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.
Computationally efficient finite element evaluation of natural patellofemoral mechanics.
Fitzpatrick, Clare K; Baldwin, Mark A; Rullkoetter, Paul J
2010-12-01
Finite element methods have been applied to evaluate in vivo joint behavior, new devices, and surgical techniques but have typically been applied to a small or single subject cohort. Anatomic variability necessitates the use of many subject-specific models or probabilistic methods in order to adequately evaluate a device or procedure for a population. However, a fully deformable finite element model can be computationally expensive, prohibiting large multisubject or probabilistic analyses. The aim of this study was to develop a group of subject-specific models of the patellofemoral joint and evaluate trade-offs in analysis time and accuracy with fully deformable and rigid body articular cartilage representations. Finite element models of eight subjects were used to tune a pressure-overclosure relationship during a simulated deep flexion cycle. Patellofemoral kinematics and contact mechanics were evaluated and compared between a fully deformable and a rigid body analysis. Additional eight subjects were used to determine the validity of the rigid body pressure-overclosure relationship as a subject-independent parameter. There was good agreement in predicted kinematics and contact mechanics between deformable and rigid analyses for both the tuned and test groups. Root mean square differences in kinematics were less than 0.5 deg and 0.2 mm for both groups throughout flexion. Differences in contact area and peak and average contact pressures averaged 5.4%, 9.6%, and 3.8%, respectively, for the tuned group and 6.9%, 13.1%, and 6.4%, respectively, for the test group, with no significant differences between the two groups. There was a 95% reduction in computational time with the rigid body analysis as compared with the deformable analysis. The tuned pressure-overclosure relationship derived from the patellofemoral analysis was also applied to tibiofemoral (TF) articular cartilage in a group of eight subjects. Differences in contact area and peak and average contact
An Efficient Vector Finite Element Method for Nonlinear Electromagnetic Modeling
Fisher, A C; White, D A; Rodrigue, G H
2006-06-27
We have developed a mixed Vector Finite Element Method (VFEM) for Maxwell's equations with a nonlinear polarization term. The method allows for discretization of complicated geometries with arbitrary order representations of the B and E fields. In this paper we will describe the method and a series of optimizations that significantly reduce the computational cost. Additionally, a series of test simulations will be presented to validate the method. Finally, a nonlinear waveguide mode mixing example is presented and discussed.
Efficient finite element simulation of slot spirals, slot radomes and microwave structures
NASA Technical Reports Server (NTRS)
Gong, J.; Volakis, J. L.
1995-01-01
This progress report contains the following two documents: (1) 'Efficient Finite Element Simulation of Slot Antennas using Prismatic Elements' - A hybrid finite element-boundary integral (FE-BI) simulation technique is discussed to treat narrow slot antennas etched on a planar platform. Specifically, the prismatic elements are used to reduce the redundant sampling rates and ease the mesh generation process. Numerical results for an antenna slot and frequency selective surfaces are presented to demonstrate the validity and capability of the technique; and (2) 'Application and Design Guidelines of the PML Absorber for Finite Element Simulations of Microwave Packages' - The recently introduced perfectly matched layer (PML) uniaxial absorber for frequency domain finite element simulations has several advantages. In this paper we present the application of PML for microwave circuit simulations along with design guidelines to obtain a desired level of absorption. Different feeding techniques are also investigated for improved accuracy.
Fuzzy logic to improve efficiency of finite element and finite difference schemes
Garcia, M.D.; Heger, A.S.
1994-05-01
This paper explores possible applications of logic in the areas of finite element and finite difference methods applied to engineering design problems. The application of fuzzy logic to both front-end selection of computational options and within the numerical computation itself are proposed. Further, possible methods of overcoming these limitations through the application of methods are explored. Decision strategy is a fundamental limitation in performing finite element calculations, such as selecting the optimum coarseness of the grid, numerical integration algorithm, element type, implicit versus explicit schemes, and the like. This is particularly true of novice analysts who are confronted with a myriad of choices in performing a calculation. The advantage of having the myriad of options available to the analyst is, however, that it improves and optimizes the design process if the appropriate ones are selected. Unfortunately, the optimum choices are not always apparent and only through the process of elimination or prior extensive experience can the optimum choices or combination of choices be selected. The knowledge of expert analysts could be integrated into a fuzzy ``front-end`` rule-based package to optimize the design process. The use of logic to capture the heuristic and human knowledge for selecting optimum solution strategies sets the framework for these proposed strategies.
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.
A numerically efficient finite element hydroelastic analysis. Volume 1: Theory and results
NASA Technical Reports Server (NTRS)
Coppolino, R. N.
1976-01-01
Symmetric finite element matrix formulations for compressible and incompressible hydroelasticity are developed on the basis of Toupin's complementary formulation of classical mechanics. Results of implementation of the new technique in the NASTRAN structural analysis program are presented which demonstrate accuracy and efficiency.
An efficient finite element method for aircraft de-icing problems
NASA Technical Reports Server (NTRS)
Huang, J. R.; Keith, Theo G., Jr.; De Witt, Kenneth J.
1992-01-01
In this paper, a finite element formulation based on an assumed states method is proposed for the solution of heat conduction problems with phase change at a fixed temperature. Attention is directed toward reduction of computer cost through the use of an efficient formulation, solver and algorithm. The procedure is applied to the analysis of an electrothermally deiced aircraft surface.
MHOST: An efficient finite element program for inelastic analysis of solids and structures
NASA Technical Reports Server (NTRS)
Nakazawa, S.
1988-01-01
An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.
Efficient evaluation of the Coulomb force in the Gaussian and finite-element Coulomb method
NASA Astrophysics Data System (ADS)
Kurashige, Yuki; Nakajima, Takahito; Sato, Takeshi; Hirao, Kimihiko
2010-06-01
We propose an efficient method for evaluating the Coulomb force in the Gaussian and finite-element Coulomb (GFC) method, which is a linear-scaling approach for evaluating the Coulomb matrix and energy in large molecular systems. The efficient evaluation of the analytical gradient in the GFC is not straightforward as well as the evaluation of the energy because the SCF procedure with the Coulomb matrix does not give a variational solution for the Coulomb energy. Thus, an efficient approximate method is alternatively proposed, in which the Coulomb potential is expanded in the Gaussian and finite-element auxiliary functions as done in the GFC. To minimize the error in the gradient not just in the energy, the derived functions of the original auxiliary functions of the GFC are used additionally for the evaluation of the Coulomb gradient. In fact, the use of the derived functions significantly improves the accuracy of this approach. Although these additional auxiliary functions enlarge the size of the discretized Poisson equation and thereby increase the computational cost, it maintains the near linear scaling as the GFC and does not affects the overall efficiency of the GFC approach.
NASA Technical Reports Server (NTRS)
Muller, A.; Hughes, T. J. R.
1984-01-01
A weak formulation in structural analysis that provides well conditioned matrices suitable for iterative solutions is presented. A mixed formulation ensures the proper representation of the problem and the constitutive relations are added in a penalized form. The problem is solved by a double conjugate gradient algorithm combined with an element by element approximate factorization procedure. The double conjugate gradient strategy resembles Uzawa's variable-length type algorithms the main difference is the presence of quadratic terms in the mixed variables. In the case of shear deformable beams these terms ensure that the proper finite thickness solution is obtained.
Felice, Maria V.; Velichko, Alexander; Wilcox, Paul D.; Barden, Tim J.; Dunhill, Tony K.
2014-02-18
A hybrid model to simulate the ultrasonic array response from stress corrosion cracks is presented. These cracks are branched and difficult to detect so the model is required to enable optimization of an array design. An efficient frequency-domain finite element method is described and selected to simulate the ultrasonic scattering. Experimental validation results are presented, followed by an example of the simulated ultrasonic array response from a real stress corrosion crack whose geometry is obtained from an X-ray Computed Tomography image. A simulation-assisted array design methodology, which includes the model and use of real crack geometries, is proposed.
On the Relationship Between Tooth Shape and Masticatory Efficiency: A Finite Element Study.
Berthaume, Michael A
2016-05-01
Dental topography has successfully linked disparate tooth shapes to distinct dietary categories, but not to masticatory efficiency. Here, the relationship between four dental topographic metrics and brittle food item breakdown efficiency during compressive biting was investigated using a parametric finite element model of a bunodont molar. Food item breakdown efficiency was chosen to represent masticatory efficiency as it isolated tooth-food item interactions, where most other categories of masticatory efficiency include several aspects of the masticatory process. As relative food item size may affect the presence/absence of any relationship, four isometrically scaled, hemispherical, proxy food items were considered. Topographic metrics were uncorrelated to food item breakdown efficiency irrespective of relative food item size, and dental topographic metrics were largely uncorrelated to one another. The lack of a correlation between topographic metrics and food item breakdown efficiency is not unexpected as not all food items break down in the same manner (e.g., nuts are crushed, leaves are sheared), and only one food item shape was considered. In addition, food item breakdown efficiency describes tooth-food item interactions and requires location and shape specific information, which are absent from dental topographic metrics. This makes it unlikely any one efficiency metric will be correlated to all topographic metrics. These results emphasize the need to take into account how food items break down during biting, ingestion, and mastication when investigating the mechanical relationship between food item shape, size, mechanical properties, and breakdown, and tooth shape. PMID:26910570
On the Relationship Between Tooth Shape and Masticatory Efficiency: A Finite Element Study.
Berthaume, Michael A
2016-05-01
Dental topography has successfully linked disparate tooth shapes to distinct dietary categories, but not to masticatory efficiency. Here, the relationship between four dental topographic metrics and brittle food item breakdown efficiency during compressive biting was investigated using a parametric finite element model of a bunodont molar. Food item breakdown efficiency was chosen to represent masticatory efficiency as it isolated tooth-food item interactions, where most other categories of masticatory efficiency include several aspects of the masticatory process. As relative food item size may affect the presence/absence of any relationship, four isometrically scaled, hemispherical, proxy food items were considered. Topographic metrics were uncorrelated to food item breakdown efficiency irrespective of relative food item size, and dental topographic metrics were largely uncorrelated to one another. The lack of a correlation between topographic metrics and food item breakdown efficiency is not unexpected as not all food items break down in the same manner (e.g., nuts are crushed, leaves are sheared), and only one food item shape was considered. In addition, food item breakdown efficiency describes tooth-food item interactions and requires location and shape specific information, which are absent from dental topographic metrics. This makes it unlikely any one efficiency metric will be correlated to all topographic metrics. These results emphasize the need to take into account how food items break down during biting, ingestion, and mastication when investigating the mechanical relationship between food item shape, size, mechanical properties, and breakdown, and tooth shape.
NASA Astrophysics Data System (ADS)
Yasin, M. Yaqoob; Kapuria, S.
2014-01-01
In this work, we present a new efficient four-node finite element for shallow multilayered piezoelectric shells, considering layerwise mechanics and electromechanical coupling. The laminate mechanics is based on the zigzag theory that has only seven kinematic degrees of freedom per node. The normal deformation of the piezoelectric layers under the electric field is accounted for without introducing any additional deflection variables. A consistent quadratic variation of the electric potential across the piezoelectric layers with the provision of satisfying the equipotential condition of electroded surfaces is adopted. The performance of the new element is demonstrated for the static response under mechanical and electric potential loads, and for free vibration response of smart shells under different boundary conditions. The predictions are found to be very close to the three dimensional piezoelasticity solutions for hybrid shells made of not only single-material composite substrates, but also sandwich substrates with a soft core for which the equivalent single layer (ESL) theories perform very badly.
General purpose software for efficient uncertainty management of large finite element models
Patelli, Edoardo; Murat Panayirci, H.; Broggi, Matteo; Goller, Barbara; Beaurepaire, Pierre; Pradlwarter, Helmut J.; Schuëller, Gerhart I.
2012-01-01
The aim of this paper is to demonstrate that stochastic analyses can be performed on large and complex models within affordable costs. Stochastic analyses offer a much more realistic approach for analysis and design of components and systems although generally computationally demanding. Hence, resorting to efficient approaches and high performance computing is required in order to reduce the execution time. A general purpose software that provides an integration between deterministic solvers (i.e. finite element solvers), efficient algorithms for uncertainty management and high performance computing is presented. The software is intended for a wide range of applications, which includes optimization analysis, life-cycle management, reliability and risk analysis, fatigue and fractures simulation, robust design. The applicability of the proposed tools for practical applications is demonstrated by means of a number of case studies of industrial interest involving detailed models. PMID:22474398
NASA Technical Reports Server (NTRS)
Walston, W. H., Jr.
1986-01-01
The comparative computational efficiencies of the finite element (FEM), boundary element (BEM), and hybrid boundary element-finite element (HVFEM) analysis techniques are evaluated for representative bounded domain interior and unbounded domain exterior problems in elastostatics. Computational efficiency is carefully defined in this study as the computer time required to attain a specified level of solution accuracy. The study found the FEM superior to the BEM for the interior problem, while the reverse was true for the exterior problem. The hybrid analysis technique was found to be comparable or superior to both the FEM and BEM for both the interior and exterior problems.
NASA Astrophysics Data System (ADS)
May, Dave; Le Pourhiet, Laetitia; Brown, Jed
2014-05-01
Here I describe a numerical method suitable for studying 3D non-linear, large deformation processes associated with crustal and lithopspheric deformation. The method employs a combination of mixed finite elements for the flow problem, coupled to the Material-Point-Method for representing material state and history variables. This computational methodology is intended to simultaneously satisfy all of the geodynamic modelling requirements. Particular emphasis is given to the development of non-linear solvers and preconditioners which are performant, practical and highly scalable - thereby enabling high resolution 3D simulations to be performed using massively parallel computational hardware. We have made a number of fundamental design choices which result in a fast, highly scalable and robust Q2P1 finite element implementation which is suitable for solving a wide range of geodynamic applications. Specifically these choices include: (i) utilizing an inf-sup stable mixed finite element (with a mapped pressure space) which provides a reliable velocity and pressure solution; (ii) expressing the problem in defect correction form so that Newton-like methods can be exploited; (iii) making extensive use of matrix-free operators which both drastically reduces the memory requirements and improves the parallel scalability of the sparse matrix-vector product; (iv) deferring a wide range of choices associated with the solver configuration to run-time. The performance characteristics of our hybrid geometric multi-grid preconditioning strategy is presented. The robustness of the preconditioner with respect to the viscosity contrast and the topology of the viscosity field, together with the parallel scalability is demonstrated. We will highlight the benefits of using hybrid coarse grid hierarchies consisting of a combination of Galerkin, assembled and matrix-free operators. The merits of using aggressive coarsening strategies will also be discussed. Examples from 3D continental
A finite element beam-model for efficient simulation of large-scale porous structures.
Stauber, Martin; Huber, Martin; Van Lenthe, G Harry; Boyd, Steven K; Müller, Ralph
2004-02-01
This paper presents a new method for the generation of a beam finite element (FE) model from a three-dimensional (3D) data set acquired by micro-computed tomography (micro-CT). This method differs from classical modeling of trabecular bone because it models a specific sample only and differs from conventional solid hexahedron element-based FE approaches in its computational efficiency. The stress-strain curve, characterizing global mechanical properties of a porous structure, could be well predicted (R(2)=0.92). Furthermore, validation of the method was achieved by comparing local displacements of element nodes with the displacements directly measured by time-lapsed imaging methods of failure, and these measures were in good agreement. The presented model is a first step in modeling specific samples for efficient strength analysis by FE modeling. We believe that with upcoming high-resolution in-vivo imaging methods, this approach could lead to a novel and accurate tool in the risk assessment for osteoporotic fractures.
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
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.
NASA Astrophysics Data System (ADS)
Kapuria, S.; Yaqoob Yasin, M.
2013-05-01
In this work, we present an electromechanically coupled efficient layerwise finite element model for the static response of piezoelectric laminated composite and sandwich plates, considering the nonlinear behavior of piezoelectric materials under strong electric field. The nonlinear model is developed consistently using a variational principle, considering a rotationally invariant second order nonlinear constitutive relationship, and full electromechanical coupling. In the piezoelectric layer, the electric potential is approximated to have a quadratic variation across the thickness, as observed from exact three dimensional solutions, and the equipotential condition of electroded piezoelectric surfaces is modeled using the novel concept of an electric node. The results predicted by the nonlinear model compare very well with the experimental data available in the literature. The effect of the piezoelectric nonlinearity on the static response and deflection/stress control is studied for piezoelectric bimorph as well as hybrid laminated plates with isotropic, angle-ply composite and sandwich substrates. For high electric fields, the difference between the nonlinear and linear predictions is large, and cannot be neglected. The error in the prediction of the smeared counterpart of the present theory with the same number of primary displacement unknowns is also examined.
Development of a Computationally Efficient, High Fidelity, Finite Element Based Hall Thruster Model
NASA Technical Reports Server (NTRS)
Jacobson, David (Technical Monitor); Roy, Subrata
2004-01-01
This report documents the development of a two dimensional finite element based numerical model for efficient characterization of the Hall thruster plasma dynamics in the framework of multi-fluid model. Effect of the ionization and the recombination has been included in the present model. Based on the experimental data, a third order polynomial in electron temperature is used to calculate the ionization rate. The neutral dynamics is included only through the neutral continuity equation in the presence of a uniform neutral flow. The electrons are modeled as magnetized and hot, whereas ions are assumed magnetized and cold. The dynamics of Hall thruster is also investigated in the presence of plasma-wall interaction. The plasma-wall interaction is a function of wall potential, which in turn is determined by the secondary electron emission and sputtering yield. The effect of secondary electron emission and sputter yield has been considered simultaneously, Simulation results are interpreted in the light of experimental observations and available numerical solutions in the literature.
Validation of composite finite elements efficiently simulating elasticity of trabecular bone.
Schwen, Lars Ole; Wolfram, Uwe
2014-01-01
Patient-specific analyses of the mechanical properties of bones become increasingly important for the management of patients with osteoporosis. The potential of composite finite elements (CFEs), a novel FE technique, to assess the apparent stiffness of vertebral trabecular bone is investigated in this study. Segmented volumes of cylindrical specimens of trabecular bone are compared to measured volumes. Elasticity under uniaxial loading conditions is simulated; apparent stiffnesses are compared to experimentally determined values. Computational efficiency is assessed and recommendations for simulation parameters are given. Validating apparent uniaxial stiffnesses results in concordance correlation coefficients 0.69 ≤ r(c) ≤ 0.92 for resolutions finer than 168 μm, and an average error of 5.8% between experimental and numerical results at 24 μm resolution. As an application, the code was used to compute local, macroscopic stiffness tensors for the trabecular structure of a lumbar vertebra. The presented technique allows for computing stiffness using smooth FE meshes at resolutions that are well achievable in peripheral high resolution quantitative CT. Therefore, CFEs could be a valuable tool for the patient-specific assessment of bone stiffness.
NASA Technical Reports Server (NTRS)
Fuh, Jon-Shen; Panda, Brahmananda; Peters, David A.
1988-01-01
A finite element approach is presented for the modeling of rotorcraft undergoing elastic deformation in addition to large rigid body motion with respect to inertial space, with particular attention given to the coupling of the rotor and fuselage subsystems subject to large relative rotations. The component synthesis technique used here allows the coupling of rotors to the fuselage for different rotorcraft configurations. The formulation is general and applicable to any rotorcraft vibration, aeroelasticity, and dynamics problem.
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Peters, Jeanne M.
1989-01-01
A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems. The procedure is based on a novel hierarchical partitioning strategy in which the response of the unsymmetric and antisymmetric response vectors (modes), each obtained by using only a fraction of the degrees of freedom of the original finite element model. The three key elements of the procedure which result in high degree of concurrency throughout the solution process are: (1) mixed (or primitive variable) formulation with independent shape functions for the different fields; (2) operator splitting or restructuring of the discrete equations at each time step to delineate the symmetric and antisymmetric vectors constituting the response; and (3) two level iterative process for generating the response of the structure. An assessment is made of the effectiveness of the procedure on the CRAY X-MP/4 computers.
Li, Mao; Wittek, Adam; Miller, Karol
2014-01-01
Biomechanical modeling methods can be used to predict deformations for medical image registration and particularly, they are very effective for whole-body computed tomography (CT) image registration because differences between the source and target images caused by complex articulated motions and soft tissues deformations are very large. The biomechanics-based image registration method needs to deform the source images using the deformation field predicted by finite element models (FEMs). In practice, the global and local coordinate systems are used in finite element analysis. This involves the transformation of coordinates from the global coordinate system to the local coordinate system when calculating the global coordinates of image voxels for warping images. In this paper, we present an efficient numerical inverse isoparametric mapping algorithm to calculate the local coordinates of arbitrary points within the eight-noded hexahedral finite element. Verification of the algorithm for a nonparallelepiped hexahedral element confirms its accuracy, fast convergence, and efficiency. The algorithm's application in warping of the whole-body CT using the deformation field predicted by means of a biomechanical FEM confirms its reliability in the context of whole-body CT registration. PMID:24828796
Efficient Computation of Info-Gap Robustness for Finite Element Models
Stull, Christopher J.; Hemez, Francois M.; Williams, Brian J.
2012-07-05
A recent research effort at LANL proposed info-gap decision theory as a framework by which to measure the predictive maturity of numerical models. Info-gap theory explores the trade-offs between accuracy, that is, the extent to which predictions reproduce the physical measurements, and robustness, that is, the extent to which predictions are insensitive to modeling assumptions. Both accuracy and robustness are necessary to demonstrate predictive maturity. However, conducting an info-gap analysis can present a formidable challenge, from the standpoint of the required computational resources. This is because a robustness function requires the resolution of multiple optimization problems. This report offers an alternative, adjoint methodology to assess the info-gap robustness of Ax = b-like numerical models solved for a solution x. Two situations that can arise in structural analysis and design are briefly described and contextualized within the info-gap decision theory framework. The treatments of the info-gap problems, using the adjoint methodology are outlined in detail, and the latter problem is solved for four separate finite element models. As compared to statistical sampling, the proposed methodology offers highly accurate approximations of info-gap robustness functions for the finite element models considered in the report, at a small fraction of the computational cost. It is noted that this report considers only linear systems; a natural follow-on study would extend the methodologies described herein to include nonlinear systems.
2006-03-08
MAPVAR-KD is designed to transfer solution results from one finite element mesh to another. MAPVAR-KD draws heavily from the structure and coding of MERLIN II, but it employs a new finite element data base, EXODUS II, and offers enhanced speed and new capabilities not available in MERLIN II. In keeping with the MERLIN II documentation, the computational algorithms used in MAPVAR-KD are described. User instructions are presented. Example problems are included to demonstrate the operationmore » of the code and the effects of various input options. MAPVAR-KD is a modification of MAPVAR in which the search algorithm was replaced by a kd-tree-based search for better performance on large problems.« less
Sjaardema, G.; Wellman, G.; Gartling, D.
2006-03-08
MAPVAR-KD is designed to transfer solution results from one finite element mesh to another. MAPVAR-KD draws heavily from the structure and coding of MERLIN II, but it employs a new finite element data base, EXODUS II, and offers enhanced speed and new capabilities not available in MERLIN II. In keeping with the MERLIN II documentation, the computational algorithms used in MAPVAR-KD are described. User instructions are presented. Example problems are included to demonstrate the operation of the code and the effects of various input options. MAPVAR-KD is a modification of MAPVAR in which the search algorithm was replaced by a kd-tree-based search for better performance on large problems.
Forsythe, C.; Smith, M.; Sjaardema, G.
2005-06-26
Exotxt is an analysis code that reads finite element results data stored in an exodusII file and generates a file in a structured text format. The text file can be edited or modified via a number of text formatting tools. Exotxt is used by analysis to translate data from the binary exodusII format into a structured text format which can then be edited or modified and then either translated back to exodusII format or to another format.
2005-06-26
Exotxt is an analysis code that reads finite element results data stored in an exodusII file and generates a file in a structured text format. The text file can be edited or modified via a number of text formatting tools. Exotxt is used by analysis to translate data from the binary exodusII format into a structured text format which can then be edited or modified and then either translated back to exodusII format or tomore » another format.« less
Sjaardema, G.; Forsythe, C.
2005-05-07
CONEX is a code for joining sequentially in time multiple exodusll database files which all represent the same base mesh topology and geometry. It is used to create a single results or restart file from multiple results or restart files which typically arise as the result of multiple restarted analyses. CONEX is used to postprocess the results from a series of finite element analyses. It can join sequentially the data from multiple results databases into a single database which makes it easier to postprocess the results data.
2005-05-07
CONEX is a code for joining sequentially in time multiple exodusll database files which all represent the same base mesh topology and geometry. It is used to create a single results or restart file from multiple results or restart files which typically arise as the result of multiple restarted analyses. CONEX is used to postprocess the results from a series of finite element analyses. It can join sequentially the data from multiple results databases intomore » a single database which makes it easier to postprocess the results data.« less
Dynamic finite-element model for efficient modelling of electric currents in electroporated tissue
Langus, J.; Kranjc, M.; Kos, B.; Šuštar, T.; Miklavčič, D.
2016-01-01
In silico experiments (numerical simulations) are a valuable tool for non-invasive research of the influences of tissue properties, electrode placement and electric pulse delivery scenarios in the process of electroporation. The work described in this article was aimed at introducing time dependent effects into a finite element model developed specifically for electroporation. Reference measurements were made ex vivo on beef liver samples and experimental data were used both as an initial condition for simulation (applied pulse voltage) and as a reference value for numerical model calibration (measured pulse current). The developed numerical model is able to predict the time evolution of an electric pulse current within a 5% error over a broad range of applied pulse voltages, pulse durations and pulse repetition frequencies. Given the good agreement of the current flowing between the electrodes, we are confident that the results of our numerical model can be used both for detailed in silico research of electroporation mechanisms (giving researchers insight into time domain effects) and better treatment planning algorithms, which predict the outcome of treatment based on both spatial and temporal distributions of applied electric pulses. PMID:27211822
Dynamic finite-element model for efficient modelling of electric currents in electroporated tissue.
Langus, J; Kranjc, M; Kos, B; Šuštar, T; Miklavčič, D
2016-01-01
In silico experiments (numerical simulations) are a valuable tool for non-invasive research of the influences of tissue properties, electrode placement and electric pulse delivery scenarios in the process of electroporation. The work described in this article was aimed at introducing time dependent effects into a finite element model developed specifically for electroporation. Reference measurements were made ex vivo on beef liver samples and experimental data were used both as an initial condition for simulation (applied pulse voltage) and as a reference value for numerical model calibration (measured pulse current). The developed numerical model is able to predict the time evolution of an electric pulse current within a 5% error over a broad range of applied pulse voltages, pulse durations and pulse repetition frequencies. Given the good agreement of the current flowing between the electrodes, we are confident that the results of our numerical model can be used both for detailed in silico research of electroporation mechanisms (giving researchers insight into time domain effects) and better treatment planning algorithms, which predict the outcome of treatment based on both spatial and temporal distributions of applied electric pulses. PMID:27211822
Dynamic finite-element model for efficient modelling of electric currents in electroporated tissue
NASA Astrophysics Data System (ADS)
Langus, J.; Kranjc, M.; Kos, B.; Šuštar, T.; Miklavčič, D.
2016-05-01
In silico experiments (numerical simulations) are a valuable tool for non-invasive research of the influences of tissue properties, electrode placement and electric pulse delivery scenarios in the process of electroporation. The work described in this article was aimed at introducing time dependent effects into a finite element model developed specifically for electroporation. Reference measurements were made ex vivo on beef liver samples and experimental data were used both as an initial condition for simulation (applied pulse voltage) and as a reference value for numerical model calibration (measured pulse current). The developed numerical model is able to predict the time evolution of an electric pulse current within a 5% error over a broad range of applied pulse voltages, pulse durations and pulse repetition frequencies. Given the good agreement of the current flowing between the electrodes, we are confident that the results of our numerical model can be used both for detailed in silico research of electroporation mechanisms (giving researchers insight into time domain effects) and better treatment planning algorithms, which predict the outcome of treatment based on both spatial and temporal distributions of applied electric pulses.
Pettit, J R; Walker, A; Cawley, P; Lowe, M J S
2014-09-01
Commercially available Finite Element packages are being used increasingly for modelling elastic wave propagation problems. Demand for improved capability has resulted in a drive to maximise the efficiency of the solver whilst maintaining a reliable solution. Modelling waves in unbound elastic media to high levels of accuracy presents a challenge for commercial packages, requiring the removal of unwanted reflections from model boundaries. For time domain explicit solvers, Absorbing Layers by Increasing Damping (ALID) have proven successful because they offer flexible application to modellers and, unlike the Perfectly Matched Layers (PMLs) approach, they are readily implemented in most commercial Finite Element software without requiring access to the source code. However, despite good overall performance, this technique requires the spatial model to extend significantly outside the domain of interest. Here, a Stiffness Reduction Method (SRM) has been developed that operates within a significantly reduced spatial domain. The technique is applied by altering the damping and stiffness matrices of the system, inducing decay of any incident wave. Absorbing region variables are expressed as a function of known model constants, helping to apply the technique to generic elastodynamic problems. The SRM has been shown to perform significantly better than ALID, with results confirmed by both numerical and analytical means. PMID:24359871
Space-time finite-element objects: Efficiently modeling physically complex flows
Dilts, G.A.
1996-03-28
Accurate modeling of high-explosive systems requires detailed consideration of many different physical properties and processes: These diverse processes generally occur in localized regions of the problem. Thus the very partial differential equations used to mathematically model the problem change from one region of space and time to another. The numerical algorithms generally used to solve these equations are frequently conceived in terms of data values for physical field variables u{sup i} defined at a number of spatial points indexed by multi-integer subscripts x{sub J}, resulting in a number of discrete state variables u{sup i}{sub J}. Instead of using as the fundamental object a physical field, which naturally maps to an array, the authors imagine a small piece of space modeled for a small amount of time, a space-time ``element``. Within it, various physical processes occur at various times. Self-contained, it gives account of what happens within its borders. It cooperates with a set of neighbors that organize into meshes, which organize into problems. The authors achieve in the software model a decoupling between the where and the how and the what, lack of which historically has been the source of a great deal of the software overhead of modelling continuum systems, and which is a necessary consequence of writing down u{sup i}{sub J}. An efficient implementation of this idea requires a reformulation of the discretization and solution of systems of conservation laws, and careful class design. A working prototype for systems in one space dimension using Mathematica and C++ is provided.
NASA Technical Reports Server (NTRS)
Cwik, Tom; Zuffada, Cinzia; Jamnejad, Vahraz
1996-01-01
Finite element modeling has proven useful for accurtely simulating scattered or radiated fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of a wavelength.
NASA Astrophysics Data System (ADS)
Nanda, Namita; Kapuria, S.; Gopalakrishnan, S.
2014-07-01
In this paper, we present a spectral finite element model (SFEM) using an efficient and accurate layerwise (zigzag) theory, which is applicable for wave propagation analysis of highly inhomogeneous laminated composite and sandwich beams. The theory assumes a layerwise linear variation superimposed with a global third-order variation across the thickness for the axial displacement. The conditions of zero transverse shear stress at the top and bottom and its continuity at the layer interfaces are subsequently enforced to make the number of primary unknowns independent of the number of layers, thereby making the theory as efficient as the first-order shear deformation theory (FSDT). The spectral element developed is validated by comparing the present results with those available in the literature. A comparison of the natural frequencies of simply supported composite and sandwich beams obtained by the present spectral element with the exact two-dimensional elasticity and FSDT solutions reveals that the FSDT yields highly inaccurate results for the inhomogeneous sandwich beams and thick composite beams, whereas the present element based on the zigzag theory agrees very well with the exact elasticity solution for both thick and thin, composite and sandwich beams. A significant deviation in the dispersion relations obtained using the accurate zigzag theory and the FSDT is also observed for composite beams at high frequencies. It is shown that the pure shear rotation mode remains always evanescent, contrary to what has been reported earlier. The SFEM is subsequently used to study wavenumber dispersion, free vibration and wave propagation time history in soft-core sandwich beams with composite faces for the first time in the literature.
Efficiency of group implicit concurrent algorithms for transient finite element analysis
NASA Technical Reports Server (NTRS)
Ortiz, M.; Sotelino, E. D.; Nour-Omid, B.
1989-01-01
The performance of group implicit algorithms is assessed on actual concurrent computers. It is shown that, as the number of subdomains is increased, performance enhancements are derived from two sources: the increased parallelism in the computations; and a reduction in equation solving effort. Moreover, these two performance enhancements are synergistic, in the sense that the corresponding speed-ups are multiplied, rather than merely added. Simulations on a 32-node hypercube are presented for which the interprocessor communications efficiencies obtained are consistently in excess of 90 percent.
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.
NASA Astrophysics Data System (ADS)
Zhou, Kan
With the modern trend of transportation electrification, electric machines are a key component of electric/hybrid electric vehicle (EV/HEV) powertrains. It is therefore important that vehicle powertrain-level and system-level designers and control engineers have access to accurate yet computationally-efficient (CE), physics-based modeling tools of the thermal and electromagnetic (EM) behavior of electric machines. In this dissertation, CE yet sufficiently-accurate thermal and EM models for electric machines, which are suitable for use in vehicle powertrain design, optimization, and control, are developed. This includes not only creating fast and accurate thermal and EM models for specific machine designs, but also the ability to quickly generate and determine the performance of new machine designs through the application of scaling techniques to existing designs. With the developed techniques, the thermal and EM performance can be accurately and efficiently estimated. Furthermore, powertrain or system designers can easily and quickly adjust the characteristics and the performance of the machine in ways that are favorable to the overall vehicle performance.
The Efficiency of Various Computers and Optimizations in Performing Finite Element Computations
NASA Technical Reports Server (NTRS)
Marcus, Martin H.; Broduer, Steve (Technical Monitor)
2001-01-01
With the advent of computers with many processors, it becomes unclear how to best exploit this advantage. For example, matrices can be inverted by applying several processors to each vector operation, or one processor can be applied to each matrix. The former approach has diminishing returns beyond a handful of processors, but how many processors depends on the computer architecture. Applying one processor to each matrix is feasible with enough ram memory and scratch disk space, but the speed at which this is done is found to vary by a factor of three depending on how it is done. The cost of the computer must also be taken into account. A computer with many processors and fast interprocessor communication is much more expensive than the same computer and processors with slow interprocessor communication. Consequently, for problems that require several matrices to be inverted, the best speed per dollar for computers is found to be several small workstations that are networked together, such as in a Beowulf cluster. Since these machines typically have two processors per node, each matrix is most efficiently inverted with no more than two processors assigned to it.
