efficient and robust computational scheme for solving 3D Navier-Stokes equations has to be implemented. Post processing software has to be adapted to visualize and analyze the computed 3D flow field. The progress made in a project to develop software for the analysis of the flow is discussed. The technical approach to the development of the finite element scheme and the relaxation procedure are discussed. The three dimensional finite element code for the compressible Navier-Stokes equations is listed.
Finite element methods for the nonlinear motion of flexible aircraft
NASA Astrophysics Data System (ADS)
Yang, Victor P.
Conventional strategies in aeroelasticity and flight dynamics for studying aircraft involve making broad assumptions based more on analytical or computational convenience rather than on physical reality. Typically in aeroelastic analyses, the study of the interaction between aircraft flexibility and aerodynamic forces, the aircraft or structural component in question is constrained in a way that is not representative of realistic flight conditions. In flight dynamics, the study of the maneuvering of aircraft, it is common to consider the vehicle as perfectly rigid. In both disciplines it is well known that such contrivances can produce incorrect results. To address these shortcomings, a finite element formulation is developed for analyzing the dynamics of flexible aircraft undergoing arbitrarily large rotation and translation. The formulation is derived in a set of body-attached axes, a frame of reference conducive to analyzing the motion and control of aircraft, and considers the structure as a whole. Several implementation issues are addressed and mitigated, including finite element interpolating functions, the use of eigenvectors as the basis for nonlinear deformation, inclusion of geometrically nonlinear effects in the strain energy, and enforcement of kinematic constraints. Numerical examples illustrate the capabilities of the latter two aspects, and a free-flying aeroelastic model problem demonstrates the overall potential of the proposed formulation. The development is approached in a general way so that the methodology can be applied to any structure that may be modeled by finite elements.
Evaluation of a Kinematically-Driven Finite Element Footstrike Model.
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.
Massively parallel computation of RCS with finite elements
NASA Technical Reports Server (NTRS)
Parker, Jay
1993-01-01
One of the promising combinations of finite element approaches for scattering problems uses Whitney edge elements, spherical vector wave-absorbing boundary conditions, and bi-conjugate gradient solution for the frequency-domain near field. Each of these approaches may be criticized. Low-order elements require high mesh density, but also result in fast, reliable iterative convergence. Spherical wave-absorbing boundary conditions require additional space to be meshed beyond the most minimal near-space region, but result in fully sparse, symmetric matrices which keep storage and solution times low. Iterative solution is somewhat unpredictable and unfriendly to multiple right-hand sides, yet we find it to be uniformly fast on large problems to date, given the other two approaches. Implementation of these approaches on a distributed memory, message passing machine yields huge dividends, as full scalability to the largest machines appears assured and iterative solution times are well-behaved for large problems. We present times and solutions for computed RCS for a conducting cube and composite permeability/conducting sphere on the Intel ipsc860 with up to 16 processors solving over 200,000 unknowns. We estimate problems of approximately 10 million unknowns, encompassing 1000 cubic wavelengths, may be attempted on a currently available 512 processor machine, but would be exceedingly tedious to prepare. The most severe bottlenecks are due to the slow rate of mesh generation on non-parallel machines and the large transfer time from such a machine to the parallel processor. One solution, in progress, is to create and then distribute a coarse mesh among the processors, followed by systematic refinement within each processor. Elimination of redundant node definitions at the mesh-partition surfaces, snap-to-surface post processing of the resulting mesh for good modelling of curved surfaces, and load-balancing redistribution of new elements after the refinement are auxiliary
Finite Element Analysis (FEA) in Design and Production.
ERIC Educational Resources Information Center
Waggoner, Todd C.; And Others
1995-01-01
Finite element analysis (FEA) enables industrial designers to analyze complex components by dividing them into smaller elements, then assessing stress and strain characteristics. Traditionally mainframe based, FEA is being increasingly used in microcomputers. (SK)
Finite Element Analysis (FEA) in Design and Production.
ERIC Educational Resources Information Center
Waggoner, Todd C.; And Others
1995-01-01
Finite element analysis (FEA) enables industrial designers to analyze complex components by dividing them into smaller elements, then assessing stress and strain characteristics. Traditionally mainframe based, FEA is being increasingly used in microcomputers. (SK)
Finite element modelling of fabric shear
NASA Astrophysics Data System (ADS)
Lin, Hua; Clifford, Mike J.; Long, Andrew C.; Sherburn, Martin
2009-01-01
In this study, a finite element model to predict shear force versus shear angle for woven fabrics is developed. The model is based on the TexGen geometric modelling schema, developed at the University of Nottingham and orthotropic constitutive models for yarn behaviour, coupled with a unified displacement-difference periodic boundary condition. A major distinction from prior modelling of fabric shear is that the details of picture frame kinematics are included in the model, which allows the mechanisms of fabric shear to be represented more accurately. Meso- and micro-mechanisms of deformation are modelled to determine their contributions to energy dissipation during shear. The model is evaluated using results obtained for a glass fibre plain woven fabric, and the importance of boundary conditions in the analysis of deformation mechanisms is highlighted. The simulation results show that the simple rotation boundary condition is adequate for predicting shear force at large deformations, with most of the energy being dissipated at higher shear angles due to yarn compaction. For small deformations, a detailed kinematic analysis is needed, enabling the yarn shear and rotation deformation mechanisms to be modelled accurately.
Finite element analysis of arc welding
Friedman, E.
1980-01-01
Analytical models of the gas tungsten-arc welding process into finite element computer programs provides a valuable tool for determining the welding thermal cycle, weld bead shape, and penetration characteristics, as well as for evaluating the stresses and distortions generated as a result of the temperature transients. The analysis procedures are applicable to planar or axisymmetric welds with arbitrary cross-sectional geometries, under quasistationary conditions. The method used for determining temperatures features an iteration procedure to accurately account for the latent heat absorbed during melting and liberated during solidification of the weld. By simulating the heat input from the arc to the workpiece by a normal distribution function, temperature transients, weld bead dimensions, and cooling rates are evaluated as functions of both the magnitude and distribution of heat input, weldment geometry, and weld speed (or duration of heating for stationary arcs). Modeling of the welding thermal cycle is a prerequisite to analytical treatments of metallurgical changes in weld metal and heat-affected zone material, residual stresses and distortions, and weld defects. A quasistationary formulation for moving welds enables temperatures to be calculated using a two-dimensional heat conduction computer program. The present limitation of high welding speed can, however, be relaxed without altering the two-dimensional framework of the procedure.
TACO: a finite element heat transfer code
Mason, W.E. Jr.
1980-02-01
TACO is a two-dimensional implicit finite element code for heat transfer analysis. It can perform both linear and nonlinear analyses and can be used to solve either transient or steady state problems. Either plane or axisymmetric geometries can be analyzed. TACO has the capability to handle time or temperature dependent material properties and materials may be either isotropic or orthotropic. A variety of time and temperature dependent loadings and boundary conditions are available including temperature, flux, convection, and radiation boundary conditions and internal heat generation. Additionally, TACO has some specialized features such as internal surface conditions (e.g., contact resistance), bulk nodes, enclosure radiation with view factor calculations, and chemical reactive kinetics. A user subprogram feature allows for any type of functional representation of any independent variable. A bandwidth and profile minimization option is also available in the code. Graphical representation of data generated by TACO is provided by a companion post-processor named POSTACO. The theory on which TACO is based is outlined, the capabilities of the code are explained, the input data required to perform an analysis with TACO are described. Some simple examples are provided to illustrate the use of the code.
VALIDATION OF ANSYS FINITE ELEMENT ANALYSIS SOFTWARE
HAMM, E.R.
2003-06-27
This document provides a record of the verification and Validation of the ANSYS Version 7.0 software that is installed on selected CH2M HILL computers. The issues addressed include: Software verification, installation, validation, configuration management and error reporting. The ANSYS{reg_sign} computer program is a large scale multi-purpose finite element program which may be used for solving several classes of engineering analysis. The analysis capabilities of ANSYS Full Mechanical Version 7.0 installed on selected CH2M Hill Hanford Group (CH2M HILL) Intel processor based computers include the ability to solve static and dynamic structural analyses, steady-state and transient heat transfer problems, mode-frequency and buckling eigenvalue problems, static or time-varying magnetic analyses and various types of field and coupled-field applications. The program contains many special features which allow nonlinearities or secondary effects to be included in the solution, such as plasticity, large strain, hyperelasticity, creep, swelling, large deflections, contact, stress stiffening, temperature dependency, material anisotropy, and thermal radiation. The ANSYS program has been in commercial use since 1970, and has been used extensively in the aerospace, automotive, construction, electronic, energy services, manufacturing, nuclear, plastics, oil and steel industries.
Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms
NASA Technical Reports Server (NTRS)
Prosser, W. H.; Hamstad, M. A.; Gary, J.; OGallagher, A.
1998-01-01
A comparison was made between two approaches to predict acoustic emission waveforms in thin plates. A normal mode solution method for Mindlin plate theory was used to predict the response of the flexural plate mode to a point source, step-function load, applied on the plate surface. The second approach used a dynamic finite element method to model the problem using equations of motion based on exact linear elasticity. Calculations were made using properties for both isotropic (aluminum) and anisotropic (unidirectional graphite/epoxy composite) materials. For simulations of anisotropic plates, propagation along multiple directions was evaluated. In general, agreement between the two theoretical approaches was good. Discrepancies in the waveforms at longer times were caused by differences in reflections from the lateral plate boundaries. These differences resulted from the fact that the two methods used different boundary conditions. At shorter times in the signals, before reflections, the slight discrepancies in the waveforms were attributed to limitations of Mindlin plate theory, which is an approximate plate theory. The advantages of the finite element method are that it used the exact linear elasticity solutions, and that it can be used to model real source conditions and complicated, finite specimen geometries as well as thick plates. These advantages come at a cost of increased computational difficulty, requiring lengthy calculations on workstations or supercomputers. The Mindlin plate theory solutions, meanwhile, can be quickly generated on personal computers. Specimens with finite geometry can also be modeled. However, only limited simple geometries such as circular or rectangular plates can easily be accommodated with the normal mode solution technique. Likewise, very limited source configurations can be modeled and plate theory is applicable only to thin plates.
3D finite element simulations of high velocity projectile impact
NASA Astrophysics Data System (ADS)
Ožbolt, Joško; İrhan, Barış; Ruta, Daniela
2015-09-01
An explicit three-dimensional (3D) finite element (FE) code is developed for the simulation of high velocity impact and fragmentation events. The rate sensitive microplane material model, which accounts for large deformations and rate effects, is used as a constitutive law. In the code large deformation frictional contact is treated by forward incremental Lagrange multiplier method. To handle highly distorted and damaged elements the approach based on the element deletion is employed. The code is then used in 3D FE simulations of high velocity projectile impact. The results of the numerical simulations are evaluated and compared with experimental results. It is shown that it realistically predicts failure mode and exit velocities for different geometries of plain concrete slab. Moreover, the importance of some relevant parameters, such as contact friction, rate sensitivity, bulk viscosity and deletion criteria are addressed.
Liu, Yanhui; Zhang, Peihua
2016-09-01
This paper presents a study of the compression behaviors of fully covered biodegradable polydioxanone biliary stents (FCBPBs) developed for human body by finite element method. To investigate the relationship between the compression force and structure parameter (monofilament diameter and braid-pin number), nine numerical models based on actual biliary stent were established, the simulation and experimental results are in good agreement with each other when calculating the compression force derived from both experiment and simulation results, indicating that the simulation results can be provided a useful reference to the investigation of biliary stents. The stress distribution on FCBPBSs was studied to optimize the structure of FCBPBSs. In addition, the plastic dissipation analysis and plastic strain of FCBPBSs were obtained via the compression simulation, revealing the structure parameter effect on the tolerance.
Solution-adaptive finite element method in computational fracture mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1993-01-01
Some recent results obtained using solution-adaptive finite element method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive finite element method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.
Modular Finite Element Methods Library Version: 1.0
2010-06-22
MFEM is a general, modular library for finite element methods. It provides a variety of finite element spaces and bilinear/linear forms in 2D and 3D. MFEM also includes classes for dealing with various types of meshes and their refinement.
Generating Finite-Element Models Of Composite Materials
NASA Technical Reports Server (NTRS)
Melis, M. E.
1993-01-01
Program starts at micromechanical level, from simple inputs supplied by user. COMGEN, COmposite Model GENerator, is interactive FORTRAN program used to create wide variety of finite-element models of continuous-fiber composite materials at micromechanical level. Quickly generates batch or "session files" to be submitted to finite-element preprocessor and postprocessor program, PATRAN. COMGEN requires PATRAN to complete model.
A computer graphics program for general finite element analyses
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Sawyer, L. M.
1978-01-01
Documentation for a computer graphics program for displays from general finite element analyses is presented. A general description of display options and detailed user instructions are given. Several plots made in structural, thermal and fluid finite element analyses are included to illustrate program options. Sample data files are given to illustrate use of the program.
Large Scale Finite Element Modeling Using Scalable Parallel Processing
NASA Technical Reports Server (NTRS)
Cwik, T.; Katz, D.; Zuffada, C.; Jamnejad, V.
1995-01-01
An iterative solver for use with finite element codes was developed for the Cray T3D massively parallel processor at the Jet Propulsion Laboratory. Finite element modeling is useful for simulating scattered or radiated electromagnetic fields from complex three-dimensional objects with geometry variations smaller than an electrical wavelength.
