Efficient finite element modeling of elastodynamic scattering
NASA Astrophysics Data System (ADS)
Wilcox, Paul D.; Velichko, Alexander
2009-03-01
The scattering of elastic waves by defects is the physical basis of ultrasonic NDE. Although analytical models exist for some canonical problems, the general case of scattering from an arbitrarily-shaped defect requires numerical methods such as finite elements (FE). In this paper, a robust and efficient FE technique is presented that is based on the premise of meshing a relatively small domain sufficient to enclose the scatterer. Plane waves are then excited from a particular direction by a numerical implementation of the Helmholtz-Kirchhoff integral that uses an encircling array of uni-modal point sources. The scattered field displacements are recorded at the same points and the field decomposed into plane waves of different modes at different angles. By repeating this procedure for different incident angles it is possible to generate the scattering- or S-matrix for the scatterer. For a given size of scatterer, all the information in an S-matrix can be represented in the Fourier domain by a limited number of complex coefficients. Thus the complete scattering behavior of an arbitrary-shaped scatterer can be characterized by a finite number of complex coefficients, that can be obtained from a relatively small number of FE model executions.
Efficient Finite Element Modelling of Elastodynamic Scattering
NASA Astrophysics Data System (ADS)
Velichko, A.; Wilcox, P. D.
2010-02-01
A robust and efficient technique for predicting the complete scattering behavior for an arbitrarily-shaped defect is presented that can be implemented in a commercial FE package. The spatial size of the modeling domain around the defect is as small as possible to minimize computational expense and a minimum number of models are executed. Example results for 2D and 3D scattering in isotropic material and guided wave scattering are presented.
Efficient finite element method for grating profile reconstruction
NASA Astrophysics Data System (ADS)
Zhang, Ruming; Sun, Jiguang
2015-12-01
This paper concerns the reconstruction of grating profiles from scattering data. The inverse problem is formulated as an optimization problem with a regularization term. We devise an efficient finite element method (FEM) and employ a quasi-Newton method to solve it. For the direct problems, the FEM stiff and mass matrices are assembled once at the beginning of the numerical procedure. Then only minor changes are made to the mass matrix at each iteration, which significantly saves the computation cost. Numerical examples show that the method is effective and robust.
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 parallel algorithms for elastic plastic finite element analysis
NASA Astrophysics Data System (ADS)
Ding, K. Z.; Qin, Q.-H.; Cardew-Hall, M.; Kalyanasundaram, S.
2008-03-01
This paper presents our new development of parallel finite element algorithms for elastic plastic problems. The proposed method is based on dividing the original structure under consideration into a number of substructures which are treated as isolated finite element models via the interface conditions. Throughout the analysis, each processor stores only the information relevant to its substructure and generates the local stiffness matrix. A parallel substructure oriented preconditioned conjugate gradient method, which is combined with MR smoothing and diagonal storage scheme are employed to solve linear systems of equations. After having obtained the displacements of the problem under consideration, a substepping scheme is used to integrate elastic plastic stress strain relations. The procedure outlined controls the error of the computed stress by choosing each substep size automatically according to a prescribed tolerance. The combination of these algorithms shows a good speedup when increasing the number of processors and the effective solution of 3D elastic plastic problems whose size is much too large for a single workstation becomes possible.
Comparative efficiency of finite, boundary and hybrid element methods in elastostatics
NASA Technical Reports Server (NTRS)
Schwartz, C. W.; Lee, C. W.
1986-01-01
The comparative computational efficiencies of the finite element (FEM), boundary element (BEM), and hybrid boundary element-finite element (HBFEM) 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.
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.
Efficient Finite Element Methods for Transient Analysis of Shells.
1985-04-01
classified as (1) implicit projection methods, such as reduced integration, and (2) explicit projection methods, such as -’. mixed methods and mode...PROJECTION METHODS In this Section a simple form of the element stiffness matrix for mixed methods will be developed and then compared to the explicit...decomposition V.’... projection methods and mixed methods appears straightforward, establishing the exact equivalence is not possible in some elements
An efficient finite-element algorithm for 3D layered complex structure modelling.
Sahalos, J N; Kyriacou, G A; Vafiadis, E
1994-05-01
In this paper an efficient finite-element method (FEM) algorithm for complicated three-dimensional (3D) layered type models has been developed. Its unique feature is that it can handle, with memory requirements within the abilities of a simple PC, arbitrarily shaped 3D elements. This task is achieved by storing only the non-zero coefficients of the sparse FEM system of equations. The algorithm is applied to the solution of the Laplace equation in models with up to 79 layers of trilinear general hexahedron elements. The system of equations is solved with the Gauss-Seidel iterative technique.
NASA Astrophysics Data System (ADS)
Alimonti, L.; Atalla, N.
2017-02-01
This work is concerned with the hybrid finite element-transfer matrix methodology recently proposed by the authors. The main assumption behind this hybrid method consists in neglecting the actual finite lateral extent of the acoustic treatment. Although a substantial increase of the computational efficiency can be achieved, the effect of the reflected field (i.e. finite size effects) may be sometimes important, preventing the hybrid model from giving quantitative meaningful results. For this reason, a correction to account for wave reflections at the lateral boundaries of the acoustic treatment is sought. It is shown in the present paper that the image source method can be successfully employed to retrieve such finite size effects. Indeed, such methodology is known to be effective when the response of the system is a smooth function of the frequency, like in the case of highly dissipative acoustic treatments. The main concern of this paper is to assess accuracy and feasibility of the image source method in the context of acoustic treatments modeling. Numerical examples show that the performance of the standard hybrid model can be substantially improved by the proposed correction without deteriorating excessively the computational efficiency.
Efficient simulation of cardiac electrical propagation using high order finite elements.
Arthurs, Christopher J; Bishop, Martin J; Kay, David
2012-05-20
We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.
Efficient simulation of cardiac electrical propagation using high order finite elements
Arthurs, Christopher J.; Bishop, Martin J.; Kay, David
2012-01-01
We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation. PMID:24976644
NASA Astrophysics Data System (ADS)
Felice, Maria V.; Velichko, Alexander; Wilcox, Paul D.; Barden, Tim J.; Dunhill, Tony K.
2014-02-01
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.
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.
NASA Astrophysics Data System (ADS)
Chen, Jiefu
2015-03-01
A discontinuous Galerkin finite element method is employed to study the responses of microresistivity imaging tools used in the oil and gas exploration industry. The multiscale structure of an imaging problem is decomposed into several nested subdomains based on its geometric characteristics. Each subdomain is discretized independently, and numerical flux is used to couple all subdomains together. The nested domain decomposition scheme will lead to a block tridiagonal linear system, and the block Thomas algorithm is utilized here to eliminate the subdomain based iteration in the step of solving the linear system. Numerical results demonstrate the validity and efficiency of this method.
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.
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.
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
Efficient inversion of three-dimensional finite element models of volcano deformation
NASA Astrophysics Data System (ADS)
Charco, M.; Galán del Sastre, P.
2014-03-01
Numerical techniques, as such as finite element method, allow for the inclusion of features, such as topography and/or mechanical heterogeneities, for the interpretation of volcanic deformation. However, models based on these numerical techniques usually are not suitable to be included in non-linear estimations of source parameters based on explorative optimization schemes because they require a calculation of the numerical approach for every evaluation of the misfit function. We present a procedure for finite element (FE) models that can be combined with explorative inversion schemes. The methodology is based on including a body force term representing an infinitesimal source in the model formulation that is responsible for pressure (volume) changes in the medium. This provides significant savings in both the time required for mesh generation and actual computational time of the numerical approach. Furthermore, we develop an inversion algorithm to estimate those parameters that characterize the changes in location and pressure (volume) of deformation sources. Both provide FE inversions in a single step, avoiding remeshing and assembly of the linear system of algebraic equations that define the numerical approach and/or the automatic mesh generation. After providing the theoretical basis for the model, the numerical approach and the algorithm for the inversions, we test the methodology using a synthetic example in a stratovolcano. Our results suggest that the FE inversion methodology can be considered suitable for efficiently save time in quantitative interpretations of volcano deformation.
Shim, Vickie B; Battley, Mark; Anderson, Iain A; Munro, Jacob T
2015-01-01
Bone in the pelvis is a composite material with a complex anatomical structure that is difficult to model computationally. Rather than assigning material properties to increasingly smaller elements to capture detail in three-dimensional finite element (FE) models, properties can be assigned to Gauss points within larger elements. As part of a validation process, we compared experimental and analytical results from a composite beam under four-point load to FE models with material properties assigned to refined elements and Gauss points within larger elements. Both FE models accurately predicted deformation and the analytical predictions of internal shear stress.
Efficient finite element modeling of scattering for 2D and 3D problems
NASA Astrophysics Data System (ADS)
Wilcox, Paul D.; Velichko, Alexander
2010-03-01
The scattering of waves by defects is central to ultrasonic NDE and SHM. In general, scattering problems must be modeled using direct numerical methods such as finite elements (FE), which is very computationally demanding. The most efficient way is to only model the scatterer itself and a minimal region of the surrounding host medium, and this was previously demonstrated for 2-dimensional (2D) bulk wave scattering problems in isotropic media. An encircling array of monopole and dipole sources is used to inject an arbitrary wavefront onto the scatterer and the scattered field is monitored by a second encircling array of monitoring points. From this data, the scattered field can be projected out to any point in space. If the incident wave is chosen to be a plane wave incident from a given angle and the scattered field is projected to distant points in the far-field of the scatterer, the far-field scattering or S-matrix may be obtained, which encodes all the available scattering information. In this paper, the technique is generalized to any elastic wave geometry in both 2D and 3D, where the latter can include guided wave scattering problems. A further refinement enables the technique to be employed with free FE meshes of triangular or tetrahedral elements.