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.
Solving finite element equations on concurrent computers
NASA Technical Reports Server (NTRS)
Nour-Omid, B.; Raefsky, A.; Lyzenga, G.
1987-01-01
This paper discusses the development of a concurrent algorithm for the solution of systems of equations arising in finite element applications. The approach is based on a hybrid of direct elimination method and preconditioned conjugate iteration. Two different preconditioners are used; diagonal scaling and a concurrent implementation of incomplete LU factorization. First, an automatic procedure is used to partition the finite element mesh into sub-structures. The particular mesh partition is chosen to minimize an estimate of the cost for evaluating the solution using this algorithm on a concurrent computer. These procedures are implemented in a finite element program on the JPL/CalTech MARK III hypercube computer. An overview of the structure of this program is presented. The performance of the solution method is demonstrated with the aid of a number of numerical test runs, and its advantages for concurrent implementations are discussed. Efficiency and speed-up factors over sequential machines for the numerical examples are highlighted.
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.
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.
Integrated transient thermal-structural finite element analysis
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Wieting, A. R.; Tamma, K. K.
1981-01-01
An integrated thermal structural finite element approach for efficient coupling of transient thermal and structural analysis is presented. Integrated thermal structural rod and one dimensional axisymmetric elements considering conduction and convection are developed and used in transient thermal structural applications. The improved accuracy of the integrated approach is illustrated by comparisons with exact transient heat conduction elasticity solutions and conventional finite element thermal finite element structural analyses.
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)
Beilina, Larisa
2016-08-01
We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the computational domain: finite difference method is used on the structured part of the computational domain and finite elements on the unstructured part of the domain. Explicit discretizations for both methods are constructed such that the finite element and the finite difference schemes coincide on the common structured overlapping layer between computational subdomains. Then the resulting approach can be considered as a pure finite element scheme which avoids instabilities at the interfaces. We derive an energy estimate for the underlying hyperbolic equation with absorbing boundary conditions and illustrate efficiency of the domain decomposition method on the reconstruction of the conductivity function in three dimensions.
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.
Ferraro, Mauro; Auricchio, Ferdinando; Boatti, Elisa; Scalet, Giulia; Conti, Michele; Morganti, Simone; Reali, Alessandro
2015-01-01
Computer-based simulations are nowadays widely exploited for the prediction of the mechanical behavior of different biomedical devices. In this aspect, structural finite element analyses (FEA) are currently the preferred computational tool to evaluate the stent response under bending. This work aims at developing a computational framework based on linear and higher order FEA to evaluate the flexibility of self-expandable carotid artery stents. In particular, numerical simulations involving large deformations and inelastic shape memory alloy constitutive modeling are performed, and the results suggest that the employment of higher order FEA allows accurately representing the computational domain and getting a better approximation of the solution with a widely-reduced number of degrees of freedom with respect to linear FEA. Moreover, when buckling phenomena occur, higher order FEA presents a superior capability of reproducing the nonlinear local effects related to buckling phenomena. PMID:26184329
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.
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
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.
NASA Astrophysics Data System (ADS)
Pettit, J. R.; Walker, A.; Lowe, M. J. S.
2014-02-01
A common goal when using Finite Element (FE) modeling in time domain wave scattering problems is to minimise model size by only considering a region immediately surrounding a defect or feature of interest. The model boundaries must simulate infinite space by minimising the reflection of incident waves. This is a significant and long-standing challenge that has only been achieved with partial success. Industrial companies wishing to perform such modeling are keen to use established commercial FE packages that offer a thorough history of validation and testing. Unfortunately, this limits the flexibility available to modelers preventing the use of popular research tools such as Perfectly Matched Layers (PML). Unlike PML, Absorbing Layers by Increasing Damping (ALID) have proven successful in this context, offering practical implementation into any solver that has representation of material damping. Despite good performance further improvements are desirable. Here, a Stiffness Reduction Method (SRM) has been developed that operates within a significantly reduced spatial domain. The technique is applied by altering damping and stiffness matrices, inducing decay of incident waves. Variables are expressed as a function of known model constants, easing implementation for generic problems. Analytical and numerical solutions have shown that SRM out performs ALID, with results approaching those of PML.
Integrated transient thermal-structural finite element analysis
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Decahaumphai, P.; Tamma, K. K.; Wieting, A. R.
1981-01-01
An integrated thermal-structural finite element approach for efficient coupling of transient thermal and structural analysis is presented. New integrated thermal-structural rod and one dimensional axisymmetric elements considering conduction and convection are developed and used in transient thermal-structural applications. The improved accuracy of the integrated approach is illustrated by comparisons with exact transient heat conduction-elasticity solutions and conventional finite element thermal-finite element structural analyses. Results indicate that the approach offers significant potential for further development with other elements.
Probabilistic finite element analysis of a craniofacial finite element model.
Berthaume, Michael A; Dechow, Paul C; Iriarte-Diaz, Jose; Ross, Callum F; Strait, David S; Wang, Qian; Grosse, Ian R
2012-05-01
We employed a probabilistic finite element analysis (FEA) method to determine how variability in material property values affects stress and strain values in a finite model of a Macaca fascicularis cranium. The material behavior of cortical bone varied in three ways: isotropic homogeneous, isotropic non-homogeneous, and orthotropic non-homogeneous. The material behavior of the trabecular bone and teeth was always treated as isotropic and homogeneous. All material property values for the cranium were randomized with a Gaussian distribution with either coefficients of variation (CVs) of 0.2 or with CVs calculated from empirical data. Latin hypercube sampling was used to determine the values of the material properties used in the finite element models. In total, four hundred and twenty six separate deterministic FE simulations were executed. We tested four hypotheses in this study: (1) uncertainty in material property values will have an insignificant effect on high stresses and a significant effect on high strains for homogeneous isotropic models; (2) the effect of variability in material property values on the stress state will increase as non-homogeneity and anisotropy increase; (3) variation in the in vivo shear strain values reported by Strait et al. (2005) and Ross et al. (2011) is not only due to variations in muscle forces and cranial morphology, but also due to variation in material property values; (4) the assumption of a uniform coefficient of variation for the material property values will result in the same trend in how moderate-to-high stresses and moderate-to-high strains vary with respect to the degree of non-homogeneity and anisotropy as the trend found when the coefficients of variation for material property values are calculated from empirical data. Our results supported the first three hypotheses and falsified the fourth. When material properties were varied with a constant CV, as non-homogeneity and anisotropy increased the level of variability in
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Voznyuk, I.; Litman, A.; Tortel, H.
2015-08-01
A Quasi-Newton method for reconstructing the constitutive parameters of three-dimensional (3D) penetrable scatterers from scattered field measurements is presented. This method is adapted for handling large-scale electromagnetic problems while keeping the memory requirement and the time flexibility as low as possible. The forward scattering problem is solved by applying the finite-element tearing and interconnecting full-dual-primal (FETI-FDP2) method which shares the same spirit as the domain decomposition methods for finite element methods. The idea is to split the computational domain into smaller non-overlapping sub-domains in order to simultaneously solve local sub-problems. Various strategies are proposed in order to efficiently couple the inversion algorithm with the FETI-FDP2 method: a separation into permanent and non-permanent subdomains is performed, iterative solvers are favorized for resolving the interface problem and a marching-on-in-anything initial guess selection further accelerates the process. The computational burden is also reduced by applying the adjoint state vector methodology. Finally, the inversion algorithm is confronted to measurements extracted from the 3D Fresnel database.
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.
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.
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.
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.
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)
Zolotareva, N. D.; Nikolaev, E. S.
2016-05-01
An iterative process implementing an adaptive hp-version of the finite element method (FEM) previously proposed by the authors for the approximate solution of boundary value problems for the stationary reaction-diffusion equation is described. The method relies on piecewise polynomial basis functions and makes use of an adaptive strategy for constructing a sequence of finite-dimensional subspaces based on the computation of correction indicators. Singularly perturbed boundary value test problems with smooth and not very smooth solutions are used to analyze the efficiency of the method in the situation when an approximate solution has to be found with high accuracy. The convergence of the approximate solution to the exact one is investigated depending on the value of the small parameter multiplying the highest derivative, on the family of basis functions and the quadrature formulas used, and on the internal parameters of the method. The method is compared with an adaptive h-version of FEM that also relies on correction indicators and with its nonadaptive variant based on the bisection of grid intervals.
Will Finite Elements Replace Structural Mechanics?
NASA Astrophysics Data System (ADS)
Ojalvo, I. U.
1984-01-01
This paper presents a personal view regarding the need for a continued interest and activity in structural methods in general, while viewing finite elements and the computer as simply two specific tools for assisting in this endeavor. An attempt is made to provide some insight as to why finite element methods seem to have "won the war," and to give examples of their more (and less) intelligent use. Items addressed include a highlight of unnecessary limitations of many existing standard finite element codes and where it is felt that further development work is needed.
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.
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:
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 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.
Finite Element Vibration Analysis of Rectangular Membrane
NASA Astrophysics Data System (ADS)
Chen, S. H.; Lin, W. J.; Leung, A. Y. T.
2010-05-01
Some pre-tensioned 4-node rectangular elements and 8-node triangular elements are constructed for the free vibration analysis of membranes by finite element. The shape functions are given to derive the element stiffness and mass matrices in accordance with the minimum potential energy principle. Two typical examples show that the calculation by the 4-node rectangular element is very close to the theoretical solution, and 8-node rectangular element has higher accuracy than the 4-node rectangular element. For dense grid, the result is almost consistent with the theoretical solution.
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.
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.
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.
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.
Finite element formulations for compressible flows
NASA Technical Reports Server (NTRS)
Tezduyar, Tayfun E.
1989-01-01
Researchers started their studies on the development and application of computational methods for compressible flows. Particular attention was given to proper numerical treatment of sharp layers occurring in such problems and to general mesh generation capabilities for intricate computational geometries. Mainly finite element methods enhanced with several state-of-the art techniques (such as the streamline-upwind/Petrov-Galerkin, discontinuity capturing, adaptive implicit-explicit, and trouped element-by-element approximate factorization schemes) were employed.
Parallel processing in finite element structural analysis
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.
1987-01-01
A brief review is made of the fundamental concepts and basic issues of parallel processing. Discussion focuses on parallel numerical algorithms, performance evaluation of machines and algorithms, and parallelism in finite element computations. A computational strategy is proposed for maximizing the degree of parallelism at different levels of the finite element analysis process including: 1) formulation level (through the use of mixed finite element models); 2) analysis level (through additive decomposition of the different arrays in the governing equations into the contributions to a symmetrized response plus correction terms); 3) numerical algorithm level (through the use of operator splitting techniques and application of iterative processes); and 4) implementation level (through the effective combination of vectorization, multitasking and microtasking, whenever available).
Finite element radiation transport in one dimension
Painter, J.F.
1997-05-09
A new physics package solves radiation transport equations in one space dimension, multiple energy groups and directions. A discontinuous finite element method discretizes radiation intensity with respect to space and angle, and a continuous finite element method discretizes electron temperature `in space. A splitting method solves the resulting linear equations. This is a one-dimensional analog of Kershaw and Harte`s two-dimensional package. This package has been installed in a two-dimensional inertial confinement fusion code, and has given excellent results for both thermal waves and highly directional radiation. In contrast, the traditional discrete ordinate and spherical harmonic methods show less accurate results in both cases.
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.
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.
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.
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.
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.
Animation of finite element models and results
NASA Technical Reports Server (NTRS)
Lipman, Robert R.
1992-01-01
This is not intended as a complete review of computer hardware and software that can be used for animation of finite element models and results, but is instead a demonstration of the benefits of visualization using selected hardware and software. The role of raw computational power, graphics speed, and the use of videotape are discussed.
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 analysis of a meniscus mirror
NASA Astrophysics Data System (ADS)
Yamashita, Y.
1989-10-01
Finite element analyses were carried out for a 7.5 m meniscus mirror of 20 cm thickness. Calculations were made for deformations of the mirror surface due to the gravity and the effect of a hole through which a lateral supporting mechanism would be installed. Vibrational eigenmodes were also calculated when the mirror is fixed by three axial and three lateral hard points.
Direct finite element equation solving algorithms
NASA Technical Reports Server (NTRS)
Melosh, R. J.; Utku, S.; Salama, M.
1985-01-01
This paper presents and examines direct solution algorithms for the linear simultaneous equations that arise when finite element models represent an engineering system. It identifies the mathematical processing of four solution methods and assesses their data processing implications using concurrent processing.
Fourier analysis of finite element preconditioned collocation schemes
NASA Technical Reports Server (NTRS)
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
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 computation with parallel VLSI
NASA Technical Reports Server (NTRS)
Mcgregor, J.; Salama, M.
1983-01-01
This paper describes a parallel processing computer consisting of a 16-bit microcomputer as a master processor which controls and coordinates the activities of 8086/8087 VLSI chip set slave processors working in parallel. The hardware is inexpensive and can be flexibly configured and programmed to perform various functions. This makes it a useful research tool for the development of, and experimentation with parallel mathematical algorithms. Application of the hardware to computational tasks involved in the finite element analysis method is demonstrated by the generation and assembly of beam finite element stiffness matrices. A number of possible schemes for the implementation of N-elements on N- or n-processors (N is greater than n) are described, and the speedup factors of their time consumption are determined as a function of the number of available parallel processors.
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
Finite Element Interface to Linear Solvers
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 themore » 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.« less
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.
Deformation modes in the finite element absolute nodal coordinate formulation
NASA Astrophysics Data System (ADS)
Sugiyama, Hiroyuki; Gerstmayr, Johannes; Shabana, Ahmed A.
2006-12-01
The objective of this study is to provide interpretation of the deformation modes in the finite element absolute nodal coordinate formulation using several strain definitions. In this finite element formulation, the nodal coordinates consist of absolute position coordinates and gradients that can be used to define a unique rotation and deformation fields within the element as well as at the nodal points. The results obtained in this study clearly show cross-section deformation modes eliminated when the number of the finite element nodal coordinates is systematically and consistently reduced. Using the procedure discussed in this paper one can obtain a reduced order dynamic model, eliminate position vector gradients that introduce high frequencies to the solution of some problems, achieve the continuity of the remaining gradients at the nodal points, and obtain a formulation that automatically satisfies the principle of work and energy. Furthermore, the resulting dynamic model, unlike large rotation finite element formulations, leads to a unique rotation field, and as a consequence, the obtained formulation does not suffer from the problem of coordinate redundancy that characterizes existing large deformation finite element formulations. In order to accurately define strain components that can have easy physical interpretation, a material coordinate system is introduced to define the material element rotation and deformation. Using the material coordinate system, the Timoshenko-Reissner and Euler -Bernoulli beam models can be systematically obtained as special cases of the absolute nodal coordinate formulation beam models. While a constraint approach is used in this study to eliminate the cross-section deformation modes, it is important to point out as mentioned in this paper that lower-order finite elements, some of which already presented in previous investigations, can be efficiently used in thin and stiff structure applications.
Finite Element Heat & Mass Transfer Code
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; andmore » double porosity and double porosity/double permeability capabilities.« less
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2016-02-01
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
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.
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.
2-d Finite Element Code Postprocessor
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 forcesmore » 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.« less
Finite Element Analysis of Honeycomb Impact Attenuator
NASA Astrophysics Data System (ADS)
Yang, Seung-Yong; Choi, Seung-Kyu; Kim, Nohyu
To participate in Student Formula Society of Automotive Engineers (SAE) competitions, it is necessary to build an impact attenuator that would give an average deceleration not to exceed 20g when it runs into a rigid wall. Students can use numerical simulations or experimental test data to show that their car satisfies this safety requirement. A student group to study formula cars at the Korea University of Technology and Education has designed a vehicle to take part in a SAE competition, and a honeycomb structure was adopted as the impact attenuator. In this paper, finite element calculations were carried out to investigate the dynamic behavior of the honeycomb attenuator. Deceleration and deformation behaviors were studied. Effect of the yield strength was checked by comparing the numerical results. ABAQUS/Explicit finite element code was used.
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 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.
Finite element based electric motor design optimization
NASA Astrophysics Data System (ADS)
Campbell, C. Warren
1993-11-01
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.
ExodusII Finite Element Data Model
2005-05-14
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. (exodus II is based on netcdf)
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 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.
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.
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 analysis of inviscid subsonic boattail flow
NASA Technical Reports Server (NTRS)
Chima, R. V.; Gerhart, P. M.
1981-01-01
A finite element code for analysis of inviscid subsonic flows over arbitrary nonlifting planar or axisymmetric bodies is described. The code solves a novel primitive variable formulation of the coupled irrotationality and compressible continuity equations. Results for flow over a cylinder, a sphere, and a NACA 0012 airfoil verify the code. Computed subcritical flows over an axisymmetric boattailed afterbody compare well with finite difference results and experimental data. Interative coupling with an integral turbulent boundary layer code shows strong viscous effects on the inviscid flow. Improvements in code efficiency and extensions to transonic flows are discussed.
NASA Astrophysics Data System (ADS)
Cheng, Jiahao; Shahba, Ahmad; Ghosh, Somnath
2016-05-01
Image-based CPFE modeling involves computer generation of virtual polycrystalline microstructures from experimental data, followed by discretization into finite element meshes. Discretization is commonly accomplished using three-dimensional four-node tetrahedral or TET4 elements, which conform to the complex geometries. It has been commonly observed that TET4 elements suffer from severe volumetric locking when simulating deformation of incompressible or nearly incompressible materials. This paper develops and examines three locking-free stabilized finite element formulations in the context of crystal plasticity finite element analysis. They include a node-based uniform strain (NUS) element, a locally integrated B-bar (LIB) based element and a F-bar patch (FP) based element. All three formulations are based on the partitioning of TET4 element meshes and integrating over patches to obtain favorable incompressibility constraint ratios without adding large degrees of freedom. The results show that NUS formulation introduces unstable spurious energy modes, while the LIB and FP elements stabilize the solutions and are preferred for reliable CPFE analysis. The FP element is found to be computationally efficient over the LIB element.
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)
Strong, Stuart L.; Meade, Andrew J., Jr.
1992-01-01
Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.
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.
Modelling the arterial wall by finite elements.
Mosora, F; Harmant, A; Bernard, C; Fossion, A; Pochet, T; Juchmes, J; Cescotto, S
1993-01-01
The mechanical behaviour of the arterial wall was determined theoretically utilizing some parameters of blood flow measured in vivo. Continuous experimental measurements of pressure and diameter were recorded in anesthetized dogs on the thoracic ascending and midabdominal aorta. The pressure was measured by using a catheter, and the diameter firstly, at the same site, by a plethysmograph with mercury gauge and secondly, by a sonomicrometer with ferroelectric ceramic transducers. The unstressed radius and thickness were measured at the end of each experiment in situ. Considering that the viscous component is not important relatively to the nonlinear component of the elasticity and utilizing several equations for Young modulus calculation (thick and thin wall circular cylindrical tube formulas and Bergel's equation) the following values were obtained for this parameter: 0.6 MPa-2 MPa in midabdominal aorta and 2 MPa-6.5 MPa in thoracic ascending aorta. The behaviour of the aorta wall was modelled considering an elastic law and using the finite element program "Lagamine" working in large deformations. The discretized equilibrium equations are non-linear and a unique axi-symmetric, iso-parametric element of 1 cm in length with 8 knots was used for this bi-dimensional problem. The theoretical estimation of radius vessel, utilizing a constant 5 MPa Young modulus and also a variable one, are in good agreement with the experimental results, showing that this finite element model can be applied to study mechanical properties of the arteries in physiological and pathological conditions.
Implicit extrapolation methods for multilevel finite element computations
Jung, M.; Ruede, U.
1994-12-31
The finite element package FEMGP has been developed to solve elliptic and parabolic problems arising in the computation of magnetic and thermomechanical fields. FEMGP implements various methods for the construction of hierarchical finite element meshes, a variety of efficient multilevel solvers, including multigrid and preconditioned conjugate gradient iterations, as well as pre- and post-processing software. Within FEMGP, multigrid {tau}-extrapolation can be employed to improve the finite element solution iteratively to higher order. This algorithm is based on an implicit extrapolation, so that the algorithm differs from a regular multigrid algorithm only by a slightly modified computation of the residuals on the finest mesh. Another advantage of this technique is, that in contrast to explicit extrapolation methods, it does not rely on the existence of global error expansions, and therefore neither requires uniform meshes nor global regularity assumptions. In the paper the authors will analyse the {tau}-extrapolation algorithm and present experimental results in the context of the FEMGP package. Furthermore, the {tau}-extrapolation results will be compared to higher order finite element solutions.
Parallel, adaptive finite element methods for conservation laws
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Devine, Karen D.; Flaherty, Joseph E.
1994-01-01
We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.
PWSCC Assessment by Using Extended Finite Element Method
NASA Astrophysics Data System (ADS)
Lee, Sung-Jun; Lee, Sang-Hwan; Chang, Yoon-Suk
2015-12-01
The head penetration nozzle of control rod driving mechanism (CRDM) is known to be susceptible to primary water stress corrosion cracking (PWSCC) due to the welding-induced residual stress. Especially, the J-groove dissimilar metal weld regions have received many attentions in the previous studies. However, even though several advanced techniques such as weight function and finite element alternating methods have been introduced to predict the occurrence of PWSCC, there are still difficulties in respect of applicability and efficiency. In this study, the extended finite element method (XFEM), which allows convenient crack element modeling by enriching degree of freedom (DOF) with special displacement function, was employed to evaluate structural integrity of the CRDM head penetration nozzle. The resulting stress intensity factors of surface cracks were verified for the reliability of proposed method through the comparison with those suggested in the American Society of Mechanical Engineering (ASME) code. The detailed results from the FE analyses are fully discussed in the manuscript.
NASA Astrophysics Data System (ADS)
Tan, E.; Choi, E.; Lavier, L. L.; Calo, V. M.
2013-12-01
Many tectonic problems treat the lithosphere as a compressible elastic material, which can also flow viscously or break in a brittle fashion depending on the stress level applied and the temperature conditions. We present a flexible methodology to address the resulting complex material response, which imposes severe challenges on the discretization and rheological models used. This robust, adaptive, multidimensional, finite element method solves the momentum balance and the heat equation in Lagrangian form with unstructured simplicial mesh (triangles in 2D and tetrahedra in 3D). The mesh locking problem is avoided by using averaged volumetric strain rate to update the stress. The solver uses contingent mesh adaptivity in places where shear strain is focused (localization) during remeshing. A simple scheme of mesh coarsening is employed to prevent tiny elements during remeshing. Lagrangian markers are used to track multiple compositions of rocks. The code is parallelized via OpenMP with graph coloring. We detail the solver and verify it in a number of benchmark problems against analytic and numerical solutions from the literature.
Adaptive mesh generation for edge-element finite element method
NASA Astrophysics Data System (ADS)
Tsuboi, Hajime; Gyimothy, Szabolcs
2001-06-01
An adaptive mesh generation method for two- and three-dimensional finite element methods using edge elements is proposed. Since the tangential component continuity is preserved when using edge elements, the strategy of creating new nodes is based on evaluation of the normal component of the magnetic vector potential across element interfaces. The evaluation is performed at the middle point of edge of a triangular element for two-dimensional problems or at the gravity center of triangular surface of a tetrahedral element for three-dimensional problems. At the boundary of two elements, the error estimator is the ratio of the normal component discontinuity to the maximum value of the potential in the same material. One or more nodes are set at the middle points of the edges according to the value of the estimator as well as the subdivision of elements where new nodes have been created. A final mesh will be obtained after several iterations. Some computation results of two- and three-dimensional problems using the proposed method are shown.
2-D Finite Element Heat Conduction
1989-10-30
AYER is a finite element program which implicitly solves the general two-dimensional equation of thermal conduction for plane or axisymmetric bodies. AYER takes into account the effects of time (transient problems), in-plane anisotropic thermal conductivity, a three-dimensional velocity distribution, and interface thermal contact resistance. Geometry and material distributions are arbitrary, and input is via subroutines provided by the user. As a result, boundary conditions, material properties, velocity distributions, and internal power generation may be mademore » functions of, e.g., time, temperature, location, and heat flux.« less
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.
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.
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.
NASA Technical Reports Server (NTRS)
Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.
1983-01-01
The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.
NASA Technical Reports Server (NTRS)
Barth, Timothy J.; Larson, Mats G.
2000-01-01
We consider a posteriori error estimates for finite volume and finite element methods on arbitrary meshes subject to prescribed error functionals. Error estimates of this type are useful in a number of computational settings: (1) quantitative prediction of the numerical solution error, (2) adaptive meshing, and (3) load balancing of work on parallel computing architectures. Our analysis recasts the class of Godunov finite volumes schemes as a particular form of discontinuous Galerkin method utilizing broken space approximation obtained via reconstruction of cell-averaged data. In this general framework, weighted residual error bounds are readily obtained using duality arguments and Galerkin orthogonality. Additional consideration is given to issues such as nonlinearity, efficiency, and the relationship to other existing methods. Numerical examples are given throughout the talk to demonstrate the sharpness of the estimates and efficiency of the techniques. Additional information is contained in the original.
Bochev, Pavel Blagoveston
2011-06-01
We develop a new formulation of the Control Volume Finite Element Method (CVFEM) with a multidimensional Scharfetter-Gummel (SG) upwinding for the drift-diffusion equations. The formulation uses standard nodal elements for the concentrations and expands the flux in terms of the lowest-order Nedelec H(curl; {Omega})-compatible finite element basis. The SG formula is applied to the edges of the elements to express the Nedelec element degree of freedom on this edge in terms of the nodal degrees of freedom associated with the endpoints of the edge. The resulting upwind flux incorporates the upwind effects from all edges and is defined at the interior of the element. This allows for accurate evaluation of integrals on the boundaries of the control volumes for arbitrary quadrilateral elements. The new formulation admits efficient implementation through a standard loop over the elements in the mesh followed by loops over the element nodes (associated with control volume fractions in the element) and element edges (associated with flux degrees of freedom). The quantities required for the SG formula can be precomputed and stored for each edge in the mesh for additional efficiency gains. For clarity the details are presented for two-dimensional quadrilateral grids. Extension to other element shapes and three dimensions is straightforward.
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%.
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.
Overcoming element erosion limitations within Lagrangian finite element codes
NASA Astrophysics Data System (ADS)
Vignjevic, Rade; Hughes, Kevin; Walker, Andrew; Taylor, Emma A.
2001-10-01
Lagrangian finite element methods have been used extensively in the past to study the non-linear transient behaviour of materials, ranging from crash test of cars to simulating bird strikes on planes.... However, as this type of space discretization does not allow for motion of the material through the mesh when modelling extremely large deformations, the mesh becomes highly distorted. This paper describes some limitations and applicability of this type of analysis for high velocity impacts. A method for dealing with this problem is by the erosion of elements is proposed where the main issue is the deformation of element failure strains. Results were compared with empirical perforation results and were found to be in good agreement. The results were then used to simulate high velocity impacts upon a multi-layered aluminium target, in order to predict a ballistic limit curve. LS-DYNA3D was used as the FE solver for all simulations. Meshes were generated with Truegrid.
Finite element methodology for transient conduction/forced-convection thermal analysis
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Wieting, A. R.
1979-01-01
Finite element methodology for steady state thermal analysis of convectively cooled structures has been extended for transient analysis. The finite elements are based on representing the fluid passages by fluid bulk-temperature nodes and fluid-solid interface nodes. The formulation of the finite element equations for a typical flow passage is based on the weighted residual method with upwind weighting functions. Computer implementation of the convective finite element methodology using explicit and implicit time integration algorithms is described. Accuracy and efficiency of the methodology is evaluated by comparisons with analytical solutions and finite-difference lumped-parameter analyses. The comparative analyses demonstrate that finite element conduction/conduction methodology may be used to predict transient temperatures with an accuracy equal or superior to the lumped-parameter finite-difference method.
A suitable low-order, eight-node tetrahedral finite element for solids
Key, S.W.; Heinstein, M.S.; Stone, C.M.; Mello, F.J.; Blanford, M.L.; Budge, K.G.
1998-03-01
To use the all-tetrahedral mesh generation existing today, the authors have explored the creation of a computationally efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping, and the element`s performance in applications are presented. In particular they examine the eight-node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hour-glass modes. In this regard it bears similarities to the eight-node, mean-quadrature hexahedral finite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, constant-strain tetrahedral finite element is a suitable replacement for the eight-node hexahedral finite element in those cases where mesh generation requires an inordinate amount of user intervention and direction to obtain acceptable mesh properties.
GPU accelerated spectral finite elements on all-hex meshes
NASA Astrophysics Data System (ADS)
Remacle, J.-F.; Gandham, R.; Warburton, T.
2016-11-01
This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes. The discrete equations are solved using a matrix-free preconditioned conjugate gradient algorithm. An additive Schwartz two-scale preconditioner is employed that allows h-independence convergence. An extensible multi-threading programming API is used as a common kernel language that allows runtime selection of different computing devices (GPU and CPU) and different threading interfaces (CUDA, OpenCL and OpenMP). Performance tests demonstrate that problems with over 50 million degrees of freedom can be solved in a few seconds on an off-the-shelf GPU.
An emulator for minimizing finite element analysis implementation resources
NASA Technical Reports Server (NTRS)
Melosh, R. J.; Utku, S.; Salama, M.; Islam, M.
1982-01-01
A finite element analysis emulator providing a basis for efficiently establishing an optimum computer implementation strategy when many calculations are involved is described. The SCOPE emulator determines computer resources required as a function of the structural model, structural load-deflection equation characteristics, the storage allocation plan, and computer hardware capabilities. Thereby, it provides data for trading analysis implementation options to arrive at a best strategy. The models contained in SCOPE lead to micro-operation computer counts of each finite element operation as well as overall computer resource cost estimates. Application of SCOPE to the Memphis-Arkansas bridge analysis provides measures of the accuracy of resource assessments. Data indicate that predictions are within 17.3 percent for calculation times and within 3.2 percent for peripheral storage resources for the ELAS code.
A finite element analysis of fatigue crack closure
NASA Technical Reports Server (NTRS)
Newman, J. C., Jr.
1974-01-01
Experiments have shown that fatigue cracks close at positive loads during constant-amplitude load cycling. The crack-closure phenomenon is caused by residual plastic deformations remaining in the wake of an advancing crack tip. The present paper is concerned with the application of a two-dimensional, nonlinear, finite-element analysis for predicting crack-closure and crack-opening stresses during cyclic loading. A two-dimensional finite-element computer program, which accounts for both elastic-plastic material behavior and changing boundary conditions associated with crack extension and intermittent contact of the crack surfaces under cyclic loading, has been developed. An efficient technique to account for changing boundary conditions was also incorporated into the nonlinear analysis program. This program was subsequently used to study crack extension and crack closure under constant-amplitude and two-level block loading. The calculated crack-closure and crack-opening stresses were qualitatively consistent with experimental observations.
Design Optimization of Coronary Stent Based on Finite Element Models
Qiu, Tianshuang; Zhu, Bao; Wu, Jinying
2013-01-01
This paper presents an effective optimization method using the Kriging surrogate model combing with modified rectangular grid sampling to reduce the stent dogboning effect in the expansion process. An infilling sampling criterion named expected improvement (EI) is used to balance local and global searches in the optimization iteration. Four commonly used finite element models of stent dilation were used to investigate stent dogboning rate. Thrombosis models of three typical shapes are built to test the effectiveness of optimization results. Numerical results show that two finite element models dilated by pressure applied inside the balloon are available, one of which with the artery and plaque can give an optimal stent with better expansion behavior, while the artery and plaque unincluded model is more efficient and takes a smaller amount of computation. PMID:24222743
Finite element prediction of vibro-acoustic environments
NASA Astrophysics Data System (ADS)
Hipol, Philip J.
1989-09-01
An efficient analytical methodology has been developed with the finite element method which may be used to predict the low frequency vibro-acoustic environment within an aerospace flight vehicle. This methodology includes general purpose capabilities for solving problems involving the effects of structure/acoustic interaction and random excitation pressure fields. Computational efficiency is enhanced by decoupling the structure from the acoustic volume, and taking advantage of reciprocity in the random vibration and vibro-acoustic formulations. The application of the analytical methodology to an example problem found good agreement with previous research, demonstrating the feasibility of the methodology described herein.
NASA Astrophysics Data System (ADS)
Ying, Jinyong; Xie, Dexuan
2015-10-01
The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.
Asymmetric quadrilateral shell elements for finite strains
NASA Astrophysics Data System (ADS)
Areias, P.; Dias-da-Costa, D.; Pires, E. B.; Van Goethem, N.
2013-07-01
Very good results in infinitesimal and finite strain analysis of shells are achieved by combining either the enhanced-metric technique or the selective-reduced integration for the in-plane shear energy and an assumed natural strain technique (ANS) in a non-symmetric Petrov-Galerkin arrangement which complies with the patch-test. A recovery of the original Wilson incompatible mode element is shown for the trial functions in the in-plane components. As a beneficial side-effect, Newton-Raphson convergence behavior for non-linear problems is improved with respect to symmetric formulations. Transverse-shear and in-plane patch tests are satisfied while distorted-mesh accuracy is higher than with symmetric formulations. Classical test functions with assumed-metric components are required for compatibility reasons. Verification tests are performed with advantageous comparisons being observed in all of them. Applications to large displacement elasticity and finite strain plasticity are shown with both low sensitivity to mesh distortion and (relatively) high accuracy. A equilibrium-consistent (and consistently linearized) updated-Lagrangian algorithm is proposed and tested. Concerning the time-step dependency, it was found that the consistent updated-Lagrangian algorithm is nearly time-step independent and can replace the multiplicative plasticity approach if only moderate elastic strains are present, as is the case of most metals.
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.
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 modeling of nanoindentation
Knapp, J.A.; Follstaedt, D.M.; Myers, S.M.; Barbour, J.C.; Friedmann, T.A.