Finite element meshing of ANSYS (trademark) solid models
NASA Technical Reports Server (NTRS)
Kelley, F. S.
1987-01-01
A large scale, general purpose finite element computer program, ANSYS, developed and marketed by Swanson Analysis Systems, Inc. is discussed. ANSYS was perhaps the first commercially available program to offer truly interactive finite element model generation. ANSYS's purpose is for solid modeling. This application is briefly discussed and illustrated.
TAURUS96. 3-D Finite Element Code Postprocessor
Brown, B.; Hallquist, J.O.; Spelce, T.E.
1993-11-30
TAURUS is an interactive post-processing application supporting visualization of finite element analysis results on unstructured grids. TAURUS provides the ability to display deformed geometries and contours or fringes of a large number of derived results on meshes consisting of beam, plate, shell, and solid type finite elements. Time history plotting is also available.
Finite-element analysis of a weld-penetration problem
NASA Technical Reports Server (NTRS)
Rogge, T. R.
1977-01-01
The stress concentration factor for a weld penetration defect is calculated by the finite-element method. A stress intensity factor is computed by use of the finite-element solution and the J-integral. The results are compared with experimental results.
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 characterization of chromatic dispersion in nonlinear holey fibers.
Fujisawa, Takeshi; Koshiba, Masanori
2003-06-30
Chromatic dispersion characteristics of nonlinear photonic crystal fibers are, for the first time to our knowledge, theoretically investigated. A self-consistent numerical approach based on the full-vector finite-element method in terms of all the components of electric fields is described for the steady-state analysis of axially-nonsymmetrical nonlinear optical fibers. Electric fields obtained with this approach can be directly utilized for evaluating nonlinear refractive index distributions. To eliminate nonphysical, spurious solutions and to accurately model curved boundaries of circular air holes, curvilinear hybrid edge/nodal elements are introduced. It is found from the numerical results that under high optical intensity, chromatic dispersion characteristics become different from those of the linear state due to optical Kerr-effect nonlinearity, especially in short wavelength region.
Practical Application of Finite Element Analysis to Aircraft Structural Design
1986-08-01
t] Cook, Robert D., "Concepts and Applications of Finite element Analysis," John Wiley & Sons, Inc., New York, 1981. [5] Rao, S. S., "The Finite...generation large-scale computer programs is discussed. V.P. Analysis of aircraft structure using applied fracture mechanics (AA) WILHEM , D. P. Northrop...Analytical, finite element for surface flaws, holes (AA) WILHEM , D. P. Northrop Corp., Hawthorne, Calif. (N5631231) Aircraft Group. In AGARD Fracture
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.
A triangular thin shell finite element: Nonlinear analysis. [structural analysis
NASA Technical Reports Server (NTRS)
Thomas, G. R.; Gallagher, R. H.
1975-01-01
Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.
Enhanced pre-computed finite element models for surgical simulation.
Zhong, Hualiang; Wachowiak, Mark P; Peters, Terry M
2005-01-01
Soft tissue modeling is an important component in effective surgical simulation systems. A pre-computed finite element method based on elastic models is well suited to modeling soft tissue deformation. This paper addresses two principal issues: the flexibility of the pre-computed FE method and the approximation approach to non-linear elastic models. We describe a dynamic mechanism of the reconfiguration of the contacted nodes and the fixed boundary, without re-computing the inverse of the global stiffness matrix. The flexibility of the pre-computed models is described for both linear and non-linear elastic models.
Galerkin finite-element simulation of a geothermal reservoir
Mercer, J.W.; Pinder, G.F.
1973-01-01
The equations describing fluid flow and energy transport in a porous medium can be used to formulate a mathematical model capable of simulating the transient response of a hot-water geothermal reservoir. The resulting equations can be solved accurately and efficiently using a numerical scheme which combines the finite element approach with the Galerkin method of approximation. Application of this numerical model to the Wairakei geothermal field demonstrates that hot-water geothermal fields can be simulated using numerical techniques currently available and under development. ?? 1973.
The sensitivity method in finite element model updating: A tutorial
NASA Astrophysics Data System (ADS)
Mottershead, John E.; Link, Michael; Friswell, Michael I.
2011-10-01
The sensitivity method is probably the most successful of the many approaches to the problem of updating finite element models of engineering structures based on vibration test data. It has been applied successfully to large-scale industrial problems and proprietary codes are available based on the techniques explained in simple terms in this article. A basic introduction to the most important procedures of computational model updating is provided, including tutorial examples to reinforce the reader's understanding and a large scale model updating example of a helicopter airframe.
Edge-based finite element method for shallow water equations
NASA Astrophysics Data System (ADS)
Ribeiro, F. L. B.; Galeão, A. C.; Landau, L.
2001-07-01
This paper describes an edge-based implementation of the generalized residual minimum (GMRES) solver for the fully coupled solution of non-linear systems arising from finite element discretization of shallow water equations (SWEs). The gain in terms of memory, floating point operations and indirect addressing is quantified for semi-discrete and space-time analyses. Stabilized formulations, including Petrov-Galerkin models and discontinuity-capturing operators, are also discussed for both types of discretization. Results illustrating the quality of the stabilized solutions and the advantages of using the edge-based approach are presented at the end of the paper. Copyright
A wave envelope finite element scheme for acoustical radiation
NASA Astrophysics Data System (ADS)
Astley, R. J.
The aeroacoustic problem associated with the radiation of fan noise from the inlet of a turbofan aircraft engine, the dimensions of which are generally many times larger than the acoustical wavelengths of the major energy-carrying frequencies, is considered. In the present approach, a conventional finite element solution in the inner region is compatibly matched to a 'wave envelope' finite element solution in a large but finite outer region. The inclusion of a wavelike variation with the correct asymptotic decay in the shape functions for the outer region preserves the correct behavior of the solution at large distances. The method is initially presented for a simple one-dimensional model based on the solution of Webster's horn equation. Results are presented for the specific case of a uniform cylindrical section joined to a conical expansion, and also for a simple axisymmetric test case of the calculation of acoustical pressure generated by a vibrating circular piston located at the center of an infinite rigid baffle.
Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis
2005-12-01
This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.
Finite element simulation of thick sheet thermoforming
NASA Astrophysics Data System (ADS)
Mercier, Daniel
This PhD was organized as collaboration between Lehigh University and the Ecole des Mines d'Albi on the subject: "Numerical simulation of thick sheet thermoforming". The research applications cover a wide range of products from thermoforming, e.g., packaging, automobile parts, appliance parts, large-scale panels and covers. Due to the special nature of this PhD, and the requirements of each hosting institutes, the research was split accordingly into two parts: At Lehigh University, under the supervision of Prof. Herman F. Nied, a full three-dimensional finite element program was developed in order to simulate the mechanical deformation during the process of thermoforming. The material behavior is considered hyperelastic with the property of incompressibility. The deformed structure may exhibit symmetries and may use a large choice of boundary conditions. A contact procedure for molds and/or displacements caused by a plug was implemented to complete the similarity with the thermoforming process. The research focused on simulating the observed nonlinear behaviors and their instabilities. The author emphasized the impact of large deformation on the numerical results and demonstrated the need for a remeshing capability. At the Ecole des Mines d'Albi, under the supervision of Prof. Fabrice Schmidt, an equi-biaxial rheometer was developed and built in order to determine the material properties during the process of thermoforming. Thermoplastic materials consist of long macromolecular chains that when stretched, during the process of sheet extrusion, exhibit a transversal isotropic behavior. The rheometer technique is the inflation of a circular membrane made of extruded thermoplastics. The resulting strain is identified by video analysis during the membrane inflation. This dissertation focused on technical issues related to heating with the goal of overcoming the difficulty of producing a homogeneous temperature distribution.
Finite element analysis of posterior cervical fixation.
Duan, Y; Wang, H H; Jin, A M; Zhang, L; Min, S X; Liu, C L; Qiu, S J; Shu, X Q
2015-02-01
Despite largely, used in the past, biomechanical test, to investigate the fixation techniques of subaxial cervical spine, information is lacking about the internal structural response to external loading. It is not yet clear which technique represents the best choice and whether stabilization devices can be efficient and beneficial for three-column injuries (TCI). The different posterior cervical fixation techniques (pedicle screw PS, lateral mass screw LS, and transarticular screw TS) have respective indications. A detailed, geometrically accurate, nonlinear C3-C7 finite element model (FEM) had been successfully developed and validated. Then three FEMs were reconstructed from different fixation techniques after C4-C6 TCI. A compressive preload of 74N combined with a pure moment of 1.8 Nm in flexion, extension, left-right lateral bending, and left-right axial rotation was applied to the FEMs. The ROM results showed that there were obvious significant differences when comparing the different fixation techniques. PS and TS techniques can provide better immediate stabilization, compared to LS technique. The stress results showed that the variability of von Mises stress in the TS fixation device was minimum and LS fixation device was maximum. Furthermore, the screws inserted by TS technique had high stress concentration at the middle part of the screws. Screw inserted by PS and LS techniques had higher stress concentration at the actual cap-rod-screw interface. The research considers that spinal surgeon should first consider using the TS technique to treat cervical TCI. If PS technique is used, we should eventually prolong the need for external bracing in order to reduce the higher risk of fracture on fixation devices. If LS technique is used, we should add anterior cervical operation for acquire a better immediate stabilization. Copyright © 2014 Elsevier Masson SAS. All rights reserved.
NASA Astrophysics Data System (ADS)
Hurtado, Daniel E.; Rojas, Guillermo
2017-08-01
Computer simulations constitute a powerful tool for studying the electrical activity of the human heart, but computational effort remains prohibitively high. In order to recover accurate conduction velocities and wavefront shapes, the mesh size in linear element (Q1) formulations cannot exceed 0.1 mm. Here we propose a novel non-conforming finite-element formulation for the non-linear cardiac electrophysiology problem that results in accurate wavefront shapes and lower mesh-dependance in the conduction velocity, while retaining the same number of global degrees of freedom as Q1 formulations. As a result, coarser discretizations of cardiac domains can be employed in simulations without significant loss of accuracy, thus reducing the overall computational effort. We demonstrate the applicability of our formulation in biventricular simulations using a coarse mesh size of ˜ 1 mm, and show that the activation wave pattern closely follows that obtained in fine-mesh simulations at a fraction of the computation time, thus improving the accuracy-efficiency trade-off of cardiac simulations.
Finite element based inversion for time-harmonic electromagnetic problems
NASA Astrophysics Data System (ADS)
Schwarzbach, Christoph; Haber, Eldad
2013-05-01
In this paper we address the inverse problem and present some recent advances in numerical methods to recover the subsurface electrical conductivity from time-harmonic electromagnetic data. We rigorously formulate and discretize both the forward and the inverse problem in the finite element framework. To solve the forward problem, we derive a finite element discretization of the first-order system of Maxwell's equations in terms of the electric field and the magnetic induction. We show that our approach is equivalent to the standard discretization of the vector Helmholtz equation in terms of the electric field and that the discretization of magnetic induction of the same approximation order is hidden in the standard discretization. We implement the forward solver on unstructured tetrahedral meshes using edge elements. Unstructured meshes are not only capable of representing complex geometry. They can also reduce the overall problem size and, thus, the size of the system of linear equations arising from the forward problem such that direct methods for its solution using a sparse matrix factorization become feasible. The inverse problem is formulated as a regularized output least squares problem. We consider two regularization functions. First, we derive a smoothness regularizer using a primal-dual mixed finite element formulation which generalizes the standard Laplacian operator for a piecewise constant conductivity model on unstructured meshes. Secondly, we derive a total variation regularizer for the same class of models. For the choice of the regularization parameter we revisit the so-called dynamic regularization and compare it to a standard regularization scheme with fixed regularization parameter. The optimization problem is solved by the Gauss-Newton method which can be efficiently implemented using sparse matrix-vector operations and exploiting the sparse matrix factorization of the forward problem system matrix. A synthetic data example from marine
Finite element thermal-structural analyses of a cable-stiffened orbiting antenna
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Pandey, A. K.
1985-01-01
Finite element thermal-structural analyses of a cable-stiffened orbiting antenna are presented. The determination of prestresses in the antenna is described first. Heating and thermal analyses for orbiting space structures are then discussed briefly. Structural deformations and stresses are presented for three finite element structural analysis approaches: (1) small deflections, (2) stress-stiffening, and (3) large deflections. The accuracy of the three analysis approaches is evaluated for the orbiting antenna at different prestress levels.
Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
NASA Astrophysics Data System (ADS)
Motamarri, P.; Nowak, M. R.; Leiter, K.; Knap, J.; Gavini, V.
2013-11-01
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss-Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100-200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn-Sham DFT problem. Our studies suggest that staggering computational savings-of the order of 1000-fold-relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn-Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using
Higher-order adaptive finite-element methods for Kohn–Sham density functional theory
Motamarri, P.; Nowak, M.R.; Leiter, K.; Knap, J.; Gavini, V.