An efficient finite element approach for modeling fibrotic clefts in the heart.
Costa, Caroline Mendonca; Campos, Fernando O; Prassl, Anton J; dos Santos, Rodrigo Weber; Sánchez-Quintana, Damián; Ahammer, Helmut; Hofer, Ernst; Plank, Gernot
2014-03-01
Advanced medical imaging technologies provide a wealth of information on cardiac anatomy and structure at a paracellular resolution, allowing to identify microstructural discontinuities which disrupt the intracellular matrix. Current state-of-the-art computer models built upon such datasets account for increasingly finer anatomical details, however, structural discontinuities at the paracellular level are typically discarded in the model generation process, owing to the significant costs which incur when using high resolutions for explicit representation. In this study, a novel discontinuous finite element (dFE) approach for discretizing the bidomain equations is presented, which accounts for fine-scale structures in a computer model without the need to increase spatial resolution. In the dFE method, this is achieved by imposing infinitely thin lines of electrical insulation along edges of finite elements which approximate the geometry of discontinuities in the intracellular matrix. Simulation results demonstrate that the dFE approach accounts for effects induced by microscopic size scale discontinuities, such as the formation of microscopic virtual electrodes, with vast computational savings as compared to high resolution continuous finite element models. Moreover, the method can be implemented in any standard continuous finite element code with minor effort.
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
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.
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.
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)
González-Estrada, Octavio A.; Natarajan, Sundararajan; Ródenas, Juan José; Nguyen-Xuan, Hung; Bordas, Stéphane P. A.
2013-07-01
An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a "smooth + singular" decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.
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.
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.
NASA Astrophysics Data System (ADS)
Cunningham, Ian A.; Westmore, Michael S.; Fenster, Aaron
1995-05-01
Image blur in digital imaging systems results from both the spatial spreading of quanta representing the image in the detector system and from the integration of quanta over the finite detector element width. Linear-systems theory has often been used to describe these blurring mechanisms as a convolution, implying the existence of a corresponding modulation transfer function (MTF) in the spatial-frequency domain. This also implies that the resulting noise- power spectrum (NPS) is modified by the square of the blurring MTF. This deterministic approach correctly describes the effect of each blurring mechanism on the overall system MTF, but does not correctly describe image noise characteristics. This is because the convolution is a deterministic calculation, and neglects the statistical properties of the image quanta. Rabbani et al. developed an expression for the NPS following a stochastic spreading mechanism that correctly accounts for these statistical properties. Use of their results requires a modification in how we should interpret the convolution theorem. We suggest the use of a `stochastic' convolution operator, that uses the Rabbani equation for the NPS rather than the deterministic result. This approach unifies the description of both image blur and image noise into a single linear-systems framework. This method is then used to develop expressions for the signal, NPS, DQE, and pixel SNR for a hypothetical digital detector design that includes the effects of conversion to secondary quanta, stochastic spreading of the secondary quanta, and a finite detector-element width.
NASA Technical Reports Server (NTRS)
Cwik, T.; Jamnejad, V.; Zuffada, C.
1993-01-01
It is often desirable to calculate the electromagnetic fields inside and about a complicated system of scattering bodies, as well as in their far-field region. The finite element method (FE) is well suited to solving the interior problem, but the domain has to be limited to a manageable size. At the truncation of the FE mesh one can either impose approximate (absorbing) boundary conditions or set up an integral equation (IE) for the fields scattered from the bodies. The latter approach is preferable since it results in higher accuracy. Hence, the two techniques can be successfully combined by introducing a surface that encloses the scatterers, applying a FE model to the inner volume and setting up an IE for the tangential fields components on the surface. Here the continuity of the tangential fields is used bo obtain a consistent solution. A few coupled FE-IE methods have recently appeared in the literature. The approach presented here has the advantage of using edge-based finite elements, a type of finite elements with degrees of freedom associated with edges of the mesh. Because of their properties, they are better suited than the conventional node based elements to represent electromagnetic fields, particularly when inhomogeneous regions are modeled, since the node based elements impose an unnatural continuity of all field components across boundaries of mesh elements. Additionally, our approach is well suited to handle large size problems and lends itself to code parallelization. We will discuss the salient features that make our approach very efficient from the standpoint of numerical computation, and the fields and RCS of a few objects are illustrated as examples.
NASA Astrophysics Data System (ADS)
Xie, Yifan; Wu, Jichun; Nan, Tongchao; Xue, Yuqun; Xie, Chunhong; Ji, Haifeng
2017-03-01
In this paper, an efficient triple-grid multiscale finite element method (ETMSFEM) is proposed for 3D groundwater simulation in heterogeneous porous media. The main idea of this method is to employ new 3D linear base functions and the domain decomposition technique to solve the local reduced elliptical problem, thereby simplifying the base function construction process and improving the efficiency. Furthermore, by using the ETMSFEM base functions, this method can solve Darcy's equation with high efficiency to obtain a continuous velocity field. Therefore, this method can considerably reduce the computational cost of solving for heads and velocities, which is crucial for large-scale 3D groundwater simulations. In the application section, we present numerical examples to compare the ETMSFEM with several classical methods to demonstrate its efficiency and effectiveness.
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.
NASA Astrophysics Data System (ADS)
Zhang, Huiming; Zhang, Min; Yuan, Weijia
2017-02-01
An efficient three dimensional (3D) finite element method numerical model is proposed for superconducting coated conductors. The model is based on the T-A formulation and can be used to tackle 3D computational challenges for superconductors with high aspect ratios. By assuming a sheet approximation for the conductors, the model can speed up the computational process. The model has been validated by established analytical solutions. Two examples with complex geometries, which can hardly be simulated by the 2D model, are given. The model could be used to characterise and design large-scale applications using superconducting coated conductors, such as high field magnets and other electrical devices.
Chang, Yia-Chung; Li, Guangwei; Chu, Hanyou; Opsal, Jon
2006-03-01
We present an efficient method for calculating the reflectivity of three-dimensional gratings on multilayer films based on a finite-element, Green's function approach. Our method scales as NlogN, where N is the number of plane waves used in the expansion. Therefore, it is much more efficient than the commonly adopted rigorous-coupled-wave analysis (RCWA), which scales as N3. We demonstrate the effectiveness of this method by applying it to a two-dimensional periodic array of contact holes on a multilayer film. We find that our Green's function approach is about one order of magnitude faster than the RCWA approach when applied to typical contact holes considered in industry. For most cases, this method is efficient enough for application as a realtime, critical-dimension metrology tool.
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.
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.
Liu, Haofei; Sun, Wei
2016-01-01
In this study, we evaluated computational efficiency of finite element (FE) simulations when a numerical approximation method was used to obtain the tangent moduli. A fiber-reinforced hyperelastic material model for nearly incompressible soft tissues was implemented for 3D solid elements using both the approximation method and the closed-form analytical method, and validated by comparing the components of the tangent modulus tensor (also referred to as the material Jacobian) between the two methods. The computational efficiency of the approximation method was evaluated with different perturbation parameters and approximation schemes, and quantified by the number of iteration steps and CPU time required to complete these simulations. From the simulation results, it can be seen that the overall accuracy of the approximation method is improved by adopting the central difference approximation scheme compared to the forward Euler approximation scheme. For small-scale simulations with about 10,000 DOFs, the approximation schemes could reduce the CPU time substantially compared to the closed-form solution, due to the fact that fewer calculation steps are needed at each integration point. However, for a large-scale simulation with about 300,000 DOFs, the advantages of the approximation schemes diminish because the factorization of the stiffness matrix will dominate the solution time. Overall, as it is material model independent, the approximation method simplifies the FE implementation of a complex constitutive model with comparable accuracy and computational efficiency to the closed-form solution, which makes it attractive in FE simulations with complex material models.
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.
Analysis of the Efficiency of an A-Posteriori Error Estimator for Linear Triangular Finite Elements
1991-06-01
2 partially/NSF CCR-88-20279 s. PERFORMING ORGANIZATION NAME AND ADDRESS I*. PROGRAM ELEMENT. PROJECT. TASKAREA & wORK UNIT NUMUERS Institute for...34’ Institute for Physical Science and Technology and Department of Mathematics, University of Mary- land, College Park, MD. 20742. The work of this...and Departamnento de Maternitica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 172, 1900 - La Plata, Argentina. (3) Institute
NASA Astrophysics Data System (ADS)
Velichko, A.; Wilcox, P. D.
2011-06-01
A robust and efficient technique for predicting the complete scattering behavior for an arbitrarily-shaped defect which is located near a free surface in an otherwise homogeneous anisotropic half-space is presented that can be implemented in a commercial FE package. The spatial size of the modeling domain around the defect is as small as possible to minimize computational expense and a minimum number of models are executed. Example results for 2D wave scattering in isotropic material are presented.
NASA Astrophysics Data System (ADS)
Velichko, A.; Wilcox, P. D.
2012-05-01
An efficient technique for predicting the complete scattering behavior for an arbitrarily-shaped scatterer is presented. The spatial size of the modeling domain around the scatterer is as small as possible to minimize computational expense and a minimum number of models are executed. This model uses non-reflecting boundary conditions on the surface surrounding the scatterer which are non-local in space. Example results for 2D and 3D scattering in isotropic material and guided wave scattering are presented.
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.
Finite element computational fluid mechanics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
Finite elements of nonlinear continua.
NASA Technical Reports Server (NTRS)
Oden, J. T.
1972-01-01
The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.
NASA Technical Reports Server (NTRS)
Tag, I. A.; Lumsdaine, E.