1999-02-01
Procedures have been developed based on finite-element modeling of nanoindentation data to obtain the mechanical properties of thin films and ion-beam-modified layers independently of the properties of the underlying substrates. These procedures accurately deduce the yield strength, Young{close_quote}s elastic modulus, and layer hardness from indentations as deep as 50{percent} of the layer thickness or more. We have used these procedures to evaluate materials ranging from ion implanted metals to deposited, diamond-like carbon layers. The technique increases the applicability of indentation testing to very thin layers, composite layers, and modulated compositions. This article presents an overview of the procedures involved and illustrates them with selected examples. {copyright} {ital 1999 American Institute of Physics.}
Finite element simulation of pipe dynamic response
Slagis, G.C.; Litton, R.W.
1996-12-01
Nonlinear finite element dynamic analyses of the response of a pipe span to controlled-displacement, sinusoidal vibration have been performed. The objective of this preliminary study is to compare strain and acceleration response data to those generated by Beaney in the Berkeley Nuclear Laboratories experiments. Results for an unpressurized, 5 Hz, carbon steel pipe are in good agreement with the experiments. Hence, it appears that analytical simulation will be useful to assess seismic margins. Recommendations for additional studies are provided. The analyses confirm the test results--dynamic response is greatly attenuated by material plasticity. Analytical strains and accelerations are about 30% higher than test data. There are several possible explanations for the differences. To assess the effect of frequency on response, the length of the pipe span was increased. Analysis of the longer, 2 Hz, pipe span shows significantly greater cyclic strains than the 5 Hz span at the same input excitation levels.
3-D Finite Element Heat Transfer
1992-02-01
TOPAZ3D is a three-dimensional implicit finite element computer code for heat transfer analysis. TOPAZ3D can be used to solve for the steady-state or transient temperature field on three-dimensional geometries. Material properties may be temperature-dependent and either isotropic or orthotropic. A variety of time-dependent and temperature-dependent boundary conditions can be specified including temperature, flux, convection, and radiation. By implementing the user subroutine feature, users can model chemical reaction kinetics and allow for any type of functionalmore » representation of boundary conditions and internal heat generation. TOPAZ3D can solve problems of diffuse and specular band radiation in an enclosure coupled with conduction in the material surrounding the enclosure. Additional features include thermal contact resistance across an interface, bulk fluids, phase change, and energy balances.« less
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.
Finite element analyses of CCAT preliminary design
NASA Astrophysics Data System (ADS)
Sarawit, Andrew T.; Kan, Frank W.
2014-07-01
This paper describes the development of the CCAT telescope finite element model (FEM) and the analyses performed to support the preliminary design work. CCAT will be a 25 m diameter telescope operating in the 0.2 to 2 mm wavelength range. It will be located at an elevation of 5600 m on Cerro Chajnantor in Northern Chile, near ALMA. The telescope will be equipped with wide-field cameras and spectrometers mounted at the two Nasmyth foci. The telescope will be inside an enclosure to protect it from wind buffeting, direct solar heating, and bad weather. The main structures of the telescope include a steel Mount and a carbon-fiber-reinforced-plastic (CFRP) primary truss. The finite element model developed in this study was used to perform modal, frequency response, seismic response spectrum, stress, and deflection analyses of telescope. Modal analyses of telescope were performed to compute the structure natural frequencies and mode shapes and to obtain reduced order modal output at selected locations in the telescope structure to support the design of the Mount control system. Modal frequency response analyses were also performed to compute transfer functions at these selected locations. Seismic response spectrum analyses of the telescope subject to the Maximum Likely Earthquake were performed to compute peak accelerations and seismic demand stresses. Stress analyses were performed for gravity load to obtain gravity demand stresses. Deflection analyses for gravity load, thermal load, and differential elevation drive torque were performed so that the CCAT Observatory can verify that the structures meet the stringent telescope surface and pointing error requirements.
NASA Technical Reports Server (NTRS)
Padovan, J.; Adams, M.; Fertis, J.; Zeid, I.; Lam, P.
1982-01-01
Finite element codes are used in modelling rotor-bearing-stator structure common to the turbine industry. Engine dynamic simulation is used by developing strategies which enable the use of available finite element codes. benchmarking the elements developed are benchmarked by incorporation into a general purpose code (ADINA); the numerical characteristics of finite element type rotor-bearing-stator simulations are evaluated through the use of various types of explicit/implicit numerical integration operators. Improving the overall numerical efficiency of the procedure is improved.
Thermal Radiation Transport on Unstructured Finite Element Meshes
R. P. Smedley-Stevenson
2000-11-12
This paper describes investigations on the use of finite element methods to solve the time-dependent thermal radiation transport equations on unstructured meshes. The solution of this equation will be incorporated in AWE's two-dimensional (2-D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic code CORVUS in order to solve complex radiation hydrodynamic problems. A 2-D discretization of the grey transport equation has been studied based on the use of lumped linear DFEs for the spatial variation and piecewise constant finite elements for the angular variation. The use of an adaptive angular approximation has been explored in order to improve the computational efficiency, together with a technique for mitigating the ray effect when it is impractical to converge the angular discretization. A revised spatial discretization is required for the diffusion synthetic acceleration (DSA) equations used to accelerate the solution of the first-order transport equation for quadrilateral elements. So far, this appears to be unconditionally efficient at accelerating the solution of the grey first-order transport equation, n the presence of large aspect ratio and/or distorted elements. The solution of the multigroup equations using the linear multi-frequency grey (LMFG) method is currently under investigation. The pseudoscattering term arising from the LMFG treatment has the same form as the fission source in neutron transport problems. The discretization of the DSA equations described in this paper will be employed for both the within-group coherent scattering contribution and the separate grey acceleration equation used to accelerate the pseudoscattering term.
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.
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).
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)
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.
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.
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.
Huang, Huajun; Xiang, Chunling; Zeng, Canjun; Ouyang, Hanbin; Wong, Kelvin Kian Loong; Huang, Wenhua
2015-12-01
We improved the geometrical modeling procedure for fast and accurate reconstruction of orthopedic structures. This procedure consists of medical image segmentation, three-dimensional geometrical reconstruction, and assignment of material properties. The patient-specific orthopedic structures reconstructed by this improved procedure can be used in the virtual surgical planning, 3D printing of real orthopedic structures and finite element analysis. A conventional modeling consists of: image segmentation, geometrical reconstruction, mesh generation, and assignment of material properties. The present study modified the conventional method to enhance software operating procedures. Patient's CT images of different bones were acquired and subsequently reconstructed to give models. The reconstruction procedures were three-dimensional image segmentation, modification of the edge length and quantity of meshes, and the assignment of material properties according to the intensity of gravy value. We compared the performance of our procedures to the conventional procedures modeling in terms of software operating time, success rate and mesh quality. Our proposed framework has the following improvements in the geometrical modeling: (1) processing time: (femur: 87.16 ± 5.90 %; pelvis: 80.16 ± 7.67 %; thoracic vertebra: 17.81 ± 4.36 %; P < 0.05); (2) least volume reduction (femur: 0.26 ± 0.06 %; pelvis: 0.70 ± 0.47, thoracic vertebra: 3.70 ± 1.75 %; P < 0.01) and (3) mesh quality in terms of aspect ratio (femur: 8.00 ± 7.38 %; pelvis: 17.70 ± 9.82 %; thoracic vertebra: 13.93 ± 9.79 %; P < 0.05) and maximum angle (femur: 4.90 ± 5.28 %; pelvis: 17.20 ± 19.29 %; thoracic vertebra: 3.86 ± 3.82 %; P < 0.05). Our proposed patient-specific geometrical modeling requires less operating time and workload, but the orthopedic structures were generated at a higher rate of success as compared with the conventional method. It is expected to benefit the surgical planning of orthopedic
Beam and Truss Finite Element Verification for DYNA3D
Rathbun, H J
2007-07-16
The explicit finite element (FE) software program DYNA3D has been developed at Lawrence Livermore National Laboratory (LLNL) to simulate the dynamic behavior of structures, systems, and components. This report focuses on verification of beam and truss element formulations in DYNA3D. An efficient protocol has been developed to verify the accuracy of these structural elements by generating a set of representative problems for which closed-form quasi-static steady-state analytical reference solutions exist. To provide as complete coverage as practically achievable, problem sets are developed for each beam and truss element formulation (and their variants) in all modes of loading and physical orientation. Analyses with loading in the elastic and elastic-plastic regimes are performed. For elastic loading, the FE results are within 1% of the reference solutions for all cases. For beam element bending and torsion loading in the plastic regime, the response is heavily dependent on the numerical integration rule chosen, with higher refinement yielding greater accuracy (agreement to within 1%). Axial loading in the plastic regime produces accurate results (agreement to within 0.01%) for all integration rules and element formulations. Truss elements are also verified to provide accurate results (within 0.01%) for elastic and elastic-plastic loading. A sample problem to verify beam element response in ParaDyn, the parallel version DYNA3D, is also presented.
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.
Finite element analysis of laminated plates and shells, volume 1
NASA Technical Reports Server (NTRS)
Seide, P.; Chang, P. N. H.
1978-01-01
The finite element method is used to investigate the static behavior of laminated composite flat plates and cylindrical shells. The analysis incorporates the effects of transverse shear deformation in each layer through the assumption that the normals to the undeformed layer midsurface remain straight but need not be normal to the mid-surface after deformation. A digital computer program was developed to perform the required computations. The program includes a very efficient equation solution code which permits the analysis of large size problems. The method is applied to the problem of stretching and bending of a perforated curved plate.
Vector algorithms for geometrically nonlinear 3D finite element analysis
NASA Technical Reports Server (NTRS)
Whitcomb, John D.
1989-01-01
Algorithms for geometrically nonlinear finite element analysis are presented which exploit the vector processing capability of the VPS-32, which is closely related to the CYBER 205. By manipulating vectors (which are long lists of numbers) rather than individual numbers, very high processing speeds are obtained. Long vector lengths are obtained without extensive replication or reordering by storage of intermediate results in strategic patterns at all stages of the computations. Comparisons of execution times with those from programs using either scalar or other vector programming techniques indicate that the algorithms presented are quite efficient.
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.
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.
Finite element modeling of retinal prosthesis mechanics
NASA Astrophysics Data System (ADS)
Basinger, B. C.; Rowley, A. P.; Chen, K.; Humayun, M. S.; Weiland, J. D.
2009-10-01
Epiretinal prostheses used to treat degenerative retina diseases apply stimulus via an electrode array fixed to the ganglion cell side of the retina. Mechanical pressure applied by these arrays to the retina, both during initial insertion and throughout chronic use, could cause sufficient retinal damage to reduce the device's effectiveness. In order to understand and minimize potential mechanical damage, we have used finite element analysis to model mechanical interactions between an electrode array and the retina in both acute and chronic loading configurations. Modeling indicates that an acute tacking force distributes stress primarily underneath the tack site and heel edge of the array, while more moderate chronic stresses are distributed more evenly underneath the array. Retinal damage in a canine model chronically implanted with a similar array occurred in correlating locations, and model predictions correlate well with benchtop eyewall compression tests. This model provides retinal prosthesis researchers with a tool to optimize the mechanical electrode array design, but the techniques used here represent a unique effort to combine a modifiable device and soft biological tissues in the same model and those techniques could be extended to other devices that come into mechanical contact with soft neural tissues.
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.
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)
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
Finite Element Model of Cardiac Electrical Conduction.
NASA Astrophysics Data System (ADS)
Yin, John Zhihao
1994-01-01
In this thesis, we develop mathematical models to study electrical conduction of the heart. One important pattern of wave propagation of electrical excitation in the heart is reentry which is believed to be the underlying mechanism of some dangerous cardiac arhythmias such as ventricular tachycardia and ventricular fibrillation. We present in this thesis a new ionic channel model of the ventricular cardiac cell membrane to study the microscopic electrical properties of myocardium. We base our model on recent single channel experiment data and a simple physical diffusion model of the calcium channel. Our ionic channel model of myocardium has simpler differential equations and fewer parameters than previous models. Further more, our ionic channel model achieves better results in simulating the strength-interval curve when we connect the membrane patch model to form a one dimensional cardiac muscle strand. We go on to study a finite element model which uses multiple states and non-nearest neighbor interactions to include curvature and dispersion effects. We create a generalized lattice randomization to overcome the artifacts generated by the interaction between the local dynamics and the regularities of the square lattice. We show that the homogeneous model does not display spontaneous wavefront breakup in a reentrant wave propagation once the lattice artifacts have been smoothed out by lattice randomization with a randomization scale larger than the characteristic length of the interaction. We further develop a finite 3-D 3-state heart model which employs a probability interaction rule. This model is applied to the simulation of Body Surface Laplacian Mapping (BSLM) using a cylindrical volume conductor as the torso model. We show that BSLM has a higher spatial resolution than conventional mapping methods in revealing the underlying electrical activities of the heart. The results of these studies demonstrate that mathematical modeling and computer simulation are very
High speed finite element simulations on the graphics card
Huthwaite, P.; Lowe, M. J. S.
2014-02-18
A software package is developed to perform explicit time domain finite element simulations of ultrasonic propagation 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 technique is compared to a commercial CPU equivalent, demonstrating an overall speedup of at least 100 for a non-destructive testing weld model.
High speed finite element simulations on the graphics card
NASA Astrophysics Data System (ADS)
Huthwaite, P.; Lowe, M. J. S.
2014-02-01
A software package is developed to perform explicit time domain finite element simulations of ultrasonic propagation 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 technique is compared to a commercial CPU equivalent, demonstrating an overall speedup of at least 100 for a non-destructive testing weld model.
Coupling finite element and integral equation solutions using decoupled boundary meshes
NASA Technical Reports Server (NTRS)
Cwik, Tom
1992-01-01
A method is outlined for calculating scattered fields from inhomogeneous penetrable objects using a coupled finite element-integral equation solution. The finite element equation can efficiently model fields in penetrable and inhomogeneous regions, while the integral equation exactly models fields on the finite element mesh boundary and in the exterior region. By decoupling the interior finite element and exterior integral equation meshes, considerable flexibility is found in both the number of field expansion points as well as their density. Only the nonmetal portions of the object need be modeled using a finite element expansion; exterior perfect conducting surfaces are modeled using an integral equation with a single unknown field since E(tan) is identically zero on these surfaces. Numerical convergence, accuracy, and stability at interior resonant frequencies are studied in detail.
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.
Finite element simulation of articular contact mechanics with quadratic tetrahedral elements.
Maas, Steve A; Ellis, Benjamin J; Rawlins, David S; Weiss, Jeffrey A
2016-03-21
Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics.
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.
Finite element-finite difference thermal/structural analysis of large space truss structures
NASA Technical Reports Server (NTRS)
Warren, Andrew H.; Arelt, Joseph E.; Eskew, William F.; Rogers, Karen M.
1992-01-01
A technique of automated and efficient thermal-structural processing of truss structures that interfaces the finite element and finite difference method was developed. The thermal-structural analysis tasks include development of the thermal and structural math models, thermal analysis, development of an interface and data transfer between the models, and finally an evaluation of the thermal stresses and displacements in the structure. Consequently, the objective of the developed technique was to minimize the model development time, in order to assure an automatic transfer of data between the thermal and structural models as well as to minimize the computer resources needed for the analysis itself. The method and techniques described are illustrated on the thermal/structural analysis of the Space Station Freedom main truss.
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
A robust, finite element model for hydrostatic surface water flows
Walters, R.A.; Casulli, V.
1998-01-01
A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.
Curved Thermopiezoelectric Shell Structures Modeled by Finite Element Analysis
NASA Technical Reports Server (NTRS)
Lee, Ho-Jun
2000-01-01
"Smart" structures composed of piezoelectric materials may significantly improve the performance of aeropropulsion systems through a variety of vibration, noise, and shape-control applications. The development of analytical models for piezoelectric smart structures is an ongoing, in-house activity at the NASA Glenn Research Center at Lewis Field focused toward the experimental characterization of these materials. Research efforts have been directed toward developing analytical models that account for the coupled mechanical, electrical, and thermal response of piezoelectric composite materials. Current work revolves around implementing thermal effects into a curvilinear-shell finite element code. This enhances capabilities to analyze curved structures and to account for coupling effects arising from thermal effects and the curved geometry. The current analytical model implements a unique mixed multi-field laminate theory to improve computational efficiency without sacrificing accuracy. The mechanics can model both the sensory and active behavior of piezoelectric composite shell structures. Finite element equations are being implemented for an eight-node curvilinear shell element, and numerical studies are being conducted to demonstrate capabilities to model the response of curved piezoelectric composite structures (see the figure).
Power flows and Mechanical Intensities in structural finite element analysis
NASA Technical Reports Server (NTRS)
Hambric, Stephen A.
1989-01-01
The identification of power flow paths in dynamically loaded structures is an important, but currently unavailable, capability for the finite element analyst. For this reason, methods for calculating power flows and mechanical intensities in finite element models are developed here. Formulations for calculating input and output powers, power flows, mechanical intensities, and power dissipations for beam, plate, and solid element types are derived. NASTRAN is used to calculate the required velocity, force, and stress results of an analysis, which a post-processor then uses to calculate power flow quantities. The SDRC I-deas Supertab module is used to view the final results. Test models include a simple truss and a beam-stiffened cantilever plate. Both test cases showed reasonable power flow fields over low to medium frequencies, with accurate power balances. Future work will include testing with more complex models, developing an interactive graphics program to view easily and efficiently the analysis results, applying shape optimization methods to the problem with power flow variables as design constraints, and adding the power flow capability to NASTRAN.
Development of a Specific Finite Element for Timber Joint Modeling
NASA Astrophysics Data System (ADS)
Descamps, Thierry; Van Parys, Laurent; Datoussaïd, Sélim
2011-01-01
Widely used for light frame structures or for heavy laminated wood structures, dowel-type fasteners are the most commonly used kind of connectors in timber construction. The purpose of this work is to develop a tool for the semi-rigid analysis and design of such joints. Firstly, interests and approaches described in literature for the semi-rigid modeling of timber plane frames are summarized. Secondly, for a better understanding of the problem, the main characteristics of wood used as a structural material are presented. Finally, a method for an efficient study of joints built with dowel-type fasteners is proposed and developed. This method consists of the introduction of a specific finite element called "Finite Semi-Rigid Element (FSRE)" between the ends of the jointed members. This joint element consists of two nodes, each with three degrees of freedom. These nodes will be tied with common beamelements during the FE analysis. The stiffness of the FSRE is computed from the geometry of the joints and embedding stiffness of all fasteners, along and perpendicular to the grain. The embedding characteristics of fasteners are defined with help of their experimental load-slip curves (fitted with Foschi's models) leading finally to the resolution of a FE non-linear problem.
Numerical algorithms for finite element computations on arrays of microprocessors
NASA Technical Reports Server (NTRS)
Ortega, J. M.
1981-01-01
The development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization.
Thermal Analysis of Thin Plates Using the Finite Element Method
NASA Astrophysics Data System (ADS)
Er, G. K.; Iu, V. P.; Liu, X. L.
2010-05-01
The isotropic thermal plate is analyzed with finite element method. The solution procedure is presented. The elementary stiffness matrix and loading vector are derived rigorously with variation principle and the principle of minimum potential energy. Numerical results are obtained based on the derived equations and tested with available exact solutions. The problems in the finite element analysis are figured out. It is found that the finite element solutions can not converge as the number of elements increases around the corners of the plate. The derived equations presented in this paper are fundamental for our further study on more complicated thermal plate analysis.
Finite element solution of optimal control problems with inequality constraints
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1990-01-01
A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.
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)
A multilevel finite element method for Fredholm integral eigenvalue problems
NASA Astrophysics Data System (ADS)
Xie, Hehu; Zhou, Tao
2015-12-01
In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.
Adaptive Mesh Refinement Algorithms for Parallel Unstructured Finite Element Codes
Parsons, I D; Solberg, J M
2006-02-03
This project produced algorithms for and software implementations of adaptive mesh refinement (AMR) methods for solving practical solid and thermal mechanics problems on multiprocessor parallel computers using unstructured finite element meshes. The overall goal is to provide computational solutions that are accurate to some prescribed tolerance, and adaptivity is the correct path toward this goal. These new tools will enable analysts to conduct more reliable simulations at reduced cost, both in terms of analyst and computer time. Previous academic research in the field of adaptive mesh refinement has produced a voluminous literature focused on error estimators and demonstration problems; relatively little progress has been made on producing efficient implementations suitable for large-scale problem solving on state-of-the-art computer systems. Research issues that were considered include: effective error estimators for nonlinear structural mechanics; local meshing at irregular geometric boundaries; and constructing efficient software for parallel computing environments.
NASA Technical Reports Server (NTRS)
Hashemi-Kia, M.; Toossi, M.
1990-01-01
As a result of this work, a reduction procedure has been developed which can be applied to large finite element model of airframe type structures. This procedure, which is tailored to be used with MSC/NASTRAN finite element code, is applied to the full airframe dynamic finite element model of AH-64A Attack Helicopter. The applicability of the resulting reduced model to parametric and optimization studies is examined. Through application of the design sensitivity analysis, the viability and efficiency of this reduction technique has been demonstrated in a vibration reduction study.
NASA Technical Reports Server (NTRS)
Atluri, S. N.; Nakagaki, M.; Kathiresan, K.
1980-01-01
In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.
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
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.
Modeling Progressive Failure of Bonded Joints Using a Single Joint Finite Element
NASA Technical Reports Server (NTRS)
Stapleton, Scott E.; Waas, Anthony M.; Bednarcyk, Brett A.
2010-01-01
Enhanced finite elements are elements with an embedded analytical solution which can capture detailed local fields, enabling more efficient, mesh-independent finite element analysis. In the present study, an enhanced finite element is applied to generate a general framework capable of modeling an array of joint types. The joint field equations are derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields are used to generate shape functions and a stiffness matrix for a single joint finite element. This single finite element thus captures the detailed stress and strain fields within the bonded joint, but it can function within a broader structural finite element model. The costs associated with a fine mesh of the joint can thus be avoided while still obtaining a detailed solution for the joint. Additionally, the capability to model non-linear adhesive constitutive behavior has been included within the method, and progressive failure of the adhesive can be modeled by using a strain-based failure criteria and re-sizing the joint as the adhesive fails. Results of the model compare favorably with experimental and finite element results.
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.
Nonlinear finite element modeling of THUNDER piezoelectric actuators
NASA Astrophysics Data System (ADS)
Taleghani, Barmac K.; Campbell, Joel F.
1999-06-01
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.
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.
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.
A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations
NASA Technical Reports Server (NTRS)
Hu, Changqing; Shu, Chi-Wang
1998-01-01
In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.
NASA Astrophysics Data System (ADS)
Koleva, M. N.
2007-10-01
We consider stationary linear and nonlinear problems on non-connected layers with distinct material properties. A version of the finite element method (FEM) is used for discretization of the continuous problems. We formulate sufficient conditions under which we prove the discrete maximum principle and convergence of the numerical higher-order finite elements solution. Efficient algorithm for solution of the FEM algebraic equations is proposed. Numerical experiments are also discussed.
NASA Technical Reports Server (NTRS)
Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume
1998-01-01
We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.
A finite element method for analysis of vibration induced by maglev trains
NASA Astrophysics Data System (ADS)
Ju, S. H.; Ho, Y. S.; Leong, C. C.
2012-07-01
This paper developed a finite element method to perform the maglev train-bridge-soil interaction analysis with rail irregularities. An efficient proportional integral (PI) scheme with only a simple equation is used to control the force of the maglev wheel, which is modeled as a contact node moving along a number of target nodes. The moving maglev vehicles are modeled as a combination of spring-damper elements, lumped mass and rigid links. The Newmark method with the Newton-Raphson method is then used to solve the nonlinear dynamic equation. The major advantage is that all the proposed procedures are standard in the finite element method. The analytic solution of maglev vehicles passing a Timoshenko beam was used to validate the current finite element method with good agreements. Moreover, a very large-scale finite element analysis using the proposed scheme was also tested in this paper.
Finite Element Transient Dynamic Analysis of Laminated Stiffened Shells
NASA Astrophysics Data System (ADS)
PRUSTY, B. GANGADHARA; SATSANGI, S. K.
2001-11-01
The present work describes the transient dynamic response of unstiffened/stiffened composite plates/shells using finite element method. Composite panels find wide applications in aerospace, marine and other engineering because of its high strength to weight ratios. These structures are often subjected to air-blast loading, underwater shock etc., which requires a thorough dynamic response analysis under such loading. A modified approach of shell and stiffener modelling is adopted here using an eight-noded isoparametric quadratic element for the shell and a three-noded curved stiffener element for the stiffeners on the concept of equal displacements at the shell-stiffener interface. The present formulation obviates the need for imposing the mesh line along the stiffeners; rather it accommodates the stiffeners elegantly anywhere placed arbitrarily inside the element with computational efficiency. Newmarks method for direct time integration has been adopted for the solution of the governing equation for undamped motion. The transient dynamic response of stiffened and unstiffened structures subjected to various kinds of time variant loading has been studied and the results are compared with the published ones.
Architecting the Finite Element Method Pipeline for the GPU
Fu, Zhisong; Lewis, T. James; Kirby, Robert M.
2014-01-01
The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers. PMID:25202164
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.
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.
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.
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.
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.
Efficient linear and nonlinear heat conduction with a quadrilateral element
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.
1984-01-01
A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2 and 1 for the normalized stabilization parameter lead to the 5-point finite difference, 9-point finite difference and fully integrated finite element operators, respectively, for rectangular meshes; numerical experiments reported here show that the three have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.
The use of Galerkin finite-element methods to solve mass-transport equations
Grove, David B.
1977-01-01
The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)
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.
Finite Element Analysis for Pseudo Hyperbolic Integral-Differential Equations
NASA Astrophysics Data System (ADS)
Cui, Xia
The finite element method and its analysis for pseudo-hyperbolic integral-differential equations with nonlinear boundary conditions is considered. A new projection is introduced to obtain optimal L2 convergence estimates. The present techniques can be applied to treat elastic wave problems with absorbing boundary conditions in porous media. Keywords: pseudo-hyperbolic integral-differential equation, finite element, Sobolev-Volterra projection, convergence analysis
Simulation of two-dimensional waterflooding using mixed finite elements
Chavent, G.; Jaffre, J.; Cohen, G.; Dupuy, M.; Dieste, I.
1982-01-01
A new method for the simulation of incompressible diphasic flows in two dimensions is presented, the distinctive features of which are: (1) reformation of the basic equation and specific choices of the finite element approximation of the same; (11) use of a mixed finite elements method, approximating both scalar and vector functions. Several test examples are shown, including gravity and capillary effects. The use of discontinuous basis functions proved successful for an accurate representation of sharp fronts. 16 refs.
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.
Finite element analysis of vibration and damping of laminated composites
NASA Astrophysics Data System (ADS)
Rikards, Rolands
Simple finite elements are used to form a special laminated beam and plate superelements excluding all degrees of freedom in the nodes of the middle layer, and the finite element analysis of this structure is performed. To estimate damping of structures, modal loss factors are calculated, using two methods: the 'exact' method of complex eigenvalues and the approximate energy method. It was found that both methods give satisfactory results. However, the energy method needs less computer time than the exact method.
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.
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.
Application of the Finite-Element Z-Matrix Method to e-H2 Collisions
NASA Technical Reports Server (NTRS)
Huo, Winifred M.; Brown, David; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
The present study adapts the Z-matrix formulation using a mixed basis of finite elements and Gaussians. This is a energy-independent basis which allows flexible boundary conditions and is amenable to efficient algorithms for evaluating the necessary matrix elements with molecular targets.
NASA Technical Reports Server (NTRS)
Vos, R. G.; Straayer, J. W.
1975-01-01
The BOPACE 3-D is a finite element computer program, which provides a general family of three-dimensional isoparametric solid elements, and includes a new algorithm for improving the efficiency of the elastic-plastic-creep solution procedure. Theoretical, user, and programmer oriented sections are presented to describe the program.
Finite element adaptive mesh analysis using a cluster of workstations
NASA Astrophysics Data System (ADS)
Wang, K. P.; Bruch, J. C., Jr.
1998-01-01
Parallel computation on clusters of workstations is becoming one of the major trends in the study of parallel computations, because of their high computing speed, cost effectiveness and scalability. This paper presents studies of using a cluster of workstations for the finite element adaptive mesh analysis of a free surface seepage problem. A parallel algorithm proven to be simple to implement and efficient is used to perform the analysis. A network of workstations is used as the hardware of a parallel system. Two parallel software packages, P4 and PVM (parallel virtual machine), are used to handle communications among networked workstations. Computational issues to be discussed are domain decomposition, load balancing, and communication time.
A Lagrange multiplier based divide and conquer finite element algorithm
NASA Technical Reports Server (NTRS)
Farhat, C.
1991-01-01
A novel domain decomposition method based on a hybrid variational principle is presented. Prior to any computation, a given finite element mesh is torn into a set of totally disconnected submeshes. First, an incomplete solution is computed in each subdomain. Next, the compatibility of the displacement field at the interface nodes is enforced via discrete, polynomial and/or piecewise polynomial Lagrange multipliers. In the static case, each floating subdomain induces a local singularity that is resolved very efficiently. The interface problem associated with this domain decomposition method is, in general, indefinite and of variable size. A dedicated conjugate projected gradient algorithm is developed for solving the latter problem when it is not feasible to explicitly assemble the interface operator. When implemented on local memory multiprocessors, the proposed methodology requires less interprocessor communication than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory and compares favorably with factorization based parallel direct methods.
Nonlinear geometrically adaptive finite element model of the coilbox
Troyani, N.
1996-12-01
Hot bar heat loss in the transfer table, the rolling stage between rougher stands and finishing stands in a hot mill, is of major concern for reasons for energy consumption, metallurgical uniformity, and rollability. A mathematical model, as well as the corresponding numerical solution, is presented for the evolution of temperature in a coiling and uncoiling bar in hot mills in the form of a parabolic partial differential equation for a shape-changing domain. The space discretization is achieved via a computationally efficient geometrically adaptive finite element scheme that accommodates the change in shape of the domain, using a computationally novel treatment of the resulting thermal contact problem due to coiling. Time is discretized according to a Crank-Nicolson scheme. Finally, some numerical results are presented.
FINITE ELEMENT MODEL FOR TIDES AND CURRENTS WITH FIELD APPLICATIONS.
Walters, Roy A.
1988-01-01
A finite element model, based upon the shallow water equations, is used to calculate tidal amplitudes and currents for two field-scale test problems. Because tides are characterized by line spectra, the governing equations are subjected to harmonic decomposition. Thus the solution variables are the real and imaginary parts of the amplitude of sea level and velocity rather than a time series of these variables. The time series is recovered through synthesis. This scheme, coupled with a modified form of the governing equations, leads to high computational efficiency and freedom from excessive numerical noise. Two test-cases are presented. The first is a solution for eleven tidal constituents in the English Channel and southern North Sea, and three constituents are discussed. The second is an analysis of the frequency response and tidal harmonics for south San Francisco Bay.
Two-dimensional finite element model of the pultrusion process
NASA Technical Reports Server (NTRS)
Hackett, Robert M.; Zhu, Si-Ze
1992-01-01
Composite materials used in the fabrication of industrial products/components are under constant development. Applications vary widely from consumer products to high-performance aerospace components. The pultrusion process is one of the important methods of production of composite materials. In order to develop a fundamental understanding of this process, a computational model employing the finite element method is developed which enables a prediction of the material temperature and degree-of-cure at any time during the process. The model is comprehensive; it can readily be employed to perform parametric studies of the process and to aid in the development of efficient design procedures for this type of material system. Comparisons are made between model predictions and experimental results and good agreement is observed.
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.
A new parallel-vector finite element analysis software on distributed-memory computers
NASA Technical Reports Server (NTRS)
Qin, Jiangning; Nguyen, Duc T.
1993-01-01
A new parallel-vector finite element analysis software package MPFEA (Massively Parallel-vector Finite Element Analysis) is developed for large-scale structural analysis on massively parallel computers with distributed-memory. MPFEA is designed for parallel generation and assembly of the global finite element stiffness matrices as well as parallel solution of the simultaneous linear equations, since these are often the major time-consuming parts of a finite element analysis. Block-skyline storage scheme along with vector-unrolling techniques are used to enhance the vector performance. Communications among processors are carried out concurrently with arithmetic operations to reduce the total execution time. Numerical results on the Intel iPSC/860 computers (such as the Intel Gamma with 128 processors and the Intel Touchstone Delta with 512 processors) are presented, including an aircraft structure and some very large truss structures, to demonstrate the efficiency and accuracy of MPFEA.
Scalable Implementation of Finite Elements by NASA _ Implicit (ScIFEi)
NASA Technical Reports Server (NTRS)
Warner, James E.; Bomarito, Geoffrey F.; Heber, Gerd; Hochhalter, Jacob D.
2016-01-01
Scalable Implementation of Finite Elements by NASA (ScIFEN) is a parallel finite element analysis code written in C++. ScIFEN is designed to provide scalable solutions to computational mechanics problems. It supports a variety of finite element types, nonlinear material models, and boundary conditions. This report provides an overview of ScIFEi (\\Sci-Fi"), the implicit solid mechanics driver within ScIFEN. A description of ScIFEi's capabilities is provided, including an overview of the tools and features that accompany the software as well as a description of the input and output le formats. Results from several problems are included, demonstrating the efficiency and scalability of ScIFEi by comparing to finite element analysis using a commercial code.
Bailey, T S; Adams, M L; Yang, B; Zika, M R
2005-07-15
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.
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.
Finite element methods for enhanced oil recovery Simulation
Cohen, M.F.
1985-02-01
A general, finite element procedure for reservoir simulation is presented. This effort is directed toward improving the numerical behavior of standard upstream, or upwind, finite difference techniques, without significantly increasing the computational costs. Two methods from previous authors' work are modified and developed: upwind finite elements and the Petrov-Galerkin method. These techniques are applied in a one- and two-dimensional, surfactant/ polymer simulator. The paper sets forth the mathematical formulation and several details concerning the implementation. The results indicate that the PetrovGalerkin method does significantly reduce numericaldiffusion errors, while it retains the stability of the first-order, upwind methods. It is also relatively simple to implement. Both the upwind, and PetrovGalerkin, finite element methods demonstrate little sensitivity to grid orientation.
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.
NASA Technical Reports Server (NTRS)
Saleeb, A. F.; Chang, T. Y. P.; Wilt, T.; Iskovitz, I.