2013-11-15
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688
Regularised finite element model updating using measured incomplete modal data
NASA Astrophysics Data System (ADS)
Chen, Hua-Peng; Maung, Than Soe
2014-10-01
This paper presents an effective approach for directly updating finite element model from measured incomplete vibration modal data with regularised algorithms. The proposed method is based on the relationship between the perturbation of structural parameters such as stiffness change and the modal data measurements of the tested structure such as measured mode shape readings. In order to adjust structural parameters at detailed locations, structural updating parameters will be selected at critical point level to reflect the modelling errors at the connections of structural elements. These updating parameters are then evaluated by an iterative or a direct solution procedure, which gives optimised solutions in the least squares sense without requiring an optimisation technique. In order to reduce the influence of modal measurement uncertainty, the Tikhonov regularisation method incorporating the L-curve criterion is employed to produce reliable solutions for the chosen updating parameters. Numerical simulation investigations and experimental studies for the laboratory tested space steel frame structure are undertaken to verify the accuracy and effectiveness of the proposed methods for adjusting the stiffness at the joints of structural members. The results demonstrate that the proposed methods provide reliable estimates of finite element model updating using the measured incomplete modal data.
Gleadall, Andrew; Pan, Jingzhe; Ding, Lifeng; Kruft, Marc-Anton; Curcó, David
2015-11-01
Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide). Copyright © 2015 Elsevier Ltd. All rights reserved.
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.
Phase-space finite elements in a least-squares solution of the transport equation
Drumm, C.; Fan, W.; Pautz, S.
2013-07-01
The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshing tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)
Discontinuous Galerkin finite element solution for poromechanics
NASA Astrophysics Data System (ADS)
Liu, Ruijie
This dissertation focuses on applying discontinuous Galerkin (DG) methods to poromechanics problems. A few challenges have been presented in traditional and popular continuous Galerkin (CG) finite element methods for solving complex coupled thermal, flow and solid mechanics. For example, nonphysical pore pressure oscillations often occur in CG solutions for poroelasticity problems with low permeability. A robust and practical numerical scheme for removing or alleviating the oscillation is not available. In modeling thermoporoelastoplasticity, CG methods require the use of very small time steps to obtain a convergent solution. The temperature profile predicted by CG methods in the fine mesh zones is often seriously polluted by large errors produced in coarse mesh zones in the case where the convection dominates the thermal process. The nonphysical oscillations in pore pressure and temperature solutions induced by CG methods at very early time stages seriously corrupt the solutions at longer time. We propose DG methods to handle these challenges because they are physics driven, provide local conservation of mass and momentum, have high stability and robustness, are locking-free, and because of their meshing and implementation capabilities. We first apply a family of DG methods, including Oden-Babuska-Baumann (OBB), Nonsymmetric Interior Penalty Galerkin (NIPG), Symmetric Interior Penalty Galerkin (SIPG) and Incomplete Interior Penalty Galerkin (IIPG), to 3D linear elasticity problems. This family of DG methods is tested and evaluated by using a cantilever beam problem with nearly incompressible materials. It is shown that DG methods are simple, robust and locking-free in dealing with nearly incompressible materials. Based on the success of DG methods in elasticity, we extend the DG theory into plasticity problems. A DG formulation has been implemented for solving 3D poroelasticity problems with low permeability. Numerical examples solved by DG methods demonstrate
A Finite Element Model for Simulation of Carbon Dioxide Sequestration
Bao, Jie; Xu, Zhijie; Fang, Yilin
2015-07-23
We present a hydro-mechanical model, followed by stress, deformation, and shear-slip failure analysis for geological sequestration of carbon dioxide (CO2). The model considers the poroelastic effects by taking into account of the two-way coupling between the geomechanical response and the fluid flow process. Analytical solutions for pressure and deformation fields were derived for a typical geological sequestration scenario in our previous work. A finite element approach is introduced here for numerically solving the hydro-mechanical model with arbitrary boundary conditions. The numerical approach was built on an open-source finite element code Elmer, and results were compared to the analytical solutions. The shear-slip failure analysis was presented based on the numerical results, where the potential failure zone is identified. Information is relevant to the prediction of the maximum sustainable injection rate or pressure. The effects of caprock permeability on the fluid pressure, deformation, stress, and the shear-slip failure zone were also quantitatively studied. It was shown that a larger permeability in caprock and base rock leads to a larger uplift but a smaller shear-slip failure zone.
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.
Calculation of protein form birefringence using the finite element method.
Pantic-Tanner, Z; Eden, D
1999-01-01
An approach based on the finite element method (FEM) is employed to calculate the optical properties of macromolecules, specifically form birefringence. Macromolecules are treated as arbitrarily shaped particles suspended in a solvent of refraction index n1. The form birefringence of the solution is calculated as the difference in its refractive index when all the particles of refractive index n2 are either parallel to or normal to the direction of the polarization of light. Since the particles of interest are small compared to the wavelength of light, a quasi-static approximation for the refractive index is used, i.e., that it is equal to the square root of the dielectric constant of the suspension. The average dielectric constant of the mixture is calculated using the finite element method. This approach has been tested for ellipsoidal particles and a good agreement with theoretical results has been obtained. Also, numerical results for the motor domains of ncd and kinesin, small arbitrarily shaped proteins with known x-ray structures, show reasonable agreement with the experimental data obtained from transient electric birefringence experiments. PMID:10354422
Aeroelastic Stability of Rotor Blades Using Finite Element Analysis
NASA Technical Reports Server (NTRS)
Chopra, I.; Sivaneri, N.
1982-01-01
The flutter stability of flap bending, lead-lag bending, and torsion of helicopter rotor blades in hover is investigated using a finite element formulation based on Hamilton's principle. The blade is divided into a number of finite elements. Quasi-steady strip theory is used to evaluate the aerodynamic loads. The nonlinear equations of motion are solved for steady-state blade deflections through an iterative procedure. The equations of motion are linearized assuming blade motion to be a small perturbation about the steady deflected shape. The normal mode method based on the coupled rotating natural modes is used to reduce the number of equations in the flutter analysis. First the formulation is applied to single-load-path blades (articulated and hingeless blades). Numerical results show very good agreement with existing results obtained using the modal approach. The second part of the application concerns multiple-load-path blades, i.e. bearingless blades. Numerical results are presented for several analytical models of the bearingless blade. Results are also obtained using an equivalent beam approach wherein a bearingless blade is modelled as a single beam with equivalent properties. Results show the equivalent beam model.
Accelerated finite element elastodynamic simulations using the GPU
Huthwaite, Peter
2014-01-15
An approach is developed to perform explicit time domain finite element simulations of elastodynamic problems on the graphical processing unit, using Nvidia's CUDA. Of critical importance for this problem is the arrangement of nodes in memory, allowing data to be loaded efficiently and minimising communication between the independently executed blocks of threads. The initial stage of memory arrangement is partitioning the mesh; both a well established ‘greedy’ partitioner and a new, more efficient ‘aligned’ partitioner are investigated. A method is then developed to efficiently arrange the memory within each partition. The software is applied to three models from the fields of non-destructive testing, vibrations and geophysics, demonstrating a memory bandwidth of very close to the card's maximum, reflecting the bandwidth-limited nature of the algorithm. Comparison with Abaqus, a widely used commercial CPU equivalent, validated the accuracy of the results and demonstrated a speed improvement of around two orders of magnitude. A software package, Pogo, incorporating these developments, is released open source, downloadable from (http://www.pogo-fea.com/) to benefit the community. -- Highlights: •A novel memory arrangement approach is discussed for finite elements on the GPU. •The mesh is partitioned then nodes are arranged efficiently within each partition. •Models from ultrasonics, vibrations and geophysics are run. •The code is significantly faster than an equivalent commercial CPU package. •Pogo, the new software package, is released open source.
Spin-Wave Excitations in Finite Rectangular Elements
NASA Astrophysics Data System (ADS)
Bayer, Christian; Jorzick, Jörg; Demokritov, Sergej O.; Slavin, Andrei N.; Guslienko, Konstantin Y.; Berkov, Dmitry V.; Gorn, Natalia L.; Kostylev, Mikhail P.; Hillebrands, Burkard
A review on recent Brillouin light scattering work on spin-wave modes in arrays of micrometer-size magnetic Ni80Fe20 stripes and rectangular elements is given. Several effects caused by the lateral confinement in the stripes are reviewed: 1. lateral quantization of dipole-dominated Damon-Eshbach spin-wave modes in a longitudinally magnetized stripe due to its finite width, 2. localization of exchange-dominated spin-wave modes near the edges and dipole-dominated spin-wave modes near the center of a transversely magnetized long magnetic stripe due to the inhomogeneity of its internal magnetic field, 3. combination of quantization and localization effects for the spin-wave modes in rectangular elements. The observed effects are analyzed using an analytical approach and numerical simulations.
Fracture and Fragmentation of Simplicial Finite Elements Meshes using Graphs
Mota, A; Knap, J; Ortiz, M
2006-10-18
An approach for the topological representation of simplicial finite element meshes as graphs is presented. It is shown that by using a graph, the topological changes induced by fracture reduce to a few, local kernel operations. The performance of the graph representation is demonstrated and analyzed, using as reference the 3D fracture algorithm by Pandolfi and Ortiz [22]. It is shown that the graph representation initializes in O(N{sub E}{sup 1.1}) time and fractures in O(N{sub I}{sup 1.0}) time, while the reference implementation requires O(N{sub E}{sup 2.1}) time to initialize and O(N{sub I}{sup 1.9}) time to fracture, where NE is the number of elements in the mesh and N{sub I} is the number of interfaces to fracture.
Edge or face based spectral finite elements for electromagnetic problems
NASA Astrophysics Data System (ADS)
Jevtic, Jovan Obrad
This work describes the development and presents a study of a finite element method (FEM) specifically designed for vector electromagnetic wave problems. Three aspects make this formulation different from the conventional FEM, namely, the selection of the unknowns, the choice of shape functions, and the approach to field matching between the elements. First, the unknowns are closely related to the tangential field components on the boundary of a finite element, an edge of a triangle in two dimensions (2D) or a face of a tetrahedron in three- dimensions (3D). This reflects the uniqueness theorem for electromagnetic fields. Second, the unknown total fields are expanded in terms of vector eigenfunctions of the wave equation within a semi-infinite domain bounded by the exact element geometry in 2D or an approximation thereof in 3D. This leads to a low phase error across an element and allows for electrically large elements. Finally, the sole numerical part of the method consist of the enforcement of the tangential field continuity over inter-element boundaries. This reflects the natural electromagnetic field boundary conditions which allows for the discontinuity of the normal field components. The 2D formulation presented herein can be thought of as an extension to higher orders of the conventional edge elements, which are based on the low order shape functions, while at the same time preserving their advantages, such as the absence of spurious modes and the ability to handle sharp edges as well as material interfaces. Furthermore, a full advantage of the higher order absorbing boundary conditions can be made. The 3D problem proved significantly more difficult, not only in terms of the conceptual development of the novel formulation, but also in terms of the associated computational issues, such as real-time determination of the zeros of associated Legendre functions and the ambiguity of eigenfunction ordering. The resolution of these issues, therefore, occupies a
Application of the Finite Element Method to Rotary Wing Aeroelasticity
NASA Technical Reports Server (NTRS)
Straub, F. K.; Friedmann, P. P.
1982-01-01
A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.
Finite-element mesh generation from mappable features
Kuniansky, Eve L.; Lowther, Robert A.
1993-01-01
A vector-based geographical information system (GIS) is used to generate a variably-sized triangular element finite-element mesh from mappable features. Important digitally-mapped features are automatically linked to nodes in the finite-element model, ensuring an efficient, virtually error-free alternative to the tedious process of mesh design and data-input preparation by other methods. The procedure permits the user to work interactively with graphically-displayed hydrologic information about the study area allowing different mesh sizes to be used as needed, based on hydrologic complexity. The mesh-generaiion programs are stand-alone macros within the GIS that set up the basic data defining a finite-element mesh for many different finite-element model programs.
A hybrid transfinite element approach for nonlinear transient thermal analysis
NASA Technical Reports Server (NTRS)
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
A new computational approach for transient nonlinear thermal analysis of structures is proposed. It is a hybrid approach which combines the modeling versatility of contemporary finite elements in conjunction with transform methods and classical Bubnov-Galerkin schemes. The present study is limited to nonlinearities due to temperature-dependent thermophysical properties. Numerical test cases attest to the basic capabilities and therein validate the transfinite element approach by means of comparisons with conventional finite element schemes and/or available solutions.
A finite element conjugate gradient FFT method for scattering
NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
Hybrid stress finite elements for large deformations of inelastic solids
NASA Technical Reports Server (NTRS)
Reed, K. W.; Atluri, S. N.
1984-01-01
A new hybrid stress finite element algorithm, based on a generalization of Fraeijs de Veubeke's complementary energy principle is presented. Analyses of large quasistatic deformation of inelastic solids (hypoelastic, plastic, viscoplastic) are within its capability. Principle variables in the formulation are the nominal stress rate and spin. A brief account is given of the boundary value problem in these variables, and the 'equivalent' variational principle. The finite element equation, along with initial positions and stresses, comprise an initial value problem. Factors affecting the choice of time integration schemes are discussed. Results found by application of the new algorithm are compared to those obtained by a velocity based finite element algorithm.
Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms
NASA Technical Reports Server (NTRS)
Kurdila, Andrew J.; Sharpley, Robert C.
1999-01-01
This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.
Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators
NASA Technical Reports Server (NTRS)
Taleghani, Barmac K.; Campbell, Joel F.
1999-01-01
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
Finite element prediction of fatigue damage growth in cancellous bone.