1978-01-01
The general non-linear three-dimensional equation for acoustic potential is derived by using a perturbation technique. The linearized axisymmetric equation is then solved by using a finite element algorithm based on the Galerkin formulation for a harmonic time dependence. The solution is carried out in complex number notation for the acoustic velocity potential. Linear, isoparametric, quadrilateral elements with non-uniform distribution across the duct section are implemented. The resultant global matrix is stored in banded form and solved by using a modified Gauss elimination technique. Sound pressure levels and acoustic velocities are calculated from post element solutions. Different duct geometries are analyzed and compared with experimental results.
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.
Finite elements: Theory and application
NASA Technical Reports Server (NTRS)
Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)
1988-01-01
Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.
Stabilized Finite Elements in FUN3D
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle; Newman, James C.; Karman, Steve L.
2017-01-01
A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.
On numerically accurate finite element
NASA Technical Reports Server (NTRS)
Nagtegaal, J. C.; Parks, D. M.; Rice, J. R.
1974-01-01
A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional element types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing finite element program, is presented. This allows accurate computations to be made even for element designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various element designs and of the new variational procedure are illustrated. Elastic-plastic computation at finite strain are discussed.
Finite element modeling and analysis of tires
NASA Technical Reports Server (NTRS)
Noor, A. K.; Andersen, C. M.
1983-01-01
Predicting the response of tires under various loading conditions using finite element technology is addressed. Some of the recent advances in finite element technology which have high potential for application to tire modeling problems are reviewed. The analysis and modeling needs for tires are identified. Reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment of combined loads, displacement-dependent and nonconservative loadings; development of simple and efficient mixed finite element models for shell analysis, identification of equivalent mixed and purely displacement models, and determination of the advantages of using mixed models; and effective computational models for large-rotation nonlinear problems, based on a total Lagrangian description of the deformation are included.
The Relation of Finite Element and Finite Difference Methods
NASA Technical Reports Server (NTRS)
Vinokur, M.
1976-01-01
Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.
Improved finite element methodology for integrated thermal structural analysis
NASA Technical Reports Server (NTRS)
Dechaumphai, P.; Thornton, E. A.
1982-01-01
An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. New thermal finite elements which yield exact nodal and element temperatures for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.
Improved finite element methodology for integrated thermal structural analysis
NASA Technical Reports Server (NTRS)
Dechaumphai, P.; Thornton, E. A.
1982-01-01
An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analyses is presented. New thermal finite elements which yield exact nodal and element temperature for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal-structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.
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.
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
ANSYS duplicate finite-element checker routine
NASA Technical Reports Server (NTRS)
Ortega, R.
1995-01-01
An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.
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.
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)
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.
O'Rourke, Dermot; Martelli, Saulo; Bottema, Murk; Taylor, Mark
2016-12-01
Assessing the sensitivity of a finite-element (FE) model to uncertainties in geometric parameters and material properties is a fundamental step in understanding the reliability of model predictions. However, the computational cost of individual simulations and the large number of required models limits comprehensive quantification of model sensitivity. To quickly assess the sensitivity of an FE model, we built linear and Kriging surrogate models of an FE model of the intact hemipelvis. The percentage of the total sum of squares (%TSS) was used to determine the most influential input parameters and their possible interactions on the median, 95th percentile and maximum equivalent strains. We assessed the surrogate models by comparing their predictions to those of a full factorial design of FE simulations. The Kriging surrogate model accurately predicted all output metrics based on a training set of 30 analyses (R2 = 0.99). There was good agreement between the Kriging surrogate model and the full factorial design in determining the most influential input parameters and interactions. For the median, 95th percentile and maximum equivalent strain, the bone geometry (60%, 52%, and 76%, respectively) was the most influential input parameter. The interactions between bone geometry and cancellous bone modulus (13%) and bone geometry and cortical bone thickness (7%) were also influential terms on the output metrics. This study demonstrates a method with a low time and computational cost to quantify the sensitivity of an FE model. It can be applied to FE models in computational orthopaedic biomechanics in order to understand the reliability of predictions.
Variational approach to probabilistic finite elements
NASA Technical Reports Server (NTRS)
Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.
1991-01-01
Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
Variational approach to probabilistic finite elements
NASA Technical Reports Server (NTRS)
Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.
1987-01-01
Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
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)
Soudah, Eduardo; Rossi, Riccardo; Idelsohn, Sergio; Oñate, Eugenio
2014-10-01
A reduced-order model for an efficient analysis of cardiovascular hemodynamics problems using multiscale approach is presented in this work. Starting from a patient-specific computational mesh obtained by medical imaging techniques, an analysis methodology based on a two-step automatic procedure is proposed. First a coupled 1D-3D Finite Element Simulation is performed and the results are used to adjust a reduced-order model of the 3D patient-specific area of interest. Then, this reduced-order model is coupled with the 1D model. In this way, three-dimensional effects are accounted for in the 1D model in a cost effective manner, allowing fast computation under different scenarios. The methodology proposed is validated using a patient-specific aortic coarctation model under rest and non-rest conditions.
Finite element coiled cochlea model
NASA Astrophysics Data System (ADS)
Isailovic, Velibor; Nikolic, Milica; Milosevic, Zarko; Saveljic, Igor; Nikolic, Dalibor; Radovic, Milos; Filipović, Nenad
2015-12-01
Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers - scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experimental measurements. Future work is needed for more realistic geometry model. Coiled model of the cochlea was created and results are compared with initial simplified coiled model of the cochlea.
Finite elements and finite differences for transonic flow calculations
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Murman, E. M.; Wellford, L. C.
1978-01-01
The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.
Element-topology-independent preconditioners for parallel finite element computations
NASA Technical Reports Server (NTRS)
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
Finite-Element Composite-Analysis Program
NASA Technical Reports Server (NTRS)
Bowles, David E.
1990-01-01
Finite Element Composite Analysis Program, FECAP, special-purpose finite-element program for analyzing behavior of composite material with microcomputer. Procedure leads to set of linear simultaneous equations relating unknown nodal displacement to applied loads. Written in HP BASIC 3.0.
Finite element analysis of helicopter structures
NASA Technical Reports Server (NTRS)
Rich, M. J.
1978-01-01
Application of the finite element analysis is now being expanded to three dimensional analysis of mechanical components. Examples are presented for airframe, mechanical components, and composite structure calculations. Data are detailed on the increase of model size, computer usage, and the effect on reducing stress analysis costs. Future applications for use of finite element analysis for helicopter structures are projected.
3-D Finite Element Code Postprocessor
1996-07-15
TAURUS is an interactive post-processing application supporting visualization of finite element analysis results on unstructured grids. TAURUS provides the ability to display deformed geometries and contours or fringes of a large number of derived results on meshes consisting of beam, plate, shell, and solid type finite elements. Time history plotting is also available.
NASA Astrophysics Data System (ADS)
Kanber, Bahattin; Bozkurt, O. Yavuz
2006-08-01
In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.
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)
Seong, Dae-Yong; Jung, ChangGyun; Yang, Dong-Yol
2007-05-01
Metallic sandwich panels composed of two face sheets and cores with low relative density have lightweight characteristics and various static and dynamic load bearing functions. To predict the forming characteristics, performance, and formability of these structured materials, full 3D modeling and analysis involving tremendous computational time and memory are required. Some constitutive continuum models including homogenization approaches to solve these problems have limitations with respect to the prediction of local buckling of face sheets and inner structures. In this work, a computationally efficient FE-analysis method incorporating a virtual equivalent projected model that enables the simulation of local buckling modes is newly introduced for analysis of metallic sandwich panels. Two-dimensional models using the projected shapes of 3D structures have the same equivalent elastic-plastic properties with original geometries that have anisotropic stiffness, yield strength, and hardening function. The sizes and isotropic properties of the virtual equivalent projected model have been estimated analytically with the same equivalent properties and face buckling strength of the full model. The 3-point bending processes with quasi-two-dimensional loads and boundary conditions are simulated to establish the validity of the proposed method. The deformed shapes and load-displacement curves of the virtual equivalent projected model are found to be almost the same as those of a full three-dimensional FE-analysis while reducing computational time drastically.
Seong, Dae-Yong; Jung, Chang Gyun; Yang, Dong-Yol
2007-05-17
Metallic sandwich panels composed of two face sheets and cores with low relative density have lightweight characteristics and various static and dynamic load bearing functions. To predict the forming characteristics, performance, and formability of these structured materials, full 3D modeling and analysis involving tremendous computational time and memory are required. Some constitutive continuum models including homogenization approaches to solve these problems have limitations with respect to the prediction of local buckling of face sheets and inner structures. In this work, a computationally efficient FE-analysis method incorporating a virtual equivalent projected model that enables the simulation of local buckling modes is newly introduced for analysis of metallic sandwich panels. Two-dimensional models using the projected shapes of 3D structures have the same equivalent elastic-plastic properties with original geometries that have anisotropic stiffness, yield strength, and hardening function. The sizes and isotropic properties of the virtual equivalent projected model have been estimated analytically with the same equivalent properties and face buckling strength of the full model. The 3-point bending processes with quasi-two-dimensional loads and boundary conditions are simulated to establish the validity of the proposed method. The deformed shapes and load-displacement curves of the virtual equivalent projected model are found to be almost the same as those of a full three-dimensional FE-analysis while reducing computational time drastically.
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.
Optimizing header strength utilizing finite element analyses
NASA Astrophysics Data System (ADS)
Burchett, S. N.