1989-01-01
The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.
An alternative Laplacian electrostatic field finite element formulation
Barber, P.F.; Lauber, T.S.
1987-01-01
An alternative finite element method for calculating three-dimensional electrostatic fields is described. The matrix equation is assembled using linear tetrahedral elements and an electrical network solution techniques known as impedance matrix building with axis discarding. The solutions of sample problems are described.
Grid generation for two-dimensional finite element flowfield computation
NASA Technical Reports Server (NTRS)
Tatum, K. E.
1980-01-01
The finite element method for fluid dynamics was used to develop a two dimensional mesh generation scheme. The method consists of shearing and conformal maps with upper and lower surfaces handled independently to allow sharp leading edges. The method also generates meshes of triangular or quadrilateral elements.
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.
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.
Exponential convergence through linear finite element discretization of stratified subdomains
NASA Astrophysics Data System (ADS)
Guddati, Murthy N.; Druskin, Vladimir; Vaziri Astaneh, Ali
2016-10-01
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The key features of the discretization are (a) use of midpoint integration to evaluate the contribution matrices, and (b) an unconventional mapping of the mesh into complex space. Named complex-length finite element method (CFEM), the technique is linked to Padé approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain. Exponential convergence facilitates drastic reduction in the number of elements. This, combined with sparse computation associated with linear finite elements, results in significant reduction in the computational cost. The paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving Laplace, Helmholtz and elastodynamics equations.
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.
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.
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
Accelerated finite element elastodynamic simulations using the GPU
NASA Astrophysics Data System (ADS)
Huthwaite, Peter
2014-01-01
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.
NASA Technical Reports Server (NTRS)
Ecer, A.; Akay, H. U.
1981-01-01
The finite element method is applied for the solution of transonic potential flows through a cascade of airfoils. Convergence characteristics of the solution scheme are discussed. Accuracy of the numerical solutions is investigated for various flow regions in the transonic flow configuration. The design of an efficient finite element computational grid is discussed for improving accuracy and convergence.
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.
NASA Astrophysics Data System (ADS)
Kouhi, Mohammad; Oñate, Eugenio
2015-07-01
A new implicit stabilized formulation for the numerical solution of the compressible Navier-Stokes equations is presented. The method is based on the finite calculus (FIC) scheme using the Galerkin finite element method (FEM) on triangular grids. Via the FIC formulation, two stabilization terms, called streamline term and transverse term, are added to the original conservation equations in the space-time domain. The non-linear system of equations resulting from the spatial discretization is solved implicitly using a damped Newton method benefiting from the exact Jacobian matrix. The matrix system is solved at each iteration with a preconditioned GMRES method. The efficiency of the proposed stabilization technique is checked out in the solution of 2D inviscid and laminar viscous flow problems where appropriate solutions are obtained especially near the boundary layer and shock waves. The work presented here can be considered as a follow up of a previous work of the authors Kouhi, Oñate (Int J Numer Methods Fluids 74:872-897, 2014). In that paper, the stabilized Galerkin FEM based on the FIC formulation was derived for the Euler equations together with an explicit scheme. In the present paper, the extension of this work to the Navier-Stokes equations using an implicit scheme is presented.
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.
Thermal Analysis of a High-Speed Aircraft Wing Using p-Version Finite Elements
NASA Technical Reports Server (NTRS)
Gould, Dana C.
2001-01-01
This paper presents the results of conceptual level thermal analyses of a High Speed Civil Transport (HSCT) wing using p-version finite elements. The work was motivated by a thermal analysis of a HSCT wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining a traditional finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Further study indicated using p-version finite elements might improve computation performance for this class of problem. Methods for determining internal radiation heat transfer were then developed and demonstrated on test problems representative of the geometry found in an aircraft wing structure. This paper presents the results of the application of these new methods to the analysis of a high speed aircraft wing. Results for both a wing box model as well as a full wing model are presented. 'Me reduced wing box model allows for a comparison of the traditional finite element method with mesh refinement (h-refinement) to the new p-version finite elements while the full wing model demonstrates the applicability and efficiency of p-version finite elements for large models.
Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint
Wang, Q.; Sprague, M. A.; Jonkman, J.; Johnson, N.
2014-01-01
This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context of LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.
Bailey, Teresa S. Adams, Marvin L. Yang, Brian Zika, Michael R.
2008-04-01
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.
Efficient linear and nonlinear heat conduction with a quadrilateral element
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.
1983-01-01
A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2, and 1 for the normalized stabilization parameter lead to the 5-point, 9-point finite difference, and fully integrated finite element operators, respectively, for rectangular meshes and have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.
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.
Flow Applications of the Least Squares Finite Element Method
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
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.
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.
Adaptive finite-element ballooning analysis of bipolar ionized fields
Al-Hamouz, Z.M.
1995-12-31
This paper presents an adaptive finite-element iterative method for the analysis of the ionized field around high-voltage bipolar direct-current (HVDC) transmission line conductors without resort to Deutsch`s assumption. A new iterative finite-element ballooning technique is proposed to solve Poisson`s equation wherein the commonly used artificial boundary around the transmission line conductors is simulated at infinity. Unlike all attempts reported in the literature for the solution of ionized field, the constancy of the conductors` surface field at the corona onset value is directly implemented in the finite-element formulation. In order to investigate the effectiveness of the proposed method, a laboratory model was built. It has been found that the calculated V-I characteristics and the ground-plane current density agreed well with those measured experimentally. The simplicity in computer programming in addition to the low number of iterations required to achieve convergence characterize this method of analysis.
Electrical and Joule heating relationship investigation using Finite Element Method
NASA Astrophysics Data System (ADS)
Thangaraju, S. K.; Munisamy, K. M.
2015-09-01
The finite element method is vastly used in material strength analysis. The nature of the finite element solver, which solves the Fourier equation of stress and strain analysis, made it possible to apply for conduction heat transfer Fourier Equation. Similarly the Current and voltage equation is also liner Fourier equation. The nature of the governing equation makes it possible to numerical investigate the electrical joule heating phenomena in electronic component. This paper highlights the Finite Element Method (FEM) application onto semiconductor interconnects to determine the specific contact resistance (SCR). Metal and semiconductor interconnects is used as model. The result confirms the possibility and validity of FEM utilization to investigate the Joule heating due electrical resistance.
Derivation of a Tappered p-Version Beam Finite Element
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1989-01-01
A tapered p-version beam finite element suitable for dynamic applications is derived. The taper in the element is represented by allowing the area moments of inertia to vary as quartic polynomials along the length of the beam, and the cross-sectional area to vary as a quadratic polynomial. The p-version finite-element characteristics are implemented through a set of polynomial shape functions. The lower-order shape functions are identical to the classical cubic and linear shape functions normally associated with a beam element. The higher-order shape functions are a hierarchical set of polynomials that are integrals of orthogonal polynomials. Explicit expressions for the mass and stiffness matrices are presented for an arbitrary value of p. The element has been verified to be numerically stable using shape functions through 22nd order.
Overview of adaptive finite element analysis in computational geodynamics
NASA Astrophysics Data System (ADS)
May, D. A.; Schellart, W. P.; Moresi, L.
2013-10-01
The use of numerical models to develop insight and intuition into the dynamics of the Earth over geological time scales is a firmly established practice in the geodynamics community. As our depth of understanding grows, and hand-in-hand with improvements in analytical techniques and higher resolution remote sensing of the physical structure and state of the Earth, there is a continual need to develop more efficient, accurate and reliable numerical techniques. This is necessary to ensure that we can meet the challenge of generating robust conclusions, interpretations and predictions from improved observations. In adaptive numerical methods, the desire is generally to maximise the quality of the numerical solution for a given amount of computational effort. Neither of these terms has a unique, universal definition, but typically there is a trade off between the number of unknowns we can calculate to obtain a more accurate representation of the Earth, and the resources (time and computational memory) required to compute them. In the engineering community, this topic has been extensively examined using the adaptive finite element (AFE) method. Recently, the applicability of this technique to geodynamic processes has started to be explored. In this review we report on the current status and usage of spatially adaptive finite element analysis in the field of geodynamics. The objective of this review is to provide a brief introduction to the area of spatially adaptive finite analysis, including a summary of different techniques to define spatial adaptation and of different approaches to guide the adaptive process in order to control the discretisation error inherent within the numerical solution. An overview of the current state of the art in adaptive modelling in geodynamics is provided, together with a discussion pertaining to the issues related to using adaptive analysis techniques and perspectives for future research in this area. Additionally, we also provide a
Parallel performance of a preconditioned CG solver for unstructured finite element applications
Shadid, J.N.; Hutchinson, S.A.; Moffat, H.K.
1994-12-31
A parallel unstructured finite element (FE) implementation designed for message passing MIMD machines is described. This implementation employs automated problem partitioning algorithms for load balancing unstructured grids, a distributed sparse matrix representation of the global finite element equations and a parallel conjugate gradient (CG) solver. In this paper a number of issues related to the efficient implementation of parallel unstructured mesh applications are presented. These include the differences between structured and unstructured mesh parallel applications, major communication kernels for unstructured CG solvers, automatic mesh partitioning algorithms, and the influence of mesh partitioning metrics on parallel performance. Initial results are presented for example finite element (FE) heat transfer analysis applications on a 1024 processor nCUBE 2 hypercube. Results indicate over 95% scaled efficiencies are obtained for some large problems despite the required unstructured data communication.
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
Finite element methods for nonlinear elastostatic problems in rubber elasticity
NASA Technical Reports Server (NTRS)
Oden, J. T.; Becker, E. B.; Miller, T. H.; Endo, T.; Pires, E. B.
1983-01-01
A number of finite element methods for the analysis of nonlinear problems in rubber elasticity are outlined. Several different finite element schemes are discussed. These include the augmented Lagrangian method, continuation or incremental loading methods, and associated Riks-type methods which have the capability of incorporating limit point behavior and bifurcations. Algorithms for the analysis of limit point behavior and bifurcations are described and the results of several numerical experiments are presented. In addition, a brief survey of some recent work on modelling contact and friction in elasticity problems is given. These results pertain to the use of new nonlocal and nonlinear friction laws.
Substructure System Identification for Finite Element Model Updating
NASA Technical Reports Server (NTRS)
Craig, Roy R., Jr.; Blades, Eric L.
1997-01-01
This report summarizes research conducted under a NASA grant on the topic 'Substructure System Identification for Finite Element Model Updating.' The research concerns ongoing development of the Substructure System Identification Algorithm (SSID Algorithm), a system identification algorithm that can be used to obtain mathematical models of substructures, like Space Shuttle payloads. In the present study, particular attention was given to the following topics: making the algorithm robust to noisy test data, extending the algorithm to accept experimental FRF data that covers a broad frequency bandwidth, and developing a test analytical model (TAM) for use in relating test data to reduced-order finite element models.
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
NASA Astrophysics Data System (ADS)
Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.
2016-09-01
In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation.
Correlation of composite material test results with finite element analysis
NASA Astrophysics Data System (ADS)
Guƫu, M.
2016-08-01
In this paper are presented some aspects regarding the method of simulation of composite materials testing with finite element analysis software. There were simulated tensile and shear tests of specimens manufactured from glass fiber reinforced polyester. For specimens manufacturing two types of fabrics were used: unidirectional and bidirectional. Experimentally determined elastic properties of composite material were used as input data. Modeling of composite architecture of the specimens was performed with ANSYS Composite PrepPost software. Finite element analysis stresses and strains on strain gauges bonding area were considered and compared with the real values in a diagram. After results comparison, potential causes of deviations were identified.
A weak Galerkin generalized multiscale finite element method
Mu, Lin; Wang, Junping; Ye, Xiu
2016-03-31
In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case.
Experimentally validated finite element model of electrocaloric multilayer ceramic structures
Smith, N. A. S. E-mail: maciej.rokosz@npl.co.uk Correia, T. M. E-mail: maciej.rokosz@npl.co.uk; Rokosz, M. K. E-mail: maciej.rokosz@npl.co.uk
2014-07-28
A novel finite element model to simulate the electrocaloric response of a multilayer ceramic capacitor (MLCC) under real environment and operational conditions has been developed. The two-dimensional transient conductive heat transfer model presented includes the electrocaloric effect as a source term, as well as accounting for radiative and convective effects. The model has been validated with experimental data obtained from the direct imaging of MLCC transient temperature variation under application of an electric field. The good agreement between simulated and experimental data, suggests that the novel experimental direct measurement methodology and the finite element model could be used to support the design of optimised electrocaloric units and operating conditions.
Development of non-linear finite element computer code
NASA Technical Reports Server (NTRS)
Becker, E. B.; Miller, T.
1985-01-01
Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein.
Finite element models of the space shuttle main engine
NASA Technical Reports Server (NTRS)
Muller, G. R.
1980-01-01
Finite element models were developed as input to dynamic simulations of the high pressure fuel turbopump (HPFTP), the high pressure oxidizer turbopump (HPOTP), and the space shuttle main engine (SSME). Descriptions are provided for the five basic finite element models: HPFTP rotor, HPFTP case, HPOTP rotor, HPOTP case, and SSME (excluding turbopumps). Modal results are presented for the HPFTP rotor, HPFTP case, HPOTP rotor, coupled HPFTP rotor and case, HPOTP case, coupled HPOTP rotor and case, SSME (excluding turbopumps), and SSME (including turbopumps). Results for the SSME (including turbopumps) model are compared to data from a SSME HPOTP modal survey.
Diffusive mesh relaxation in ALE finite element numerical simulations
Dube, E.I.
1996-06-01
The theory for a diffusive mesh relaxation algorithm is developed for use in three-dimensional Arbitary Lagrange/Eulerian (ALE) finite element simulation techniques. This mesh relaxer is derived by a variational principle for an unstructured 3D grid using finite elements, and incorporates hourglass controls in the numerical implementation. The diffusive coefficients are based on the geometric properties of the existing mesh, and are chosen so as to allow for a smooth grid that retains the general shape of the original mesh. The diffusive mesh relaxation algorithm is then applied to an ALE code system, and results from several test cases are discussed.
Discontinuous Galerkin finite element methods for gradient plasticity.
Garikipati, Krishna.; Ostien, Jakob T.
2010-10-01
In this report we apply discontinuous Galerkin finite element methods to the equations of an incompatibility based formulation of gradient plasticity. The presentation is motivated with a brief overview of the description of dislocations within a crystal lattice. A tensor representing a measure of the incompatibility with the lattice is used in the formulation of a gradient plasticity model. This model is cast in a variational formulation, and discontinuous Galerkin machinery is employed to implement the formulation into a finite element code. Finally numerical examples of the model are shown.
Robust Hybrid Finite Element Methods for Antennas and Microwave Circuits
NASA Technical Reports Server (NTRS)
Gong, J.; Volakis, John L.
1996-01-01
One of the primary goals in this dissertation is concerned with the development of robust hybrid finite element-boundary integral (FE-BI) techniques for modeling and design of conformal antennas of arbitrary shape. Both the finite element and integral equation methods will be first overviewed in this chapter with an emphasis on recently developed hybrid FE-BI methodologies for antennas, microwave and millimeter wave applications. The structure of the dissertation is then outlined. We conclude the chapter with discussions of certain fundamental concepts and methods in electromagnetics, which are important to this study.
Two-dimensional finite-element temperature variance analysis
NASA Technical Reports Server (NTRS)
Heuser, J. S.
1972-01-01
The finite element method is extended to thermal analysis by forming a variance analysis of temperature results so that the sensitivity of predicted temperatures to uncertainties in input variables is determined. The temperature fields within a finite number of elements are described in terms of the temperatures of vertices and the variational principle is used to minimize the integral equation describing thermal potential energy. A computer calculation yields the desired solution matrix of predicted temperatures and provides information about initial thermal parameters and their associated errors. Sample calculations show that all predicted temperatures are most effected by temperature values along fixed boundaries; more accurate specifications of these temperatures reduce errors in thermal calculations.
Finite element microscopic stress analysis of cracked composite systems
NASA Technical Reports Server (NTRS)
Ko, W. L.
1978-01-01
This paper considers the stress concentration problems of two types of cracked composite systems: (1) a composite system with a broken fiber (a penny-shaped crack problem), and (2) a composite system with a cracked matrix (an annular crack problem). The cracked composite systems are modeled with triangular and trapezoidal ring finite elements. Using NASTRAN (NASA Structural Analysis) finite element computer program, the stress and deformation fields in the cracked composite systems are calculated. The effect of fiber-matrix material combination on the stress concentrations and on the crack opening displacements is studied.
Higher-order adaptive finite-element methods for orbital-free density functional theory
Motamarri, Phani; Iyer, Mrinal; Knap, Jaroslaw; Gavini, Vikram
2012-08-15
In the present work, we study various numerical aspects of higher-order finite-element discretizations of the non-linear saddle-point formulation of orbital-free density-functional theory. We first investigate the robustness of viable solution schemes by analyzing the solvability conditions of the discrete problem. We find that a staggered solution procedure where the potential fields are computed consistently for every trial electron-density is a robust solution procedure for higher-order finite-element discretizations. We next study the convergence properties of higher-order finite-element discretizations of orbital-free density functional theory by considering benchmark problems that include calculations involving both pseudopotential as well as Coulomb singular potential fields. Our numerical studies suggest close to optimal rates of convergence on all benchmark problems for various orders of finite-element approximations considered in the present study. We finally investigate the computational efficiency afforded by various higher-order finite-element discretizations, which constitutes the main aspect of the present work, by measuring the CPU time for the solution of discrete equations on benchmark problems that include large Aluminum clusters. In these studies, we use mesh coarse-graining rates that are derived from error estimates and an a priori knowledge of the asymptotic solution of the far-field electronic fields. Our studies reveal a significant 100-1000 fold computational savings afforded by the use of higher-order finite-element discretization, alongside providing the desired chemical accuracy. We consider this study as a step towards developing a robust and computationally efficient discretization of electronic structure calculations using the finite-element basis.
Finite Element Model Development and Validation 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. The increased frequency range results in a corresponding increase in the number of modes, modal density and spatial resolution requirements. In this study, conventional modal tests using accelerometers are complemented with Scanning Laser Doppler Velocimetry and Electro-Optic Holography measurements to further resolve the spatial response characteristics. Whenever possible, component and subassembly modal tests are used to validate the finite element models at lower levels of assembly. Normal mode predictions for different finite element representations of components and assemblies are compared with experimental results to assess the most accurate techniques for modeling aircraft fuselage type structures.
Finite element method for optimal guidance of an advanced launch vehicle
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.; Calise, Anthony J.; Leung, Martin
1992-01-01
A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.
A comparative study of an ABC and an artificial absorber for truncating finite element meshes
NASA Technical Reports Server (NTRS)
Oezdemir, T.; Volakis, John L.
1993-01-01
The type of mesh termination used in the context of finite element formulations plays a major role on the efficiency and accuracy of the field solution. The performance of an absorbing boundary condition (ABC) and an artificial absorber (a new concept) for terminating the finite element mesh was evaluated. This analysis is done in connection with the problem of scattering by a finite slot array in a thick ground plane. The two approximate mesh truncation schemes are compared with the exact finite element-boundary integral (FEM-BI) method in terms of accuracy and efficiency. It is demonstrated that both approximate truncation schemes yield reasonably accurate results even when the mesh is extended only 0.3 wavelengths away from the array aperture. However, the artificial absorber termination method leads to a substantially more efficient solution. Moreover, it is shown that the FEM-BI method remains quite competitive with the FEM-artificial absorber method when the FFT is used for computing the matrix-vector products in the iterative solution algorithm. These conclusions are indeed surprising and of major importance in electromagnetic simulations based on the finite element method.
Numerical techniques in linear duct acoustics. [finite difference and finite element analyses
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1980-01-01
Both finite difference and finite element analyses of small amplitude (linear) sound propagation in straight and variable area ducts with flow, as might be found in a typical turboject engine duct, muffler, or industrial ventilation system, are reviewed. Both steady state and transient theories are discussed. Emphasis is placed on the advantages and limitations associated with the various numerical techniques. Examples of practical problems are given for which the numerical techniques have been applied.
The Elastic Behaviour of Sintered Metallic Fibre Networks: A Finite Element Study by Beam Theory
Bosbach, Wolfram A.
2015-01-01
Background The finite element method has complimented research in the field of network mechanics in the past years in numerous studies about various materials. Numerical predictions and the planning efficiency of experimental procedures are two of the motivational aspects for these numerical studies. The widespread availability of high performance computing facilities has been the enabler for the simulation of sufficiently large systems. Objectives and Motivation In the present study, finite element models were built for sintered, metallic fibre networks and validated by previously published experimental stiffness measurements. The validated models were the basis for predictions about so far unknown properties. Materials and Methods The finite element models were built by transferring previously published skeletons of fibre networks into finite element models. Beam theory was applied as simplification method. Results and Conclusions The obtained material stiffness isn’t a constant but rather a function of variables such as sample size and boundary conditions. Beam theory offers an efficient finite element method for the simulated fibre networks. The experimental results can be approximated by the simulated systems. Two worthwhile aspects for future work will be the influence of size and shape and the mechanical interaction with matrix materials. PMID:26569603
FEWA: a Finite Element model of Water flow through Aquifers
Yeh, G.T.; Huff, D.D.
1983-11-01
This report documents the implementation and demonstration of a Finite Element model of Water flow through Aquifers (FEWA). The particular features of FEWA are its versatility and flexibility to deal with as many real-world problems as possible. Point as well as distributed sources/sinks are included to represent recharges/pumpings and rainfall infiltrations. All sources/sinks can be transient or steady state. Prescribed hydraulic head on the Dirichlet boundaries and fluxes on Neumann or Cauchy boundaries can be time-dependent or constant. Source/sink strength over each element and node, hydraulic head at each Dirichlet boundary node, and flux at each boundary segment can vary independently of each other. Either completely confined or completely unconfined aquifers, or partially confined and partially unconfined aquifers can be dealt with effectively. Discretization of a compound region with very irregular curved boundaries is made easy by including both quadrilateral and triangular elements in the formulation. Large-field problems can be solved efficiently by including a pointwise iterative solution strategy as an optional alternative to the direct elimination solution method for the matrix equation approximating the partial differential equation of groundwater flow. FEWA also includes transient flow through confining leaky aquifers lying above and/or below the aquifer of interest. The model is verified against three simple cases to which analytical solutions are available. It is then demonstrated by two examples of how the model can be applied to heterogeneous and anisotropic aquifers with transient boundary conditions, time-dependent sources/sinks, and confining aquitards for a confined aquifer of variable thickness and for a free surface problem in an unconfined aquifer, respectively. 20 references, 25 figures, 8 tables.
New hybrid quadrilateral finite element for Mindlin plate
NASA Astrophysics Data System (ADS)
Chin, Yi; Zhang, Jingyu
1994-02-01
A new quadrilateral plate element concerning the effect of transverse shear strain was presented. It was derived from the hybrid finite element model based on the principles of virtual work. The outstanding advantage of this element was to use more rational trial functions of the displacements. For this reason, every variety of plate deformation can be simulated really while the least degrees of freedom was employed. A wide range of numerical tests was conducted and the results illustrate that this element has a very wide application scope to the thickness of plates and satisfactory accuracy can be obtained by coarse mesh for all kinds of examples.
ATESHIAN, GERARD A.; ALBRO, MICHAEL B.; MAAS, STEVE; WEISS, JEFFREY A.
2012-01-01
Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechano-chemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechano-chemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http://mrl.sci.utah.edu/software). PMID:21950898
NASA Technical Reports Server (NTRS)
Seybert, A. F.; Wu, T. W.; Wu, X. F.
1994-01-01
This research report is presented in three parts. In the first part, acoustical analyses were performed on modes of vibration of the housing of a transmission of a gear test rig developed by NASA. The modes of vibration of the transmission housing were measured using experimental modal analysis. The boundary element method (BEM) was used to calculate the sound pressure and sound intensity on the surface of the housing and the radiation efficiency of each mode. The radiation efficiency of each of the transmission housing modes was then compared to theoretical results for a finite baffled plate. In the second part, analytical and experimental validation of methods to predict structural vibration and radiated noise are presented. A rectangular box excited by a mechanical shaker was used as a vibrating structure. Combined finite element method (FEM) and boundary element method (BEM) models of the apparatus were used to predict the noise level radiated from the box. The FEM was used to predict the vibration, while the BEM was used to predict the sound intensity and total radiated sound power using surface vibration as the input data. Vibration predicted by the FEM model was validated by experimental modal analysis; noise predicted by the BEM was validated by measurements of sound intensity. Three types of results are presented for the total radiated sound power: sound power predicted by the BEM model using vibration data measured on the surface of the box; sound power predicted by the FEM/BEM model; and sound power measured by an acoustic intensity scan. In the third part, the structure used in part two was modified. A rib was attached to the top plate of the structure. The FEM and BEM were then used to predict structural vibration and radiated noise respectively. The predicted vibration and radiated noise were then validated through experimentation.
A General-Purpose Mesh Generator for Finite Element Codes.
1984-02-28
Version 00 INGEN is a general-purpose mesh generator for use in conjunction with two and three dimensional finite element programs. The basic components of INGEN are surface and three-dimensional region generators that use linear-blending interpolation formulae. These generators are based on an i, j, k index scheme, which is used to number nodal points, construct elements, and develop displacement and traction boundary conditions.
A finite element code for electric motor design
NASA Technical Reports Server (NTRS)
Campbell, C. Warren
1994-01-01
FEMOT is a finite element program for solving the nonlinear magnetostatic problem. This version uses nonlinear, Newton first order elements. The code can be used for electric motor design and analysis. FEMOT can be embedded within an optimization code that will vary nodal coordinates to optimize the motor design. The output from FEMOT can be used to determine motor back EMF, torque, cogging, and magnet saturation. It will run on a PC and will be available to anyone who wants to use it.
HEAT2. Two-Dimensional Heat Transfer Finite Element Code
Charman, C.
1993-08-01
HEAT2 is a finite element program for the transient and steady-state, thermal analysis of two-dimensional solids. Calculates detailed temperature distributions in MHTGR prismatic fuel elements side reflector and core support blocks. Non-linear effects of time and temperature dependent boundary conditions, and heat source generation and material properties are included with user supplied subroutines NPBC, QAREA, SOURCE, and MPROP.
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.
The strain-based beam finite elements in multibody dynamics
NASA Astrophysics Data System (ADS)
Gams, M.; Planinc, I.; Saje, M.
2007-08-01
We present a strain-based finite-element formulation for the dynamic analysis of flexible elastic planar multibody systems, composed of planar beams. We consider finite displacements, rotations and strains. The discrete dynamic equations of motion are obtained by the collocation method. The strains are the basic interpolated variables, which makes the formulation different from other formulations. The further speciality of the formulation is the strong satisfaction of the cross-sectional constitutive conditions at collocation points. In order to avoid the nested integrations, a special algorithm for the numerical integration over the length of the finite element is proposed. The midpoint scheme is used for the time integration. The performance of the formulation is illustrated via numerical examples, including a stiff multibody system.
Finite element forced vibration analysis of rotating cyclic structures
NASA Technical Reports Server (NTRS)
Elchuri, V.; Smith, G. C. C.
1981-01-01
A capability was added to the general purpose finite element program NASTRAN Level 17.7 to conduct forced vibration analysis of tuned cyclic structures rotating about their axes of symmetry. The effects of Coriolis and centripetal accelerations together with those due to linear acceleration of the axis of rotation were included. The theoretical development of this capability is presented.
Spanwise variation of potential form drag. [finite element method
NASA Technical Reports Server (NTRS)
Clever, W. C.
1977-01-01
The finite element method is used to calculate the spanwise variation of potential form drag of a wing at subsonic and supersonic speeds using linearly varying panels. The wing may be of arbitrary planform and nonplanar provided the wing panels are parallel to the aircraft axis.
Experiences in interfacing NASTRAN with another finite element program
NASA Technical Reports Server (NTRS)
Schwerzler, D. D.; Leverenz, R. K.
1972-01-01
The coupling of NASTRAN to another finite element program developed for the static analysis of automotive structures is discussed. The two programs were coupled together to use the substructuring capability of the in-house program and the normal mode analysis capability of NASTRAN. Modifications were made to the NASTRAN program in order to make the coupling feasible.
Finite-element analysis of end-notch flexure specimens
NASA Technical Reports Server (NTRS)
Mall, S.; Kochhar, N. K.
1986-01-01
A finite-element analysis of the end-notch flexure specimen for Mode II interlaminar fracture toughness measurement was conducted. The effects of friction between the crack faces and large deflection on the evaluation of G(IIc) from this specimen were investigated. Results of this study are presented in this paper.
Finite element analysis of end notch flexure specimen
NASA Technical Reports Server (NTRS)
Mall, S.; Kochhar, N. K.
1986-01-01
A finite element analysis of the end notch flexure specimen for mode II interlaminar fracture toughness measurement was conducted. The effect of friction between the crack faces and large deflection on the evaluation of G sub IIc from this specimen were investigated. Results of this study are presented in this paper.
SUPG Finite Element Simulations of Compressible Flows for Aerothermodynamic Applications
NASA Technical Reports Server (NTRS)
Kirk, Benjamin S.
2007-01-01
This viewgraph presentation reviews the Streamline-Upwind Petrov-Galerkin (SUPG) Finite Element Simulation. It covers the background, governing equations, weak formulation, shock capturing, inviscid flux discretization, time discretization, linearization, and implicit solution strategies. It also reviews some applications such as Type IV Shock Interaction, Forward-Facing Cavity and AEDC Sharp Double Cone.
Boundary control of parabolic systems - Finite-element approximation
NASA Technical Reports Server (NTRS)
Lasiecka, I.
1980-01-01
The finite element approximation of a Dirichlet type boundary control problem for parabolic systems is considered. An approach based on the direct approximation of an input-output semigroup formula is applied. Error estimates are derived for optimal state and optimal control, and it is noted that these estimates are actually optimal with respect to the approximation theoretic properties.
Finite Element Studies Of Tangent Mounted Conical Optics
NASA Astrophysics Data System (ADS)
Stoneking, J.; Casstevens, J.; Stillman, D.
1982-12-01
This paper presents experimental and analytical results from a study investigating the effect of centrifugal force and gravity on two candidate mirror fixture designs to be used on a diamond-turning ma-chine. The authors illustrate and discuss the use of the finite element method as an aid in the design and fabrication of high precision metallic optical components.
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.
Finite-Element Analysis of Multiphase Immiscible Flow Through Soils
NASA Astrophysics Data System (ADS)
Kuppusamy, T.; Sheng, J.; Parker, J. C.; Lenhard, R. J.
1987-04-01
A finite-element model is developed for multiphase flow through soil involving three immiscible fluids: namely, air, water, and a nonaqueous phase liquid (NAPL). A variational method is employed for the finite-element formulation corresponding to the coupled differential equations governing flow in a three-fluid phase porous medium system with constant air phase pressure. Constitutive relationships for fluid conductivities and saturations as functions of fluid pressures, which are derived in a companion paper by J. C. Parker et al. (this issue) and which may be calibrated from two-phase laboratory measurements, are employed in the finite-element program. The solution procedure uses backward time integration with iteration by a modified Picard method to handle the nonlinear properties. Laboratory experiments involving water displacement from soil columns by p cymene (a benzene-derivative hydrocarbon) under constant pressure were simulated by the finite-element program to validate the numerical model and formulation for constitutive properties. Transient water outflow predicted using independently measured saturation-capillary head data agreed with observed outflow data within the limits of precision of the predictions as estimated by a first-order Taylor series approximation considering parameter uncertainty due to experimental reproducability and constitutive model accuracy. Two-dimensional simulations are presented for a hypothetical field case involving introduction of NAPL near the soil surface due to leakage from an underground storage tank. Subsequent transport of NAPL in the variably saturated vadose and groundwater zones is analyzed.
NASA Astrophysics Data System (ADS)
Chi, Heng; Lopez-Pamies, Oscar; Paulino, Glaucio H.
2016-02-01
This paper presents a new variational principle in finite elastostatics applicable to arbitrary elastic solids that may contain constitutively rigid spatial domains (e.g., rigid inclusions). The basic idea consists in describing the constitutive rigid behavior of a given spatial domain as a set of kinematic constraints over the boundary of the domain. From a computational perspective, the proposed formulation is shown to reduce to a set of algebraic constraints that can be implemented efficiently in terms of both single-field and mixed finite elements of arbitrary order. For demonstration purposes, applications of the proposed rigid-body-constraint formulation are illustrated within the context of elastomers, reinforced with periodic and random distributions of rigid filler particles, undergoing finite deformations.
Taylor, G.; Dong, C.; Sun, S.
2010-03-18
A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods, i.e. mixed finite element (MFE) and the finite volume methods. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocities field for both the fractures and matrix which are crucial to the convection part of the transport equation. The finite volume method and the standard MFE method are used to approximate the convection and dispersion terms respectively. The model is used to investigate the interaction of adsorption with transport and to extract information on effective adsorption distribution coefficients. Numerical examples in different fractured media illustrate the robustness and efficiency of the proposed numerical model.
Consistent finite-element approach to Brownian polymer dynamics with anisotropic friction.
Cyron, Christian J; Wall, Wolfgang A
2010-12-01
In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Here we present a mathematically consistent finite element approach to the simulation of Brownian polymer dynamics. The viscous damping forces are accounted for by an anisotropic friction model. By comparison with theoretical predictions and experimental data we demonstrate the reliability and efficiency of this method. PMID:21230752
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;…
A Taylor-Galerkin finite element algorithm for transient nonlinear thermal-structural analysis
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.
1986-01-01
A Taylor-Galerkin finite element method for solving large, nonlinear thermal-structural problems is presented. The algorithm is formulated for coupled transient and uncoupled quasistatic thermal-structural problems. Vectorizing strategies ensure computational efficiency. Two applications demonstrate the validity of the approach for analyzing transient and quasistatic thermal-structural problems.