Hambli, Ridha; Frikha, Sana; Toumi, Hechmi; Tavares, João Manuel R S
2016-01-01
Cyclic stresses applied to bones generate fatigue damage that affects the bone stiffness and its elastic modulus. This paper proposes a finite element model for the prediction of fatigue damage accumulation and failure in cancellous bone at continuum scale. The model is based on continuum damage mechanics and incorporates crack closure effects in compression. The propagation of the cracks is completely simulated throughout the damaged area. In this case, the stiffness of the broken element is reduced by 98% to ensure no stress-carrying capacities of completely damaged elements. Once a crack is initiated, the propagation direction is simulated by the propagation of the broken elements of the mesh. The proposed model suggests that damage evolves over a real physical time variable (cycles). In order to reduce the computation time, the integration of the damage growth rate is based on the cycle blocks approach. In this approach, the real number of cycles is reduced (divided) into equivalent blocks of cycles. Damage accumulation is computed over the cycle blocks and then extrapolated over the corresponding real cycles. The results show a clear difference between local tensile and compressive stresses on damage accumulation. Incorporating stiffness reduction also produces a redistribution of the peak stresses in the damaged region, which results in a delay in damage fracture.
NASA Astrophysics Data System (ADS)
Zhu, Song; Liu, Hui-Ping; Yi, Lin
2010-09-01
A generalized finite element formulation is proposed for the study of the spin-dependent ballistic transport of electron through the two-dimensional quantum structures with Rashba spin-orbit interactions (SOI). The transmission coefficient, conductance, the total and local polarization are numerically calculated and discussed as the Rashba coefficient, the geometric sizes, and incident energy are changed in the T-shaped devices. Some interesting features are found in the proper parameter regime. The polarization has an enhancement as the Rashba coefficient becomes stronger. The polarization valley is rigid in the regime of the conductance plateaus since the local interference among the polarized multi-wave modes. The Rashba interactions coupling to geometry in sizes could form the structure-induced Fano-Rashba resonance. In the wider stub, the localized spin lattice of electron could be produced. The conductance plateaus correspond to weak polarizations. Strong polarizations appear when the stub sizes, incident energy, and the Rashba coupling coefficient are matched. The resonances are formed in a wide Fermi energy segment easily.
Martínez-Martínez, F; Rupérez-Moreno, M J; Martínez-Sober, M; Solves-Llorens, J A; Lorente, D; Serrano-López, A J; Martínez-Sanchis, S; Monserrat, C; Martín-Guerrero, J D
2017-09-28
This work presents a data-driven method to simulate, in real-time, the biomechanical behavior of the breast tissues in some image-guided interventions such as biopsies or radiotherapy dose delivery as well as to speed up multimodal registration algorithms. Ten real breasts were used for this work. Their deformation due to the displacement of two compression plates was simulated off-line using the finite element (FE) method. Three machine learning models were trained with the data from those simulations. Then, they were used to predict in real-time the deformation of the breast tissues during the compression. The models were a decision tree and two tree-based ensemble methods (extremely randomized trees and random forest). Two different experimental setups were designed to validate and study the performance of these models under different conditions. The mean 3D Euclidean distance between nodes predicted by the models and those extracted from the FE simulations was calculated to assess the performance of the models in the validation set. The experiments proved that extremely randomized trees performed better than the other two models. The mean error committed by the three models in the prediction of the nodal displacements was under 2 mm, a threshold usually set for clinical applications. The time needed for breast compression prediction is sufficiently short to allow its use in real-time (<0.2 s). Copyright © 2017 Elsevier Ltd. All rights reserved.
Bourke, Jason; Wroe, Stephen; Moreno, Karen; McHenry, Colin; Clausen, Philip
2008-05-21
Models of the mammalian jaw have predicted that bite force is intimately linked to jaw gape and to tooth position. Despite widespread use, few empirical studies have provided evidence to validate these models in non-human mammals and none have considered the influence of gape angle on the distribution of stress. Here using a multi-property finite element (FE) model of Canis lupus dingo, we examined the influence of gape angle and bite point on both bite force and cranial stress. Bite force data in relation to jaw gape and along the tooth row, are in broad agreement with previously reported results. However stress data showed that the skull of C. l. dingo is mechanically suited to withstand stresses at wide gapes; a result that agreed well with previously held views regarding carnivoran evolution. Stress data, combined with bite force information, suggested that there is an optimal bite angle of between 25 degrees and 35 degrees in C. l. dingo. The function of these rather small bite angles remains unclear.
Finite Element Anlaysis of Laminated Composite Plates
1988-09-01
4.2, results depicting maximum displacement obtained using 2 x 2 integration points, 3 x 3 integration points and ’ heterosis ’ [Ref. 4] elements are...thick and thin plates. This element gives better predictions for thick plates than heterosis ele- ment, however, for thin plates, heterosis element...results showing the normalized maximum displacements are shown in Figure 4.8. The heterosis element results in about ten percent error while the
Validating Finite Element Models of Assembled Shell Structures
NASA Technical Reports Server (NTRS)
Hoff, Claus
2006-01-01
The validation of finite element models of assembled shell elements is presented. The topics include: 1) Problems with membrane rotations in assembled shell models; 2) Penalty stiffness for membrane rotations; 3) Physical stiffness for membrane rotations using shell elements with 6 dof per node; and 4) Connections avoiding rotations.
NASA Astrophysics Data System (ADS)
Raffler, Marco; Sevarin, Alessio; Ellersdorfer, Christian; Heindl, Simon F.; Breitfuss, Christoph; Sinz, Wolfgang
2017-08-01
In this research, a parameterized beam-element-based mechanical modeling approach for cylindrical lithium ion batteries is developed. With the goal to use the cell model in entire vehicle crash simulations, focus of development is on minimizing the computational effort whilst simultaneously obtaining accurate mechanical behavior. The cylindrical cell shape is approximated by radial beams connected to each other in circumferential and longitudinal directions. The discrete beam formulation is used to define an anisotropic material behavior. An 18650 lithium ion cell model constructed in LS-Dyna is used to show the high degree of parameterization of the approach. A criterion which considers the positive pole deformation and the radial deformation of the cell is developed for short circuit prediction during simulation. An abuse testing program, consisting of radial crush, axial crush, and penetration is performed to evaluate the mechanical properties and internal short circuit behavior of a commercially available 18650 lithium cell. Additional 3-point-bending tests are performed to verify the approach objectively. By reducing the number of strength-related elements to 1600, a fast and accurate cell model can be created. Compared to typical cell models in technical literature, simulation time of a single cell load case can be reduced by approx. 90%.
A Method for Connecting Dissimilar Finite Element Meshes in Three Dimensions
Dohrmann, C.R.; Heinstein, M.W.; Key, S.W.
1998-11-12
A method is presented for connecting dissimilar finite element meshes in three dimensions. The method combines the concept of master and slave surfaces with the uniform strain approach for surface, corrections finite elements- By modifyhg the are made to element formulations boundaries of elements on the slave such that first-order patch tests are passed. The method can be used to connect meshes which use different element types. In addition, master and slave surfaces can be designated independently of relative mesh resolutions. Example problems in three-dimensional linear elasticity are presented.
Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.
2012-09-20
The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered
Finite element techniques applied to cracks interacting with selected singularities
NASA Technical Reports Server (NTRS)
Conway, J. C.
1975-01-01
The finite-element method for computing the extensional stress-intensity factor for cracks approaching selected singularities of varied geometry is described. Stress-intensity factors are generated using both displacement and J-integral techniques, and numerical results are compared to those obtained experimentally in a photoelastic investigation. The selected singularities considered are a colinear crack, a circular penetration, and a notched circular penetration. Results indicate that singularities greatly influence the crack-tip stress-intensity factor as the crack approaches the singularity. In addition, the degree of influence can be regulated by varying the overall geometry of the singularity. Local changes in singularity geometry have little effect on the stress-intensity factor for the cases investigated.
Superconvergence in the Generalized Finite Element Method
2005-01-01
Galerkin method for elliptic equations based on tensor products of piecewise polynomials. RAIRO Anal. Numer., 8:61– 66, 1974. [19] M. Kř́ıžek...London, 1986. [22] P. Lesaint and M. Zlámal. Superconvergence of the gradient of finite ele- ment solutions. RAIRO Anal. Numer., 13:139–166, 1979. [23] Q
Application of Mass Lumped Higher Order Finite Elements
Chen, J.; Strauss, H. R.; Jardin, S. C.; Park, W.; Sugiyama, L. E.; G. Fu; Breslau, J.
2005-11-01
There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied.
NASA Astrophysics Data System (ADS)
Kanber, Bahattin; Bozkurt, O. Yavuz
2006-08-01
In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.
Finite element analysis to evaluate optical mirror deformations
NASA Astrophysics Data System (ADS)
Izazaga-Pérez, R.; Aguirre-Aguirre, D.; Villalobos-Mendoza, B.
2015-10-01
In this work we describe the use of Finite Element Analysis software to simulate the deformations of an optical mirror. We use Finite Element Method software as a tool to simulate the mirror deformations assuming that it is a thin plate that can be mechanically tensed or compressed; the Finite Element Analysis give us information about the displacements of the mirror from an initial position and the tensions that remains in the surface. The information obtained by means of Finite Element Analysis can be easily exported to a coordinate system and processed in a simulation environment. Finally, a ray-tracing subroutine is used in the obtained data giving us information in terms of aberration coefficients. We present some results of the simulations describing the followed procedure.
Adaptive Finite-Element Computation In Fracture Mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1995-01-01
Report discusses recent progress in use of solution-adaptive finite-element computational methods to solve two-dimensional problems in linear elastic fracture mechanics. Method also shown extensible to three-dimensional problems.
Validation of High Displacement Piezoelectric Actuator Finite Element Models
NASA Technical Reports Server (NTRS)
Taleghani, B. K.
2000-01-01
The paper presents the results obtained by using NASTRAN(Registered Trademark) and ANSYS(Regitered Trademark) finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness are important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN(Registered Trademark) and ANSYS(Registered Trademark) used different methods for modeling piezoelectric effects. In NASTRAN(Registered Trademark), a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS(Registered Trademark) processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.
Scalable, Finite Element Analysis of Electromagnetic Scattering and Radiation
NASA Technical Reports Server (NTRS)
Cwik, T.; Lou, J.; Katz, D.
1997-01-01
In this paper a method for simulating electromagnetic fields scattered from complex objects is reviewed; namely, an unstructured finite element code that does not use traditional mesh partitioning algorithms.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Error analysis of finite element solutions for postbuckled cylinders
NASA Technical Reports Server (NTRS)
Sistla, Rajaram; Thurston, Gaylen A.
1989-01-01
A general method of error analysis and correction is investigated for the discrete finite-element results for cylindrical shell structures. The method for error analysis is an adaptation of the method of successive approximation. When applied to the equilibrium equations of shell theory, successive approximations derive an approximate continuous solution from the discrete finite-element results. The advantage of this continuous solution is that it contains continuous partial derivatives of an order higher than the basis functions of the finite-element solution. Preliminary numerical results are presented in this paper for the error analysis of finite-element results for a postbuckled stiffened cylindrical panel modeled by a general purpose shell code. Numerical results from the method have previously been reported for postbuckled stiffened plates. A procedure for correcting the continuous approximate solution by Newton's method is outlined.
Scalable, Finite Element Analysis of Electromagnetic Scattering and Radiation
NASA Technical Reports Server (NTRS)
Cwik, T.; Lou, J.; Katz, D.
1997-01-01
In this paper a method for simulating electromagnetic fields scattered from complex objects is reviewed; namely, an unstructured finite element code that does not use traditional mesh partitioning algorithms.
The finite element machine: An experiment in parallel processing
NASA Technical Reports Server (NTRS)
Storaasli, O. O.; Peebles, S. W.; Crockett, T. W.; Knott, J. D.; Adams, L.
1982-01-01
The finite element machine is a prototype computer designed to support parallel solutions to structural analysis problems. The hardware architecture and support software for the machine, initial solution algorithms and test applications, and preliminary results are described.
Validation of high displacement piezoelectric actuator finite element models
NASA Astrophysics Data System (ADS)
Taleghani, Barmac K.
2000-08-01
The paper presents the results obtained by using NASTRAN and ANSYS finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness and important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN and ANSYS used different methods for modeling piezoelectric effects. In NASTRAN, a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.
Optimal least-squares finite element method for elliptic problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Povinelli, Louis A.
1991-01-01
An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.
Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector
NASA Technical Reports Server (NTRS)
Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)
2001-01-01
Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.
Finite Element Modeling of the Posterior Eye in Microgravity
NASA Technical Reports Server (NTRS)
Feola, Andrew; Raykin, Julia; Mulugeta, Lealem; Gleason, Rudolph; Myers, Jerry G.; Nelson, Emily S.; Samuels, Brian; Ethier, C. Ross
2015-01-01
Microgravity experienced during spaceflight affects astronauts in various ways, including weakened muscles and loss of bone density. Recently, visual impairment and intracranial pressure (VIIP) syndrome has become a major concern for space missions lasting longer than 30 days. Astronauts suffering from VIIP syndrome have changes in ocular anatomical and visual impairment that persist after returning to earth. It is hypothesized that a cephalad fluid shift in microgravity may increase the intracranial pressure (ICP), which leads to an altered biomechanical environment of the posterior globe and optic nerve sheath (ONS).Currently, there is a lack of knowledge of how elevated ICP may lead to vision impairment and connective tissue changes in VIIP. Our goal was to develop a finite element model to simulate the acute effects of elevated ICP on the posterior eye and optic nerve sheath. We used a finite element (FE) analysis approach to understand the response of the lamina cribrosa and optic nerve to the elevations in ICP thought to occur in microgravity and to identify which tissue components have the greatest impact on strain experienced by optic nerve head tissues.