Finite element techniques have been successfully applied as a design tool in the optimization of high strength headers for pyrotechnic-driven actuators. These techniques have been applied to three aspects of the design process of a high strength header. The design process was a joint effort of experts from several disciplines including design engineers, material scientists, test engineers, manufacturing engineers, and structural analysts. Following material selection, finite element techniques were applied to evaluate the residual stresses due to manufacturing which were developed in the high strength glass ceramic-to-metal seal headers. Results from these finite element analyses were used to identify header designs which were manufacturable and had a minimum residual stress state. Finite element techniques were than applied to obtain the response of the header due to pyrotechnic burn. The results provided realistic upper bounds on the pressure containment ability of various preliminary header designs and provided a quick and inexpensive method of strengthening and refining the designs. Since testing of the headers was difficult and sometimes destructive, results of the analyses were also used to interpret test results and identify failure modes. In this paper, details of the finite element element techniques including the models used, material properties, material failure models, and loading will be presented. Results from the analyses showing the header failure process will also be presented. This paper will show that significant gains in capability and understanding can result when finite element techniques are included as an integral part of the design process of complicated high strength headers.
Visualization of higher order finite elements.
Thompson, David C.; Pebay, Philippe Pierre; Crawford, Richard H.; Khardekar, Rahul Vinay
2004-04-01
Finite element meshes are used to approximate the solution to some differential equation when no exact solution exists. A finite element mesh consists of many small (but finite, not infinitesimal or differential) regions of space that partition the problem domain, {Omega}. Each region, or element, or cell has an associated polynomial map, {Phi}, that converts the coordinates of any point, x = ( x y z ), in the element into another value, f(x), that is an approximate solution to the differential equation, as in Figure 1(a). This representation works quite well for axis-aligned regions of space, but when there are curved boundaries on the problem domain, {Omega}, it becomes algorithmically much more difficult to define {Phi} in terms of x. Rather, we define an archetypal element in a new coordinate space, r = ( r s t ), which has a simple, axis-aligned boundary (see Figure 1(b)) and place two maps onto our archetypal element:
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.
Quadratic finite elements and incompressible viscous flows.
Dohrmann, Clark R.; Gartling, David K.
2005-01-01
Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.
Finite element analysis of 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.
Model Reduction of Viscoelastic Finite Element Models
NASA Astrophysics Data System (ADS)
Park, C. H.; Inman, D. J.; Lam, M. J.
1999-01-01
This paper examines a method of adding viscoelastic properties to finite element models by using additional co-ordinates to account for the frequency dependence usually associated with such damping materials. Several such methods exist and all suffer from an increase in order of the final finite model which is undesirable in many applications. Here we propose to combine one of these methods, the GHM (Golla-Hughes-McTavish) method, with model reduction techniques to remove the objection of increased model order. The result of combining several methods is an ability to add the effects of visoelastic components to finite element or other analytical models without increasing the order of the system. The procedure is illustrated by a numerical example. The method proposed here results in a viscoelastic finite element of a structure without increasing the order of the original model.
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.
Higher-Order Finite Elements for Computing Thermal Radiation
NASA Technical Reports Server (NTRS)
Gould, Dana C.
2004-01-01
unrealistic physical conditions are assumed. Instead, the equations of radiative heat transfer are integrated numerically over the parent finite elements by use of a computationally efficient Gaussian integration scheme.
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.
The GPRIME approach to finite element modeling
NASA Technical Reports Server (NTRS)
Wallace, D. R.; Mckee, J. H.; Hurwitz, M. M.
1983-01-01
GPRIME, an interactive modeling system, runs on the CDC 6000 computers and the DEC VAX 11/780 minicomputer. This system includes three components: (1) GPRIME, a user friendly geometric language and a processor to translate that language into geometric entities, (2) GGEN, an interactive data generator for 2-D models; and (3) SOLIDGEN, a 3-D solid modeling program. Each component has a computer user interface of an extensive command set. All of these programs make use of a comprehensive B-spline mathematics subroutine library, which can be used for a wide variety of interpolation problems and other geometric calculations. Many other user aids, such as automatic saving of the geometric and finite element data bases and hidden line removal, are available. This interactive finite element modeling capability can produce a complete finite element model, producing an output file of grid and element data.
Quadrilateral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Benzley, Steven E
2012-10-16
Techniques for coarsening a quadrilateral mesh are described. These techniques include identifying a coarsening region within the quadrilateral mesh to be coarsened. Quadrilateral elements along a path through the coarsening region are removed. Node pairs along opposite sides of the path are identified. The node pairs along the path are then merged to collapse the path.
Waveguide finite elements for curved structures
NASA Astrophysics Data System (ADS)
Finnveden, Svante; Fraggstedt, Martin
2008-05-01
A waveguide finite element formulation for the analysis of curved structures is introduced. The formulation is valid for structures that along one axis have constant properties. It is based on a modified Hamilton's principle valid for general linear viscoelastic motion, which is derived here. Using this principle, material properties such as losses may be distributed in the system and may vary with frequency. Element formulations for isoparametric solid elements and deep shell elements are presented for curved waveguides as well as for straight waveguides. In earlier works, the curved elements have successfully been used to model a passenger car tyre. Here a simple validation example and convergence study is presented, which considers a finite length circular cylinder and all four elements presented are used, in turn, to model this structure. Calculated results compare favourably to those in the literature.
Exact finite elements for conduction and convection
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507
Exact finite elements for conduction and convection
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.
Visualizing higher order finite elements. Final report
Thompson, David C; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elements into regions appropriate for isosurfacing and proves the conditions under which the algorithm will terminate. Finite elements are used to create piecewise polynomial approximants to the solution of partial differential equations for which no analytical solution exists. These polynomials represent fields such as pressure, stress, and momentum. In the past, these polynomials have been linear in each parametric coordinate. Each polynomial coefficient must be uniquely determined by a simulation, and these coefficients are called degrees of freedom. When there are not enough degrees of freedom, simulations will typically fail to produce a valid approximation to the solution. Recent work has shown that increasing the number of degrees of freedom by increasing the order of the polynomial approximation (instead of increasing the number of finite elements, each of which has its own set of coefficients) can allow some types of simulations to produce a valid approximation with many fewer degrees of freedom than increasing the number of finite elements alone. However, once the simulation has determined the values of all the coefficients in a higher-order approximant, tools do not exist for visual inspection of the solution. This report focuses on a technique for the visual inspection of higher-order finite element simulation results based on decomposing each finite element into simplicial regions where existing visualization algorithms such as isosurfacing will work. The requirements of the isosurfacing algorithm are enumerated and related to the places where the partial derivatives of the polynomial become zero. The original isosurfacing algorithm is then applied to each of these regions in turn.
Finite Element Analysis of Pipe Elbows.
1980-02-01
AD-AO81 077 DAVD TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CE--ETC F/B 13/11 FINITE ELEMENT ANALYSIS OF PIPE ELBOWS .(U) FE SO M S MARCUS, B C...TAYLOR NAVAL SHIP i RESEARCH AND DEVELOPMENT CENTER Bethesda, Md. 20084 4 FINITE ELEMENT ANALYSIS OF PIPE ELBOWS by 0 Melvyn S. Marcus and Gordon C...a 90-degree pipe elbow to determine principal stresses due to internal pressure, inplane bending, out-of-plane bending, and torsion moment loadings
Finite Element Model to Reduce Fire and Blast Vulnerability
2013-01-01
Finite Element Analysis FEM Finite Element Model NAVAIR...and probabilistic analysis are need to address these challenges. The objective of this effort is to develop a finite element model of a soldier to...UNCLASSIFIED FINITE ELEMENT MODEL TO REDUCE FIRE AND BLAST VULNERABILITY INTERIM REPORT TFLRF No. 439 by W. Loren Francis
Studies of finite element analysis of composite material structures
NASA Technical Reports Server (NTRS)
Douglas, D. O.; Holzmacher, D. E.; Lane, Z. C.; Thornton, E. A.
1975-01-01
Research in the area of finite element analysis is summarized. Topics discussed include finite element analysis of a picture frame shear test, BANSAP (a bandwidth reduction program for SAP IV), FEMESH (a finite element mesh generation program based on isoparametric zones), and finite element analysis of a composite bolted joint specimens.
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.
Finite element wavelets with improved quantitative properties
NASA Astrophysics Data System (ADS)
Nguyen, Hoang; Stevenson, Rob
2009-08-01
In [W. Dahmen, R. Stevenson, Element-by-element construction of wavelets satisfying stability and moment conditions, SIAM J. Numer. Anal. 37 (1) (1999) 319-352 (electronic)], finite element wavelets were constructed on polygonal domains or Lipschitz manifolds that are piecewise parametrized by mappings with constant Jacobian determinants. The wavelets could be arranged to have any desired order of cancellation properties, and they generated stable bases for the Sobolev spaces Hs for (or s<=1 on manifolds). Unfortunately, it appears that the quantitative properties of these wavelets are rather disappointing. In this paper, we modify the construction from the above-mentioned work to obtain finite element wavelets which are much better conditioned.
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.
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.
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.
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.
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.
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.
Finite Element Modelling and Analysis of Conventional Pultrusion Processes
NASA Astrophysics Data System (ADS)
Akishin, P.; Barkanov, E.; Bondarchuk, A.
2015-11-01
Pultrusion is one of many composite manufacturing techniques and one of the most efficient methods for producing fiber reinforced polymer composite parts with a constant cross-section. Numerical simulation is helpful for understanding the manufacturing process and developing scientific means for the pultrusion tooling design. Numerical technique based on the finite element method has been developed for the simulation of pultrusion processes. It uses the general purpose finite element software ANSYS Mechanical. It is shown that the developed technique predicts the temperature and cure profiles, which are in good agreement with those published in the open literature.
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.
Probabilistic finite elements for transient analysis in nonlinear continua
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.; Mani, A.
1985-01-01
The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
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.
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
A new formulation of hybrid/mixed finite element
NASA Technical Reports Server (NTRS)
Pian, T. H. H.; Kang, D.; Chen, D.-P.