Multiphase control volume finite element simulations of fractured reservoirs
NASA Astrophysics Data System (ADS)
Fu, Yao
With rapid evolution of hardware and software techniques in energy sector, reservoir simulation has become a powerful tool for field development planning and reservoir management. Many of the widely used commercial simulators were originally designed for structured grids and implemented with finite difference method (FDM). In recent years, technical advances in griding, fluid modeling, linear solver, reservoir and geological modeling, etc. have created new opportunities. At the same time, new reservoir simulation technology is required for solving large-scale heterogeneous problems. A three-dimensional, three-phase black-oil reservoir simulator has been developed using the control volume finite element (CVFE) formulation. Flux-based upstream weighting is employed to ensure flux continuity. The CVFE method is embedded in a fully-implicit formulation. State-of-the-art parallel, linear solvers are used. The implementation takes the advantages of object-oriented programming capabilities of C++ to provide maximum reuse and extensibility for future students. The results from the simulator have excellent agreement with those from commercial simulators. The convergence properties of the new simulator are verified using the method of manufactured solutions. The pressure and saturation solutions are verified to be first-order convergent as expected. The efficiency of the simulators and their capability to handle real large-scale field models are improved by implementing the models in parallel. Another aspect of the work dealt with multiphase flow of fractured reservoirs was performed. The discrete-fracture model is implemented in the simulator. Fractures and faults are represented by lines and planes in two- and three-dimensional spaces, respectively. The difficult task of generating an unstructured mesh for complex domains with fractures and faults is accomplished in this study. Applications of this model for two-phase and three-phase simulations in a variety of fractured
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.
Finite Elements in Ab Initio Electronic-Structure Calulations
NASA Astrophysics Data System (ADS)
Pask, J. E.; Sterne, P. A.
Over the course of the past two decades, the density functional theory (DFT) (see e.g., [1]) of Hohenberg, Kohn, and Sham has proven to be an accurate and reliable basis for the understanding and prediction of a wide range of materials properties from first principles (ab initio), with no experimental input or empirical parameters. However, the solution of the Kohn-Sham equations of DFT is a formidable task and this has limited the range of physical systems which can be investigated by such rigorous, quantum mechanical means. In order to extend the interpretive and predictive power of such quantum mechanical theories further into the domain of "real materials", involving nonstoichiometric deviations, defects, grain boundaries, surfaces, interfaces, and the like; robust and efficient methods for the solution of the associated quantum mechanical equations are critical. The finite-element (FE) method (see e.g., [2]) is a general method for the solution of partial differential and integral equations which has found wide application in diverse fields ranging from particle physics to civil engineering. Here, we discuss its application to large-scale ab initio electronic-structure calculations.
Finite element based simulation of dry sliding wear
NASA Astrophysics Data System (ADS)
Hegadekatte, V.; Huber, N.; Kraft, O.
2005-01-01
In order to predict wear and eventually the life-span of complex mechanical systems, several hundred thousand operating cycles have to be simulated. Therefore, a finite element (FE) post-processor is the optimum choice, considering the computational expense. A wear simulation approach based on Archard's wear law is implemented in an FE post-processor that works in association with a commercial FE package, ABAQUS, for solving the general deformable-deformable contact problem. Local wear is computed and then integrated over the sliding distance using the Euler integration scheme. The wear simulation tool works in a loop and performs a series of static FE-simulations with updated surface geometries to get a realistic contact pressure distribution on the contacting surfaces. It will be demonstrated that this efficient approach can simulate wear on both two-dimensional and three-dimensional surface topologies. The wear on both the interacting surfaces is computed using the contact pressure distribution from a two-dimensional or three-dimensional simulation, depending on the case. After every wear step the geometry is re-meshed to correct the deformed mesh due to wear, thus ensuring a fairly uniform mesh for further processing. The importance and suitability of such a wear simulation tool will be enunciated in this paper.
ELLIPT2D: A Flexible Finite Element Code Written Python
Pletzer, A.; Mollis, J.C.
2001-03-22
The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research.
Finite element-wavelet hybrid algorithm for atmospheric tomography.
Yudytskiy, Mykhaylo; Helin, Tapio; Ramlau, Ronny
2014-03-01
Reconstruction of the refractive index fluctuations in the atmosphere, or atmospheric tomography, is an underlying problem of many next generation adaptive optics (AO) systems, such as the multiconjugate adaptive optics or multiobject adaptive optics (MOAO). The dimension of the problem for the extremely large telescopes, such as the European Extremely Large Telescope (E-ELT), suggests the use of iterative schemes as an alternative to the matrix-vector multiply (MVM) methods. Recently, an algorithm based on the wavelet representation of the turbulence has been introduced in [Inverse Probl.29, 085003 (2013)] by the authors to solve the atmospheric tomography using the conjugate gradient iteration. The authors also developed an efficient frequency-dependent preconditioner for the wavelet method in a later work. In this paper we study the computational aspects of the wavelet algorithm. We introduce three new techniques, the dual domain discretization strategy, a scale-dependent preconditioner, and a ground layer multiscale method, to derive a method that is globally O(n), parallelizable, and compact with respect to memory. We present the computational cost estimates and compare the theoretical numerical performance of the resulting finite element-wavelet hybrid algorithm with the MVM. The quality of the method is evaluated in terms of an MOAO simulation for the E-ELT on the European Southern Observatory (ESO) end-to-end simulation system OCTOPUS. The method is compared to the ESO version of the Fractal Iterative Method [Proc. SPIE7736, 77360X (2010)] in terms of quality.
Finite element-wavelet hybrid algorithm for atmospheric tomography.
Yudytskiy, Mykhaylo; Helin, Tapio; Ramlau, Ronny
2014-03-01
Reconstruction of the refractive index fluctuations in the atmosphere, or atmospheric tomography, is an underlying problem of many next generation adaptive optics (AO) systems, such as the multiconjugate adaptive optics or multiobject adaptive optics (MOAO). The dimension of the problem for the extremely large telescopes, such as the European Extremely Large Telescope (E-ELT), suggests the use of iterative schemes as an alternative to the matrix-vector multiply (MVM) methods. Recently, an algorithm based on the wavelet representation of the turbulence has been introduced in [Inverse Probl.29, 085003 (2013)] by the authors to solve the atmospheric tomography using the conjugate gradient iteration. The authors also developed an efficient frequency-dependent preconditioner for the wavelet method in a later work. In this paper we study the computational aspects of the wavelet algorithm. We introduce three new techniques, the dual domain discretization strategy, a scale-dependent preconditioner, and a ground layer multiscale method, to derive a method that is globally O(n), parallelizable, and compact with respect to memory. We present the computational cost estimates and compare the theoretical numerical performance of the resulting finite element-wavelet hybrid algorithm with the MVM. The quality of the method is evaluated in terms of an MOAO simulation for the E-ELT on the European Southern Observatory (ESO) end-to-end simulation system OCTOPUS. The method is compared to the ESO version of the Fractal Iterative Method [Proc. SPIE7736, 77360X (2010)] in terms of quality. PMID:24690653
Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis
NASA Technical Reports Server (NTRS)
Nguyen, Duc T.; Tungkahotara, Siroj; Watson, Willie R.; Rajan, Subramaniam D.
2005-01-01
A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.
Finite element code development for modeling detonation of HMX composites
NASA Astrophysics Data System (ADS)
Duran, Adam; Sundararaghavan, Veera
2015-06-01
In this talk, we present a hydrodynamics code for modeling shock and detonation waves in HMX. A stable efficient solution strategy based on a Taylor-Galerkin finite element (FE) discretization was developed to solve the reactive Euler equations. In our code, well calibrated equations of state for the solid unreacted material and gaseous reaction products have been implemented, along with a chemical reaction scheme and a mixing rule to define the properties of partially reacted states. A linear Gruneisen equation of state was employed for the unreacted HMX calibrated from experiments. The JWL form was used to model the EOS of gaseous reaction products. It is assumed that the unreacted explosive and reaction products are in both pressure and temperature equilibrium. The overall specific volume and internal energy was computed using the rule of mixtures. Arrhenius kinetics scheme was integrated to model the chemical reactions. A locally controlled dissipation was introduced that induces a non-oscillatory stabilized scheme for the shock front. The FE model was validated using analytical solutions for sod shock and ZND strong detonation models and then used to perform 2D and 3D shock simulations. We will present benchmark problems for geometries in which a single HMX crystal is subjected to a shock condition. Our current progress towards developing microstructural models of HMX/binder composite will also be discussed.
Advance finite element modeling of rotor blade aeroelasticity
NASA Technical Reports Server (NTRS)
Straub, F. K.; Sangha, K. B.; Panda, B.
1994-01-01
An advanced beam finite element has been developed for modeling rotor blade dynamics and aeroelasticity. This element is part of the Element Library of the Second Generation Comprehensive Helicopter Analysis System (2GCHAS). The element allows modeling of arbitrary rotor systems, including bearingless rotors. It accounts for moderately large elastic deflections, anisotropic properties, large frame motion for maneuver simulation, and allows for variable order shape functions. The effects of gravity, mechanically applied and aerodynamic loads are included. All kinematic quantities required to compute airloads are provided. In this paper, the fundamental assumptions and derivation of the element matrices are presented. Numerical results are shown to verify the formulation and illustrate several features of the element.
High-order Finite Element Analysis of Boundary Layer Flows
NASA Astrophysics Data System (ADS)
Zhang, Alvin; Sahni, Onkar
2014-11-01
Numerical analysis of boundary layer flows requires careful approximations, specifically the use of a mesh with layered and graded elements near the (viscous) walls. This is referred to as a boundary layer mesh, which for complex geometries is composed of triangular elements on the walls that are inflated or extruded into the volume along the wall-normal direction up to a desired height while the rest of the domain is filled with unstructured tetrahedral elements. Linear elements with C0 inter-element continuity are employed and in some situations higher order C0 elements are also used. However, these elements only enforce continuity whereas high-order smoothness is not attained as will be the case with C1 inter-element continuity and higher. As a result, C0 elements result in a poor approximation of the high-order boundary layer behavior. To achieve greater inter-element continuity in boundary layer region, we employ B-spline basis functions along the wall-normal direction (i.e., only in the layered portion of the mesh). In the rest of the fully unstructured mesh, linear or higher order C0 elements are used as appropriate. In this study we demonstrate the benefits of finite-element analysis based on such higher order and continuity basis functions for boundary layer flows.
Discontinuous dual-primal mixed finite elements for elliptic problems
NASA Technical Reports Server (NTRS)
Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo
2000-01-01
We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.
Finite Element Modeling of the NASA Langley Aluminum Testbed Cylinder
NASA Technical Reports Server (NTRS)
Grosveld, Ferdinand W.; Pritchard, Joselyn I.; Buehrle, Ralph D.; Pappa, Richard S.
2002-01-01
The NASA Langley Aluminum Testbed Cylinder (ATC) was designed to serve as a universal structure for evaluating structural acoustic codes, modeling techniques and optimization methods used in the prediction of aircraft interior noise. Finite element models were developed for the components of the ATC based on the geometric, structural and material properties of the physical test structure. Numerically predicted modal frequencies for the longitudinal stringer, ring frame and dome component models, and six assembled ATC configurations were compared with experimental modal survey data. The finite element models were updated and refined, using physical parameters, to increase correlation with the measured modal data. Excellent agreement, within an average 1.5% to 2.9%, was obtained between the predicted and measured modal frequencies of the stringer, frame and dome components. The predictions for the modal frequencies of the assembled component Configurations I through V were within an average 2.9% and 9.1%. Finite element modal analyses were performed for comparison with 3 psi and 6 psi internal pressurization conditions in Configuration VI. The modal frequencies were predicted by applying differential stiffness to the elements with pressure loading and creating reduced matrices for beam elements with offsets inside external superelements. The average disagreement between the measured and predicted differences for the 0 psi and 6 psi internal pressure conditions was less than 0.5%. Comparably good agreement was obtained for the differences between the 0 psi and 3 psi measured and predicted internal pressure conditions.
Finite element dynamic analysis on CDC STAR-100 computer
NASA Technical Reports Server (NTRS)
Noor, A. K.; Lambiotte, J. J., Jr.
1978-01-01
Computational algorithms are presented for the finite element dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order finite elements. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell elements having 80 degrees of freedom.
Finite Element Modelling of Fluid Coupling in the Coiled Cochlea
NASA Astrophysics Data System (ADS)
Ni, Guangjian; Elliott, S. J.; Lineton, B.; Saba, R.
2011-11-01
A finite element model is first used to calculate the modal pressure difference for a box model of the cochlea, which shows that the number of fluid elements across the width of the cochlea determines the accuracy with which the near field, or short wavenumber, component of the fluid coupling is reproduced. Then results are compared with the analytic results to validate the accuracy of the FE model. It is, however, the far field, or long wavelength, component of the fluid coupling that is most affected by the geometry. A finite element model of the coiled cochlea is then used to calculate fluid coupling in this case, which has similar characteristics to the uncoiled model.
EXODUS: A finite element file format for pre- and postprocessing
Mills-Curran, W.C.; Gilkey, A.P.; Flanagan, D.P.
1988-09-01
The EXODUS format defines a binary file which is used for finite element analysis pre- and postprocessing. It includes data to define the finite element mesh and label both boundary condition and load application points. EXODUS accommodates multiple element types and is sufficiently general format for analysis results. A benefit of combining the mesh definition data and the results data in the same file is that the user is assured that the results data are consistent with the model. EXODUS is currently in use by the entire range of Department 1520 codes (including preprocessors, translators, linear and nonlinear analyses, and postprocessors) and is finding applications in codes outside Department 1520. 2 refs., 2 figs., 1 tab.
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 fast method of numerical quadrature for p-version finite element matrices
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1993-01-01
A new technique of numerical quadrature especially suited for p-version finite element matrices is presented. This new technique separates the integrand into two parts, and numerically operates on each part separately. The objective of this scheme is to minimize the computational cost of integrating the entire element matrix as opposed to minimizing the cost of integrating a single function. The efficiency of the new technique is compared with Gaussian quadrature and found to take a small fraction of the computational effort.
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.
Hierarchicalp-version finite elements for radiation heat transfer
NASA Astrophysics Data System (ADS)
Gould, Dana Craig
Methods to compute surface-to-surface radiation heat transfer between diffuse-gray surfaces using hierarchical p-version finite elements have been developed and applied to the analysis of a high-speed aircraft wing. A review of traditional methods for surface-to-surface radiation exchange is given. Traditional methods rely on the assumption of isothermal surfaces with incoming and outgoing radiation heat flux assumed constant over the surface. These assumptions are not appropriate for p-version finite elements, so new methods for evaluating the incoming and outgoing radiation flux over a finite element surface were required. Two methods for computing the surface-to-surface radiation heat transfer that do not rely on the above assumptions are developed and validated. The first approach uses traditional methods to compute the radiation exchange on an element sub-mesh, then transfers this data back to the parent element for the computation of the radiation heat flux. The second method requires the numerical integration of the net radiation exchange equation for each element. The methods are validated and evaluated using simple problems with analytical solutions. The radiation sub-element method is less costly than the direct integration method, but it is also less accurate. Both methods are computationally more expensive than traditional methods for a given number of degrees of freedom; however, for a given accuracy, they are less expensive. The new methods are used to analyze the wing of a High Speed Civil Transport vehicle. The p-elements were effective in capturing significant temperature variations over large sections of the wing and reduced the mesh complexity and associated modeling time while maintaining accuracy.
Efficient Controls for Finitely Convergent Sequential Algorithms
Chen, Wei; Herman, Gabor T.
2010-01-01
Finding a feasible point that satisfies a set of constraints is a common task in scientific computing: examples are the linear feasibility problem and the convex feasibility problem. Finitely convergent sequential algorithms can be used for solving such problems; an example of such an algorithm is ART3, which is defined in such a way that its control is cyclic in the sense that during its execution it repeatedly cycles through the given constraints. Previously we found a variant of ART3 whose control is no longer cyclic, but which is still finitely convergent and in practice it usually converges faster than ART3 does. In this paper we propose a general methodology for automatic transformation of finitely convergent sequential algorithms in such a way that (i) finite convergence is retained and (ii) the speed of convergence is improved. The first of these two properties is proven by mathematical theorems, the second is illustrated by applying the algorithms to a practical problem. PMID:20953327
Finite element evaluation of erosion/corrosion affected reducing elbow
Basavaraju, C.
1996-12-01
Erosion/corrosion is a primary source for wall thinning or degradation of carbon steel piping systems in service. A number of piping failures in the power industry have been attributed to erosion/corrosion. Piping elbow is one of such susceptible components for erosion/corrosion because of increased flow turbulence due to its geometry. In this paper, the acceptability of a 12 in. x 8 in. reducing elbow in RHR service water pump discharge piping, which experienced significant degradation due to wall thinning in localized areas, was evaluated using finite element analysis methodology. Since the simplified methods showed very small margin and recommended replacement of the elbow, a detailed 3-D finite element model was built using shell elements and analyzed for internal pressure and moment loadings. The finite element analysis incorporated the U.T. measured wall thickness data at various spots that experienced wall thinning. The results showed that the elbow is acceptable as-is until the next fuel cycle. FEA, though cumbersome, and time consuming is a valuable analytical tool in making critical decisions with regard to component replacement of border line situation cases, eliminating some conservatism while not compromising the safety.
FECAP - FINITE ELEMENT COMPOSITE ANALYSIS PROGRAM FOR A MICROCOMPUTER
NASA Technical Reports Server (NTRS)
Bowles, D. E.
1994-01-01
Advanced composite materials have gained use in the aerospace industry over the last 20 years because of their high specific strength and stiffness, and low coefficient of thermal expansion. Design of composite structures requires the analysis of composite material behavior. The Finite Element Composite Analysis Program, FECAP, is a special purpose finite element analysis program for analyzing composite material behavior with a microcomputer. Composite materials, in regard to this program, are defined as the combination of at least two distinct materials to form one nonhomogeneous anisotropic material. FECAP assumes a state of generalized plane strain exists in a material consisting of two or more orthotropic phases, subjected to mechanical and/or thermal loading. The finite element formulation used in FECAP is displacement based and requires the minimization of the total potential energy for each element with respect to the unknown variables. This procedure leads to a set of linear simultaneous equations relating the unknown nodal displacements to the applied loads. The equations for each element are assembled into a global system, the boundary conditions are applied, and the system is solved for the nodal displacements. The analysis may be performed using either 4-mode linear or 8-mode quadratic isoparametric elements. Output includes the nodal displacements, and the element stresses and strains. FECAP was written for a Hewlett Packard HP9000 Series 200 Microcomputer with the HP Basic operating system. It was written in HP BASIC 3.0 and requires approximately 0.5 Mbytes of RAM in addition to what is required for the operating system. A math coprocessor card is highly recommended. FECAP was developed in 1988.
Effect of geometric shape on two-dimensional finite elements
Cook, W.A.
1981-01-01
Three quadrilateral elements are defined. These are an eight-nodal-point serendipity element (QUAD8s), a nine-nodal-point serendipity element (QUAD9s), and a nine-nodal-point quadrilateral element composed of two six-nodal-point triangular elements (QUAD9t). The effect that the geometric shape of the element has on the approximation function of each element is discussed. Two beam problems demonstrate that when the shape of the elements becomes skewed, the QUAD9t element significantly improves the calculated results. Finally, a recommendation is made for the QUAD8s and QUAD9t to be used together for the most efficient and accurate results.
Experience with automatic, dynamic load balancing and adaptive finite element computation
Wheat, S.R.; Devine, K.D.; Maccabe, A.B.
1993-10-01
Distributed memory, Massively Parallel (MP), MIMD technology has enabled the development of applications requiring computational resources previously unobtainable. Structural mechanics and fluid dynamics applications, for example, are often solved by finite element methods (FEMs) requiring, millions of degrees of freedom to accurately simulate physical phenomenon. Adaptive methods, which automatically refine or coarsen meshes and vary the order of accuracy of the numerical solution, offer greater robustness and computational efficiency than traditional FEMs by reducing the amount of computation required away from physical structures such as shock waves and boundary layers. On MP computers, FEMs frequently result in distributed processor load imbalances. To overcome load imbalance, many MP FEMs use static load balancing as a preprocessor to the finite element calculation. Adaptive methods complicate the load imbalance problem since the work per element is not uniform across the solution domain and changes as the computation proceeds. Therefore, dynamic load balancing is required to maintain global load balance. We describe a dynamic, fine-grained, element-based data migration system that maintains global load balance and is effective in the presence of changing work loads. Global load balance is achieved by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. The method utilizes an automatic element management system library to which a programmer integrates the application`s computational description. The library`s flexibility supports a large class of finite element and finite difference based applications.
Structural health monitoring system design using finite element analysis
Stinemates, D. W.; Bennett, J. G.
2002-01-01
The project described in this report was performed to couple experimental and analytical techniques in the field of structural health monitoring and damage identification. To do this, a finite element model was constructed of a simulated three-story building used for damage identification experiments. The model was used in conjunction with data from the physical structure to research damage identification algorithms. Of particular interest was modeling slip in joints as a function of bolt torque and predicting the smallest change of torque that could be detected experimentally. After being validated with results from the physical structure, the model was used to produce data to test the capabilities of damage identification algorithms. This report describes the finite element model constructed, the results obtained, and proposed future use of the model.
A fast hidden line algorithm for plotting finite element models
NASA Technical Reports Server (NTRS)
Jones, G. K.
1982-01-01
Effective plotting of finite element models requires the use of fast hidden line plot techniques that provide interactive response. A high speed hidden line technique was developed to facilitate the plotting of NASTRAN finite element models. Based on testing using 14 different models, the new hidden line algorithm (JONES-D) appears to be very fast: its speed equals that for normal (all lines visible) plotting and when compared to other existing methods it appears to be substantially faster. It also appears to be very reliable: no plot errors were observed using the new method to plot NASTRAN models. The new algorithm was made part of the NPLOT NASTRAN plot package and was used by structural analysts for normal production tasks.
Finite element thermo-viscoplastic analysis of aerospace structures
NASA Technical Reports Server (NTRS)
Pandey, Ajay K.; Dechaumphai, Pramote; Thornton, Earl A.
1990-01-01
The time-dependent thermo-viscoplastic response of aerospace structures subjected to intense aerothermal loads is predicted using the finite-element method. The finite-element analysis uses the Bodner-Partom unified viscoplastic constitutive relations to determine rate-dependent nonlinear material behavior. The methodology is verified by comparison with experimental data and other numerical results for a uniaxially-loaded bar. The method is then used (1) to predict the structural response of a rectangular plate subjected to line heating along a centerline, and (2) to predict the thermal-structural response of a convectively-cooled engine cowl leading edge subjected to aerodynamic shock-shock interference heating. Compared to linear elastic analysis, the viscoplastic analysis results in lower peak stresses and regions of plastic deformations.
Finite element model of magnetoconvection of a ferrofluid
NASA Astrophysics Data System (ADS)
Snyder, Suzanne M.; Cader, Tahir; Finlayson, Bruce A.
2003-06-01
Combined natural and magnetic convective heat transfer through a ferrofluid in a cubic enclosure is simulated numerically. The momentum equation includes a magnetic term that arises when a magnetic fluid is in the presence of a magnetic field gradient and a temperature gradient. In order to validate the theory, the wall temperature isotherms and Nusselt numbers are compared to experimental work of Sawada et al. (Int. J. Appl. Electromagn. Mater. 4 (1994) 329). Results are obtained using standard computational fluid dynamics codes, with modifications to account for the Langevin factor when needed. The CFD code FIDAP uses the finite element method, sometimes with a user-defined subroutine. The CFD code FEMLAB uses the finite element method with a user-supplied body force.
Weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1991-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1990-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1989-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
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.
Sensitive analysis of a finite element model of orthogonal cutting
NASA Astrophysics Data System (ADS)
Brocail, J.; Watremez, M.; Dubar, L.
2011-01-01
This paper presents a two-dimensional finite element model of orthogonal cutting. The proposed model has been developed with Abaqus/explicit software. An Arbitrary Lagrangian-Eulerian (ALE) formulation is used to predict chip formation, temperature, chip-tool contact length, chip thickness, and cutting forces. This numerical model of orthogonal cutting will be validated by comparing these process variables to experimental and numerical results obtained by Filice et al. [1]. This model can be considered to be reliable enough to make qualitative analysis of entry parameters related to cutting process and frictional models. A sensitivity analysis is conducted on the main entry parameters (coefficients of the Johnson-Cook law, and contact parameters) with the finite element model. This analysis is performed with two levels for each factor. The sensitivity analysis realised with the numerical model on the entry parameters has allowed the identification of significant parameters and the margin identification of parameters.
A finite element model of ferroelectric/ferroelastic polycrystals
HWANG,STEPHEN C.; MCMEEKING,ROBERT M.
2000-02-17
A finite element model of polarization switching in a polycrystalline ferroelectric/ferroelastic ceramic is developed. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. Each crystallite is represented by a finite element with the possible dipole directions assigned randomly subject to crystallographic constraints. The model accounts for both electric field induced (i.e. ferroelectric) switching and stress induced (i.e. ferroelastic) switching with piezoelectric interactions. Experimentally measured elastic, dielectric, and piezoelectric constants are used consistently, but different effective critical energy barriers are selected phenomenologically. Electric displacement versus electric field, strain versus electric field, stress versus strain, and stress versus electric displacement loops of a ceramic lead lanthanum zirconate titanate (PLZT) are modeled well below the Curie temperature.
Finite element modelling of the 1969 Portuguese tsunami
NASA Astrophysics Data System (ADS)
Guesmia, M.; Heinrich, Ph.; Mariotti, C.
1996-03-01
On the 28 th February 1969, the coasts of Portugal, Spain and Morocco were affected by water waves generated by a submarine earthquake (Ms=7.3) with epicenter located off Portugal. The propagation of this tsunami has been simulated by a finite element numerical model solving the Boussinesq equations. These equations have been discretized using the finite element Galerkin method and a Crank-Nicholson scheme in time. The 2-D simulation of the 1969 tsunami is carried out using the hydraulic source calculated from the geophysical model of Okada and seismic parameters of Fukao. The modeled waves are compared with the recorded waves with respect to the travel times, the maximum amplitudes, the periods of the signal. Good agreement is found for most of the studied gauges. The comparison between Boussinesq and shallow-water models shows that the effects of frequency dispersion are minor using Fukao's seismic parameters.
Finite element calculation of residual stress in dental restorative material
NASA Astrophysics Data System (ADS)
Grassia, Luigi; D'Amore, Alberto
2012-07-01
A finite element methodology for residual stresses calculation in dental restorative materials is proposed. The material under concern is a multifunctional methacrylate-based composite for dental restorations, activated by visible light. Reaction kinetics, curing shrinkage, and viscoelastic relaxation functions were required as input data on a structural finite element solver. Post cure effects were considered in order to quantify the residual stresses coming out from natural contraction with respect to those debited to the chemical shrinkage. The analysis showed for a given test case that residual stresses frozen in the dental restoration at uniform temperature of 37°C are of the same order of magnitude of the strength of the dental composite material per se.
Exemplifying Quantum Systems in a Finite Element Basis
Young, Toby D.
2009-08-13
This paper presents a description of the abstractions required for the expression and solution of the linear single-particle Schroedinger equation in a finite element basis. This paper consists of two disparate themes: First, to layout and establish the foundations of finite element analysis as an approximate numerical solution to extendable quantum mechanical systems; and second, to promote a high-performance open-source computational model for the approximate numerical solution to quantum mechanical systems. The structural foundation of the one-and two-dimensional time-independent Schroedinger equation describing an infinite potential well is explored and a brief overview of the hierarchal design of the computational library written in C++ is given.
An emulator for minimizing computer resources for finite element analysis
NASA Technical Reports Server (NTRS)
Melosh, R.; Utku, S.; Islam, M.; Salama, M.
1984-01-01
A computer code, SCOPE, has been developed for predicting the computer resources required for a given analysis code, computer hardware, and structural problem. The cost of running the code is a small fraction (about 3 percent) of the cost of performing the actual analysis. However, its accuracy in predicting the CPU and I/O resources depends intrinsically on the accuracy of calibration data that must be developed once for the computer hardware and the finite element analysis code of interest. Testing of the SCOPE code on the AMDAHL 470 V/8 computer and the ELAS finite element analysis program indicated small I/O errors (3.2 percent), larger CPU errors (17.8 percent), and negligible total errors (1.5 percent).
Finite element analyses of two antirotational designs of implant fixtures.
Akour, Salih N; Fayyad, Mohammed A; Nayfeh, Jamal F
2005-03-01
The purpose of this study was to compare the effect of cyclic compressive forces on loosening of the abutment retaining screw of dental implant fixtures with two different antirotational designs using the finite element analysis. A three-dimensional model of externally hexed and trichannel dental implant fixtures with their corresponding abutments and retaining screws was developed. Comparison between the two designs was carried out using finite element analysis. The results revealed that the externally hexed design has significantly higher overall stress, contact stress, and deflection compared with the trichannel design. The trichannel antirotational design has the least potential for fracture of the implant/abutment assembly in addition to its capability for preventing rotation of the prosthesis and loosening of the screw.
Finite Element Analysis Applied to Dentoalveolar Trauma: Methodology Description
da Silva, B. R.; Moreira Neto, J. J. S.; da Silva, F. I.; de Aguiar, A. S. W.
2011-01-01
Dentoalveolar traumatic injuries are among the clinical conditions most frequently treated in dental practice. However, few studies so far have addressed the biomechanical aspects of these events, probably as a result of difficulties in carrying out satisfactory experimental and clinical studies as well as the unavailability of truly scientific methodologies. The aim of this paper was to describe the use of finite element analysis applied to the biomechanical evaluation of dentoalveolar trauma. For didactic purposes, the methodological process was divided into steps that go from the creation of a geometric model to the evaluation of final results, always with a focus on methodological characteristics, advantages, and disadvantages, so as to allow the reader to customize the methodology according to specific needs. Our description shows that the finite element method can faithfully reproduce dentoalveolar trauma, provided the methodology is closely followed and thoroughly evaluated. PMID:21991463
A finite element model for residual stress in repair welds
Feng, Z.; Wang, X.L.; Spooner, S.; Goodwin, G.M.; Maziasz, P.J.; Hubbard, C.R.; Zacharia, T.
1996-03-28
This paper describes a three-dimensional finite element model for calculation of the residual stress distribution caused by repair welding. Special user subroutines were developed to simulate the continuous deposition of filler metal during welding. The model was then tested by simulating the residual stress/strain field of a FeAl weld overlay clad on a 2{1/4}Cr-1 Mo steel plate, for which neutron diffraction measurement data of the residual strain field were available. It is shown that the calculated residual stress distribution was consistent with that determined with neutron diffraction. High tensile residual stresses in both the longitudinal and transverse directions were observed around the weld toe at the end of the weld. The strong spatial dependency of the residual stresses in the region around the weld demonstrates that the common two-dimensional cross-section finite element models should not be used for repair welding analysis.
Tube Bulge Process : Theoretical Analysis And Finite Element Simulations
Velasco, Raphaeel; Boudeau, Nathalie
2007-04-07
This paper is focused on the determination of mechanics characteristics for tubular materials, using tube bulge process. A comparative study is made between two different models: theoretical model and finite element analysis. The theoretical model is completely developed, based first on a geometrical analysis of the tube profile during bulging, which is assumed to strain in arc of circles. Strain and stress analysis complete the theoretical model, which allows to evaluate tube thickness and state of stress, at any point of the free bulge region. Free bulging of a 304L stainless steel is simulated using Ls-Dyna 970. To validate FE simulations approach, a comparison between theoretical and finite elements models is led on several parameters such as: thickness variation at the free bulge region pole with bulge height, tube thickness variation with z axial coordinate, and von Mises stress variation with plastic strain.
Finite element modeling of an electrically variable inductor
Bi, Y.; Jiles, D.C.
1999-09-01
A new type of electrically variable inductor has been investigated. This uses an ac excitation field with an orthogonal dc bias field to control the properties of the device. Measurements showed that the effective inductance can be decreased by increasing the orthogonal dc bias field. With an appropriate current in the orthogonal bias coils, an inductance plateau can be reached in which the inductance remains stable over a range of excitation currents. The inductance value can be adjusted by controlling the orthogonal current. Based on an existing anhysteretic magnetization model, nonlinear 3D finite element modeling was successfully used to model the distribution of flux density and to identify the region of saturation which is believed to result in the decrease in effective inductance of the inductor. The effective inductance of the device was also modeled using numerical finite element calculations. The modeled inductance showed broad agreement with experimental results and predicted the observed trend in inductance.
Finite Element Modeling of Micromachined MEMS Photon Devices
Datskos, P.G.; Evans, B.M.; Schonberger, D.
1999-09-20
The technology of microelectronics that has evolved over the past half century is one of great power and sophistication and can now be extended to many applications (MEMS and MOEMS) other than electronics. An interesting application of MEMS quantum devices is the detection of electromagnetic radiation. The operation principle of MEMS quantum devices is based on the photoinduced stress in semiconductors, and the photon detection results from the measurement of the photoinduced bending. These devices can be described as micromechanical photon detectors. In this work, we have developed a technique for simulating electronic stresses using finite element analysis. We have used our technique to model the response of micromechanical photon devices to external stimuli and compared these results with experimental data. Material properties, geometry, and bimaterial design play an important role in the performance of micromechanical photon detectors. We have modeled these effects using finite element analysis and included the effects of bimaterial thickness coating, effective length of the device, width, and thickness.
A finite-element analysis of bipolar ionized field
Abdel-Salam, M.; Al-Hamouz, Z.
1995-05-01
This paper describes a new iterative method for the analysis of the bipolar ionized field in HVDC transmission lines without resorting to Deutsch`s assumption. The finite-element technique (FET) is used to solve Poisson`s equation where the constancy of the conductors` surface field at the corona inception value is directly implemented in the finite-element formulation. The proposed method has been tested on laboratory and full-scale models. The calculated V-I characteristics agreed well with those calculated and measured previously. The dependence of the corona current as well as its monopolar and bipolar components on the conductor height is discussed. The simplicity in computer programming in addition to the low number of iterations required to achieve convergence characterize the proposed method of analysis.
Finite element analysis of fiber-reinforced fixed partial dentures.