Superaccurate finite element eigenvalues via a Rayleigh quotient correction
NASA Astrophysics Data System (ADS)
Fried, Isaac; Leong, Kaiwen
2005-11-01
The consistent finite element formulation of the vibration problem generates upper bounds on the corresponding exact eigenvalues but requires the solution of the highly expensive general algebraic eigenproblem Kx=λMx with a global matrix M that is of the same sparsity pattern as the global stiffness K. The lumped, diagonal, mass matrix finite element formulation is no longer variationally correct but results in a simplified algebraic eigenproblem of comparable accuracy. We may write the mass matrix as a linear matrix function, M(γ)=M1+γM2, of parameter γ such that M(γ=1) is the (diagonal) lumped mass matrix and M(γ=0) is the consistent mass matrix. It has been shown that an optimal γ exists between these two states which results in superaccurate eigenvalues. What detracts from the appeal of this approach is that the superior accuracy thus achieved comes at the hefty price of having to solve the still general algebraic eigenproblem with a nondiagonal mass matrix. In this note we show that the same superior accuracy can be had by first computing an eigenvector u from Ku=λDu, in which D=M1+M2 is the lumped, diagonal, mass matrix, and then obtaining the corresponding, superaccurate, eigenvalue from the Rayleigh quotient R[u]=uTKu/uTM(γ)u, M(γ)=M1+γM2 for an optimal γ.
The future of finite element applications on massively parallel supercomputers
Christon, M.
1994-07-05
The current focus in large scale scientific computing is upon parallel supercomputers. While still relatively unproven, these machines are being slated for production-oriented, general purpose supercomputing applications. The promise, of course, is to use massively parallel computers to venture further into scientific realisms by performing computations with anywhere from 10{sup 6} to 10{sup 9} grid points thereby, in principle, obtaining a deeper understanding of physical processes. In approaching this brave new world of computing with finite element applications, many technical issues become apparent. This paper attempts to reveal some of the applications-oriented issues which are facing code developers and ultimately the users of engineering and scientific applications on parallel supercomputers, but which seem to be remaining unanswered by vendors, researchers and centralized computing facilities. At risk is the fundamental way in which analysis is performed in a production sense, and the insight into physical problems which results. while at first this treatise may seem to advocate traditional register-to-register vector supercomputers, the goal of this paper is simply an attempt to point out what is missing from the massively parallel computing picture not only for production finite element applications, but also for grand challenge problems. the limiting issues for the use of FEM applications on parallel supercomputers are centered about the need for adequate disk space, archival storage, high bandwidth networks, and continued software development for mesh generation, scientific visualization, linear equation solvers and parallel input/output.
Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector
NASA Technical Reports Server (NTRS)
Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)
2001-01-01
Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.
Patient-specific finite element modeling for femoral bone augmentation
Basafa, Ehsan; Armiger, Robert S.; Kutzer, Michael D.; Belkoff, Stephen M.; Mears, Simon C.; Armand, Mehran
2015-01-01
The aim of this study was to provide a fast and accurate finite element (FE) modeling scheme for predicting bone stiffness and strength suitable for use within the framework of a computer-assisted osteoporotic femoral bone augmentation surgery system. The key parts of the system, i.e. preoperative planning and intraoperative assessment of the augmentation, demand the finite element model to be solved and analyzed rapidly. Available CT scans and mechanical testing results from nine pairs of osteoporotic femur bones, with one specimen from each pair augmented by polymethylmethacrylate (PMMA) bone cement, were used to create FE models and compare the results with experiments. Correlation values of R2 = 0.72–0.95 were observed between the experiments and FEA results which, combined with the fast model convergence (~3 min for ~250,000 degrees of freedom), makes the presented modeling approach a promising candidate for the intended application of preoperative planning and intraoperative assessment of bone augmentation surgery. PMID:23375663
Progress in Developing Finite Element Models Replicating Flexural Graphite Testing
Robert Bratton
2010-06-01
This report documents the status of flexural strength evaluations from current ASTM procedures and of developing finite element models predicting the probability of failure. This work is covered under QLD REC-00030. Flexural testing procedures of the American Society for Testing and Materials (ASTM) assume a linear elastic material that has the same moduli for tension and compression. Contrary to this assumption, graphite is known to have different moduli for tension and compression. A finite element model was developed and demonstrated that accounts for the difference in moduli tension and compression. Brittle materials such as graphite exhibit significant scatter in tensile strength, so probabilistic design approaches must be used when designing components fabricated from brittle materials. ASTM procedures predicting probability of failure in ceramics were compared to methods from the current version of the ASME graphite core components rules predicting probability of failure. Using the ASTM procedures yields failure curves at lower applied forces than the ASME rules. A journal paper was published in the Journal of Nuclear Engineering and Design exploring the statistical models of fracture in graphite.
Simple bounds on limit loads by elastic finite element analysis
Mackenzie, D.; Nadarajah, C.; Shi, J.; Boyle, J.T. . Dept. of Mechanical Engineering)
1993-02-01
A method for bounding limit loads by an iterative elastic continuum finite element analysis procedure, referred to as the elastic compensation method, is proposed. A number of sample problems are considered, based on both exact solutions and finite element analysis, and it is concluded that the method may be used to obtain limit-load bounds for pressure vessel design by analysis applications with useful accuracy.
Examples of finite element mesh generation using SDRC IDEAS
NASA Technical Reports Server (NTRS)
Zapp, John; Volakis, John L.
1990-01-01
IDEAS (Integrated Design Engineering Analysis Software) offers a comprehensive package for mechanical design engineers. Due to its multifaceted capabilities, however, it can be manipulated to serve the needs of electrical engineers, also. IDEAS can be used to perform the following tasks: system modeling, system assembly, kinematics, finite element pre/post processing, finite element solution, system dynamics, drafting, test data analysis, and project relational database.
Global/local finite element analysis of composite materials
NASA Technical Reports Server (NTRS)
Griffin, O. Hayden, Jr.; Vidussoni, M. A.
1988-01-01
The motivation for performing global/local finite element analysis in composite materials is described. An example of such an analysis of a composite plate with a central circular hole is presented. Deformed finite element grids and interlaminar normal stress distributions are presented to aid understanding of the plate response. Such distribution at the plate edge is shown to be basically unaffected, although transverse displacements of the edge were slightly different from an analysis of a similar plate with no hole.
Finite element analysis to model complex mitral valve repair.
Labrosse, Michel; Mesana, Thierry; Baxter, Ian; Chan, Vincent
2016-01-01
Although finite element analysis has been used to model simple mitral repair, it has not been used to model complex repair. A virtual mitral valve model was successful in simulating normal and abnormal valve function. Models were then developed to simulate an edge-to-edge repair and repair employing quadrangular resection. Stress contour plots demonstrated increased stresses along the mitral annulus, corresponding to the annuloplasty. The role of finite element analysis in guiding clinical practice remains undetermined.
Finite element analysis of a composite wheelchair wheel design
NASA Technical Reports Server (NTRS)
Ortega, Rene
1994-01-01
The finite element analysis of a composite wheelchair wheel design is presented. The design is the result of a technology utilization request. The designer's intent is to soften the riding feeling by incorporating a mechanism attaching the wheel rim to the spokes that would allow considerable deflection upon compressive loads. A finite element analysis was conducted to verify proper structural function. Displacement and stress results are presented and conclusions are provided.
An Adaptive Multiscale Finite Element Method for Large Scale Simulations
2015-09-28
the method . Using the above definitions , the weak statement of the non-linear local problem at the kth 4 DISTRIBUTION A: Distribution approved for...AFRL-AFOSR-VA-TR-2015-0305 An Adaptive Multiscale Finite Element Method for Large Scale Simulations Carlos Duarte UNIVERSITY OF ILLINOIS CHAMPAIGN...14-07-2015 4. TITLE AND SUBTITLE An Adaptive Multiscale Generalized Finite Element Method for Large Scale Simulations 5a. CONTRACT NUMBER 5b
Nonlinear Finite Element Analysis of Composite Flextensional Transducer Shell
1993-03-01
4 TITLE AND SUBTITLE s FUNDING NUMbE;h NONLINEAR FINITE ELEMENT ANALYSIS OF COMPOSITE FLEXTENSIONAL PR: SV70 TRANSDUCER SHELL PE: 020431 IN 6 AUFTHOA...D NSN 7540-01-280-5500 ,ssard tr,298 IBACI UiNCLA-SSIFlED NONLINEAR FINITE ELEMENT ANALYSIS OF COMPOSITE FLEXTENSIONAL TRANSDUCER SHELL R. C. SliAW...its correlation with test data for a Class IV flextensional underwater acoustic transducer . The thick. elliptical fiberglass/epoxy shell of the
Finite element modeling of electromagnetic propagation in composite structures
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1987-01-01
A finite element Galerkin formulation has been developed to study electromagnetic propagation in complex two-dimensional absorbing ducts. The reflection and transmission at entrance and exit boundaries are determined by coupling the finite element solutions at the entrance and exit to the eigenfunctions of an infinite uniform perfect conducting duct. Example solutions are presented for electromagnetic propagation with absorbing duct walls and propagating through dielectric-metallic matrix materials.
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.
Evaluation of a hybrid, anisotropic, multilayered, quadrilateral finite element
NASA Technical Reports Server (NTRS)
Robinson, J. C.; Blackburn, C. L.
1978-01-01
A multilayered finite element with bending-extensional coupling is evaluated for: (1) buckling of general laminated plates; (2) thermal stresses of laminated plates cured at elevated temperatures; (3) displacements of a bimetallic beam; and (4) displacement and stresses of a single-cell box beam with warped cover panels. Also, displacements and stresses for flat and spherical orthotropic and anisotropic segments are compared with results from higher order plate and shell finite-element analyses.
Applications of finite element simulation in orthopedic and trauma surgery
Herrera, Antonio; Ibarz, Elena; Cegoñino, José; Lobo-Escolar, Antonio; Puértolas, Sergio; López, Enrique; Mateo, Jesús; Gracia, Luis
2012-01-01
Research in different areas of orthopedic and trauma surgery requires a methodology that allows both a more economic approach and the ability to reproduce different situations in an easy way. Simulation models have been introduced recently in bioengineering and could become an essential tool in the study of any physiological unity, regardless of its complexity. The main problem in modeling with finite elements simulation is to achieve an accurate reproduction of the anatomy and a perfect correlation of the different structures, in any region of the human body. Authors have developed a mixed technique, joining the use of a three-dimensional laser scanner Roland Picza captured together with computed tomography (CT) and 3D CT images, to achieve a perfect reproduction of the anatomy. Finite element (FE) simulation lets us know the biomechanical changes that take place after hip prostheses or osteosynthesis implantation and biological responses of bone to biomechanical changes. The simulation models are able to predict changes in bone stress distribution around the implant, so allowing preventing future pathologies. The development of a FE model of lumbar spine is another interesting application of the simulation. The model allows research on the lumbar spine, not only in physiological conditions but also simulating different load conditions, to assess the impact on biomechanics. Different degrees of disc degeneration can also be simulated to determine the impact on adjacent anatomical elements. Finally, FE models may be useful to test different fixation systems, i.e., pedicular screws, interbody devices or rigid fixations compared with the dynamic ones. We have also developed models of lumbar spine and hip joint to predict the occurrence of osteoporotic fractures, based on densitometric determinations and specific biomechanical models, including approaches from damage and fracture mechanics. FE simulations also allow us to predict the behavior of orthopedic splints
Applications of finite element simulation in orthopedic and trauma surgery.
Herrera, Antonio; Ibarz, Elena; Cegoñino, José; Lobo-Escolar, Antonio; Puértolas, Sergio; López, Enrique; Mateo, Jesús; Gracia, Luis
2012-04-18
Research in different areas of orthopedic and trauma surgery requires a methodology that allows both a more economic approach and the ability to reproduce different situations in an easy way. Simulation models have been introduced recently in bioengineering and could become an essential tool in the study of any physiological unity, regardless of its complexity. The main problem in modeling with finite elements simulation is to achieve an accurate reproduction of the anatomy and a perfect correlation of the different structures, in any region of the human body. Authors have developed a mixed technique, joining the use of a three-dimensional laser scanner Roland Picza captured together with computed tomography (CT) and 3D CT images, to achieve a perfect reproduction of the anatomy. Finite element (FE) simulation lets us know the biomechanical changes that take place after hip prostheses or osteosynthesis implantation and biological responses of bone to biomechanical changes. The simulation models are able to predict changes in bone stress distribution around the implant, so allowing preventing future pathologies. The development of a FE model of lumbar spine is another interesting application of the simulation. The model allows research on the lumbar spine, not only in physiological conditions but also simulating different load conditions, to assess the impact on biomechanics. Different degrees of disc degeneration can also be simulated to determine the impact on adjacent anatomical elements. Finally, FE models may be useful to test different fixation systems, i.e., pedicular screws, interbody devices or rigid fixations compared with the dynamic ones. We have also developed models of lumbar spine and hip joint to predict the occurrence of osteoporotic fractures, based on densitometric determinations and specific biomechanical models, including approaches from damage and fracture mechanics. FE simulations also allow us to predict the behavior of orthopedic splints
Recent developments in finite element analysis for transonic airfoils
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Murman, E. M.