1983-01-01
A new formulation of finite element method is accomplished by the Hellinger-Reissner principle for which the stress equilibrium conditions are not introduced initially but are brought-in through the use of additional internal displacement parameters. The method can lead to the same result as the assumed stress hybrid model. However, it is more general and more flexible. The use of natural coordinates for stress assumptions leads to elements which are less sensitive to the choice of reference coordinates. Numerical solutions by 3-D solid element indicate that more efficient elements can be constructed by assumed stresses which only partially satisfy the equilibrium conditions.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2015-12-21
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying a series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2015-12-21
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less
Finite Element Heat & Mass Transfer Code
Trease, Lynn
1996-10-10
FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; and double porosity and double porosity/double permeability capabilities.
Finite Element Analysis of Piping Tees.
1980-06-01
Combustion Engineering, Inc., performed an experimental stress analysis3 on an ANSI B16.9 carbon steelt tee designated T-12. Pipe extensions were welded to...AD-ASS? 353 DAVID If TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CE--ETC F/S 13/11 FINITE ELEENT ANALYSIS OF PIPING TEES.(U) JUN 8 A J QUEZON. S C...DAVID W. TAYLOR NAVAL SHIP SRESEARCH AND DEVELOPMENT CENTER Bethesa Md. 20084 FINITE ELEMENT ANALYSIS OF PIPING TEES by Antonio J. Quezon, Gordon C
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 modelling of SAW correlator
NASA Astrophysics Data System (ADS)
Tikka, Ajay C.; Al-Sarawi, Said F.; Abbott, Derek
2007-12-01
Numerical simulations of SAW correlators so far are limited to delta function and equivalent circuit models. These models are not accurate as they do not replicate the actual behaviour of the device. Manufacturing a correlator to specifically realise a different configuration is both expensive and time consuming. With the continuous improvement in computing capacity, switching to finite element modelling would be more appropriate. In this paper a novel way of modelling a SAW correlator using finite element analysis is presented. This modelling approach allows the consideration of different code implementation and device structures. This is demonstrated through simulation results for a 5×2-bit Barker sequence encoded SAW correlator. These results show the effect of both bulk and leaky modes on the device performance at various operating frequencies. Moreover, the ways in which the gain of the correlator can be optimised though variation of design parameters will also be outlined.
Finite element modeling of permanent magnet devices
NASA Astrophysics Data System (ADS)
Brauer, J. R.; Larkin, L. A.; Overbye, V. D.
1984-03-01
New techniques are presented for finite element modeling of permanent magnets in magnetic devices such as motors and generators. These techniques extend a previous sheet-current permanent magnet model that applies only for straight line B-H loops and rectangular-shaped magnets. Here Maxwell's equations are used to derive the model of a permanent magnet having a general curved B-H loop and any geometric shape. The model enables a nonlinear magnetic finite element program to use Newton-Raphson iteration to solve for saturable magnetic fields in a wide variety of devices containing permanent magnets and steels. The techniques are applied to a brushless dc motor with irregular-shaped permanent magnets. The calculated motor torque agrees well with measured torque.
EC Vacuum Vessel Finite Element Analysis
Rudland, D.; Luther, R.; /Fermilab
1992-02-04
This Note contains a summary of the results of the finite element analysis of the EC Cryostat vacuum vessel performed by Dave Rudland in 1987. The results are used in the structural evaluation of the EC cryostats presented in Engineering Note 194. It should also be noted that the adequacy of the design of the vacuum vessels was reviewed and verified by the Battelle Memorial Institute. Battelle used a shell of revolution program to essentially duplicate the FEA analysis with similar results. It should be noted that no plots of the finite element mesh were retained from the analysis, and these can not be easily reproduced due to a change in the version of the ANSYS computer program shortly after the analysis was completed.
Finite element 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
Sanford, L. A.; Hallquist, J. O.
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forces along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.
Finite element concepts in computational aerodynamics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1978-01-01
Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.
Finite 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: Principles for Their Selection.
1983-02-01
the finite element methods. 39 Various statements in the literature that certain mixed methods work well inspite of the fact that the LBB (BB...method, displacement and mixed methods , various adaptive approaches, etc. The examples discussed in Sections 2 and 3 show that the same computational...performance and their relation to mixed methods , SIAM J. Num. Anal., to appear. 5. F. Brezzi, On the existence uniqueness and approximation of saddle-point
Finite Element Output Bounds for Hyperbolic Problems
Machiels, L.
2000-03-27
We propose a Neumann-subproblem a posteriori finite element error bound technique for linear stationary scalar advection problems. The method is similar in many respects to the previous output bound technique developed for elliptic problems. In the new approach, however, the primal residual is enhanced with a streamline diffusion term. We first formulate the bound algorithm, with particular emphasis on the proof of the bounding properties; then, we provide numerical results for an illustrative example.
Finite element analysis of wrinkling membranes
NASA Technical Reports Server (NTRS)
Miller, R. K.; Hedgepeth, J. M.; Weingarten, V. I.; Das, P.; Kahyai, S.
1984-01-01
The development of a nonlinear numerical algorithm for the analysis of stresses and displacements in partly wrinkled flat membranes, and its implementation on the SAP VII finite-element code are described. A comparison of numerical results with exact solutions of two benchmark problems reveals excellent agreement, with good convergence of the required iterative procedure. An exact solution of a problem involving axisymmetric deformations of a partly wrinkled shallow curved membrane is also reported.
Finite Element 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.
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.
Solution Techniques in Finite Element Analysis.
1983-05-01
CR 83.027 NAVAL CIVIL ENGINEERING LABORATORY Port Hueneme, California Sponsored by NAVAL FACILITIES ENGINEERING COMMAND ___ SOLUTION TECHNIQUES IN...CATALOG NUMBER CR 83.027 A bA/Z3 SZ *4 TITLE fori SoobIt, S TYPE F REP RT II PERIOD COVERED SOLUTION TECHNIQUES IN FINITE ELEMENT Not 192in Jna98 ANALYSIS...elements; nonlinear algebraic equations; numierical solution methods 20 ABSTRACT (Contlinue mI e.se mde It nc..Ac.. Wd ordonhifI, by block .- abe,) ,A
Finite element modeling of lipid bilayer membranes
NASA Astrophysics Data System (ADS)
Feng, Feng; Klug, William S.
2006-12-01
A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic model for these membranes employs a two-dimensional-fluid-like elastic constitutive law which is sensitive to curvature, and subjects vesicles to physically imposed constraints on surface area and volume. This model is implemented numerically via the use of C1-conforming triangular Loop subdivision finite elements. The validity of the framework is tested by computing equilibrium shapes from previously-determined axisymmetric shape-phase diagram of lipid bilayer vesicles with homogeneous material properties. Some of the benefits and challenges of finite element modeling of lipid bilayer systems are discussed, and it is indicated how this framework is natural for future investigation of biologically realistic bilayer structures involving nonaxisymmetric geometries, binding and adhesive interactions, heterogeneous mechanical properties, cytoskeletal interactions, and complex loading arrangements. These biologically relevant features have important consequences for the shape mechanics of nonidealized vesicles and cells, and their study requires not simply advances in theory, but also advances in numerical simulation techniques, such as those presented here.
Gauge finite element method for incompressible flows
NASA Astrophysics Data System (ADS)
E, Weinan; Liu, Jian-Guo
2000-12-01
A finite element method for computing viscous incompressible flows based on the gauge formulation introduced in [Weinan E, Liu J-G. Gauge method for viscous incompressible flows. Journal of Computational Physics (submitted)] is presented. This formulation replaces the pressure by a gauge variable. This new gauge variable is a numerical tool and differs from the standard gauge variable that arises from decomposing a compressible velocity field. It has the advantage that an additional boundary condition can be assigned to the gauge variable, thus eliminating the issue of a pressure boundary condition associated with the original primitive variable formulation. The computational task is then reduced to solving standard heat and Poisson equations, which are approximated by straightforward, piecewise linear (or higher-order) finite elements. This method can achieve high-order accuracy at a cost comparable with that of solving standard heat and Poisson equations. It is naturally adapted to complex geometry and it is much simpler than traditional finite element methods for incompressible flows. Several numerical examples on both structured and unstructured grids are presented. Copyright
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.
Dynamic quasistatic characterization of finite elements for shell structures.
Thomas, Jesse David
2010-11-01
Finite elements for shell structures have been investigated extensively, with numerous formulations offered in the literature. These elements are vital in modern computational solid mechanics due to their computational efficiency and accuracy for thin and moderately thick shell structures, allowing larger and more comprehensive (e.g. multi-scale and multi-physics) simulations. Problems now of interest in the research and development community are routinely pushing our computational capabilities, and thus shell finite elements are being used to deliver efficient yet high quality computations. Much work in the literature is devoted to the formulation of shell elements and their numerical accuracy, but there is little published work on the computational characterization and comparison of shell elements for modern solid mechanics problems. The present study is a comparison of three disparate shell element formulations in the Sandia National Laboratories massively parallel Sierra Solid Mechanics code. A constant membrane and bending stress shell element (Key and Hoff, 1995), a thick shell hex element (Key et al., 2004) and a 7-parameter shell element (Buechter et al., 1994) are available in Sierra Solid Mechanics for explicit transient dynamic, implicit transient dynamic and quasistatic calculations. Herein these three elements are applied to a set of canonical dynamic and quasistatic problems, and their numerical accuracy, computational efficiency and scalability are investigated. The results show the trade-off between the relative inefficiency and improved accuracy of the latter two high quality element types when compared with the highly optimized and more widely used constant membrane and bending stress shell element.
Visualization of transient finite element analyses on large unstructured grids
Dovey, D.
1995-03-22
Three-dimensional transient finite element analysis is performed on unstructured grids. A trend toward running larger analysis problems, combined with a desire for interactive animation of analysis results, demands efficient visualization techniques. This paper discusses a set of data structures and algorithms for visualizing transient analysis results on unstructured grids and introduces some modifications in order to better support large grids. In particular, an element grouping approach is used to reduce the amount of memory needed for external surface determination and to speed up ``point in element`` tests. The techniques described lend themselves to visualization of analyses carried out in parallel on a massively parallel computer (MPC).