Nakamura, Takashi; Ohyama, Tatsuo; Waki, Tomonori; Kinuta, Soichiro; Wakabayashi, Kazumichi; Takano, Naoki; Yatani, Hirofumi
2005-06-01
Two-dimensional finite element models were created for a three-unit posterior fixed partial denture. An experimental resin-impregnated glass fiber was used as the fiber-reinforced composite (FRC) for the framework. The FRC was evaluated using varying combinations of position and thickness, alongside with two types of veneering composite. A load of 50 N simulating bite force was applied at the pontic in a vertical direction. Tensile stress was examined using a finite element analysis program. Model without FRC showed tensile stress concentrations within the veneering composite on the cervical side of the pontic--from the connector area to the bottom of the pontic. Model with FRC at the top of the pontic had almost the same stress distribution as the model without FRC. Models with 0.4-0.8 mm thick FRC positioned at the bottom of the pontic showed maximum tensile stresses reduced by 4-19% within the veneering composite. PMID:16022451
Surface subsidence prediction by nonlinear finite-element analysis
Najjar, Y. . Dept. of Civil Engineering); Zaman, M. . School of Civil Engineering and Environmental Science)
1993-11-01
An improved two-dimensional plane-strain numerical procedure based on the incremental-iterative nonlinear finite-element is developed to predict ground subsidence caused by underground mining. The procedure emphasizes the use of the following features: (1) an appropriate constitutive model that can accurately describe the nonlinear behavior of geological strata; and (2) an accurate algorithm for simulation of excavation sequences consistent with the actual underground mining process. The computer code is used to analyze a collapse that occurred in the Blue Goose Lease [number sign]1 Mine in northeastern Oklahoma. A parametric study is conducted to investigate the effects of some selected factors on the shape and extent of subsidence profiles. Analyses of the numerical results indicate that the nonlinear finite-element technique can be employed to meaningfully predict and characterize the potential for ground subsidence due to underground mining.
Finite element analysis of electrically excited quartz tuning fork devices.
Oria, Roger; Otero, Jorge; González, Laura; Botaya, Luis; Carmona, Manuel; Puig-Vidal, Manel
2013-05-30
Quartz Tuning Fork (QTF)-based Scanning Probe Microscopy (SPM) is an important field of research. A suitable model for the QTF is important to obtain quantitative measurements with these devices. Analytical models have the limitation of being based on the double cantilever configuration. In this paper, we present an electromechanical finite element model of the QTF electrically excited with two free prongs. The model goes beyond the state-of-the-art of numerical simulations currently found in the literature for this QTF configuration. We present the first numerical analysis of both the electrical and mechanical behavior of QTF devices. Experimental measurements obtained with 10 units of the same model of QTF validate the finite element model with a good agreement.
Finite-element thermo-viscoplastic analysis of aerospace structures
NASA Technical Reports Server (NTRS)
Pandey, Ajay; Dechaumphai, Pramote; Thornton, Earl A.
1990-01-01
The time-dependent thermo-viscoplastic response of aerospace structures subjected to intense aerothermal loads is predicted using the finite-element method. The finite-element analysis uses the Bodner-Partom unified viscoplastic constitutive relations to determine rate-dependent nonlinear material behavior. The methodology is verified by comparison with experimental data and other numerical results for a uniaxially-loaded bar. The method is then used (1) to predict the structural response of a rectangular plate subjected to line heating along a centerline, and (2) to predict the thermal-structural response of a convectively-cooled engine cowl leading edge subjected to aerodynamic shock-shock interference heating. Compared to linear elastic analysis, the viscoplastic analysis results in lower peak stresses and regions of plastic deformations.
ORION96. 2-d Finite Element Code Postprocessor
Sanford, L.A.; Hallquist, J.O.
1992-02-02
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.
Crack modeling of rotating blades with cracked hexahedral finite element method
NASA Astrophysics Data System (ADS)
Liu, Chao; Jiang, Dongxiang
2014-06-01
Dynamic analysis is the basis in investigating vibration features of cracked blades, where the features can be applied to monitor health state of blades, detect cracks in an early stage and prevent failures. This work presents a cracked hexahedral finite element method for dynamic analysis of cracked blades, with the purpose of addressing the contradiction between accuracy and efficiency in crack modeling of blades in rotor system. The cracked hexahedral element is first derived with strain energy release rate method, where correction of stress intensity factors of crack front and formulation of load distribution of crack surface are carried out to improve the modeling accuracy. To consider nonlinear characteristics of time-varying opening and closure effects caused by alternating loads, breathing function is proposed for the cracked hexahedral element. Second, finite element method with contact element is analyzed and used for comparison. Finally, validation of the cracked hexahedral element is carried out in terms of breathing effects of cracked blades and natural frequency in different crack depths. Good consistency is acquired between the results with developed cracked hexahedral element and contact element, while the computation time is significantly reduced in the previous one. Therefore, the developed cracked hexahedral element achieves good accuracy and high efficiency in crack modeling of rotating blades.
Study of the available finite element software packages at KSC
NASA Technical Reports Server (NTRS)
Lu, Chu-Ho
1990-01-01
The interaction among the three finite element software packages, SDRCI/I-DEAS, MSC/NASTRAN, and I/FEM, used at NASA, Kennedy Space Center is addressed. The procedures for using more than one of these application software packages to model and analyze a structure design are discussed. Design and stress analysis of a solid rocket booster fixture is illustrated by using four different combinations of the three software packages. Their results are compared and show small yet acceptable differences.
Finite Element Composite Analysis Program (FECAP) for a microcomputer
NASA Technical Reports Server (NTRS)
Bowles, David E.
1988-01-01
A special purpose finite element composite analysis program for analyzing composite material behavior with a microcomputer is described. The formulation assumes a state of generalized plane strain in a material consisting of two or more orthotropic phases. Loading can be mechanical and/or thermal. The theoretical background, computer implementation, and program users guide are described in detail. A sample program is solved showing the required user input and computer generated output.
[Whiplash injury analysis of cervical vertebra by finite element method].
Wang, Tao; Li, Zheng-Dong; Shao, Yu; Chen, Yi-Jiu
2015-02-01
Finite element method (FEM) is an effective mathematical method for stress analysis, and has been gradually applied in the study of biomechanics of human body structures. This paper reviews the construction, development, materials assignment and verification of FEM model of cervical vertebra, and it also states the research results of injury mechanism of whiplash injury and biomechanical response analysis of the cervical vertebra using FEM by researchers at home and abroad. PMID:26058135
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.
An interactive virtual environment for finite element analysis
Bradshaw, S.; Canfield, T.; Kokinis, J.; Disz, T.
1995-06-01
Virtual environments (VE) provide a powerful human-computer interface that opens the door to exciting new methods of interaction with high-performance computing applications in several areas of research. The authors are interested in the use of virtual environments as a user interface to real-time simulations used in rapid prototyping procedures. Consequently, the authors are developing methods for coupling finite element models of complex mechanical systems with a VE interface for real-time interaction.
Application of Finite Element Method to Analyze Inflatable Waveguide Structures
NASA Technical Reports Server (NTRS)
Deshpande, M. D.
1998-01-01
A Finite Element Method (FEM) is presented to determine propagation characteristics of deformed inflatable rectangular waveguide. Various deformations that might be present in an inflatable waveguide are analyzed using the FEM. The FEM procedure and the code developed here are so general that they can be used for any other deformations that are not considered in this report. The code is validated by applying the present code to rectangular waveguide without any deformations and comparing the numerical results with earlier published results.
Piezoelectric theory for finite element analysis of ultrasonic motors
Emery, J.D.; Mentesana, C.P.
1997-06-01
The authors present the fundamental equations of piezoelectricity and references. They show how a second form of the equations and a second set of coefficients can be found, through inversions involving the elasticity tensor. They show how to compute the clamped permittivity matrix from the unclamped matrix. The authors list the program pzansys.ftn and present examples of its use. This program does the conversions and calculations needed by the finite element program ANSYS.
Discontinuous Galerkin Finite Element Method for Parabolic Problems
NASA Technical Reports Server (NTRS)
Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.
2004-01-01
In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of parallel ut(t) parallel Lz(omega) = parallel ut parallel2, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also included.
Three-dimensional finite element modeling of liquid crystal devices
NASA Astrophysics Data System (ADS)
Vanbrabant, Pieter J. M.; James, Richard; Beeckman, Jeroen; Neyts, Kristiaan; Willman, Eero; Fernandez, F. Anibal
2011-03-01
A finite element framework is presented to combine advanced three-dimensional liquid crystal director calculations with a full-vector beam propagation analysis. This approach becomes especially valuable to analyze and design structures in which disclinations or diffraction effects play an important role. The wide applicability of the approach is illustrated in our overview from several examples including small pixel LCOS microdisplays with homeotropic alignment.
Stability and Convergence of Underintegrated Finite Element Approximations
NASA Technical Reports Server (NTRS)
Oden, J. T.
1984-01-01
The effects of underintegration on the numerical stability and convergence characteristics of certain classes of finite element approximations were analyzed. Particular attention is given to hourglassing instabilities that arise from underintegrating the stiffness matrix entries and checkerboard instabilities that arise from underintegrating constrain terms such as those arising from incompressibility conditions. A fundamental result reported here is the proof that the fully integrated stiffness is restored in some cases through a post-processing operation.
Finite element methods for non-Newtonian flows
Gartling, D.K.
1986-01-01
The application of the finite element method to problems in non-Newtonian fluid mechanics is described. The formulation of the basic equations is presented for both inelastic and viscoelastic constitutive models. Solution algorithms for treating the material nonlinearities associated with inealstic fluids are described; typical solution procedures for the implicit stress-rate equations of viscoelastic fluids are also presented. Simple example analyses are included for both types of fluid models. 65 refs., 21 figs.
A verification procedure for MSC/NASTRAN Finite Element Models
NASA Technical Reports Server (NTRS)
Stockwell, Alan E.
1995-01-01
Finite Element Models (FEM's) are used in the design and analysis of aircraft to mathematically describe the airframe structure for such diverse tasks as flutter analysis and actively controlled landing gear design. FEM's are used to model the entire airplane as well as airframe components. The purpose of this document is to describe recommended methods for verifying the quality of the FEM's and to specify a step-by-step procedure for implementing the methods.
Finite Element Method Applied to Fuse Protection Design
NASA Astrophysics Data System (ADS)
Li, Sen; Song, Zhiquan; Zhang, Ming; Xu, Liuwei; Li, Jinchao; Fu, Peng; Wang, Min; Dong, Lin
2014-03-01
In a poloidal field (PF) converter module, fuse protection is of great importance to ensure the safety of the thyristors. The fuse is pre-selected in a traditional way and then verified by finite element analysis. A 3D physical model is built by ANSYS software to solve the thermal-electric coupled problem of transient process in case of external fault. The result shows that this method is feasible.
Enhanced finite element scheme for vibrational and flow induced sound
NASA Astrophysics Data System (ADS)
Kaltenbacher, M.; Triebenbacher, S.; Wohlmuth, B.; Zörnre, S.
2010-06-01
The paper presents Finite Element (FE) methods for classical vibroacoustics as well as computational aeroacoustics. Therewith, we can handle different grid sizes in different regions and ensure a correct coupling at the interfaces by applying the Mortar FE method. Furthermore, we can fully take into account free radiation by a new Perfectly Matched Layer (PML) technique, which is stable even for long term computations. The applicability of our developed numerical methods will be demonstrated by simulation results of the human phonation.
Transient Finite Element Computations on a Variable Transputer System
NASA Technical Reports Server (NTRS)
Smolinski, Patrick J.; Lapczyk, Ireneusz
1993-01-01
A parallel program to analyze transient finite element problems was written and implemented on a system of transputer processors. The program uses the explicit time integration algorithm which eliminates the need for equation solving, making it more suitable for parallel computations. An interprocessor communication scheme was developed for arbitrary two dimensional grid processor configurations. Several 3-D problems were analyzed on a system with a small number of processors.
Least-squares finite element method for fluid dynamics
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Povinelli, Louis A.
1989-01-01
An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.
High speed inviscid compressible flow by the finite element method
NASA Technical Reports Server (NTRS)
Zienkiewicz, O. C.; Loehner, R.; Morgan, K.
1984-01-01
The finite element method and an explicit time stepping algorithm which is based on Taylor-Galerkin schemes with an appropriate artificial viscosity is combined with an automatic mesh refinement process which is designed to produce accurate steady state solutions to problems of inviscid compressible flow in two dimensions. The results of two test problems are included which demonstrate the excellent performance characteristics of the proposed procedures.
Finite element model for brittle fracture and fragmentation
Li, Wei; Delaney, Tristan J.; Jiao, Xiangmin; Samulyak, Roman; Lu, Cao
2016-06-01
A new computational model for brittle fracture and fragmentation has been developed based on finite element analysis of non-linear elasticity equations. The proposed model propagates the cracks by splitting the mesh nodes alongside the most over-strained edges based on the principal direction of strain tensor. To prevent elements from overlapping and folding under large deformations, robust geometrical constraints using the method of Lagrange multipliers have been incorporated. In conclusion, the model has been applied to 2D simulations of the formation and propagation of cracks in brittle materials, and the fracture and fragmentation of stretched and compressed materials.
Periodic Boundary Conditions in the ALEGRA Finite Element Code
AIDUN,JOHN B.; ROBINSON,ALLEN C.; WEATHERBY,JOE R.
1999-11-01
This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given.
Interactive Finite Elements for General Engine Dynamics Analysis
NASA Technical Reports Server (NTRS)
Adams, M. L.; Padovan, J.; Fertis, D. G.
1984-01-01
General nonlinear finite element codes were adapted for the purpose of analyzing the dynamics of gas turbine engines. In particular, this adaptation required the development of a squeeze-film damper element software package and its implantation into a representative current generation code. The ADINA code was selected because of prior use of it and familiarity with its internal structure and logic. This objective was met and the results indicate that such use of general purpose codes is viable alternative to specialized codes for general dynamics analysis of engines.
Finite Element Method for Thermal Analysis. [with computer program
NASA Technical Reports Server (NTRS)
Heuser, J.
1973-01-01
A two- and three-dimensional, finite-element thermal-analysis program which handles conduction with internal heat generation, convection, radiation, specified flux, and specified temperature boundary conditions is presented. Elements used in the program are the triangle and tetrahedron for two- and three-dimensional analysis, respectively. The theory used in the program is developed, and several sample problems demonstrating the capability and reliability of the program are presented. A guide to using the program, description of the input cards, and program listing are included.
Hopenfeld, Bruce
2006-01-01
Background In some cases, it may be necessary to combine distinct finite element meshes into a single system. The present work describes a scheme for coupling a finite element mesh, which may have curvilinear elements, to a voxel based finite element mesh. Methods The method is described with reference to a sample problem that involves combining a heart, which is defined by a curvilinear mesh, with a voxel based torso mesh. The method involves the creation of a temporary (scaffolding) mesh that couples the outer surface of the heart mesh to a voxel based torso mesh. The inner surface of the scaffolding mesh is the outer heart surface, and the outer surface of the scaffolding mesh is defined by the nodes in the torso mesh that are nearest (but outside of) the heart. The finite element stiffness matrix for the scaffolding mesh is then computed. This stiffness matrix includes extraneous nodes that are then removed, leaving a coupling matrix that couples the original outer heart surface nodes to adjacent nodes in the torso voxel mesh. Finally, a complete system matrix is assembled from the pre-existing heart stiffness matrix, the heart/torso coupling matrix, and the torso stiffness matrix. Results Realistic body surface electrocardiograms were generated. In a test involving a dipole embedded in a spherical shell, relative error of the scheme rapidly converged to slightly over 4%, although convergence thereafter was relatively slow. Conclusion The described method produces reasonably accurate results and may be best suited for problems where computational speed and convenience have a higher priority than very high levels of accuracy. PMID:17112373
Nonlinear vibration of axially moving membrane by finite element method
NASA Astrophysics Data System (ADS)
Koivurova, H.; Pramila, A.
A theoretical and numerical formulation for nonlinear axially moving membrane is presented. The model is based on a Lagrangian description of the continuum problem in the context of dynamics of initially stressed solids. Membrane elasticity is included via a finite strain model and the membrane transport speed is included by using conservation of the membrane mass. Hamilton's principle provides nonlinear equations, which describe the three-dimensional motion of the membrane. The incremental equations of Hamilton's principle are discretized by the finite element method. The formulation includes geometrically nonlinear effects: large displacements, variation of membrane tension and variations in axial velocity due to deformation. Implementation of this novel numerical model was done by adding an axially moving membrane element into a FEM program, which contains acoustic fluid elements and contact algorithms. Hence, analysis of problems containing interaction with the surrounding air field and contact between supporting structures was possible. The model was tested by comparing previous linear and present nonlinear dynamic behaviour of an axially moving web. The effects of contact between finite rolls and the membrane and interaction between the surrounding air and the membrane were included in the model. The results show, that nonlinearities and coupling phenomena have a considerable effect on the dynamic behaviour of the system.
Nonlinear probabilistic finite element models of laminated composite shells
NASA Technical Reports Server (NTRS)
Engelstad, S. P.; Reddy, J. N.
1993-01-01
A probabilistic finite element analysis procedure for laminated composite shells has been developed. A total Lagrangian finite element formulation, employing a degenerated 3-D laminated composite shell with the full Green-Lagrange strains and first-order shear deformable kinematics, forms the modeling foundation. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed and results are presented in the form of mean and variance of the structural response. The effects of material nonlinearity are included through the use of a rate-independent anisotropic plasticity formulation with the macroscopic point of view. Both ply-level and micromechanics-level random variables can be selected, the latter by means of the Aboudi micromechanics model. A number of sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. Experimental data is compared in many cases, and the Monte Carlo simulation method is used to check the probabilistic results. In general, the procedure is quite effective in modeling the mean and variance response of the linear and nonlinear behavior of laminated composite shells.
Finite element analysis of the cyclic indentation of bilayer enamel
NASA Astrophysics Data System (ADS)
Jia, Yunfei; Xuan, Fu-zhen; Chen, Xiaoping; Yang, Fuqian
2014-04-01
Tooth enamel is often subjected to repeated contact and often experiences contact deformation in daily life. The mechanical strength of the enamel determines the biofunctionality of the tooth. Considering the variation of the rod arrangement in outer and inner enamel, we approximate enamel as a bilayer structure and perform finite element analysis of the cyclic indentation of the bilayer structure, to mimic the repeated contact of enamel during mastication. The dynamic deformation behaviour of both the inner enamel and the bilayer enamel is examined. The material parameters of the inner and outer enamel used in the analysis are obtained by fitting the finite element results with the experimental nanoindentation results. The penetration depth per cycle at the quasi-steady state is used to describe the depth propagation speed, which exhibits a two-stage power-law dependence on the maximum indentation load and the amplitude of the cyclic load, respectively. The continuous penetration of the indenter reflects the propagation of the plastic zone during cyclic indentation, which is related to the energy dissipation. The outer enamel serves as a protective layer due to its great resistance to contact deformation in comparison to the inner enamel. The larger equivalent plastic strain and lower stresses in the inner enamel during cyclic indentation, as calculated from the finite element analysis, indicate better crack/fracture resistance of the inner enamel.
Interpreting finite element results for brittle materials in endodontic restorations
2011-01-01
Background Finite element simulation has been used in last years for analysing the biomechanical performance of post-core restorations in endodontics, but results of these simulations have been interpreted in most of the works using von Mises stress criterion. However, the validity of this failure criterion for brittle materials, which are present in these restorations, is questionable. The objective of the paper is to analyse how finite element results for brittle materials of endodontic restorations should be interpreted to obtain correct conclusions about the possible failure in the restoration. Methods Different failure criteria (Von Mises, Rankine, Coulomb-Mohr, Modified Mohr and Christensen) and material strength data (diametral tensile strength and flexural strength) were considered in the study. Three finite element models (FEM) were developed to simulate an endodontic restoration and two typical material tests: diametral tensile test and flexural test. Results Results showed that the Christensen criterion predicts similar results as the Von Mises criterion for ductile components, while it predicts similar results to all other criteria for brittle components. The different criteria predict different failure points for the diametral tensile test, all of them under multi-axial stress states. All criteria except Von Mises predict failure for flexural test at the same point of the specimen, with this point under uniaxial tensile stress. Conclusions From the results it is concluded that the Christensen criterion is recommended for FEM result interpretation in endodontic restorations and that the flexural test is recommended to estimate tensile strength instead of the diametral tensile test. PMID:21635759
Nonlinear explicit transient finite element analysis on the Intel Delta
Plaskacz, E.J. ); Ramirez, M.R.; Gupta, S. . Dept. of Civil Engineering)
1993-01-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Nonlinear explicit transient finite element analysis on the Intel Delta
Plaskacz, E.J.; Ramirez, M.R.; Gupta, S.
1993-03-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
A phenomenological finite element model of stereolithography processing
Chambers, R.S.; Guess, T.R.; Hinnerichs, T.D.
1996-03-01
In the stereolithography process, three dimensional parts are built layer by layer using a laser to selectively cure slices of a photocurable resin, one on top of another. As the laser spot passes over the surface of the resin, the ensuing chemical reaction causes the resin to shrink and stiffen during solidification. When laser paths cross or when new layers are cured on top of existing layers, residual stresses are generated as the cure shrinkage of the freshly gelled resin is constrained by the adjoining previously-cured material. These internal stresses can cause curling in the compliant material. A capability for performing finite element analyses of the stereolithography process has been developed. Although no attempt has been made to incorporate all the physics of the process, a numerical platform suitable for such development has been established. A methodology and code architecture have been structured to allow finite elements to be birthed (activated) according to a prescribed order mimicking the procedure by which a laser is used to cure and build-up surface layers of resin to construct a three dimensional geometry. In its present form, the finite element code incorporates a simple phenomenological viscoelastic material model of solidification that is based on the shrinkage and relaxation observed following isolated, uncoupled laser exposures. The phenomenological material model has been used to analyze the curl in a simple cantilever beam and to make qualitative distinctions between two contrived build styles.
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.
Automated Finite Element Modeling of Wing Structures for Shape Optimization
NASA Technical Reports Server (NTRS)
Harvey, Michael Stephen
1993-01-01
The displacement formulation of the finite element method is the most general and most widely used technique for structural analysis of airplane configurations. Modem structural synthesis techniques based on the finite element method have reached a certain maturity in recent years, and large airplane structures can now be optimized with respect to sizing type design variables for many load cases subject to a rich variety of constraints including stress, buckling, frequency, stiffness and aeroelastic constraints (Refs. 1-3). These structural synthesis capabilities use gradient based nonlinear programming techniques to search for improved designs. For these techniques to be practical a major improvement was required in computational cost of finite element analyses (needed repeatedly in the optimization process). Thus, associated with the progress in structural optimization, a new perspective of structural analysis has emerged, namely, structural analysis specialized for design optimization application, or.what is known as "design oriented structural analysis" (Ref. 4). This discipline includes approximation concepts and methods for obtaining behavior sensitivity information (Ref. 1), all needed to make the optimization of large structural systems (modeled by thousands of degrees of freedom and thousands of design variables) practical and cost effective.
HYDRA, A finite element computational fluid dynamics code: User manual
Christon, M.A.
1995-06-01
HYDRA is a finite element code which has been developed specifically to attack the class of transient, incompressible, viscous, computational fluid dynamics problems which are predominant in the world which surrounds us. The goal for HYDRA has been to achieve high performance across a spectrum of supercomputer architectures without sacrificing any of the aspects of the finite element method which make it so flexible and permit application to a broad class of problems. As supercomputer algorithms evolve, the continuing development of HYDRA will strive to achieve optimal mappings of the most advanced flow solution algorithms onto supercomputer architectures. HYDRA has drawn upon the many years of finite element expertise constituted by DYNA3D and NIKE3D Certain key architectural ideas from both DYNA3D and NIKE3D have been adopted and further improved to fit the advanced dynamic memory management and data structures implemented in HYDRA. The philosophy for HYDRA is to focus on mapping flow algorithms to computer architectures to try and achieve a high level of performance, rather than just performing a port.
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.
A hybrid-stress finite element for linear anisotropic elasticity
NASA Technical Reports Server (NTRS)
Fly, Gerald W.; Oden, J. Tinsley; Pearson, Mark L.
1988-01-01
Standard assumed displacement finite elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased.
Effect of grid system on finite element calculation
NASA Technical Reports Server (NTRS)
Lee, K. D.; Yen, S. M.
1980-01-01
Detailed parametric studies of the effect of grid system on finite element calculation for potential flows were made. These studies led to the formulation of a design criteria for optimum mesh system and the development of two methods to generate the optimum mesh system. The guidelines for optimum mesh system are: (1) the mesh structure should be regular; (2) the element should be as regular and equilateral as possible; (3) the distribution of size of element should be consistent with that of flow variables to insure maximum uniformity in error distribution; (4) for non-Dirichlet boundary conditions, smaller boundary elements or higher order interpolation functions should be used; and (5) the mesh should accommodate the boundary geometry as accurately as possible. The results of the parametric studies are presented.
Higher Order Lagrange Finite Elements In M3D
J. Chen; H.R. Strauss; S.C. Jardin; W. Park; L.E. Sugiyama; G. Fu; J. Breslau
2004-12-17
The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles.
NASA Technical Reports Server (NTRS)
Averill, Ronald C.
2002-01-01
An effective and robust interface element technology able to connect independently modeled finite element subdomains has been developed. This method is based on the use of penalty constraints and allows coupling of finite element models whose nodes do not coincide along their common interface. Additionally, the present formulation leads to a computational approach that is very efficient and completely compatible with existing commercial software. A significant effort has been directed toward identifying those model characteristics (element geometric properties, material properties, and loads) that most strongly affect the required penalty parameter, and subsequently to developing simple 'formulae' for automatically calculating the proper penalty parameter for each interface constraint. This task is especially critical in composite materials and structures, where adjacent sub-regions may be composed of significantly different materials or laminates. This approach has been validated by investigating a variety of two-dimensional problems, including composite laminates.
Finite element model update via Bayesian estimation and minimization of dynamic residuals
Alvin, K.F.
1996-12-31
An algorithm is presented for updating finite element models based upon a minimization of dynamic residuals. The dynamic residual of interest is the force unbalance in the homogeneous form of the equations of motion arising from errors in the model`s mass and stiffness when evaluated with the identified modal parameters. The present algorithm is a modification and extension of a previously-developed Sensitivity-Based Element-By-Element (SB-EBE) method for damage detection and finite element model up- dating. In the present algorithm, SB-EBE has been generalized to minimize a dynamic displacement residual quantity, which is shown to improve test- analysis mode correspondence. Furthermore, the algorithm has been modified to include Bayesian estimation concepts, and the underlying nonlinear optimization problem has been consistently linearized to improve the convergence properties. The resulting algorithm is demonstrated via numerical and experimental examples to be an efficient and robust method for both localizing model errors and estimating physical parameters.
Lee, W; Kim, T-S; Cho, M; Lee, S
2005-01-01
In studying bioelectromagnetic problems, finite element method offers several advantages over other conventional methods such as boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropy. Mesh generation is the first requirement in the finite element analysis and there are many different approaches in mesh generation. However conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes, resulting in numerous elements in the smaller volume regions, thereby increasing computational load and demand. In this work, we present an improved content-adaptive mesh generation scheme that is efficient and fast along with options to change the contents of meshes. For demonstration, mesh models of the head from a volume MRI are presented in 2-D and 3-D.
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.
Comparison of boundary element and finite element methods in spur gear root stress analysis
NASA Technical Reports Server (NTRS)
Sun, H.; Mavriplis, D.; Huston, R. L.; Oswald, F. B.
1989-01-01
The boundary element method (BEM) is used to compute fillet stress concentration in spur gear teeth. The results are shown to compare favorably with analogous results obtained using the finite element method (FEM). A partially supported thin rim gear is studied. The loading is applied at the pitch point. A three-dimensional analysis is conducted using both the BEM and FEM (NASTRAN). The results are also compared with those of a two-dimensional finite element model. An advantage of the BEM over the FEM is that fewer elements are needed with the BEM. Indeed, in the current study the BEM used 92 elements and 270 nodes whereas the FEM used 320 elements and 2037 nodes. Moreover, since the BEM is especially useful in problems with high stress gradients it is potentially a very useful tool for fillet stress analyses.
Dohrmann, C.R.; Heinstein, M.W.; Jung, J.; Key, S.W.
1999-01-01
This report documents a collection of papers on a family of uniform strain tetrahedral finite elements and their connection to different element types. Also included in the report are two papers which address the general problem of connecting dissimilar meshes in two and three dimensions. Much of the work presented here was motivated by the development of the tetrahedral element described in the report "A Suitable Low-Order, Eight-Node Tetrahedral Finite Element For Solids," by S. W. Key {ital et al.}, SAND98-0756, March 1998. Two basic issues addressed by the papers are: (1) the performance of alternative tetrahedral elements with uniform strain and enhanced uniform strain formulations, and (2) the proper connection of tetrahedral and other element types when two meshes are "tied" together to represent a single continuous domain.
Extraction and applications of skeletons in finite element mesh generation.
Quadros, William Roshan
2010-05-01
This paper focuses on the extraction of skeletons of CAD models and its applications in finite element (FE) mesh generation. The term 'skeleton of a CAD model' can be visualized as analogous to the 'skeleton of a human body'. The skeletal representations covered in this paper include medial axis transform (MAT), Voronoi diagram (VD), chordal axis transform (CAT), mid surface, digital skeletons, and disconnected skeletons. In the literature, the properties of a skeleton have been utilized in developing various algorithms for extracting skeletons. Three main approaches include: (1) the bisection method where the skeleton exists at equidistant from at least two points on boundary, (2) the grassfire propagation method in which the skeleton exists where the opposing fronts meet, and (3) the duality method where the skeleton is a dual of the object. In the last decade, the author has applied different skeletal representations in all-quad meshing, hex meshing, mid-surface meshing, mesh size function generation, defeaturing, and decomposition. A brief discussion on the related work from other researchers in the area of tri meshing, tet meshing, and anisotropic meshing is also included. This paper concludes by summarizing the strengths and weaknesses of the skeleton-based approaches in solving various geometry-centered problems in FE mesh generation. The skeletons have proved to be a great shape abstraction tool in analyzing the geometric complexity of CAD models as they are symmetric, simpler (reduced dimension), and provide local thickness information. However, skeletons generally require some cleanup, and stability and sensitivity of the skeletons should be controlled during extraction. Also, selecting a suitable application-specific skeleton and a computationally efficient method of extraction is critical.
Finite volume and finite element methods applied to 3D laminar and turbulent channel flows
Louda, Petr; Příhoda, Jaromír; Sváček, Petr; Kozel, Karel
2014-12-10
The work deals with numerical simulations of incompressible flow in channels with rectangular cross section. The rectangular cross section itself leads to development of various secondary flow patterns, where accuracy of simulation is influenced by numerical viscosity of the scheme and by turbulence modeling. In this work some developments of stabilized finite element method are presented. Its results are compared with those of an implicit finite volume method also described, in laminar and turbulent flows. It is shown that numerical viscosity can cause errors of same magnitude as different turbulence models. The finite volume method is also applied to 3D turbulent flow around backward facing step and good agreement with 3D experimental results is obtained.
Finite Element Analysis of Tube Hydroforming in Non-Symmetrical Dies
NASA Astrophysics Data System (ADS)
Nulkar, Abhishek V.; Gu, Randy; Murty, Pilaka
2011-08-01
Tube hydroforming has been studied intensively using commercial finite element programs. A great deal of the investigations dealt with models with symmetric cross-sections. It is known that additional constraints due to symmetry may be imposed on the model so that it is properly supported. For a non-symmetric model, these constraints become invalid and the model does not have sufficient support resulting in a singular finite element system. Majority of commercial codes have a limited capability in solving models with insufficient supports. Recently, new algorithms using penalty variable and air-like contact element (ALCE) have been developed to solve positive semi-definite finite element systems such as those in contact mechanics. In this study the ALCE algorithm is first validated by comparing its result against a commercial code using a symmetric model in which a circular tube is formed to polygonal dies with symmetric shapes. Then, the study investigates the accuracy and efficiency of using ALCE in analyzing hydroforming of tubes with various cross-sections in non-symmetrical dies in 2-D finite element settings.
NASA Technical Reports Server (NTRS)
Gong, J.; Volakis, J. L.; Chatterjee, A.; Jin, J. M.
1992-01-01
A hybrid finite element boundary integral formulation is developed using tetrahedral and/or triangular elements for discretizing the cavity and/or aperture of microstrip antenna arrays. The tetrahedral elements with edge based linear expansion functions are chosen for modeling the volume region and triangular elements are used for discretizing the aperture. The edge based expansion functions are divergenceless thus removing the requirement to introduce a penalty term and the tetrahedral elements permit greater geometrical adaptability than the rectangular bricks. The underlying theory and resulting expressions are discussed in detail together with some numerical scattering examples for comparison and demonstration.
A finite element simulation of sound attenuation in a finite duct with a peripherally variable liner
NASA Technical Reports Server (NTRS)
Watson, W. R.
1977-01-01
Using multimodal analysis, a variational finite element method is presented for analyzing sound attenuation in a three-dimensional finite duct with a peripherally variable liner in the absence of flow. A rectangular element, with cubic shaped functions, is employed. Once a small portion of a peripheral liner is removed, the attenuation rate near the frequency where maximum attenuation occurs drops significantly. The positioning of the liner segments affects the attenuation characteristics of the liner. Effects of the duct termination are important in the low frequency ranges. The main effect of peripheral variation of the liner is a broadening of the attenuation characteristics in the midfrequency range. Because of matrix size limitations of the presently available computer program, the eigenvalue equations should be solved out of core in order to handle realistic sources.
Adaptation of a program for nonlinear finite element analysis to the CDC STAR 100 computer
NASA Technical Reports Server (NTRS)
Pifko, A. B.; Ogilvie, P. L.
1978-01-01
The conversion of a nonlinear finite element program to the CDC STAR 100 pipeline computer is discussed. The program called DYCAST was developed for the crash simulation of structures. Initial results with the STAR 100 computer indicated that significant gains in computation time are possible for operations on gloval arrays. However, for element level computations that do not lend themselves easily to long vector processing, the STAR 100 was slower than comparable scalar computers. On this basis it is concluded that in order for pipeline computers to impact the economic feasibility of large nonlinear analyses it is absolutely essential that algorithms be devised to improve the efficiency of element level computations.
Experimental and three-dimensional finite element investigation of fatigue
NASA Astrophysics Data System (ADS)
Bomidi, John A. R.