1979-01-01
The prediction of aerodynamic forces in the transonic regime generally requires a flow field calculation to solve the governing non-linear mixed elliptic-hyperbolic partial differential equations. Finite difference techniques were developed to the point that design and analysis application are routine, and continual improvements are being made by various research groups. The principal limitation in extending finite difference methods to complex three-dimensional geometries is the construction of a suitable mesh system. Finite element techniques are attractive since their application to other problems have permitted irregular mesh elements to be employed. The purpose of this paper is to review the recent developments in the application of finite element methods to transonic flow problems and to report some recent results.
Dynamical observer for a flexible beam via finite element approximations
NASA Technical Reports Server (NTRS)
Manitius, Andre; Xia, Hong-Xing
1994-01-01
The purpose of this view-graph presentation is a computational investigation of the closed-loop output feedback control of a Euler-Bernoulli beam based on finite element approximation. The observer is part of the classical observer plus state feedback control, but it is finite-dimensional. In the theoretical work on the subject it is assumed (and sometimes proved) that increasing the number of finite elements will improve accuracy of the control. In applications, this may be difficult to achieve because of numerical problems. The main difficulty in computing the observer and simulating its work is the presence of high frequency eigenvalues in the finite-element model and poor numerical conditioning of some of the system matrices (e.g. poor observability properties) when the dimension of the approximating system increases. This work dealt with some of these difficulties.
Nonlinear Finite Element Analysis of Sandwich Composites.
1981-03-01
to the element midsurface z - z(x,y) at all points. An additional coordinate r is used to describe the distance away from the midsurface at any point...It is assumed that on the element level, the shell is shallow, so that z2 2 (56) ,y everywhere. The unit vector normal to the shell midsurface at a...relations above do not involve the orientation of the displaced midsurface normal, and, therefore, apply to arbitrarily large displacements and rotations
A simple finite element method for non-divergence form elliptic equation
Mu, Lin; Ye, Xiu
2017-03-01
Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.
Finite element analysis of the SDC barrel and endcap calorimeters
Guarino, V.; Hill, N.; Nasiakta, J.
1992-03-11
In designing the SCD barrel and endcap calorimeters, the inter-module connecting forces must be known in order to determine the required size and number of connecting links between modules, and in order to understand how individual modules will be affected by these forces when assembled to form a full barrel and endcap. The connecting forces were found by analyzing three-dimensional Finite Element Models of both the barrel and endcap. This paper is divided into two parts, the first part will describe in detail the results of the barrel analysis and the second part will describe the results obtained from the endcap analysis. A similar approach was used in constructing the models for both analysis.
Finite element simulation of mechanical properties of graphene sheets
NASA Astrophysics Data System (ADS)
Khandoker, N.; Islam, S.; Hiung, Y. S.
2017-06-01
Graphene is the material for the twenty first century applications. In this paper, the elastic properties of monolayer and double layer Graphene sheets, typically less than 10nm in size are investigated through linear finite element simulations. The effect of aspect ratio, sizes and chirality of the Graphene sheet on the Young’s modulus, Shear modulus and Poisson’s ratio are studied. By using structural mechanics approach combining atomistic and equivalent continuum techniques, the Young’s modulus, shear modulus and the Poisson ratio were found and they slightly increase with the aspect ratio but decrease with the size of the Graphene sheet. These simulated properties compliment the mechanical properties of Graphene found in literature.
A responsive finite element method to aid interactive geometric modeling.
Umetani, N; Takayama, K; Mitani, J; Igarashi, T
2011-01-01
Current computer-aided engineering systems use numerical-simulation methods mainly as offline verification tools to reject designs that don't satisfy the required constraints, rather than as tools to guide users toward better designs. However, integrating real-time finite element method (FEM) into interactive geometric modeling can provide user guidance. During interactive editing, real-time feedback from numerical simulation guides users toward an improved design without tedious trial-and-error iterations. Careful reuse of previous computation results, such as meshes and matrices, on the basis of speed and accuracy trade-offs, have helped produce fast FEM analysis during interactive editing. Several 2D example applications and informal user studies show this approach's effectiveness. Such tools could help nonexpert users design objects that satisfy physical constraints and help those users understand the underlying physical properties.
Application of physical parameter identification to finite element models
NASA Technical Reports Server (NTRS)
Bronowicki, Allen J.; Lukich, Michael S.; Kuritz, Steven P.
1986-01-01
A time domain technique for matching response predictions of a structural dynamic model to test measurements is developed. Significance is attached to prior estimates of physical model parameters and to experimental data. The Bayesian estimation procedure allows confidence levels in predicted physical and modal parameters to be obtained. Structural optimization procedures are employed to minimize an error functional with physical model parameters describing the finite element model as design variables. The number of complete FEM analyses are reduced using approximation concepts, including the recently developed convoluted Taylor series approach. The error function is represented in closed form by converting free decay test data to a time series model using Prony' method. The technique is demonstrated on simulated response of a simple truss structure.
Finite Element Modeling and Optimization of Mechanical Joining Technology
NASA Astrophysics Data System (ADS)
Chenot, Jean-Loup; Bouchard, Pierre-Olivier; Massoni, Elisabeth; Mocellin, Katia; Lasne, Patrice
2011-05-01
The main scientific ingredients are recalled for developing a general finite element code and model accurately large plastic deformation of metallic materials during joining processes. Multi material contact is treated using the classical master and slave approach. Rupture may occur in joining processes or even be imposed in self piercing riveting and it must be predicted to evaluate the ultimate strength of joins. Damage is introduced with a generalized uncoupled damage criterion, or by utilizing a coupled formulation with a Lemaître law. Several joining processes are briefly analyzed in term of specific scientific issues: riveting, self piercing riveting, clinching, crimping, hemming and screwing. It is shown that not only the joining process can be successfully simulated and optimized, but also the strength of the assembly can be predicted in tension and in shearing.
Finite element analysis of the SDC barrel and endcap calorimeters
Guarino, V.; Hill, N.; Nasiakta, J.
1992-03-11
In designing the SCD barrel and endcap calorimeters, the inter-module connecting forces must be known in order to determine the required size and number of connecting links between modules, and in order to understand how individual modules will be affected by these forces when assembled to form a full barrel and endcap. The connecting forces were found by analyzing three-dimensional Finite Element Models of both the barrel and endcap. This paper is divided into two parts, the first part will describe in detail the results of the barrel analysis and the second part will describe the results obtained from the endcap analysis. A similar approach was used in constructing the models for both analysis.
Numerical Analysis of a Finite Element/Volume Penalty Method
NASA Astrophysics Data System (ADS)
Maury, Bertrand
The penalty method makes it possible to incorporate a large class of constraints in general purpose Finite Element solvers like freeFEM++. We present here some contributions to the numerical analysis of this method. We propose an abstract framework for this approach, together with some general error estimates based on the discretization parameter ɛ and the space discretization parameter h. As this work is motivated by the possibility to handle constraints like rigid motion for fluid-particle flows, we shall pay a special attention to a model problem of this kind, where the constraint is prescribed over a subdomain. We show how the abstract estimate can be applied to this situation, in the case where a non-body-fitted mesh is used. In addition, we describe how this method provides an approximation of the Lagrange multiplier associated to the constraint.
Large deformation finite element analysis of undrained pile installation
NASA Astrophysics Data System (ADS)
Konkol, Jakub; Bałachowski, Lech
2016-03-01
In this paper, a numerical undrained analysis of pile jacking into the subsoil using Abaqus software suit has been presented. Two different approaches, including traditional Finite Element Method (FEM) and Arbitrary Lagrangian-Eulerian (ALE) formulation, were tested. In the first method, the soil was modelled as a two-phase medium and effective stress analysis was performed. In the second one (ALE), a single-phase medium was assumed and total stress analysis was carried out. The fitting between effective stress parameters and total stress parameters has been presented and both solutions have been compared. The results, discussion and verification of numerical analyzes have been introduced. Possible applications and limitations of large deformation modelling techniques have been explained.
Geometrical nonlinearity of 14-node brick finite element
NASA Astrophysics Data System (ADS)
Chandan, Swet; Chauhan, Alok P. S.
2017-01-01
The present work depicts the geometrical nonlinearity analysis for the finite element, PN5X1. Here, the general problem of elasticity is numerically solved using iteration method. The proposed element is passed through different tests in order to prove that it works not only for modeling sheet metal forming process but also for other large deformation problems.
An alternative to Guyan reduction of finite-element models
NASA Technical Reports Server (NTRS)
Lin, Jiguan Gene
1988-01-01
Structural modeling is a key part of structural system identification for large space structures. Finite-element structural models are commonly used in practice because of their general applicability and availability. The initial models generated by using a standard computer program such as NASTRAN, ANSYS, SUPERB, STARDYNE, STRUDL, etc., generally contain tens of thousands of degrees of freedom. The models must be reduced for purposes of identification. Not only does the magnitude of the identification effort grow exponentially as a function of the number of degrees of freedom, but numerical procedures may also break down because of accumulated round-off errors. Guyan reduction is usually applied after a static condensation. Misapplication of Guyan reduction can lead to serious modeling errors. It is quite unfortunate and disappointing, since the accuracy of the original detailed finite-element model one tries very hard to achieve is lost by the reduction. First, why and how Guyan reduction always causes loss of accuracy is examined. An alternative approach is then introduced. The alternative can be thought of as an improvement of Guyan reduction, the Rayleigh-Ritz method, and in particular the recent algorithm of Wilson, Yuan, and Dickens. Unlike Guyan reduction, the use of the alternative does not need any special insight, experience, or skill for partitioning the structural degrees of freedom. In addition to model condensation, this alternative approach can also be used for predicting analytically, quickly, and economically, what are those structural modes that are excitable by a force actuator at a given trial location. That is, in the excitation of the structural modes for identification, it can be used for guiding the placement of the force actuators.
An alternative to Guyan reduction of finite-element models
NASA Technical Reports Server (NTRS)
Lin, Jiguan Gene
1988-01-01
Structural modeling is a key part of structural system identification for large space structures. Finite-element structural models are commonly used in practice because of their general applicability and availability. The initial models generated by using a standard computer program such as NASTRAN, ANSYS, SUPERB, STARDYNE, STRUDL, etc., generally contain tens of thousands of degrees of freedom. The models must be reduced for purposes of identification. Not only does the magnitude of the identification effort grow exponentially as a function of the number of degrees of freedom, but numerical procedures may also break down because of accumulated round-off errors. Guyan reduction is usually applied after a static condensation. Misapplication of Guyan reduction can lead to serious modeling errors. It is quite unfortunate and disappointing, since the accuracy of the original detailed finite-element model one tries very hard to achieve is lost by the reduction. First, why and how Guyan reduction always causes loss of accuracy is examined. An alternative approach is then introduced. The alternative can be thought of as an improvement of Guyan reduction, the Rayleigh-Ritz method, and in particular the recent algorithm of Wilson, Yuan, and Dickens. Unlike Guyan reduction, the use of the alternative does not need any special insight, experience, or skill for partitioning the structural degrees of freedom. In addition to model condensation, this alternative approach can also be used for predicting analytically, quickly, and economically, what are those structural modes that are excitable by a force actuator at a given trial location. That is, in the excitation of the structural modes for identification, it can be used for guiding the placement of the force actuators.
Finite Element Model Development For Aircraft Fuselage Structures
NASA Technical Reports Server (NTRS)
Buehrle, Ralph D.; Fleming, Gary A.; Pappa, Richard S.; Grosveld, Ferdinand W.
2000-01-01
The ability to extend the valid frequency range for finite element based structural dynamic predictions using detailed models of the structural components and attachment interfaces is examined for several stiffened aircraft fuselage structures. This extended dynamic prediction capability is needed for the integration of mid-frequency noise control technology. Beam, plate and solid element models of the stiffener components are evaluated. Attachment models between the stiffener and panel skin range from a line along the rivets of the physical structure to a constraint over the entire contact surface. The finite element models are validated using experimental modal analysis results.
Preconditioned CG-solvers and finite element grids
Bauer, R.; Selberherr, S.
1994-12-31
To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.
Radiosity algorithms using higher order finite element methods
Troutman, R.; Max, N.
1993-08-01
Many of the current radiosity algorithms create a piecewise constant approximation to the actual radiosity. Through interpolation and extrapolation, a continuous solution is obtained. An accurate solution is found by increasing the number of patches which describe the scene. This has the effect of increasing the computation time as well as the memory requirements. By using techniques found in the finite element method, we can incorporate an interpolation function directly into our form factor computation. We can then use less elements to achieve a more accurate solution. Two algorithms, derived from the finite element method, are described and analyzed.
Finite element analysis of two disk rotor system
Dixit, Harsh Kumar
2016-05-06
A finite element model of simple horizontal rotor system is developed for evaluating its dynamic behaviour. The model is based on Timoshenko beam element and accounts for the effect of gyroscopic couple and other rotational forces. Present rotor system consists of single shaft which is supported by bearings at both ends and two disks are mounted at different locations. The natural frequencies, mode shapes and orbits of rotating system for a specific range of rotation speed are obtained by developing a MATLAB code for solving the finite element equations of rotary system. Consequently, Campbell diagram is plotted for finding a relationship between natural whirl frequencies and rotation of the rotor.