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.
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 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
Mixed Finite Element Method for Melt Migration
NASA Astrophysics Data System (ADS)
Taicher, A. L.; Hesse, M. A.; Arbogast, T.
2012-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium. Therefore, a numerical method must also carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. The finite element framework provides support for additional analysis of error and convergence. Moreover, both mesh refinement and anisotropy are naturally incorporated into finite elements. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. Mixed methods also produce discretely conservative fluxes that are required for the transport problem to remains stable without violating conservation of mass. Based preliminary investigations in 1D and derived energy estimates, we present a mixed formulation for the Darcy-Stokes system. Next, using novel elements of lowest order and
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.
NASA Technical Reports Server (NTRS)
Aberson, J. A.; Anderson, J. M.
1973-01-01
The recent introduction of special crack-tip singularity elements, usually referred to as cracked elements, has brought the power and flexibility of the finite-element method to bear much more effectively on fracture mechanics problems. This paper recalls the development of two cracked elements and presents the results of some applications proving their accuracy and economy. Judging from the available literature on numerical methods in fracture mechanics, it seems clear that the elements described have been used more extensively than any others in practical fracture mechanics applications.
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.
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.
Edge-based finite element scheme for the Euler equations
NASA Astrophysics Data System (ADS)
Luo, Hong; Baum, Joseph D.; Loehner, Rainald
1994-06-01
This paper describes the development, validation, and application of a new finite element scheme for the solution of the compressible Euler equations on unstructured grids. The implementation of the numerical scheme is based on an edge-based data structure, as opposed to a more element-based data structure. The use of this edge-based data structure not only improves the efficiency of the algorithm but also enables a straightforward implementation of the upwind schemes in the context of finite element methods. The algorithm has been tested and validated on some well documented configurations. A flow solution about a complete F-18 fighter is shown to demonstrate the accuracy and robustness of the proposed algorithm.
Edge-based finite element scheme for the Euler equations
NASA Astrophysics Data System (ADS)
Luo, Hong; Baum, Joseph D.; Lohner, Rainald
1994-06-01
This paper describes the development, validation, and application of a new finite element scheme for the solution of the compressible Euler equations on unstructured grids. The implementation of the numerical scheme is based on an edge-based data structure, as opposed to a more traditional element-based data structure. The use of this edge-based data structure not only improves the efficiency of the algorithm but also enables a straightforward implementation of upwind schemes in the context of finite element methods. The algorithm has been tested and validated on some well-documented configurations. A flow solution about a complete F-18 fighter is shown to demonstrate the accuracy and robustness of the proposed algorithm.
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.
System software for the finite element machine
NASA Technical Reports Server (NTRS)
Crockett, T. W.; Knott, J. D.
1985-01-01
The Finite Element Machine is an experimental parallel computer developed at Langley Research Center to investigate the application of concurrent processing to structural engineering analysis. This report describes system-level software which has been developed to facilitate use of the machine by applications researchers. The overall software design is outlined, and several important parallel processing issues are discussed in detail, including processor management, communication, synchronization, and input/output. Based on experience using the system, the hardware architecture and software design are critiqued, and areas for further work are suggested.
Algebraic surface design and finite element meshes
NASA Technical Reports Server (NTRS)
Bajaj, Chandrajit L.
1992-01-01
Some of the techniques are summarized which are used in constructing C sup 0 and C sup 1 continuous meshes of low degree, implicitly defined, algebraic surface patches in three dimensional space. These meshes of low degree algebraic surface patches are used to construct accurate computer models of physical objects. These meshes are also used in the finite element simulation of physical phenomena (e.g., heat dissipation, stress/strain distributions, fluid flow characteristics) required in the computer prototyping of both the manufacturability and functionality of the geometric design.
Chemorheology of reactive systems: Finite element analysis
NASA Technical Reports Server (NTRS)
Douglas, C.; Roylance, D.
1982-01-01
The equations which govern the nonisothermal flow of reactive fluids are outlined, and the means by which finite element analysis is used to solve these equations for the sort of arbitrary boundary conditions encountered in industrial practice are described. The performance of the computer code is illustrated by several trial problems, selected more for their value in providing insight to polymer processing flows than as practical production problems. Although a good deal remains to be learned as to the performance and proper use of this numerical technique, it is undeniably useful in providing better understanding of today's complicated polymer processing problems.
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.
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.
NASA Technical Reports Server (NTRS)
Tsai, C.; Szabo, B. A.
1973-01-01
An approch to the finite element method which utilizes families of conforming finite elements based on complete polynomials is presented. Finite element approximations based on this method converge with respect to progressively reduced element sizes as well as with respect to progressively increasing orders of approximation. Numerical results of static and dynamic applications of plates are presented to demonstrate the efficiency of the method. Comparisons are made with plate elements in NASTRAN and the high-precision plate element developed by Cowper and his co-workers. Some considerations are given to implementation of the constraint method into general purpose computer programs such as NASTRAN.
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.
Recent advances in hybrid/mixed finite elements
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1985-01-01
In formulations of Hybrid/Mixed finite element methods respectively by the Hellinger-Reissner principle and the Hu-Washizu principle, the stress equilibrium equations are brought in as conditions of constraint through the introduction of additional internal displacement parameters. These two approaches are more flexible and have better computing efficiencies. A procedure for the choice of assumed stress terms for 3-D solids is suggested. Example solutions are given for plates and shells using the present formulations and the idea of semiloof elements.
Mixed Finite Element Methods for Melt Migration
NASA Astrophysics Data System (ADS)
Taicher, A. L.
2013-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium so must carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. We present a mixed formulation for the Darcy-Stokes system. Next, we present novel elements of lowest order and compatible with both Darcy and Stokes flow Finally, we present our 2D mixed FEM code result for solving Stokes and Darcy flow as well as the coupled Darcy-Stokes system the mid-ocean ridge or corner flow problem.
Finite element analysis enhancement of cryogenic testing
NASA Astrophysics Data System (ADS)
Thiem, Clare D.; Norton, Douglas A.
1991-12-01
Finite element analysis (FEA) of large space optics enhances cryogenic testing by providing an analytical method by which to ensure that a test article survives proposed testing. The analyses presented in this paper were concerned with determining the reliability of a half meter mirror in an environment where the exact environmental profile was unknown. FEA allows the interaction between the test object and the environment to be simulated to detect potential problems prior to actual testing. These analyses examined worse case scenerios related to cooling the mirror, its structural integrity for the proposed test environment, and deformation of the reflective surface. The FEA was conducted in-house on the System's Reliability Division's VAX 11-750 and Decstation 3100 using Engineering Mechanics Research Corporation's numerically integrated elements for systems analysis finite element software. The results of the analyses showed that it would take at least 48 hours to cool the mirror to its desired testing temperature. It was also determined that the proposed mirror mount would not cause critical concentrated thermal stresses that would fracture the mirror. FEA and actual measurements of the front reflective face were compared and good agreement between computer simulation and physical tests were seen. Space deployment of large optics requires lightweight mirrors which can perform under the harsh conditions of space. The physical characteristics of these mirrors must be well understood in order that their deployment and operation are successful. Evaluating design approaches by analytical simulation, like FEA, verifies the reliability and structural integrity of a space optic during design prior to prototyping and testing. Eliminating an optic's poor design early in its life saves money, materials, and human resources while ensuring performance.
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.
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 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.
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.
Patient-specific finite element modeling of bones.
Poelert, Sander; Valstar, Edward; Weinans, Harrie; Zadpoor, Amir A
2013-04-01
Finite element modeling is an engineering tool for structural analysis that has been used for many years to assess the relationship between load transfer and bone morphology and to optimize the design and fixation of orthopedic implants. Due to recent developments in finite element model generation, for example, improved computed tomography imaging quality, improved segmentation algorithms, and faster computers, the accuracy of finite element modeling has increased vastly and finite element models simulating the anatomy and properties of an individual patient can be constructed. Such so-called patient-specific finite element models are potentially valuable tools for orthopedic surgeons in fracture risk assessment or pre- and intraoperative planning of implant placement. The aim of this article is to provide a critical overview of current themes in patient-specific finite element modeling of bones. In addition, the state-of-the-art in patient-specific modeling of bones is compared with the requirements for a clinically applicable patient-specific finite element method, and judgment is passed on the feasibility of application of patient-specific finite element modeling as a part of clinical orthopedic routine. It is concluded that further development in certain aspects of patient-specific finite element modeling are needed before finite element modeling can be used as a routine clinical tool.
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.
Quality management of finite element analysis
NASA Astrophysics Data System (ADS)
Barlow, John
1991-09-01
A quality management system covering the use of finite element analysis is described. The main topics are as follows: acquisition, development and verification of software (including the software suppliers software quality control system), support, documentation, error control, internal software, software acceptance and release; development and qualification of analysis methods, including software evaluation, analysis procedure qualification and documentation, procedure quality checks, control of analysis procedure errors; product design and integrity analysis, including project quality assurance and analysis planning, task specification and allocation, analysis, execution, results checking and analysis records. Other issues include the commercial and business advantages of quality systems, project and technical management and the training and experience of personnel. The items are correlated with the requirements of International Standard Organization 9001.
Adaptive finite element methods in electrochemistry.