Materials often fail at cyclic loads that are lower than their ultimate strength or even their yield strength due to progressive internal material degradation; commonly known as fatigue. Moreover, there is a wide scatter in observed fatigue lives of mechanical components operating under identical loading conditions. The randomness of fatigue failure is considered to be linked to basic microstructural effects such as random microstructure topology and the initiation/growth of cracks along inter/transgranular planes. Several modeling approaches have been previously presented ranging from 2D discrete element to 3D Finite Element methods with explicit representation of microstructure topology and continuum damage mechanics to capture dispersion in rolling contact fatigue life and fatigue spalling. There is, however, a need to compare the modeling approach with experimental fatigue test conditions in order to verify and as required enhance the modeling approach to capture observed fatigue failure. This dissertation presents experimental test results and three-dimensional modeling approach that capture fatigue failure. The three-dimensional modeling approach is enhanced according to the experimental observations to consider inter/trans granular failure, different modes of fatigue initiation and propagation and finally for considering effect of plasticity in fatigue of rolling contacts. The following phenomena have been investigated: (1) Fatigue of microbeams: (a )Results of fatigue life and failure from 3D modeling of intergranular fatigue in microbeams are compared with experimental observations reported in literature (2) Tensile fatigue of thin sheets: (a) A test rig with a new grip and alignment system is developed to address the challenges associated with thin sheet testing and conduct fatigue experiments. (b) The 3D fatigue model is enhanced to capture the dominant transgranular fatigue observed in the experiments. The observed and modeled fatigue life and failure
An implementation analysis of the linear discontinuous finite element method
Becker, T. L.
2013-07-01
This paper provides an implementation analysis of the linear discontinuous finite element method (LD-FEM) that spans the space of (l, x, y, z). A practical implementation of LD includes 1) selecting a computationally efficient algorithm to solve the 4 x 4 matrix system Ax = b that describes the angular flux in a mesh element, and 2) choosing how to store the data used to construct the matrix A and the vector b to either reduce memory consumption or increase computational speed. To analyze the first of these, three algorithms were selected to solve the 4 x 4 matrix equation: Cramer's rule, a streamlined implementation of Gaussian elimination, and LAPACK's Gaussian elimination subroutine dgesv. The results indicate that Cramer's rule and the streamlined Gaussian elimination algorithm perform nearly equivalently and outperform LAPACK's implementation of Gaussian elimination by a factor of 2. To analyze the second implementation detail, three formulations of the discretized LD-FEM equations were provided for implementation in a transport solver: 1) a low-memory formulation, which relies heavily on 'on-the-fly' calculations and less on the storage of pre-computed data, 2) a high-memory formulation, which pre-computes much of the data used to construct A and b, and 3) a reduced-memory formulation, which lies between the low - and high-memory formulations. These three formulations were assessed in the Jaguar transport solver based on relative memory footprint and computational speed for increasing mesh size and quadrature order. The results indicated that the memory savings of the low-memory formulation were not sufficient to warrant its implementation. The high-memory formulation resulted in a significant speed advantage over the reduced-memory option (10-50%), but also resulted in a proportional increase in memory consumption (5-45%) for increasing quadrature order and mesh count; therefore, the practitioner should weigh the system memory constraints against any
Simulating Space Capsule Water Landing with Explicit Finite Element Method
NASA Technical Reports Server (NTRS)
Wang, John T.; Lyle, Karen H.
2007-01-01
A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.
Finite Element Analysis of the LOLA Receiver Telescope Lens
NASA Technical Reports Server (NTRS)
Matzinger, Elizabeth
2007-01-01
This paper presents the finite element stress and distortion analysis completed on the Receiver Telescope lens of the Lunar Orbiter Laser Altimeter (LOLA). LOLA is one of six instruments on the Lunar Reconnaissance Orbiter (LRO), scheduled to launch in 2008. LOLA's main objective is to produce a high-resolution global lunar topographic model to aid in safe landings and enhance surface mobility in future exploration missions. The Receiver Telescope captures the laser pulses transmitted through a diffractive optical element (DOE) and reflected off the lunar surface. The largest lens of the Receiver Telescope, Lens 1, is a 150 mm diameter aspheric lens originally designed to be made of BK7 glass. The finite element model of the Receiver Telescope Lens 1 is comprised of solid elements and constrained in a manner consistent with the behavior of the mounting configuration of the Receiver Telescope tube. Twenty-one temperature load cases were mapped to the nodes based on thermal analysis completed by LOLA's lead thermal analyst, and loads were applied to simulate the preload applied from the ring flexure. The thermal environment of the baseline design (uncoated BK7 lens with no baffle) produces large radial and axial gradients in the lens. These large gradients create internal stresses that may lead to part failure, as well as significant bending that degrades optical performance. The high stresses and large distortions shown in the analysis precipitated a design change from BK7 glass to sapphire.
NASA Technical Reports Server (NTRS)
Nakazawa, Shohei
1989-01-01
The internal structure is discussed of the MHOST finite element program designed for 3-D inelastic analysis of gas turbine hot section components. The computer code is the first implementation of the mixed iterative solution strategy for improved efficiency and accuracy over the conventional finite element method. The control structure of the program is covered along with the data storage scheme and the memory allocation procedure and the file handling facilities including the read and/or write sequences.
IFEMS, an Interactive Finite Element Modeling System Using a CAD/CAM System
NASA Technical Reports Server (NTRS)
Mckellip, S.; Schuman, T.; Lauer, S.
1980-01-01
A method of coupling a CAD/CAM system with a general purpose finite element mesh generator is described. The three computer programs which make up the interactive finite element graphics system are discussed.
NASA Technical Reports Server (NTRS)
Cerracchio, Priscilla; Gherlone, Marco; Di Sciuva, Marco; Tessler, Alexander
2013-01-01
The marked increase in the use of composite and sandwich material systems in aerospace, civil, and marine structures leads to the need for integrated Structural Health Management systems. A key capability to enable such systems is the real-time reconstruction of structural deformations, stresses, and failure criteria that are inferred from in-situ, discrete-location strain measurements. This technology is commonly referred to as shape- and stress-sensing. Presented herein is a computationally efficient shape- and stress-sensing methodology that is ideally suited for applications to laminated composite and sandwich structures. The new approach employs the inverse Finite Element Method (iFEM) as a general framework and the Refined Zigzag Theory (RZT) as the underlying plate theory. A three-node inverse plate finite element is formulated. The element formulation enables robust and efficient modeling of plate structures instrumented with strain sensors that have arbitrary positions. The methodology leads to a set of linear algebraic equations that are solved efficiently for the unknown nodal displacements. These displacements are then used at the finite element level to compute full-field strains, stresses, and failure criteria that are in turn used to assess structural integrity. Numerical results for multilayered, highly heterogeneous laminates demonstrate the unique capability of this new formulation for shape- and stress-sensing.
Reflections of AE Waves in Finite Plates: Finite Element Modeling and Experimental Measurements
NASA Technical Reports Server (NTRS)
Prosser, W. H.; Hamstad, M. A.; Gary, J.; OGallagher, A.
1999-01-01
The capability of a three-dimensional dynamic finite element method for predicting far-field acoustic emission signals in thin plates of finite lateral extent, including their reflections from the plate edges, was investigated. A lead break (Hsu-Neilsen) source to simulate AE was modeled and used in the experimental measurements. For the thin plate studied, the signals were primarily composed of the lowest order symmetric (S0) and antisymmetric (A0) Lamb modes. Experimental waveforms were detected with an absolutely calibrated, wideband, conical element transducer. The conditions of lead fractures both on the surface of the plate as well as on the edge of the plate were investigated. Surface lead breaks preferentially generate the A0 mode while edge lead breaks generate the S0 mode. Reflections of developed plate waves from both normal and oblique incidence angles were evaluated. Particularly interesting for the case of the lead break on the plate edge were S0 waves produced by the interaction of a Rayleigh wave with the plate corner and by a bulk shear wave mode converting at the side edge. The Rayleigh wave, in this case, propagated along the specimen edge. For all cases considered, the experimental measurements were in good agreement with the predictions of the finite element model.
Galerkin finite element scheme for magnetostrictive structures and composites
NASA Astrophysics Data System (ADS)
Kannan, Kidambi Srinivasan
The ever increasing-role of magnetostrictives in actuation and sensing applications is an indication of their importance in the emerging field of smart structures technology. As newer, and more complex, applications are developed, there is a growing need for a reliable computational tool that can effectively address the magneto-mechanical interactions and other nonlinearities in these materials and in structures incorporating them. This thesis presents a continuum level quasi-static, three-dimensional finite element computational scheme for modeling the nonlinear behavior of bulk magnetostrictive materials and particulate magnetostrictive composites. Models for magnetostriction must deal with two sources of nonlinearities-nonlinear body forces/moments in equilibrium equations governing magneto-mechanical interactions in deformable and magnetized bodies; and nonlinear coupled magneto-mechanical constitutive models for the material of interest. In the present work, classical differential formulations for nonlinear magneto-mechanical interactions are recast in integral form using the weighted-residual method. A discretized finite element form is obtained by applying the Galerkin technique. The finite element formulation is based upon three dimensional eight-noded (isoparametric) brick element interpolation functions and magnetostatic infinite elements at the boundary. Two alternative possibilities are explored for establishing the nonlinear incremental constitutive model-characterization in terms of magnetic field or in terms of magnetization. The former methodology is the one most commonly used in the literature. In this work, a detailed comparative study of both methodologies is carried out. The computational scheme is validated, qualitatively and quantitatively, against experimental measurements published in the literature on structures incorporating the magnetostrictive material Terfenol-D. The influence of nonlinear body forces and body moments of magnetic origin
A finite element model for sound transmission through panels
NASA Technical Reports Server (NTRS)
Ramakrishnan, J. V.; Koval, L. R.
1983-01-01
A finite element method (FEM) is applied to predicting coupled frequencies and pressures within an acoustic cavity in order to characterize sound transmission through a panel. Structural equations of motion are defined and the FEM model is configured with four-noded plate elements, the lateral displacement and two slopes being the unknowns at every node. Each element then has 12 degrees of freedom (DOF) and the displacement variation is expressed by a 12-term nonconforming polynomial. A consistent mass matrix is used to represent the panel mass matrix and a wave equation governs the acoustic volume. Analysis of pressure and displacement over the panel yields a square coupling matrix, and an eigenanalysis leads to a solution of the forced vibration problem.
Most efficient quantum thermoelectric at finite power output.
Whitney, Robert S
2014-04-01
Machines are only Carnot efficient if they are reversible, but then their power output is vanishingly small. Here we ask, what is the maximum efficiency of an irreversible device with finite power output? We use a nonlinear scattering theory to answer this question for thermoelectric quantum systems, heat engines or refrigerators consisting of nanostructures or molecules that exhibit a Peltier effect. We find that quantum mechanics places an upper bound on both power output and on the efficiency at any finite power. The upper bound on efficiency equals Carnot efficiency at zero power output but decays with increasing power output. It is intrinsically quantum (wavelength dependent), unlike Carnot efficiency. This maximum efficiency occurs when the system lets through all particles in a certain energy window, but none at other energies. A physical implementation of this is discussed, as is the suppression of efficiency by a phonon heat flow.
A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions
NASA Astrophysics Data System (ADS)
Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.
2014-01-01
We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.
Progress on hybrid finite element methods for scattering by bodies of revolution
NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Volakis, John L.
1992-01-01
Progress on the development and implementation of hybrid finite element methods for scattering by bodies of revolution are described. It was found that earlier finite element-boundary integral formulations suffered from convergence difficulties when applied to large and thin bodies of revolution. An alternative implementation is described where the finite element method is terminated with an absorbing termination boundary. In addition, an alternative finite element-boundary integral implementation is discussed for improving the convergence of the original code.
Finite element modeling for validation of structural damage identification experimentation.
Stinemates, D. W.; Bennett, J. G.
2001-01-01
The project described in this report was performed to couple experimental and analytical techniques in the field of structural health monitoring and darnage identification. To do this, a finite dement model was Constructed of a simulated three-story building used for damage identification experiments. The model was used in conjunction with data from thie physical structure to research damage identification algorithms. Of particular interest was modeling slip in joints as a function of bolt torque and predicting the smallest change of torque that could be detected experimentally. After being validated with results from the physical structure, the model was used to produce data to test the capabilities of damage identification algorithms. This report describes the finite element model constructed, the results obtained, and proposed future use of the model.
Least-squares finite element methods for quantum chromodynamics
Ketelsen, Christian; Brannick, J; Manteuffel, T; Mccormick, S
2008-01-01
A significant amount of the computational time in large Monte Carlo simulations of lattice quantum chromodynamics (QCD) is spent inverting the discrete Dirac operator. Unfortunately, traditional covariant finite difference discretizations of the Dirac operator present serious challenges for standard iterative methods. For interesting physical parameters, the discretized operator is large and ill-conditioned, and has random coefficients. More recently, adaptive algebraic multigrid (AMG) methods have been shown to be effective preconditioners for Wilson's discretization of the Dirac equation. This paper presents an alternate discretization of the Dirac operator based on least-squares finite elements. The discretization is systematically developed and physical properties of the resulting matrix system are discussed. Finally, numerical experiments are presented that demonstrate the effectiveness of adaptive smoothed aggregation ({alpha}SA ) multigrid as a preconditioner for the discrete field equations resulting from applying the proposed least-squares FE formulation to a simplified test problem, the 2d Schwinger model of quantum electrodynamics.
Large-eddy simulation using the finite element method
McCallen, R.C.; Gresho, P.M.; Leone, J.M. Jr.; Kollmann, W.
1993-10-01
In a large-eddy simulation (LES) of turbulent flows, the large-scale motion is calculated explicitly (i.e., approximated with semi-empirical relations). Typically, finite difference or spectral numerical schemes are used to generate an LES; the use of finite element methods (FEM) has been far less prominent. In this study, we demonstrate that FEM in combination with LES provides a viable tool for the study of turbulent, separating channel flows, specifically the flow over a two-dimensional backward-facing step. The combination of these methodologies brings together the advantages of each: LES provides a high degree of accuracy with a minimum of empiricism for turbulence modeling and FEM provides a robust way to simulate flow in very complex domains of practical interest. Such a combination should prove very valuable to the engineering community.
Improved inhomogeneous finite elements for fabric reinforced composite mechanics analysis
NASA Technical Reports Server (NTRS)
Foye, R. L.
1992-01-01
There is a need to do routine stress/failure analysis of fabric reinforced composite microstructures to provide additional confidence in critical applications and guide materials development. Conventional methods of 3-D stress analysis are time consuming to set up, run and interpret. A need exists for simpler methods of modeling these structures and analyzing the models. The principal difficulty is the discrete element mesh generation problem. Inhomogeneous finite elements are worth investigating for application to these problems because they eliminate the mesh generation problem. However, there are penalties associated with these elements. Their convergence rates can be slow compared to homogeneous elements. Also, there is no accepted method for obtaining detailed stresses in the constituent materials of each element. This paper shows that the convergence rate can be significantly improved by a simple device which substitutes homogeneous elements for the inhomogeneous ones. The device is shown to work well in simple one and two dimensional problems. However, demonstration of the application to more complex two and three dimensional problems remains to be done. Work is also progressing toward more realistic fabric microstructural geometries.
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.
Application of finite-element method to three-dimensional nuclear reactor analysis
Cheung, K.Y.
1985-01-01
The application of the finite element method to solve a realistic one-or-two energy group, multiregion, three-dimensional static neutron diffusion problem is studied. Linear, quadratic, and cubic serendipity box-shape elements are used. The resulting sets of simultaneous algebraic equations with thousands of unknowns are solved by the conjugate gradient method, without forming the large coefficient matrix explicitly. This avoids the complicated data management schemes to store such a large coefficient matrix. Three finite-element computer programs: FEM-LINEAR, FEM-QUADRATIC and FEM-CUBIC were developed, using the linear, quadratic, and cubic box-shape elements respectively. They are self-contained, using simple nodal labeling schemes, without the need for separate finite element mesh generating routines. The efficiency and accuracy of these computer programs are then compared among themselves, and with other computer codes. The cubic element model is not recommended for practical usage because it gives almost identical results as the quadratic model, but it requires considerably longer computation time. The linear model is less accurate than the quadratic model, but it requires much shorter computation time. For a large 3-D problem, the linear model is to be preferred since it gives acceptable accuracy. The quadratic model may be used if improved accuracy is desired.
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.
NASA Technical Reports Server (NTRS)
Hamilton, H. B.; Strangas, E.
1980-01-01
The time dependent solution of the magnetic field is introduced as a method for accounting for the variation, in time, of the machine parameters in predicting and analyzing the performance of the electrical machines. The method of time dependent finite element was used in combination with an also time dependent construction of a grid for the air gap region. The Maxwell stress tensor was used to calculate the airgap torque from the magnetic vector potential distribution. Incremental inductances were defined and calculated as functions of time, depending on eddy currents and saturation. The currents in all the machine circuits were calculated in the time domain based on these inductances, which were continuously updated. The method was applied to a chopper controlled DC series motor used for electric vehicle drive, and to a salient pole sychronous motor with damper bars. Simulation results were compared to experimentally obtained ones.
NASA Technical Reports Server (NTRS)
Ko, William L.; Olona, Timothy; Muramoto, Kyle M.
1990-01-01
Different finite element models previously set up for thermal analysis of the space shuttle orbiter structure are discussed and their shortcomings identified. Element density criteria are established for the finite element thermal modelings of space shuttle orbiter-type large, hypersonic aircraft structures. These criteria are based on rigorous studies on solution accuracies using different finite element models having different element densities set up for one cell of the orbiter wing. Also, a method for optimization of the transient thermal analysis computer central processing unit (CPU) time is discussed. Based on the newly established element density criteria, the orbiter wing midspan segment was modeled for the examination of thermal analysis solution accuracies and the extent of computation CPU time requirements. The results showed that the distributions of the structural temperatures and the thermal stresses obtained from this wing segment model were satisfactory and the computation CPU time was at the acceptable level. The studies offered the hope that modeling the large, hypersonic aircraft structures using high-density elements for transient thermal analysis is possible if a CPU optimization technique was used.
Finite element analysis of heat transport in a hydrothermal zone
Bixler, N.E.; Carrigan, C.R.
1987-01-01
Two-phase heat transport in the vicinity of a heated, subsurface zone is important for evaluation of nuclear waste repository design and estimation of geothermal energy recovery, as well as prediction of magma solidification rates. Finite element analyses of steady, two-phase, heat and mass transport have been performed to determine the relative importance of conduction and convection in a permeable medium adjacent to a hot, impermeable, vertical surface. The model includes the effects of liquid flow due to capillarity and buoyancy and vapor flow due to pressure gradients. Change of phase, with its associated latent heat effects, is also modeled. The mechanism of capillarity allows for the presence of two-phase zones, where both liquid and vapor can coexist, which has not been considered in previous investigations. The numerical method employs the standard Galerkin/finite element method, using eight-node, subparametric or isoparametric quadrilateral elements. In order to handle the extreme nonlinearities inherent in two-phase, nonisothermal, porous-flow problems, steady-state results are computed by integrating transients out to a long time (a method that is highly robust).
Merging of intersecting triangulations for finite element modeling.
Cebral, J R; Löhner, R; Choyke, P L; Yim, P J
2001-06-01
Surface mesh generation over intersecting triangulations is a problem common to many branches of biomechanics. A new strategy for merging intersecting triangulations is described. The basis of the method is that object surfaces are represented as the zero-level iso-surface of the distance-to-surface function defined on a background grid. Thus, the triangulation of intersecting objects reduces to the extraction of an iso-surface from an unstructured grid. In a first step, a regular background mesh is constructed. For each point of the background grid, the closest distance to the surface of each object is computed. Background points are then classified as external or internal by checking the direction of the surface normal at the closest location and assigned a positive or negative distance, respectively. Finally, the zero-level iso-surface is constructed. This is the final triangulation of the intersecting objects. The overall accuracy is enhanced by adaptive refinement of the background grid elements. The resulting surface models are used as support surfaces to generate three-dimensional grids for finite element analysis. The algorithms are demonstrated by merging arterial branches independently reconstructed from contrast-enhanced magnetic resonance images and by adding extra features such as vascular stents. Although the methodology is presented in the context of finite element analysis of blood flow, the algorithms are general and can be applied in other areas as well. PMID:11470121
Elliptic interface problem solved using the mixed finite element method
NASA Astrophysics Data System (ADS)
Wang, Shuqiang
2007-05-01
The elliptic boundary value/interface problem is very important in many applications, for example, in incompressible flow and MHD. Many methods are used to solve these problems in a complex domain, including the finite volume method, the finite element method and the boundary element method. For a complex computational domain, the better choice of the partition of the computational domain is to use an unstructured grid. However, it is not a straight forward task to implement a mesh generation program. Such a program requires extra computing time and resources (such as computer memory). Thus people like to use a structured mesh if possible, especially a cartesian mesh. Popular methods using structured cartesian grids for the elliptic boundary value/interface problem include the immersed boundary method, the immersed interface method, the ghost fluid method, and the embedded boundary method. This thesis solves the elliptic problem using several versions of the mixed nite element method on an unstructured mesh. The results are compared for speed and accuracy to the embedded boundary method. A ghost fluid method for elliptic boundary value/interface problems is also investigated. Finally, a simple test of the 2D Rayleigh-Taylor instability is performed using the FronTier-Lite package. Key Words. Elliptic Boundary Value, Interface, Mesh Generation, Quadtree, Octree, Front Tracking.
Automated Finite Element Analysis of Elastically-Tailored Plates
NASA Technical Reports Server (NTRS)
Jegley, Dawn C. (Technical Monitor); Tatting, Brian F.; Guerdal, Zafer
2003-01-01
A procedure for analyzing and designing elastically tailored composite laminates using the STAGS finite element solver has been presented. The methodology used to produce the elastic tailoring, namely computer-controlled steering of unidirectionally reinforced composite material tows, has been reduced to a handful of design parameters along with a selection of construction methods. The generality of the tow-steered ply definition provides the user a wide variety of options for laminate design, which can be automatically incorporated with any finite element model that is composed of STAGS shell elements. Furthermore, the variable stiffness parameterization is formulated so that manufacturability can be assessed during the design process, plus new ideas using tow steering concepts can be easily integrated within the general framework of the elastic tailoring definitions. Details for the necessary implementation of the tow-steering definitions within the STAGS hierarchy is provided, and the format of the ply definitions is discussed in detail to provide easy access to the elastic tailoring choices. Integration of the automated STAGS solver with laminate design software has been demonstrated, so that the large design space generated by the tow-steering options can be traversed effectively. Several design problems are presented which confirm the usefulness of the design tool as well as further establish the potential of tow-steered plies for laminate design.
Binary tree eigen solver in finite element analysis
NASA Technical Reports Server (NTRS)
Akl, F. A.; Janetzke, D. C.; Kiraly, L. J.
1993-01-01
This paper presents a transputer-based binary tree eigensolver for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on the method of recursive doubling, which parallel implementation of a number of associative operations on an arbitrary set having N elements is of the order of o(log2N), compared to (N-1) steps if implemented sequentially. The hardware used in the implementation of the binary tree consists of 32 transputers. The algorithm is written in OCCAM which is a high-level language developed with the transputers to address parallel programming constructs and to provide the communications between processors. The algorithm can be replicated to match the size of the binary tree transputer network. Parallel and sequential finite element analysis programs have been developed to solve for the set of the least-order eigenpairs using the modified subspace method. The speed-up obtained for a typical analysis problem indicates close agreement with the theoretical prediction given by the method of recursive doubling.
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.
Binary tree eigen solver in finite element analysis
Akl, F.A.; Janetzke, D.C.; Kiraly, L.J.
1993-01-01
This paper presents a transputer-based binary tree eigensolver for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on the method of recursive doubling, which parallel implementation of a number of associative operations on an arbitrary set having N elements is of the order of o(log2N), compared to (N-1) steps if implemented sequentially. The hardware used in the implementation of the binary tree consists of 32 transputers. The algorithm is written in OCCAM which is a high-level language developed with the transputers to address parallel programming constructs and to provide the communications between processors. The algorithm can be replicated to match the size of the binary tree transputer network. Parallel and sequential finite element analysis programs have been developed to solve for the set of the least-order eigenpairs using the modified subspace method. The speed-up obtained for a typical analysis problem indicates close agreement with the theoretical prediction given by the method of recursive doubling. 5 refs.
Finite-element impact response of debonded composite turbine blades
NASA Astrophysics Data System (ADS)
Dey, Sudip; Karmakar, Amit
2014-02-01
This paper investigates on the transient behavior of debonded composite pretwisted rotating shallow conical shells which could be idealized as turbine blades subjected to low velocity normal impact using finite-element method. Lagrange's equation of motion is used to derive the dynamic equilibrium equation and the moderate rotational speeds are considered neglecting the Coriolis effect. An eight-noded isoparametric plate bending element is employed in the finite element formulation incorporating rotary inertia and effects of transverse shear deformation based on Mindlin's theory. The modified Hertzian contact law which accounts for permanent indentation is utilized to compute the impact parameters. The time-dependent equations are solved by using Newmark's time integration scheme. Parametric studies are performed to investigate the effects of triggering parameters like angle of twist, rotational speed, laminate configuration and location of debonding considering low velocity normal impact at the center of eight-layered graphite-epoxy composite cantilevered conical shells with bending stiff ([0o2/{±} 30o]s), torsion stiff ([45°/-45°/-45°/45°]s) and cross-ply ([0°/90°/0°/90°]s) laminate configurations.
Simplified Finite Element Modelling of Acoustically Treated Structures
NASA Astrophysics Data System (ADS)
Carfagni, M.; Citti, P.; Pierini, M.
1997-07-01
The application of non-optimized damping and phono-absorbent materials to automotive systems has not proved fully satisfactory in abating noise and vibration. The objective of this work was to develop a simple finite element modelling procedure that would allow optimizing structures such as a car body-in-white in terms of vibroacoustic behavior from the design stage. A procedure was developed to determine the modifications to be made in the mass, stiffness and damping characteristics in the finite element (FE) modelling of a metal structure meshed with shell elements so that the model would describe the behavior of the acoustically treated structure. To validate the modifications, a numerical-experimental comparison of the velocities on the vibrating surface was carried out, followed by a numerical-experimental comparison of the sound pressures generated by the vibrating plate. In the comparison a simple monopole model was used, in which each area of vibrating surface could be likened to a point source. The simulation and experimental procedures, previously validated for the metal structure, were then applied to multi-layered panels. Good agreement between the experimental and simulated velocities and sound pressures resulted for all the multi-layered panel configurations examined.
Loveday, Philip W
2007-10-01
A finite-element modeling procedure for computing the frequency response of piezoelectric transducers attached to infinite constant cross-section waveguides, as encountered in guided wave ultrasonic inspection, is presented. Two-dimensional waveguide finite elements are used to model the waveguide. Conventional three-dimensional finite elements are used to model the piezoelectric transducer. The harmonic forced response of the waveguide is used to obtain a dynamic stiffness matrix (complex and frequency dependent), which represents the waveguide in the transducer model. The electrical and mechanical frequency response of the transducer, attached to the waveguide, can then be computed. The forces applied to the waveguide are calculated and are used to determine the amplitude of each mode excited in the waveguide. The method is highly efficient compared to time integration of a conventional finite-element model of a length of waveguide. In addition, the method provides information about each mode that is excited in the waveguide. The method is demonstrated by modeling a sandwich piezoelectric transducer exciting a waveguide of rectangular cross section, although it could be applied to more complex situations. It is expected that the modeling method will be useful during the optimization of piezoelectric transducers for exciting specific wave propagation modes in waveguides.
NASA Technical Reports Server (NTRS)
Gupta, K. K.; Lawson, C. L.; Ahmad, A. R.
1992-01-01
The paper first presents the details of the development of a new six-noded plane triangular finite dynamic element. A block Lanczos algorithm is developed next for the accurate and efficient solution of the quadratic matrix eigenvalue problem associated with the finite dynamic element formulation. The resulting computer program fully exploits matrix sparsity inherent in such a discretization and proves to be most efficient for the extraction of the usually required first few roots and vectors, including repeated ones. Most importantly, the present eigenproblem solution is shown to be comparable to that of the corresponding finite element analysis, thereby rendering the associated dynamic element method rather attractive owing to superior convergence characteristics of such elements, presented herein.
Cwik, T.; Katz, D.S.
1996-12-31
Finite element modeling has proven useful for accurately simulating scattered or radiated electromagnetic fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of an electrical wavelength. An unstructured finite element model of realistic objects leads to a large, sparse, system of equations that needs to be solved efficiently with regard to machine memory and execution time. Both factorization and iterative solvers can be used to produce solutions to these systems of equations. Factorization leads to high memory requirements that limit the electrical problem size of three-dimensional objects that can be modeled. An iterative solver can be used to efficiently solve the system without excessive memory use and in a minimal amount of time if the convergence rate is controlled.
Some Observations on the Current Status of Performing Finite Element Analyses
NASA Technical Reports Server (NTRS)
Raju, Ivatury S.; Knight, Norman F., Jr; Shivakumar, Kunigal N.
2015-01-01
Aerospace structures are complex high-performance structures. Advances in reliable and efficient computing and modeling tools are enabling analysts to consider complex configurations, build complex finite element models, and perform analysis rapidly. Many of the early career engineers of today are very proficient in the usage of modern computers, computing engines, complex software systems, and visualization tools. These young engineers are becoming increasingly efficient in building complex 3D models of complicated aerospace components. However, the current trends demonstrate blind acceptance of the results of the finite element analysis results. This paper is aimed at raising an awareness of this situation. Examples of the common encounters are presented. To overcome the current trends, some guidelines and suggestions for analysts, senior engineers, and educators are offered.
Simulation of 3D tumor cell growth using nonlinear finite element method.
Dong, Shoubing; Yan, Yannan; Tang, Liqun; Meng, Junping; Jiang, Yi
2016-01-01
We propose a novel parallel computing framework for a nonlinear finite element method (FEM)-based cell model and apply it to simulate avascular tumor growth. We derive computation formulas to simplify the simulation and design the basic algorithms. With the increment of the proliferation generations of tumor cells, the FEM elements may become larger and more distorted. Then, we describe a remesh and refinement processing of the distorted or over large finite elements and the parallel implementation based on Message Passing Interface to improve the accuracy and efficiency of the simulation. We demonstrate the feasibility and effectiveness of the FEM model and the parallelization methods in simulations of early tumor growth. PMID:26213205
Finite element analysis of notch behavior using a state variable constitutive equation
NASA Technical Reports Server (NTRS)
Dame, L. T.; Stouffer, D. C.; Abuelfoutouh, N.
1985-01-01
The state variable constitutive equation of Bodner and Partom was used to calculate the load-strain response of Inconel 718 at 649 C in the root of a notch. The constitutive equation was used with the Bodner-Partom evolution equation and with a second evolution equation that was derived from a potential function of the stress and state variable. Data used in determining constants for the constitutive models was from one-dimensional smooth bar tests. The response was calculated for a plane stress condition at the root of the notch with a finite element code using constant strain triangular elements. Results from both evolution equations compared favorably with the observed experimental response. The accuracy and efficiency of the finite element calculations also compared favorably to existing methods.
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 of thumb carpometacarpal joint implants
Nielsen, C.
1995-11-01
The thumb carpometacarpal joint is frequently replaced in women who have developed severe osteoarthritis of the hand. A new, privately developed implant design consists of two components, trapezial and metacarpal, each with a saddle-shaped articulating surface. A three dimensional finite element model of this implant has been developed to analyze stresses on the device. The first simulations using the model involve loading the implant with forces normal to the trapezial component. Preliminary results show contact stress distributions at the particulating surfaces of the implant.
Finite Element Modeling of Transient Thermography Inspection of Composite Materials
NASA Technical Reports Server (NTRS)
Chu, Tsuchin Philip
1998-01-01
Several finite element models of defects such as debond and void have been developed for composite panels subjected to transient thermography inspection. Since the exact nature of the heat generated from the flash lamps is unknown, direct comparison between FEA and experimental results is not possible. However, some similarity of the results has been observed. The shape of the time curve that simulates the heat flux from the flash lamps has minimal effect on the temperature profiles. Double the number of flash lamps could increase the contrast of thermal image and define the shape of defect better.
Visualizing Higher Order Finite Elements: FY05 Yearly Report.
Thompson, David; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elementsinto regions appropriate for isosurfacing and proves the conditions under which thealgorithm will terminate. Finite elements are used to create piecewise polynomialapproximants to the solution of partial differential equations for which no analyticalsolution exists. These polynomials represent fields such as pressure, stress, and mo-mentim. In the past, these polynomials have been linear in each parametric coordinate.Each polynomial coefficient must be uniquely determined by a simulation, and thesecoefficients are called degrees of freedom. When there are not enough degrees of free-dom, 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 increas-ing the order of the polynomial approximation (instead of increasing the number offinite elements, each of which has its own set of coefficients) can allow some typesof simulations to produce a valid approximation with many fewer degrees of freedomthan increasing the number of finite elements alone. However, once the simulation hasdetermined the values of all the coefficients in a higher-order approximant, tools donot exist for visual inspection of the solution.This report focuses on a technique for the visual inspection of higher-order finiteelement simulation results based on decomposing each finite element into simplicialregions where existing visualization algorithms such as isosurfacing will work. Therequirements of the isosurfacing algorithm are enumerated and related to the placeswhere the partial derivatives of the polynomial become zero. The original isosurfacingalgorithm is then applied to each of these regions in turn.3 AcknowledgementThe authors would like to thank David Day and Louis Romero for their insight into poly-nomial system solvers and the LDRD Senior Council for the opportunity to pursue thisresearch. The authors were
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.
Seakeeping with the semi-Lagrangian particle finite element method
NASA Astrophysics Data System (ADS)
Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio
2016-07-01
The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.
Analysis of Waveguide Junction Discontinuities Using Finite Element Method
NASA Technical Reports Server (NTRS)
Deshpande, Manohar D.
1997-01-01
A Finite Element Method (FEM) is presented to determine reflection and transmission coefficients of rectangular waveguide junction discontinuities. An H-plane discontinuity, an E-plane ridge discontinuity, and a step discontinuity in a concentric rectangular waveguide junction are analyzed using the FEM procedure. Also, reflection and transmission coefficients due to presence of a gap between two sections of a rectangular waveguide are determined using the FEM. The numerical results obtained by the present method are in excellent agreement with the earlier published results. The numerical results obtained by the FEM are compared with the numerical results obtained using the Mode Matching Method (MMM) and also with the measured data.