Finite element analysis of shear deformable laminated composite plates
Kam, T.Y.; Chang, R.R. )
1993-03-01
A shear deformable finite element is developed for the analysis of thick laminated composite plates. The finite element formulation is based on Mindlin's plate theory in which shear correction factors are derived from the exact expressions for orthotropic materials. The element is used to solve a variety of problems on deflection, stress distribution, natural frequency and buckling of laminated composite plates. The effects of material properties, plate aspect ratio, length-to-thickness ratio, number of layers and lamination angle on the mechanical behaviors of laminated composite plates are investigated. Optimal lamination arrangements of layers for laminated composite plates of particular applications are determined.
Time domain finite element analysis of multimode microwave applicators
Dibben, D.C.; Metaxas, R.
1996-05-01
Analysis of multimode applicators in the frequency domain via the finite element technique produces a set of very ill-conditioned equations. This paper outlines a time domain finite element method (TDFE) for analyzing three dimensional microwave applicators where this ill-conditioning is avoided. Edge elements are used in order to handle sharp metal edges and to avoid spurious solutions. Analysis in the time domain allows field distributions at a range of different frequencies to be obtained with a single calculation. Lumping is investigated as a means of reducing the time taken for the calculation. The reflection coefficient is also obtained.
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.
Adaptive grid finite element model of the tokamak scrapeoff layer
Kuprat, A.P.; Glasser, A.H.
1995-07-01
The authors discuss unstructured grids for application to transport in the tokamak edge SOL. They have developed a new metric with which to judge element elongation and resolution requirements. Using this method, the authors apply a standard moving finite element technique to advance the SOL equations while inserting/deleting dynamically nodes that violate an elongation criterion. In a tokamak plasma, this method achieves a more uniform accuracy, and results in highly stretched triangular finite elements, except near separatrix X-point where transport is more isotropic.
Finite element analysis of two disk rotor system
NASA Astrophysics Data System (ADS)
Dixit, Harsh Kumar
2016-05-01
A finite element model of simple horizontal rotor system is developed for evaluating its dynamic behaviour. The model is based on Timoshenko beam element and accounts for the effect of gyroscopic couple and other rotational forces. Present rotor system consists of single shaft which is supported by bearings at both ends and two disks are mounted at different locations. The natural frequencies, mode shapes and orbits of rotating system for a specific range of rotation speed are obtained by developing a MATLAB code for solving the finite element equations of rotary system. Consequently, Campbell diagram is plotted for finding a relationship between natural whirl frequencies and rotation of the rotor.
A finite element method to study multimaterial wind towers
NASA Astrophysics Data System (ADS)
Pascoal-Faria, P.; Dias, C.; Oliveira, M.; Alves, N.
2017-07-01
Wind towers are used to produce electrical energy from the wind. A significant number of towers is manufactured using tubular separately steel or concrete, having limitations such as maximum diameter and height imposed essentially by transportation limitations. Developed computational studies on structural design of towers have been mainly focused on a single material. This investigation aims to develop a finite element method able to study structural design of wind towers combining different materials. The finite element model combines solid and shell elements encompassing different geometries. Several case studies are considered to validate the proposed method and accurate results are obtained.
Numerical Differentiation for Adaptively Refined Finite Element Meshes
NASA Technical Reports Server (NTRS)
Borgioli, Andrea; Cwik, Tom
1998-01-01
Postprocessing of point-wise data is a fundamental process in many fields of research. Numerical differentiation is a key operation in computational electromagnetics. In the case of data obtained from a finite element method with automatic mesh refinement much work needs still to be done. This paper addresses some issues in differentiating data obtained from a finite element electromagnetic code with adaptive mesh refinement, and it proposes a methodology for deriving the electric field given the magnetic field on a mesh of linear triangular elements. The procedure itself is nevertheless more general and might be extended for numerically differentiating any point-wise solution based on triangular meshes.
Footbridge between finite volumes and finite elements with applications to CFD
NASA Astrophysics Data System (ADS)
Pascal, Frédéric; Ghidaglia, Jean-Michel
2001-12-01
The aim of this paper is to introduce a new algorithm for the discretization of second-order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier-Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided. Copyright
Design and finite element analysis of oval man way
Hari, Y.; Gryder, B.
1996-12-01
This paper presents the design of an oval man way in the side wall of a cylindrical pressure vessel. ASME Code Section 8 is used to obtain the design parameters of the oval man way, man way cover and bolts. The code calculations require some assumptions which may not be valid. A typical design example is taken. STAAD III finite element code with plate elements is used to model the oval man way, man way cover and bolts. The stresses calculated using ASME Code Section 8 and other analytical formulas for plate and shells are compared with the stresses obtained by Finite Element Modeling. This paper gives the designer of oval man way the ability to perform a finite element analysis and compare it with the analytical calculations and assumptions made. This gives added confidence to the designer as to the validity of his calculations and assumptions.
A finite element simulation scheme for biological muscular hydrostats.
Liang, Y; McMeeking, R M; Evans, A G
2006-09-07
An explicit finite element scheme is developed for biological muscular hydrostats such as squid tentacles, octopus arms and elephant trunks. The scheme is implemented by embedding muscle fibers in finite elements. In any given element, the fiber orientation can be assigned arbitrarily and multiple muscle directions can be simulated. The mechanical stress in each muscle fiber is the sum of active and passive parts. The active stress is taken to be a function of activation state, muscle fiber shortening velocity and fiber strain; while the passive stress depends only on the strain. This scheme is tested by simulating extension of a squid tentacle during prey capture; our numerical predictions are in close correspondence with existing experimental results. It is shown that the present finite element scheme can successfully simulate more complex behaviors such as torsion of a squid tentacle and the bending behavior of octopus arms or elephant trunks.
Finite element analysis for acoustic characteristics of a magnetostrictive transducer
NASA Astrophysics Data System (ADS)
Kim, Jaehwan; Jung, Eunmi
2005-12-01
This paper presents a finite element analysis for a magnetostrictive transducer by taking into account the nonlinear behavior of the magnetostrictive material and fluid interaction. A finite element formulation is derived for the coupling of magnetostrictive and elastic materials based upon a separated magnetic and displacement field calculation and a curve fitting technique of material properties. The fluid and structure coupled problem is taken into account based upon pressure and velocity potential fields formulation. Infinite wave envelope elements are introduced at an artificial boundary to deal with the infinite fluid domain. A finite element code for the analysis of a magnetostrictive transducer is developed. A magnetostrictive tonpilz transducer is taken as an example and verification for the developed program is made by comparing with a commercial code. The acoustic characteristics of the magnetostrictive tonpilz transducer are calculated in terms of radiation pattern and transmitted current response.
Solution Techniques in Finite Element Analysis.
1983-05-01
7. we show a plane strain rubber block subjected to large deforma- tion. We employ a 4-node element and a Mooney - Rivlin material as described in...0 Rubber Block U: 0.30 Figure 7. Large Deformation Analysis of the R ubber Block with Mooney - Rivlin Material Model. GEOMETRY node iE 10 4 -0.3 1.0 1
Guo, Hongqiang; Shah, Mitul; Spilker, Robert L.
2014-01-01
The study of biphasic soft tissues contact is fundamental to understanding the biomechanical behavior of human diarthrodial joints. However, to date, few biphasic finite element contact analysis for 3D physiological geometries under finite deformation has been developed. The objective of this paper is to develop a hyperelastic biphasic contact implementation for finite deformation and sliding problem. An augmented Lagrangian method was used to enforce the continuity of contact traction and fluid pressure across the contact interface. The finite element implementation was based on a general purpose software, COMSOL Multiphysics. The accuracy of the implementation is verified using example problems, for which solutions are available by alternative analyses. The implementation was proven to be robust and able to handle finite deformation and sliding. PMID:24496915
Taylor, Z A; Cheng, M; Ourselin, S
2008-05-01
The use of biomechanical modelling, especially in conjunction with finite element analysis, has become common in many areas of medical image analysis and surgical simulation. Clinical employment of such techniques is hindered by conflicting requirements for high fidelity in the modelling approach, and fast solution speeds. We report the development of techniques for high-speed nonlinear finite element analysis for surgical simulation. We use a fully nonlinear total Lagrangian explicit finite element formulation which offers significant computational advantages for soft tissue simulation. However, the key contribution of the work is the presentation of a fast graphics processing unit (GPU) solution scheme for the finite element equations. To the best of our knowledge, this represents the first GPU implementation of a nonlinear finite element solver. We show that the present explicit finite element scheme is well suited to solution via highly parallel graphics hardware, and that even a midrange GPU allows significant solution speed gains (up to 16.8 x) compared with equivalent CPU implementations. For the models tested the scheme allows real-time solution of models with up to 16,000 tetrahedral elements. The use of GPUs for such purposes offers a cost-effective high-performance alternative to expensive multi-CPU machines, and may have important applications in medical image analysis and surgical simulation.
A software framework for solving bioelectrical field problems based on finite elements.
Sachse, F B; Cole, M J; Stinstra, J G
2006-01-01
Computational modeling and simulation can provide important insights into the electrical and electrophysiological properties of cells, tissues, and organs. Commonly, the modeling is based on Maxwell's and Poisson's equations for electromagnetic and electric fields, respectively, and numerical techniques are applied for field calculation such as the finite element and finite differences methods. Focus of this work are finite element methods, which are based on an element-wise discretization of the spatial domain. These methods can be classified on the element's geometry, e.g. triangles, tetrahedrons and hexahedrons, and the underlying interpolation functions, e.g. polynomials of various order. Aim of this work is to describe finite element-based approaches and their application to extend the problem-solving environment SCIRun/BioPSE. Finite elements of various types were integrated and methods for interpolation and integration were implemented. General methods for creation of finite element system matrices and boundary conditions were incorporated. The extension provides flexible means for geometric modeling, physical simulation, and visualization with particular application in solving bioelectric field problems.
Adaptive implicit-explicit finite element algorithms for fluid mechanics problems
NASA Technical Reports Server (NTRS)
Tezduyar, T. E.; Liou, J.
1988-01-01
The adaptive implicit-explicit (AIE) approach is presented for the finite-element solution of various problems in computational fluid mechanics. In the AIE approach, the elements are dynamically (adaptively) arranged into differently treated groups. The differences in treatment could be based on considerations such as the cost efficiency, the type of spatial or temporal discretization employed, the choice of field equations, etc. Several numerical tests are performed to demonstrate that this approach can achieve substantial savings in CPU time and memory.
Adaptive implicit-explicit finite element algorithms for fluid mechanics problems
NASA Technical Reports Server (NTRS)
Tezduyar, T. E.; Liou, J.
1988-01-01
The adaptive implicit-explicit (AIE) approach is presented for the finite-element solution of various problems in computational fluid mechanics. In the AIE approach, the elements are dynamically (adaptively) arranged into differently treated groups. The differences in treatment could be based on considerations such as the cost efficiency, the type of spatial or temporal discretization employed, the choice of field equations, etc. Several numerical tests are performed to demonstrate that this approach can achieve substantial savings in CPU time and memory.
Finite element analysis of partly wrinkled reinforced prestressed membranes
NASA Astrophysics Data System (ADS)
Gil, Antonio J.; Bonet, Javier
2007-08-01
Wrinkling is a well known phenomenon experimented by tension membranes in Civil Engineering applications. This paper will present an efficient numerical technique for the computational simulation of such wrinkles in a prestressed membrane. In particular, the relaxed energy approach (Pipkin in IMA J Appl Math 36:85-99, 1986) is particularized for prestressed membranes (Gil in Textile composites and inflatable structures, CIMNE, 2003) undergoing moderate strains. Wrinkling conditions in terms of the Euler-Lagrange finite deformation tensor along principal directions will be obtained. This will provide a framework to describe properly the initial instant when wrinkles start to be encountered in a prestressed Saint Venant-Kirchhoff hyperelastic membrane. Subsequently, a modified Helmholtz’s free energy functional will be introduced with the purpose of describing the modified constitutive behaviour of the continuum after the onset of wrinkling. Consistent derivations of the stress tensor as well as the constitutive tensor will de depicted. The results will be particularized for membranes and cables in a Finite Element discretization basis. Some numerical examples will prove the accuracy and robustness of the described algorithm.
New triangular and quadrilateral plate-bending finite elements
NASA Technical Reports Server (NTRS)
Narayanaswami, R.
1974-01-01
A nonconforming plate-bending finite element of triangular shape and associated quadrilateral elements are developed. The transverse displacement is approximated within the element by a quintic polynomial. The formulation takes into account the effects of transverse shear deformation. Results of the static and dynamic analysis of a square plate, with edges simply supported or clamped, are compared with exact solutions. Good accuracy is obtained in all calculations.
Variational formulation of high performance finite elements: Parametrized variational principles
NASA Technical Reports Server (NTRS)
Felippa, Carlos A.; Militello, Carmello
1991-01-01
High performance elements are simple finite elements constructed to deliver engineering accuracy with coarse arbitrary grids. This is part of a series on the variational basis of high-performance elements, with emphasis on those constructed with the free formulation (FF) and assumed natural strain (ANS) methods. Parametrized variational principles that provide a foundation for the FF and ANS methods, as well as for a combination of both are presented.