Gavaghan, David J; Gillow, Kathryn; Süli, Endre
2006-12-05
In this article, we review some of our previous work that considers the general problem of numerical simulation of the currents at microelectrodes using an adaptive finite element approach. Microelectrodes typically consist of an electrode embedded (or recessed) in an insulating material. For all such electrodes, numerical simulation is made difficult by the presence of a boundary singularity at the electrode edge (where the electrode meets the insulator), manifested by the large increase in the current density at this point, often referred to as the edge effect. Our approach to overcoming this problem has involved the derivation of an a posteriori bound on the error in the numerical approximation for the current that can be used to drive an adaptive mesh-generation algorithm, allowing calculation of the quantity of interest (the current) to within a prescribed tolerance. We illustrate the generic applicability of the approach by considering a broad range of steady-state applications of the technique.
NASA Astrophysics Data System (ADS)
Sarakorn, Weerachai
2017-04-01
In this research, the finite element (FE) method incorporating quadrilateral elements for solving 2-D MT modeling was presented. The finite element software was developed, employing a paving algorithm to generate the unstructured quadrilateral mesh. The accuracy, efficiency, reliability, and flexibility of our FE forward modeling are presented, compared and discussed. The numerical results indicate that our FE codes using an unstructured quadrilateral mesh provide good accuracy when the local mesh refinement is applied around sites and in the area of interest, with superior results when compared to other FE methods. The reliability of the developed codes was also confirmed when comparing both analytical solutions and COMMEMI2D model. Furthermore, our developed FE codes incorporating an unstructured quadrilateral mesh showed useful and powerful features such as handling irregular and complex subregions and providing local refinement of the mesh for a 2-D domain as closely as unstructured triangular mesh but it requires less number of elements in a mesh.
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
Generalization of mixed multiscale finite element methods with applications
Lee, C S
2016-08-01
Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii
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.
A finite element solver for 3-D compressible viscous flows
NASA Technical Reports Server (NTRS)
Reddy, K. C.; Reddy, J. N.; Nayani, S.
1990-01-01
Computation of the flow field inside a space shuttle main engine (SSME) requires the application of state of the art computational fluid dynamic (CFD) technology. Several computer codes are under development to solve 3-D flow through the hot gas manifold. Some algorithms were designed to solve the unsteady compressible Navier-Stokes equations, either by implicit or explicit factorization methods, using several hundred or thousands of time steps to reach a steady state solution. A new iterative algorithm is being developed for the solution of the implicit finite element equations without assembling global matrices. It is an efficient iteration scheme based on a modified nonlinear Gauss-Seidel iteration with symmetric sweeps. The algorithm is analyzed for a model equation and is shown to be unconditionally stable. Results from a series of test problems are presented. The finite element code was tested for couette flow, which is flow under a pressure gradient between two parallel plates in relative motion. Another problem that was solved is viscous laminar flow over a flat plate. The general 3-D finite element code was used to compute the flow in an axisymmetric turnaround duct at low Mach numbers.
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.
Impact of new computing systems on finite element computations
NASA Technical Reports Server (NTRS)
Noor, A. K.; Storassili, O. O.; Fulton, R. E.
1983-01-01
Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified.
Improved finite-element methods for rotorcraft structures
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1991-01-01
An overview of the research directed at improving finite-element methods for rotorcraft airframes is presented. The development of a modification to the finite element method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick finite element program.
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.
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).
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.
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.
Ablative Thermal Response Analysis Using the Finite Element Method
NASA Technical Reports Server (NTRS)
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
Leapfrog/Finite Element Method for Fractional Diffusion Equation
Zhao, Zhengang; Zheng, Yunying
2014-01-01
We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an L 2-error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis. PMID:24955431
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.
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.
Dual Methods for Optimizing Finite Element Flexural Systems.
1981-02-01
ADAIO2. T.7 LIEGE UNIV -(BEL-GIUM) LABORATOIRE DE TECHNIQUES AERON--ETC F/B 13/13 DUAL METHODS FOR OPTIMIZING FINITE ELEMENT FLEXURAL SYSTEMS. (U...FEB 81 C FLEURY. G SANDER AFOSR-80-0060 UNLSSIFIED LTASSA-87 AFOSR-TR-8 -0601 NL *soonmmnmi GRANT AFOSR - 80 - 000 REPORT SA-87 DUAL METHODS FOR...block number) Modern numerical methods for the optimization of large discretized systems are now well developed and highly efficient in the case of
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.
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
Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
NASA Astrophysics Data System (ADS)
Motamarri, P.; Nowak, M. R.; Leiter, K.; Knap, J.; Gavini, V.
2013-11-01
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss-Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100-200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn-Sham DFT problem. Our studies suggest that staggering computational savings-of the order of 1000-fold-relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn-Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Decahaumphai, P.; Wieting, A. R.
1980-01-01
An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. An integrated thermal-structural rod element is developed and used in four thermal-structural applications; the accuracy of this integrated approach is illustrated by comparisons with the customary approach of finite difference thermal-finite element structural analyses. Results show that integrated thermal-structural analysis of structures modeled with rod elements is more accurate than conventional analysis, and that its further development promises significant results.
VALIDATION OF ANSYS FINITE ELEMENT ANALYSIS SOFTWARE
HAMM, E.R.
2003-06-27
This document provides a record of the verification and Validation of the ANSYS Version 7.0 software that is installed on selected CH2M HILL computers. The issues addressed include: Software verification, installation, validation, configuration management and error reporting. The ANSYS{reg_sign} computer program is a large scale multi-purpose finite element program which may be used for solving several classes of engineering analysis. The analysis capabilities of ANSYS Full Mechanical Version 7.0 installed on selected CH2M Hill Hanford Group (CH2M HILL) Intel processor based computers include the ability to solve static and dynamic structural analyses, steady-state and transient heat transfer problems, mode-frequency and buckling eigenvalue problems, static or time-varying magnetic analyses and various types of field and coupled-field applications. The program contains many special features which allow nonlinearities or secondary effects to be included in the solution, such as plasticity, large strain, hyperelasticity, creep, swelling, large deflections, contact, stress stiffening, temperature dependency, material anisotropy, and thermal radiation. The ANSYS program has been in commercial use since 1970, and has been used extensively in the aerospace, automotive, construction, electronic, energy services, manufacturing, nuclear, plastics, oil and steel industries.
A composite nodal finite element for hexagons
Hennart, J.P.; Mund, E.H. |; Valle, E. Del
1997-10-01
A nodal algorithm for the solution of the multigroup diffusion equations in hexagonal arrays is analyzed. Basically, the method consists of dividing each hexagon into four quarters and mapping the hexagon quarters onto squares. The resulting boundary value problem on a quadrangular domain is solved in primal weak formulation. Nodal finite element methods like the Raviart-Thomas RTk schemes provide accurate analytical expansions of the solution in the hexagons. Transverse integration cannot be performed on the equations in the quadrangular domain as simply as it is usually done on squares because these equations have essentially variable coefficients. However, by considering an auxiliary problem with constant coefficients (on the same quadrangular domain) and by using a preconditioning approach, transverse integration can be performed as for rectangular geometry. A description of the algorithm is given for a one-group diffusion equation. Numerical results are presented for a simple model problem with a known analytical solution and for k{sub eff} evaluations of some benchmark problems proposed in the literature. For the analytical problem, the results indicate that the theoretical convergence orders of RTk schemes (k = 0,1) are obtained, yielding accurate solutions at the expense of a few preconditioning iterations.
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 modelling of fabric shear
NASA Astrophysics Data System (ADS)
Lin, Hua; Clifford, Mike J.; Long, Andrew C.; Sherburn, Martin
2009-01-01
In this study, a finite element model to predict shear force versus shear angle for woven fabrics is developed. The model is based on the TexGen geometric modelling schema, developed at the University of Nottingham and orthotropic constitutive models for yarn behaviour, coupled with a unified displacement-difference periodic boundary condition. A major distinction from prior modelling of fabric shear is that the details of picture frame kinematics are included in the model, which allows the mechanisms of fabric shear to be represented more accurately. Meso- and micro-mechanisms of deformation are modelled to determine their contributions to energy dissipation during shear. The model is evaluated using results obtained for a glass fibre plain woven fabric, and the importance of boundary conditions in the analysis of deformation mechanisms is highlighted. The simulation results show that the simple rotation boundary condition is adequate for predicting shear force at large deformations, with most of the energy being dissipated at higher shear angles due to yarn compaction. For small deformations, a detailed kinematic analysis is needed, enabling the yarn shear and rotation deformation mechanisms to be modelled accurately.
Finite element analysis of arc welding
Friedman, E.
1980-01-01
Analytical models of the gas tungsten-arc welding process into finite element computer programs provides a valuable tool for determining the welding thermal cycle, weld bead shape, and penetration characteristics, as well as for evaluating the stresses and distortions generated as a result of the temperature transients. The analysis procedures are applicable to planar or axisymmetric welds with arbitrary cross-sectional geometries, under quasistationary conditions. The method used for determining temperatures features an iteration procedure to accurately account for the latent heat absorbed during melting and liberated during solidification of the weld. By simulating the heat input from the arc to the workpiece by a normal distribution function, temperature transients, weld bead dimensions, and cooling rates are evaluated as functions of both the magnitude and distribution of heat input, weldment geometry, and weld speed (or duration of heating for stationary arcs). Modeling of the welding thermal cycle is a prerequisite to analytical treatments of metallurgical changes in weld metal and heat-affected zone material, residual stresses and distortions, and weld defects. A quasistationary formulation for moving welds enables temperatures to be calculated using a two-dimensional heat conduction computer program. The present limitation of high welding speed can, however, be relaxed without altering the two-dimensional framework of the procedure.
Intra Plate Stresses Using Finite Element Modelling
NASA Astrophysics Data System (ADS)
Jayalakshmi, S.; Raghukanth, S. T. G.