Modelling the viscoelasticity of ceramic tiles by finite element
NASA Astrophysics Data System (ADS)
Pavlovic, Ana; Fragassa, Cristiano
2016-05-01
This research details a numerical method aiming at investigating the viscoelastic behaviour of a specific family of ceramic material, the Grès Porcelain, during an uncommon transformation, known as pyroplasticity, which occurs when a ceramic tile bends under a combination of thermal stress and own weight. In general, the theory of viscoelasticity can be considered extremely large and precise, but its application on real cases is particularly delicate. A time-depending problem, as viscoelasticity naturally is, has to be merged with a temperature-depending situation. This paper investigates how the viscoelastic response of bending ceramic materials can be modelled by commercial Finite Elements codes.
Finite-element simulation of myocardial electrical excitation
NASA Astrophysics Data System (ADS)
Vasserman, I. N.; Matveenko, V. P.; Shardakov, I. N.; Shestakov, A. P.
2014-01-01
Based on a single-domain model of myocardial conduction, isotropic and anisotropic finite element models of the myocardium are developed allowing excitation wave propagation to be studied. The Aliev-Panfilov phenomenological equations were used as the relations between the transmembrane current and the transmembrane potential. Interaction of an additional source of initial excitation with an excitation wave that passed and the spread of the excitation wave are studied using heart tomograms. A numerical solution is obtained using a splitting algorithm that allows the nonlinear boundary-value problem to be reduced to a sequence of simpler problems: ordinary differential equations and linear boundary-value problems in partial derivatives.
Finite element model of thermal processes in retinal photocoagulation
NASA Astrophysics Data System (ADS)
Sramek, Christopher; Paulus, Yannis M.; Nomoto, Hiroyuki; Huie, Phil; Palanker, Daniel
2009-02-01
Short duration (< 20 ms) pulses are desirable in patterned scanning laser photocoagulation to confine thermal damage to the photoreceptor layer, decrease overall treatment time and reduce pain. However, short exposures have a smaller therapeutic window (defined as the ratio of rupture threshold power to that of light coagulation). We have constructed a finite-element computational model of retinal photocoagulation to predict spatial damage and improve the therapeutic window. Model parameters were inferred from experimentally measured absorption characteristics of ocular tissues, as well as the thresholds of vaporization, coagulation, and retinal pigment epithelial (RPE) damage. Calculated lesion diameters showed good agreement with histological measurements over a wide range of pulse durations and powers.
Finite element modelling of a rotating piezoelectric ultrasonic motor.
Frangi, A; Corigliano, A; Binci, M; Faure, P
2005-10-01
The evaluation of the performance of ultrasonic motors as a function of input parameters such as the driving frequency, voltage input and pre-load on the rotor is of key importance to their development and is here addressed by means of a finite element three-dimensional model. First the stator is simulated as a fully deformable elastic body and the travelling wave dynamics is accurately reproduced; secondly the interaction through contact between the stator and the rotor is accounted for by assuming that the rotor behaves as a rigid surface. Numerical results for the whole motor are finally compared to available experimental data.
Finite element analysis of the stiffness of fabric reinforced composites
NASA Technical Reports Server (NTRS)
Foye, R. L.
1992-01-01
The objective of this work is the prediction of all three dimensional elastic moduli of textile fabric reinforced composites. The analysis is general enough for use with complex reinforcing geometries and capable of subsequent improvements. It places no restrictions on fabric microgeometry except that the unit cell be determinate and rectangular. The unit cell is divided into rectangular subcells in which the reinforcing geometries are easier to define and analyze. The analysis, based on inhomogeneous finite elements, is applied to a variety of weave, braid, and knit reinforced composites. Some of these predictions are correlated to test data.
Finite-element approach to Brownian dynamics of polymers.
Cyron, Christian J; Wall, Wolfgang A
2009-12-01
In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Such simulation tools have been applied to a large variety of problems and accelerated the scientific progress significantly. However, the currently most frequently used explicit bead models exhibit severe limitations, especially with respect to time step size, the necessity of artificial constraints and the lack of a sound mathematical foundation. Here we present a framework for simulations of Brownian polymer dynamics based on the finite-element method. This approach allows simulating a wide range of physical phenomena at a highly attractive computational cost on the basis of a far-developed mathematical background.
Finite Element Analysis of Brain Injury due to Head Impact
NASA Astrophysics Data System (ADS)
Suh, Chang Min; Kim, Sung Ho; Goldsmith, Werner
Traumatic Brain Injury (TBI) due to head impact by external impactor was analyzed using Finite Element Method (FEM). Two-dimensiona modeling was performed according to Magnetic Resonance Imaging (MRI) data of Mongolian subject. Pressure variation in a cranium due to external impact was analyzed in order to simulate Nahum et al.'s cadaver test.6 And, analyzed results were compared with Nahum et al.'s experimental data.6 As results, stress and strain behaviors of the brain during impact were accorded with experimental data qualitatively even though there were some differences in quantitative values. In addition, they were accorded with other references about brain injury as well.
Plane-wave fluorescence tomography with adaptive finite elements.
Joshi, Amit; Bangerth, Wolfgang; Hwang, Kildong; Rasmussen, John; Sevick-Muraca, Eva M
2006-01-15
We present three-dimensional fluorescence yield tomography of a tissue phantom in a noncontact reflectance imaging setup. The method employs planar illumination with modulated light and frequency domain fluorescence measurements made on the illumination plane. An adaptive finite-element algorithm is used to handle the ill-posed and computationally demanding inverse image reconstruction problem. Tomographic images of fluorescent targets buried at 1-2 cm depths from the illumination surface demonstrate the feasibility of fluorescence tomography from reflectance tomography in clinically relevant tissue volumes.
Finite element methods for non-Newtonian flows
Gartling, D.K.
1992-10-01
The application of the finite element method to problems in non-Newtonian fluid mechanics is described. The formulation of the basic equations is presented for both inelastic and viscoelastic constitutive models. Solution algorithms for treating the material nonlinearities associated with inelastic fluids are described; typical solution procedures for the implicit stress-rate equations of viscoelastic fluids are also presented. Methods for the simulation of various types of free-surface flows are also outlined. Simple example analyses are included for both types of fluid models.
Finite Element Modeling Techniques for Analysis of VIIP
NASA Technical Reports Server (NTRS)
Feola, Andrew J.; Raykin, J.; Gleason, R.; Mulugeta, Lealem; Myers, Jerry G.; Nelson, Emily S.; Samuels, Brian C.; Ethier, C. Ross
2015-01-01
Visual Impairment and Intracranial Pressure (VIIP) syndrome is a major health concern for long-duration space missions. Currently, it is thought that a cephalad fluid shift in microgravity causes elevated intracranial pressure (ICP) that is transmitted along the optic nerve sheath (ONS). We hypothesize that this in turn leads to alteration and remodeling of connective tissue in the posterior eye which impacts vision. Finite element (FE) analysis is a powerful tool for examining the effects of mechanical loads in complex geometries. Our goal is to build a FE analysis framework to understand the response of the lamina cribrosa and optic nerve head to elevations in ICP in VIIP.
Dual Formulations of Mixed Finite Element Methods with Applications.
Gillette, Andrew; Bajaj, Chandrajit
2011-10-01
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail.
SPAR data set contents. [finite element structural analysis system
NASA Technical Reports Server (NTRS)
Cunningham, S. W.
1981-01-01
The contents of the stored data sets of the SPAR (space processing applications rocket) finite element structural analysis system are documented. The data generated by each of the system's processors are stored in a data file organized as a library. Each data set, containing a two-dimensional table or matrix, is identified by a four-word name listed in a table of contents. The creating SPAR processor, number of rows and columns, and definitions of each of the data items are listed for each data set. An example SPAR problem using these data sets is also presented.
Finite Element Analysis of 2-D Elastic Contacts Involving FGMs
NASA Astrophysics Data System (ADS)
Abhilash, M. N.; Murthy, H.
2014-05-01
The response of elastic indenters in contact with Functionally Graded Material (FGM) coated homogeneous elastic half space has been presented in the current paper. Finite element analysis has been used due to its ability to handle complex geometry, material, and boundary conditions. Indenters of different typical surface profiles have been considered and the problem has been idealized as a two-dimensional (2D) plane strain problem considering only normal loads. Initially, indenters were considered to be rigid and the results were validated with the solutions presented in the literature. The analysis has then been extended to the case of elastic indenters on FGM-coated half spaces and the results are discussed.
Ateshian, Gerard A.; Maas, Steve; Weiss, Jeffrey A.
2010-01-01
Background This study formulates and implements a finite element contact algorithm for solid-fluid (biphasic) mixtures, accommodating both finite deformation and sliding. The finite element source code is made available to the general public. Methods The algorithm uses a penalty method regularized with an augmented Lagrangian method to enforce the continuity of contact traction and normal component of fluid flux across the contact interface. The formulation addresses the need to automatically enforce free-draining conditions outside of the contact interface. The formulation addresses the need to automatically enforce free-draining conditions outside of the contact interface. Results The accuracy of the implementation is verified using contact problems for which exact solutions are obtained by alternative analyses. Illustrations are also provided that demonstrate large deformations and sliding under configurations relevant to biomechanical applications such as articular contact. Conclusions This study addresses an important computational need in the biomechanics of porous-permeable soft tissues. Placing the source code in the public domain provides a useful resource to the biomechanics community. PMID:20887031
Driessen, B.J.; Dohner, J.L.
1998-08-01
In this paper a hybrid, finite element--boundary element method which can be used to solve for particle advection-diffusion in infinite domains with variable advective fields is presented. In previous work either boundary element, finite element, or difference methods have been used to solve for particle motion in advective-diffusive domains. These methods have a number of limitations. Due to the complexity of computing spatially dependent Green`s functions, the boundary element method is limited to domains containing only constant advective fields, and due to their inherent formulation, finite element and finite difference methods are limited to only domains of finite spatial extent. Thus, finite element and finite difference methods are limited to finite space problems for which the boundary element method is not, and the boundary element method is limited to constant advection field problems for which finite element and finite difference methods are not. In this paper it is proposed to split a domain into two sub-domains, and for each of these sub domains, apply the appropriate solution method; thereby, producing a method for the total infinite space, variable advective field domain.
Higher order finite element analysis of thick composite laminates
NASA Technical Reports Server (NTRS)
Goering, J.; Kim, H. J.
1992-01-01
A higher order, sub-parametric, laminated, 3D solid finite element was used for the analysis of very thick laminated composite plates. The geometry of this element is defined by four nodes in the X-Y plane which define a prism of material through the thickness of the laminate. There are twenty-four degrees of freedom at each node; translations at the upper and lower surfaces of the laminate in each of the three coordinate directions, and the derivatives of these translations with respect to each coordinate. This choice of degrees of freedom leads to displacement and strain compatibility at the corners. Stacking sequence effects are accounted for by explicitly integrating the strain energy density through the thickness of the element. The laminated solid element was combined with a gap-contact element to analyze thick laminated composite lugs loaded through flexible pins. The resulting model accounts for pin bending effects that produce non-uniform bearing stresses through the thickness of the lug. A thick composite lug experimental test program was performed, and provided data that was used to validate the analytical model. Two lug geometries and three stacking sequences were tested.
An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations
Key, S.W.; Heinstein, M.W.; Stone, C.M.
1997-12-31
Considerable effort has been expended in perfecting the algorithmic properties of 8-node hexahedral finite elements. Today the element is well understood and performs exceptionally well when used in modeling three-dimensional explicit transient dynamic events. However, the automatic generation of all-hexahedral meshes remains an elusive achievement. The alternative of automatic generation for all-tetrahedral finite element is a notoriously poor performer, and the 10-node quadratic tetrahedral finite element while a better performer numerically is computationally expensive. To use the all-tetrahedral mesh generation extant today, the authors have explored the creation of a quality 8-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four midface nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping and the element`s performance in applications are presented. In particular, they examine the 80node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element only samples constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the 8-node, mean-quadrature hexahedral finite element. Given automatic all-tetrahedral meshing, the 8-node, constant-strain tetrahedral finite element is a suitable replacement for the 8-node hexahedral finite element and handbuilt meshes.
Miles, Brad; Kolos, Elizabeth; Walter, William L; Appleyard, Richard; Shi, Angela; Li, Qing; Ruys, Andrew J
2015-06-01
Subject-specific finite element (FE) modeling methodology could predict peri-prosthetic femoral fracture (PFF) for cementless hip arthoplasty in the early postoperative period. This study develops methodology for subject-specific finite element modeling by using the element deactivation technique to simulate bone failure and validate with experimental testing, thereby predicting peri-prosthetic femoral fracture in the early postoperative period. Material assignments for biphasic and triphasic models were undertaken. Failure modeling with the element deactivation feature available in ABAQUS 6.9 was used to simulate a crack initiation and propagation in the bony tissue based upon a threshold of fracture strain. The crack mode for the biphasic models was very similar to the experimental testing crack mode, with a similar shape and path of the crack. The fracture load is sensitive to the friction coefficient at the implant-bony interface. The development of a novel technique to simulate bone failure by element deactivation of subject-specific finite element models could aid prediction of fracture load in addition to fracture risk characterization for PFF. PMID:25937546
Cwik, T.; Jamnejad, V.; Zuffada, C.
1994-12-31
The usefulness of finite element modeling follows from the ability to accurately simulate the geometry and three-dimensional fields on the scale of a fraction of a wavelength. To make this modeling practical for engineering design, it is necessary to integrate the stages of geometry modeling and mesh generation, numerical solution of the fields-a stage heavily dependent on the efficient use of a sparse matrix equation solver, and display of field information. The stages of geometry modeling, mesh generation, and field display are commonly completed using commercially available software packages. Algorithms for the numerical solution of the fields need to be written for the specific class of problems considered. Interior problems, i.e. simulating fields in waveguides and cavities, have been successfully solved using finite element methods. Exterior problems, i.e. simulating fields scattered or radiated from structures, are more difficult to model because of the need to numerically truncate the finite element mesh. To practically compute a solution to exterior problems, the domain must be truncated at some finite surface where the Sommerfeld radiation condition is enforced, either approximately or exactly. Approximate methods attempt to truncate the mesh using only local field information at each grid point, whereas exact methods are global, needing information from the entire mesh boundary. In this work, a method that couples three-dimensional finite element (FE) solutions interior to the bounding surface, with an efficient integral equation (IE) solution that exactly enforces the Sommerfeld radiation condition is developed. The bounding surface is taken to be a surface of revolution (SOR) to greatly reduce computational expense in the IE portion of the modeling.
Finite element dependence of stress evaluation for human trabecular bone.
Depalle, B; Chapurlat, R; Walter-Le-Berre, H; Bou-Saïd, B; Follet, H
2013-02-01
Numerical simulation using finite element models (FEM) has become more and more suitable to estimate the mechanical properties of trabecular bone. The size and kind of elements involved in the models, however, may influence the results. The purpose of this study is to analyze the influence of hexahedral elements formulation on the evaluation of mechanical stress applied to trabeculae bone during a compression test simulation. Trabecular bone cores were extracted from 18 L2 vertebrae (12 women and 6 men, mean age: 76 ± 11, BV/TV=7.5 ± 1.9%). Samples were micro-CT scanned at 20 μm isotropic voxel size. Micro-CT images have been sub-sampled (20, 40 and 80 μm) to create 5.6 mm cubic FEM. For each sample, a compression test FEM has been created, using either 8-nodes linear hexahedral elements with full or reduced integration or 20-nodes quadratic hexahedral elements fully integrated, resulting in nine models per samples. Bone mechanical properties have been assumed isotropic, homogenous and to follow a linear elastic behavior law (Young modulus: 8 GPa, Poisson ratio: 0.3). Despite micro-architecture modifications (loss of connectivity, trabeculae thickening) due to voxel size increase, apparent mechanical properties calculated with low resolution models are significantly correlated with high resolution results, no matter the element formulation. However, stress distributions are more sensitive to both resolution and element formulation modifications. With linear elements, increasing voxel size leads to an alteration of stress concentration areas due to stiffening errors. On the opposite, the use of reduced integration induces severe smoothing and underestimation of stress fields resulting in stress raisers loss. Notwithstanding their high computational cost, quadratic elements are most appropriate for stress prediction in low resolution trabecular bone FEM. These observations are dependent on trabecular bone micro-architecture, and are more significant for low
NASA Astrophysics Data System (ADS)
Stupkiewicz, Stanisław
2009-10-01
Soft elastohydrodynamic lubrication (EHL) problem is studied for a reciprocating elastomeric seal with full account of finite configuration changes. The fluid part is described by the Reynolds equation which is formulated on the deformed boundary of the seal treated as a hyperelastic body. The paper is concerned with the finite element (FE) treatment of this soft EHL problem. Displacement-based FE discretization is applied for the solid part. The Reynolds equation is discretized using the FE method or, alternatively, the discontinuous Galerkin method, both employing higher-order interpolation of pressure. The performance of both methods is assessed by studying convergence and stability of the solution for a benchmark problem of an O-ring seal. It is shown that the solution may exhibit spurious oscillations which occur in severe lubrication conditions. Mesh refinement results in reduction of these oscillations, while increasing the pressure interpolation order or application of the discontinuous Galerkin method does not help significantly.
Maximum windmill efficiency in finite time
NASA Astrophysics Data System (ADS)
Huleihil, Mahmoud
2009-05-01
The fraction of the kinetic energy of the wind impinging on the rotor-swept area that a wind turbine can convert to useful power has been shown by Betz in an idealized laminar-flow model to have an upper limit of 16/27 or 59% approximately [I. H. Shames, Mechanics of Fluids, 2nd ed. (McGraw-Hill, New York, 1982), pp. A26-A31]. This figure is known as Betz number. Other studies [A. Rauh and W. Seelret, Appl. Energy 17, 15 (1984)] suggested that this figure should be considered as a guideline. In this paper, a new model is introduced and its efficiency at maximum power output is derived. The derived value is shown to be a function of the Betz number B and given by the formula ηmp=1-√1-B . This value is 36.2%, which agrees well with those of actually operating wind turbines. As a guideline, the wind turbine efficiency can be considered to be within the range of the two numbers of merit, the Betz number and ηmp.
Multigrid waveform relaxation on spatial finite element meshes
Janssen, J.; Vandewalle, S.
1994-12-31
The authors shall discuss the numerical solution of a parabolic partial differential equation {partial_derivative}u/{partial_derivative}t(x,t) = Lu(x,t) + f(x,t), x{element_of}{Omega}, t>0, (1) supplied with a boundary condition and given initial values. The spatial finite element discretization of (1) on a discrete grid {Omega}{sub h} leads to an initial value problem of the form B{dot u} + Au = f, u(0) = u{sub o}, t > 0, (2) with B a non-singular matrix. The waveform relaxation method is a method for solving ordinary differential equations. It differs from most standard iterative techniques in that it is a continuous-time method, iterating with functions in time, and thereby well-suited for parallel computation.
3D unstructured mesh discontinuous finite element hydro
Prasad, M.K.; Kershaw, D.S.; Shaw, M.J.
1995-07-01
The authors present detailed features of the ICF3D hydrodynamics code used for inertial fusion simulations. This code is intended to be a state-of-the-art upgrade of the well-known fluid code, LASNEX. ICF3D employs discontinuous finite elements on a discrete unstructured mesh consisting of a variety of 3D polyhedra including tetrahedra, prisms, and hexahedra. The authors discussed details of how the ROE-averaged second-order convection was applied on the discrete elements, and how the C++ coding interface has helped to simplify implementing the many physics and numerics modules within the code package. The author emphasized the virtues of object-oriented design in large scale projects such as ICF3D.
Automation Tools for Finite Element Analysis of Adhesively Bonded Joints
NASA Technical Reports Server (NTRS)
Tahmasebi, Farhad; Brodeur, Stephen J. (Technical Monitor)
2002-01-01
This article presents two new automation creation tools that obtain stresses and strains (Shear and peel) in adhesively bonded joints. For a given adhesively bonded joint Finite Element model, in which the adhesive is characterised using springs, these automation tools read the corresponding input and output files, use the spring forces and deformations to obtain the adhesive stresses and strains, sort the stresses and strains in descending order, and generate plot files for 3D visualisation of the stress and strain fields. Grids (nodes) and elements can be numbered in any order that is convenient for the user. Using the automation tools, trade-off studies, which are needed for design of adhesively bonded joints, can be performed very quickly.
Dynamic Analysis of Geared Rotors by Finite Elements
NASA Technical Reports Server (NTRS)
Kahraman, A.; Ozguven, H. Nevzat; Houser, D. R.; Zakrajsek, J. J.
1992-01-01
A finite element model of a geared rotor system on flexible bearings has been developed. The model includes the rotary inertia of on shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis geared rotors by calculating the critical speeds and determining the response of any point on the shafts to mass unbalances, geometric eccentricities of gears, and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.
Probabilistic finite elements for fatigue and fracture analysis
NASA Technical Reports Server (NTRS)
Belytschko, Ted; Liu, Wing Kam
1993-01-01
An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.
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.
Finite element simulation of adaptive aerospace structures with SMA actuators
NASA Astrophysics Data System (ADS)
Frautschi, Jason; Seelecke, Stefan
2003-07-01
The particular demands of aerospace engineering have spawned many of the developments in the field of adaptive structures. Shape memory alloys are particularly attractive as actuators in these types of structures due to their large strains, high specific work output and potential for structural integration. However, the requisite extensive physical testing has slowed development of potential applications and highlighted the need for a simulation tool for feasibility studies. In this paper we present an implementation of an extended version of the M'ller-Achenbach SMA model into a commercial finite element code suitable for such studies. Interaction between the SMA model and the solution algorithm for the global FE equations is thoroughly investigated with respect to the effect of tolerances and time step size on convergence, computational cost and accuracy. Finally, a simulation of a SMA-actuated flexible trailing edge of an aircraft wing modeled with beam elements is presented.
Dynamic analysis of geared rotors by finite elements
NASA Technical Reports Server (NTRS)
Kahraman, Ahmet; Ozguven, H. Nevzat; Houser, Donald R.; Zakrajsek, James J.
1990-01-01
A finite-element model of a geared rotor system on flexible bearings was developed. The model includes the rotary inertia of shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis of geared rotors by calculating the critical speeds and determining the response of any point on the shaft to mass unbalances, geometric eccentricities of gears and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.
Mohamed, M. Shadi; Seaid, Mohammed; Trevelyan, Jon; Laghrouche, Omar
2013-10-15
We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach can be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.
NASA Astrophysics Data System (ADS)
Cimrman, Robert; Tůma, Miroslav; Novák, Matyáš; Čertík, Ondřej; Plešek, Jiří; Vackář, Jiří
2013-10-01
Ab-initio calculations of electronic states within the density-functional framework has been performed by means of the open source finite element package SfePy (Simple Finite Elements in Python, http://sfepy.org). We describe a new robust ab-initio real-space code based on (i) density functional theory, (ii) finite element method and (iii) environment-reflecting pseudopotentials. This approach brings a new quality to solving Kohn-Sham equations, calculating electronic states, total energy, Hellmann-Feynman forces and material properties particularly for non-crystalline, non-periodic structures. The main asset of the above approach is an efficient combination of excellent convergence control of standard, universal basis used in industrially proved finite-element method, high precision of ab-initio environment-reflecting pseudopotentials, and applicability not restricted to electrically neutral periodic environment. We present also numerical examples illustrating the outputs of the method.
A finite element method for solving the shallow water equations on the sphere
NASA Astrophysics Data System (ADS)
Comblen, Richard; Legrand, Sébastien; Deleersnijder, Eric; Legat, Vincent
Within the framework of ocean general circulation modeling, the present paper describes an efficient way to discretize partial differential equations on curved surfaces by means of the finite element method on triangular meshes. Our approach benefits from the inherent flexibility of the finite element method. The key idea consists in a dialog between a local coordinate system defined for each element in which integration takes place, and a nodal coordinate system in which all local contributions related to a vectorial degree of freedom are assembled. Since each element of the mesh and each degree of freedom are treated in the same way, the so-called pole singularity issue is fully circumvented. Applied to the shallow water equations expressed in primitive variables, this new approach has been validated against the standard test set defined by [Williamson, D.L., Drake, J.B., Hack, J.J., Jakob, R., Swarztrauber, P.N., 1992. A standard test set for numerical approximations to the shallow water equations in spherical geometry. Journal of Computational Physics 102, 211-224]. Optimal rates of convergence for the P1NC-P1 finite element pair are obtained, for both global and local quantities of interest. Finally, the approach can be extended to three-dimensional thin-layer flows in a straightforward manner.
NASA Technical Reports Server (NTRS)
Gherlone, Marco; Cerracchio, Priscilla; Mattone, Massimiliano; Di Sciuva, Marco; Tessler, Alexander
2011-01-01
A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.
Bouayed, Kaïss; Hamdi, Mohamed-Ali
2012-08-01
This paper presents numerical and experimental validation of results obtained by a shell finite element, which has been developed for modeling of the dynamic behavior of sandwich multilayered structures with a viscoelastic core. The proposed shell finite element is very easy to implement in existing finite element solvers, since it uses only the displacements as degrees of freedom at external faces and at inter-layer interfaces. The displacement field is linearly interpolated in the thickness direction of each layer, and analytical integration is made in the thickness direction in order to avoid meshing of each sandwich layer by solid elements. Only the two dimensional mid-surface of reference is meshed, facilitating the mesh generation task. A simplified modal approach using a real modal basis is also proposed to efficiently calculate the dynamic response of the sandwich structure. The proposed method reduces the memory size and computing time and takes into account the frequency-dependence of the polymer core mechanical properties. Results obtained by the proposed element in conjunction with the simplified modal method have been numerically and experimentally validated by comparison to results obtained by commercial software codes (MSC/NASTRAN and ESI/RAYON-VTM), and to measurements done on automobile windscreens. PMID:22894198
NASA Astrophysics Data System (ADS)
Song, Huimin
In the aerospace and automotive industries, many finite element analyses use lower-dimensional finite elements such as beams, plates and shells, to simplify the modeling. These simplified models can greatly reduce the computation time and cost; however, reduced-dimensional models may introduce inaccuracies, particularly near boundaries and near portions of the structure where reduced-dimensional models may not apply. Another factor in creation of such models is that beam-like structures frequently have complex geometry, boundaries and loading conditions, which may make them unsuitable for modeling with single type of element. The goal of this dissertation is to develop a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. The first chapter of the thesis gives the background of the present work and some related previous work. The second chapter is focused on formulating a system of equations that govern the joining of a 2D model with a beam model for planar deformation. The essential aspect of this formulation is to find the transformation matrices to achieve deflection and load continuity on the interface. Three approaches are provided to obtain the transformation matrices. An example based on joining a beam to a 2D finite element model is examined, and the accuracy of the analysis is studied by comparing joint results with the full 2D analysis. The third chapter is focused on formulating the system of equations for joining a beam to a 3D finite element model for static and free-vibration problems. The transition between the 3D elements and beam elements is achieved by use of the stress recovery technique of the variational-asymptotic method as implemented in VABS (the Variational Asymptotic Beam Section analysis). The formulations for an interface transformation matrix and
Distributed Finite Element Analysis Using a Transputer Network
NASA Technical Reports Server (NTRS)
Watson, James; Favenesi, James; Danial, Albert; Tombrello, Joseph; Yang, Dabby; Reynolds, Brian; Turrentine, Ronald; Shephard, Mark; Baehmann, Peggy
1989-01-01
The principal objective of this research effort was to demonstrate the extraordinarily cost effective acceleration of finite element structural analysis problems using a transputer-based parallel processing network. This objective was accomplished in the form of a commercially viable parallel processing workstation. The workstation is a desktop size, low-maintenance computing unit capable of supercomputer performance yet costs two orders of magnitude less. To achieve the principal research objective, a transputer based structural analysis workstation termed XPFEM was implemented with linear static structural analysis capabilities resembling commercially available NASTRAN. Finite element model files, generated using the on-line preprocessing module or external preprocessing packages, are downloaded to a network of 32 transputers for accelerated solution. The system currently executes at about one third Cray X-MP24 speed but additional acceleration appears likely. For the NASA selected demonstration problem of a Space Shuttle main engine turbine blade model with about 1500 nodes and 4500 independent degrees of freedom, the Cray X-MP24 required 23.9 seconds to obtain a solution while the transputer network, operated from an IBM PC-AT compatible host computer, required 71.7 seconds. Consequently, the $80,000 transputer network demonstrated a cost-performance ratio about 60 times better than the $15,000,000 Cray X-MP24 system.
Finite element visualization in the cave virtual reality environment
Plaskacz, E.J.; Kuhn, M.A.
1996-03-01
Through the use of the post-processing software, Virtual Reality visualization (VRviz), and the Cave Automatic Virtual Environment (CAVE), finite element representations can be viewed as they would be in real life. VRviz is a program written in ANSI C to translate the mathematical results generated by finite element analysis programs into a virtual representation. This virtual representation is projected into the CAVE environment and the results are animated. The animation is fully controllable. A user is able to translate the image, rotate about any axis and scale the image at any time. The user is also able to freeze the animation at any time step and control the image update rate. This allows the user to navigate around, or even inside, the image in order to effectively analyze possible failure points and redesign as necessary. Through the use of the CAVE and the real life image that is being produced by VRviz, engineers are able to save considerable time, money, and effort in the design process.
Finite Element Reconstruction of a Mandibular First Molar
Ehsani, Sara; Mirhashemi, Fatemeh Sadat; Asgary, Saeed
2013-01-01
Introduction Mandibular first molar is the most important tooth with complicated morphology. In finite element (FE) studies, investigators usually prefer to model anterior teeth with a simple and single straight root; it makes the results deviate from the actual case. The most complicated and time-consuming step in FE studies is modeling of the desired tooth, thus this study was performed to establish a finite element method (FEM) of reconstructing a mandibular first molar with the greatest precision. Materials and Methods An extracted mandibular first molar was digitized, and then radiographed from different aspects to achieve its outer and inner morphology. The solid model of tooth and root canals were constructed according to this data as well as the anatomy of mandibular first molar described in the literature. Result A three-dimensional model of mandibular first molar was created, giving special consideration to shape and root canal system dimensions. Conclusion This model may constitute a basis for investigating the effect of different clinical situations on mandibular first molars in vitro, especially on its root canal system. The method described here seems feasible and reasonably precise foundation for investigations. PMID:23717327
Immersed finite element method and its applications to biological systems
Liu, Wing Kam; Liu, Yaling; Farrell, David; Zhang, Lucy; Wang, X. Sheldon; Fukui, Yoshio; Patankar, Neelesh; Zhang, Yongjie; Bajaj, Chandrajit; Lee, Junghoon; Hong, Juhee; Chen, Xinyu; Hsu, Huayi
2009-01-01
This paper summarizes the newly developed immersed finite element method (IFEM) and its applications to the modeling of biological systems. This work was inspired by the pioneering work of Professor T.J.R. Hughes in solving fluid–structure interaction problems. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans the entire computational domain. Hence, mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element method and the continuity between the fluid and solid subdomains is enforced via the interpolation of the velocities and the distribution of the forces with the reproducing Kernel particle method (RKPM) delta function. The proposed method is used to study the fluid–structure interaction problems encountered in human cardiovascular systems. Currently, the heart modeling is being constructed and the deployment process of an angioplasty stent has been simulated. Some preliminary results on monocyte and platelet deposition are presented. Blood rheology, in particular, the shear-rate dependent de-aggregation of red blood cell (RBC) clusters and the transport of deformable cells, are modeled. Furthermore, IFEM is combined with electrokinetics to study the mechanisms of nano/bio filament assembly for the understanding of cell motility. PMID:20200602
Finite element modeling of electrically rectified piezoelectric energy harvesters
NASA Astrophysics Data System (ADS)
Wu, P. H.; Shu, Y. C.
2015-09-01
Finite element models are developed for designing electrically rectified piezoelectric energy harvesters. They account for the consideration of common interface circuits such as the standard and parallel-/series-SSHI (synchronized switch harvesting on inductor) circuits, as well as complicated structural configurations such as arrays of piezoelectric oscillators. The idea is to replace the energy harvesting circuit by the proposed equivalent load impedance together with the capacitance of negative value. As a result, the proposed framework is capable of being implemented into conventional finite element solvers for direct system-level design without resorting to circuit simulators. The validation based on COMSOL simulations carried out for various interface circuits by the comparison with the standard modal analysis model. The framework is then applied to the investigation on how harvested power is reduced due to fabrication deviations in geometric and material properties of oscillators in an array system. Remarkably, it is found that for a standard array system with strong electromechanical coupling, the drop in peak power turns out to be insignificant if the optimal load is carefully chosen. The second application is to design broadband energy harvesting by developing array systems with suitable interface circuits. The result shows that significant broadband is observed for the parallel (series) connection of oscillators endowed with the parallel-SSHI (series-SSHI) circuit technique.
Adaptive Finite Element Methods for Continuum Damage Modeling
NASA Technical Reports Server (NTRS)
Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.
1995-01-01
The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.
Validation of a finite element model of the human metacarpal.
Barker, D S; Netherway, D J; Krishnan, J; Hearn, T C
2005-03-01
Implant loosening and mechanical failure of components are frequently reported following metacarpophalangeal (MCP) joint replacement. Studies of the mechanical environment of the MCP implant-bone construct are rare. The objective of this study was to evaluate the predictive ability of a finite element model of the intact second human metacarpal to provide a validated baseline for further mechanical studies. A right index human metacarpal was subjected to torsion and combined axial/bending loading using strain gauge (SG) and 3D finite element (FE) analysis. Four different representations of bone material properties were considered. Regression analyses were performed comparing maximum and minimum principal surface strains taken from the SG and FE models. Regression slopes close to unity and high correlation coefficients were found when the diaphyseal cortical shell was modelled as anisotropic and cancellous bone properties were derived from quantitative computed tomography. The inclusion of anisotropy for cortical bone was strongly influential in producing high model validity whereas variation in methods of assigning stiffness to cancellous bone had only a minor influence. The validated FE model provides a tool for future investigations of current and novel MCP joint prostheses.