Effective Finite Elements for Shell Analysis.
1984-02-20
important mode of deformation , and when an element is not capable of representing inextensional bending, parasitic membrane energy is generated in many modes...of deformation . In the same manner that parasitic shear causes shear locking, this spurious membrane energy causes membrane locking. Membrane locking...dominant mode of deformation . (cont.) 20. OISTRIBUTION/AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION UNCLASSIFIEO/UNLIMITEO X SAME AS
The Mathematics of Finite Elements and Applications
1993-04-30
suitable geometrical mapping between the parametric u,v-plane and the physical xy- plane. In the u,v-plane the geometry of the elements is linear. In...the plate. For thin plates there may be a boundary layer, the existence and structure of which depends on the boundary conditions, the plate geometry ...exhibits a boundary layer except for very special data or plate geometry . The bending moment tensor and shear force vector have more pronounced boundary
Finite element analysis and performance evaluation of synthetic jet actuators
NASA Astrophysics Data System (ADS)
Ro, Jeng-Jong; Wu, K. C.
2002-11-01
The primary objective of active flow control research is to develop a cost-effective technology that has the potential for revolutionary advances in aerodynamic performance and maneuvering compared to conventional approaches. The development of such systems have many implications for aerospace vehicles including: reducing mechanical complexity and hydraulic failure, reducing noise and weight, lowering energy and fuel consumption, lowering downtime and maintenance, enhancing maneuvering and agility with enhanced aerodynamic performance and safety. Interest in active flow control for aerospace applications has stimulated the recent development of innovative actuator designs that create localized disturbances in a flowfield. A novel class of devices, known as synthetic jet actuator, has been demonstrated to exhibit promising flow control capabilities including separation control and thrust vectoring. The basic components of a synthetic jet actuator are made of cavity and oscillating materials. The synthetic jet actuator developed at NASA LaRC has a small housing in which a cylindrical cavity is enclosed by two metal diaphragms, 50 mm in diameter, placed opposite each other. A circular piezoelectric wafer is attached to the center of the outside face of each metal diaphragm. The pair of piezoelectric metal diaphragms is operated with a 180° phase differential at the same sinusoidal voltage and frequency. With actuation, a synthetic jet issues from a 35.5mm long by 0.5mm wide slot on the top of the device. In this study, a finite element model of synthetic jet actuator developed at NASA LaRC is investigated. The developed finite element model can be utilized to design and determine the performance of synthetic jet actuator. The analysis includes the FE model of circular plate, FE model of piezoelectric actuator/circular plate, piezoelectric (electrical field)/circular plate (structural field)/cavity (flow field) coupled system and experimental validation. The phase
Stabilized plane and axisymmetric Lobatto finite element models
NASA Astrophysics Data System (ADS)
Hu, Y. C.; Sze, K. Y.; Zhou, Y. X.
2015-11-01
High order elements are renowned for their high accuracy and convergence. Among them, Lobatto spectral finite elements are commonly used in explicit dynamic analyses as their mass matrices when evaluated by the Lobatto integration rule are diagonal. While there are numerous advanced first and second order elements, advanced high order elements are rarely seen. In this paper, generic stabilization schemes are devised for the reduced integrated plane and axisymmetric elements. Static and explicit dynamic tests are considered for evaluating the relatively merits of the stabilized and conventional elements. The displacement errors of the stabilized elements are less than those of the conventional Lobatto elements. When the material is nearly incompressible, the stabilized elements are also more accurate in terms of the energy error norm. This advantage is of practical importance for bio-tissue and hydrated soil analyses.
A simple triangular finite element for nonlinear thin shells: statics, dynamics and anisotropy
NASA Astrophysics Data System (ADS)
Viebahn, Nils; Pimenta, Paulo M.; Schröder, Jörg
2016-11-01
This work presents a simple finite element implementation of a geometrically exact and fully nonlinear Kirchhoff-Love shell model. Thus, the kinematics are based on a deformation gradient written in terms of the first- and second-order derivatives of the displacements. The resulting finite element formulation provides C^1 -continuity using a penalty approach, which penalizes the kinking at the edges of neighboring elements. This approach enables the application of well-known C^0 -continuous interpolations for the displacements, which leads to a simple finite element formulation, where the only unknowns are the nodal displacements. On the basis of polyconvex strain energy functions, the numerical framework for the simulation of isotropic and anisotropic thin shells is presented. A consistent plane stress condition is incorporated at the constitutive level of the model. A triangular finite element, with a quadratic interpolation for the displacements and a one-point integration for the enforcement of the C^1 -continuity at the element interfaces leads to a robust shell element. Due to the simple nature of the element, even complex geometries can be meshed easily, which include folded and branched shells. The reliability and flexibility of the element formulation is shown in a couple of numerical examples, including also time dependent boundary value problems. A plane reference configuration is assumed for the shell mid-surface, but initially curved shells can be accomplished if one regards the initial configuration as a stress-free deformed state from the plane position, as done in previous works.
A simple triangular finite element for nonlinear thin shells: statics, dynamics and anisotropy
NASA Astrophysics Data System (ADS)
Viebahn, Nils; Pimenta, Paulo M.; Schröder, Jörg
2017-02-01
This work presents a simple finite element implementation of a geometrically exact and fully nonlinear Kirchhoff-Love shell model. Thus, the kinematics are based on a deformation gradient written in terms of the first- and second-order derivatives of the displacements. The resulting finite element formulation provides C^1-continuity using a penalty approach, which penalizes the kinking at the edges of neighboring elements. This approach enables the application of well-known C^0-continuous interpolations for the displacements, which leads to a simple finite element formulation, where the only unknowns are the nodal displacements. On the basis of polyconvex strain energy functions, the numerical framework for the simulation of isotropic and anisotropic thin shells is presented. A consistent plane stress condition is incorporated at the constitutive level of the model. A triangular finite element, with a quadratic interpolation for the displacements and a one-point integration for the enforcement of the C^1-continuity at the element interfaces leads to a robust shell element. Due to the simple nature of the element, even complex geometries can be meshed easily, which include folded and branched shells. The reliability and flexibility of the element formulation is shown in a couple of numerical examples, including also time dependent boundary value problems. A plane reference configuration is assumed for the shell mid-surface, but initially curved shells can be accomplished if one regards the initial configuration as a stress-free deformed state from the plane position, as done in previous works.
The Constraint Method for Solid Finite Elements.
1982-11-30
Sciences 13 . NUMBER S Bolling Air Force Base, DC 20332 - -Jfi’ 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) IS. SECURITY CVASS...1- 4)Q2 (n) (’+C) Higher degree elements add edge modes, face modes and internal modes. More details are given in [12, 13 ]. triangular prism A...23) N2 (L2 , L3)(l-z) edge u (31) N2 (L3 ’ L)(1-z) nodes s u s (45). N2 (L1, L2 )z uso (56) N2 (L2, L3 )z K - 13 - nodal variable shape function u
NAFEMS Finite Element Benchmarks for MDG Code Verification
Greer, R; Ferencz, R M
2004-02-24
NAFEMS was originally founded at the United Kingdom's National Engineering Laboratory as the National Agency for Finite Element Methods and Standards. It was subsequently privatized as the not-for-profit organization NAFEMS, Ltd., but retains its mission ''To promote the safe and reliable use of finite element and related technology''. That mission has been pursued in part by sponsoring a series of studies that published benchmarked deemed suitable to assess the basic accuracy of engineering simulation tools. The early studies focused on FEA for linear solid and structural mechanics and then extended to nonlinear solid mechanics, eventually including contact. These benchmarks are complemented by educational materials concerning analysis technologies and approaches. More recently NAFEMS is expanding to consider thermal-fluid problems. Further information is available at www.nafems.org. Essentially all major commercial firms selling FEA for solid mechanics are members of NAFEMS and it seemed clear that Methods Development Group should leverage from this information resource, too. In 2002, W Program ASCI funding purchased a three-year membership in NAFEMS. In the summer of 2003 the first author hosted a summer graduate student to begin modeling some of the benchmark problems. We concentrated on NIKE3D, as the benchmarks are most typically problems most naturally run with implicit FEA. Also, this was viewed as a natural path to generate verification problems that could be subsequently incorporated into the Diablo code's test suite. This report documents and archives our initial efforts. The intent is that this will be a ''living document'' that can be expanded as further benchmarks are generated, run, interpreted and documented. To this end each benchmark, or related grouping, is localized in its own section with its own pagination. Authorship (test engineers) will be listed section by section.
Finite Element Method for Capturing Ultra-relativistic Shocks
NASA Technical Reports Server (NTRS)
Richardson, G. A.; Chung, T. J.
2003-01-01
While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.
Hybrid finite element-finite difference method for thermal analysis of blood vessels.
Blanchard, C H; Gutierrez, G; White, J A; Roemer, R B
2000-01-01
A hybrid finite-difference/finite-element technique for the thermal analysis of blood vessels embedded in perfused tissue has been developed and evaluated. This method provides efficient and accurate solutions to the conjugated heat transfer problem of convection by blood coupled to conduction in the tissue. The technique uses a previously developed 3D automatic meshing method for creating a finite element mesh in the tissue surrounding the vessels, coupled iteratively with a 1-D marching finite difference method for the interior of the vessels. This hybrid technique retains the flexibility and ease of automated finite-element meshing techniques for modelling the complex geometry of blood vessels and irregularly shaped tissues, and speeds the solution time by using a simple finite-difference method to calculate the bulk mean temperatures within all blood vessels. The use of the 1D finite-difference technique in the blood vessels also eliminates the large computer memory requirements needed to accurately solve large vessel network problems when fine FE meshes are used in the interior of vessels. The accuracy of the hybrid technique has been verified against previously verified numerical solutions. In summary, the hybrid technique combines the accuracy and flexibility found in automated finite-element techniques, with the speed and reduction of computational memory requirements associated with the 1D finite-difference technique, something which has not been done before. This method, thus, has the potential to provide accurate, flexible and relatively fast solutions for the thermal analysis of coupled perfusion/blood vessel problems, and large vessel network problems.
Optimal mapping of irregular finite element domains to parallel processors
NASA Technical Reports Server (NTRS)
Flower, J.; Otto, S.; Salama, M.
1987-01-01
Mapping the solution domain of n-finite elements into N-subdomains that may be processed in parallel by N-processors is an optimal one if the subdomain decomposition results in a well-balanced workload distribution among the processors. The problem is discussed in the context of irregular finite element domains as an important aspect of the efficient utilization of the capabilities of emerging multiprocessor computers. Finding the optimal mapping is an intractable combinatorial optimization problem, for which a satisfactory approximate solution is obtained here by analogy to a method used in statistical mechanics for simulating the annealing process in solids. The simulated annealing analogy and algorithm are described, and numerical results are given for mapping an irregular two-dimensional finite element domain containing a singularity onto the Hypercube computer.
Finite element methods for nonlinear acoustics in fluids.
Walsh, Timothy Francis
2005-06-01
In this paper, weak formulations and finite element discretizations of the governing partial differential equations of three-dimensional nonlinear acoustics in absorbing fluids are presented. The fluid equations are considered in an Eulerian framework, rather than a displacement framework, since in the latter case the corresponding finite element formulations suffer from spurious modes and numerical instabilities. When taken with the governing partial differential equations of a solid body and the continuity conditions, a coupled formulation is derived. The change in solid/fluid interface conditions when going from a linear acoustic fluid to a nonlinear acoustic fluid is demonstrated. Finite element discretizations of the coupled problem are then derived, and verification examples are presented that demonstrate the correctness of the implementations. We demonstrate that the time step size necessary to resolve the wave decreases as steepening occurs. Finally, simulation results are presented on a resonating acoustic cavity, and a coupled elastic/acoustic system consisting of a fluid-filled spherical tank.
Finite element methods on supercomputers - The scatter-problem
NASA Technical Reports Server (NTRS)
Loehner, R.; Morgan, K.
1985-01-01
Certain problems arise in connection with the use of supercomputers for the implementation of finite-element methods. These problems are related to the desirability of utilizing the power of the supercomputer as fully as possible for the rapid execution of the required computations, taking into account the gain in speed possible with the aid of pipelining operations. For the finite-element method, the time-consuming operations may be divided into three categories. The first two present no problems, while the third type of operation can be a reason for the inefficient performance of finite-element programs. Two possibilities for overcoming certain difficulties are proposed, giving attention to a scatter-process.
An Object Oriented, Finite Element Framework for Linear Wave Equations
Koning, Joseph M.
2004-03-01
This dissertation documents an object oriented framework which can be used to solve any linear wave equation. The linear wave equations are expressed in the differential forms language. This differential forms expression allows a strict discrete interpretation of the system. The framework is implemented using the Galerkin Finite Element Method to define the discrete differential forms and operators. Finite element basis functions including standard scalar Nodal and vector Nedelec basis functions are used to implement the discrete differential forms resulting in a mixed finite element system. Discretizations of scalar and vector wave equations in the time and frequency domains will be demonstrated in both differential forms and vector calculi. This framework conserves energy, maintains physical continuity, is valid on unstructured grids, conditionally stable and second order accurate. Examples including linear electrodynamics, acoustics, elasticity and magnetohydrodynamics are demonstrated.