2016-10-01
One of the most challenging problems in the estimation of seismic hazard is the ability to quantify seismic activity. Empirical models based on the available earthquake catalogue are often used to obtain activity of source regions. The major limitation with this approach is the lack of sufficient data near a specified source. The non-availability of data poses difficulties in obtaining distribution of earthquakes with large return periods. Such events recur over geological time scales during which tectonic processes, including mantle convection, formation of faults and new plate boundaries, are likely to take place. The availability of geometries of plate boundaries, plate driving forces, lithospheric stress field and GPS measurements has provided numerous insights on the mechanics of tectonic plates. In this article, a 2D finite element model of Indo-Australian plate is developed with the focus of representing seismic activity in India. The effect of large scale geological features including sedimentary basins, fold belts and cratons on the stress field in India is explored in this study. In order to address long term behaviour, the orientation of stress field and tectonic faults of the present Indo- Australian plate are compared with a reconstructed stress field from the early Miocene (20 Ma).
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)
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.
Thermal-structural finite element analysis using linear flux formulation
NASA Technical Reports Server (NTRS)
Pandey, Ajay K.; Dechaumphai, Pramote; Wieting, Allan R.
1990-01-01
A linear flux approach is developed for a finite element thermal-structural analysis of steady state thermal and structural problems. The element fluxes are assumed to vary linearly in the same form as the element unknown variables, and the finite element matrices are evaluated in closed form. Since numerical integration is avoided, significant computational time saving is achieved. Solution accuracy and computational speed improvements are demonstrated by solving several two and three dimensional thermal-structural examples.
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.
The simulation of Lamb waves in a cracked plate using the scaled boundary finite element method.
Gravenkamp, Hauke; Prager, Jens; Saputra, Albert A; Song, Chongmin
2012-09-01
The scaled boundary finite element method is applied to the simulation of Lamb waves for ultrasonic testing applications. With this method, the general elastodynamic problem is solved, while only the boundary of the domain under consideration has to be discretized. The reflection of the fundamental Lamb wave modes from cracks of different geometry in a steel plate is modeled. A test problem is compared with commercial finite element software, showing the efficiency and convergence of the scaled boundary finite element method. A special formulation of this method is utilized to calculate dispersion relations for plate structures. For the discretization of the boundary, higher-order elements are employed to improve the efficiency of the simulations. The simplicity of mesh generation of a cracked plate for a scaled boundary finite element analysis is illustrated.
Finite element meshing of ANSYS (trademark) solid models
NASA Technical Reports Server (NTRS)
Kelley, F. S.
1987-01-01
A large scale, general purpose finite element computer program, ANSYS, developed and marketed by Swanson Analysis Systems, Inc. is discussed. ANSYS was perhaps the first commercially available program to offer truly interactive finite element model generation. ANSYS's purpose is for solid modeling. This application is briefly discussed and illustrated.
Generating Finite-Element Models Of Composite Materials
NASA Technical Reports Server (NTRS)
Melis, M. E.
1993-01-01
Program starts at micromechanical level, from simple inputs supplied by user. COMGEN, COmposite Model GENerator, is interactive FORTRAN program used to create wide variety of finite-element models of continuous-fiber composite materials at micromechanical level. Quickly generates batch or "session files" to be submitted to finite-element preprocessor and postprocessor program, PATRAN. COMGEN requires PATRAN to complete model.
A computer graphics program for general finite element analyses
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Sawyer, L. M.
1978-01-01
Documentation for a computer graphics program for displays from general finite element analyses is presented. A general description of display options and detailed user instructions are given. Several plots made in structural, thermal and fluid finite element analyses are included to illustrate program options. Sample data files are given to illustrate use of the program.
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.
Finite-element analysis of a weld-penetration problem
NASA Technical Reports Server (NTRS)
Rogge, T. R.
1977-01-01
The stress concentration factor for a weld penetration defect is calculated by the finite-element method. A stress intensity factor is computed by use of the finite-element solution and the J-integral. The results are compared with experimental results.
TAURUS96. 3-D Finite Element Code Postprocessor
Brown, B.; Hallquist, J.O.; Spelce, T.E.
1993-11-30
TAURUS is an interactive post-processing application supporting visualization of finite element analysis results on unstructured grids. TAURUS provides the ability to display deformed geometries and contours or fringes of a large number of derived results on meshes consisting of beam, plate, shell, and solid type finite elements. Time history plotting is also available.
Practical Application of Finite Element Analysis to Aircraft Structural Design
1986-08-01
t] Cook, Robert D., "Concepts and Applications of Finite element Analysis," John Wiley & Sons, Inc., New York, 1981. [5] Rao, S. S., "The Finite...generation large-scale computer programs is discussed. V.P. Analysis of aircraft structure using applied fracture mechanics (AA) WILHEM , D. P. Northrop...Analytical, finite element for surface flaws, holes (AA) WILHEM , D. P. Northrop Corp., Hawthorne, Calif. (N5631231) Aircraft Group. In AGARD Fracture
Finite element based inversion for time-harmonic electromagnetic problems
NASA Astrophysics Data System (ADS)
Schwarzbach, Christoph; Haber, Eldad
2013-05-01
In this paper we address the inverse problem and present some recent advances in numerical methods to recover the subsurface electrical conductivity from time-harmonic electromagnetic data. We rigorously formulate and discretize both the forward and the inverse problem in the finite element framework. To solve the forward problem, we derive a finite element discretization of the first-order system of Maxwell's equations in terms of the electric field and the magnetic induction. We show that our approach is equivalent to the standard discretization of the vector Helmholtz equation in terms of the electric field and that the discretization of magnetic induction of the same approximation order is hidden in the standard discretization. We implement the forward solver on unstructured tetrahedral meshes using edge elements. Unstructured meshes are not only capable of representing complex geometry. They can also reduce the overall problem size and, thus, the size of the system of linear equations arising from the forward problem such that direct methods for its solution using a sparse matrix factorization become feasible. The inverse problem is formulated as a regularized output least squares problem. We consider two regularization functions. First, we derive a smoothness regularizer using a primal-dual mixed finite element formulation which generalizes the standard Laplacian operator for a piecewise constant conductivity model on unstructured meshes. Secondly, we derive a total variation regularizer for the same class of models. For the choice of the regularization parameter we revisit the so-called dynamic regularization and compare it to a standard regularization scheme with fixed regularization parameter. The optimization problem is solved by the Gauss-Newton method which can be efficiently implemented using sparse matrix-vector operations and exploiting the sparse matrix factorization of the forward problem system matrix. A synthetic data example from marine
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 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
Finite element simulation of thick sheet thermoforming
NASA Astrophysics Data System (ADS)
Mercier, Daniel
This PhD was organized as collaboration between Lehigh University and the Ecole des Mines d'Albi on the subject: "Numerical simulation of thick sheet thermoforming". The research applications cover a wide range of products from thermoforming, e.g., packaging, automobile parts, appliance parts, large-scale panels and covers. Due to the special nature of this PhD, and the requirements of each hosting institutes, the research was split accordingly into two parts: At Lehigh University, under the supervision of Prof. Herman F. Nied, a full three-dimensional finite element program was developed in order to simulate the mechanical deformation during the process of thermoforming. The material behavior is considered hyperelastic with the property of incompressibility. The deformed structure may exhibit symmetries and may use a large choice of boundary conditions. A contact procedure for molds and/or displacements caused by a plug was implemented to complete the similarity with the thermoforming process. The research focused on simulating the observed nonlinear behaviors and their instabilities. The author emphasized the impact of large deformation on the numerical results and demonstrated the need for a remeshing capability. At the Ecole des Mines d'Albi, under the supervision of Prof. Fabrice Schmidt, an equi-biaxial rheometer was developed and built in order to determine the material properties during the process of thermoforming. Thermoplastic materials consist of long macromolecular chains that when stretched, during the process of sheet extrusion, exhibit a transversal isotropic behavior. The rheometer technique is the inflation of a circular membrane made of extruded thermoplastics. The resulting strain is identified by video analysis during the membrane inflation. This dissertation focused on technical issues related to heating with the goal of overcoming the difficulty of producing a homogeneous temperature distribution.
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.
The mixed finite element multigrid method for stokes equations.
Muzhinji, K; Shateyi, S; Motsa, S S
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results.
The Mixed Finite Element Multigrid Method for Stokes Equations
Muzhinji, K.; Shateyi, S.; Motsa, S. S.
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361
Multiscale finite-element method for linear elastic geomechanics
NASA Astrophysics Data System (ADS)
Castelletto, Nicola; Hajibeygi, Hadi; Tchelepi, Hamdi A.
2017-02-01
The demand for accurate and efficient simulation of geomechanical effects is widely increasing in the geoscience community. High resolution characterizations of the mechanical properties of subsurface formations are essential for improving modeling predictions. Such detailed descriptions impose severe computational challenges and motivate the development of multiscale solution strategies. We propose a multiscale solution framework for the geomechanical equilibrium problem of heterogeneous porous media based on the finite-element method. After imposing a coarse-scale grid on the given fine-scale problem, the coarse-scale basis functions are obtained by solving local equilibrium problems within coarse elements. These basis functions form the restriction and prolongation operators used to obtain the coarse-scale system for the displacement-vector. Then, a two-stage preconditioner that couples the multiscale system with a smoother is derived for the iterative solution of the fine-scale linear system. Various numerical experiments are presented to demonstrate accuracy and robustness of the method.
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)
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.
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)
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 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 Astrophysics Data System (ADS)
Chen, Jiefu; Zeng, Shubin; Dong, Qiuzhao; Huang, Yueqin
2017-02-01
An axisymmetric semianalytical finite element method is proposed and employed for rapid simulations of electromagnetic telemetry in layered underground formation. In this method, the layered media is decomposed into several subdomains and the interfaces between subdomains are discretized by conventional finite elements. Then a Riccati equation based high precision integration scheme is applied to exploit the homogeneity along the vertical direction in each layer. This semianalytical finite element scheme is very efficient in modeling electromagnetic telemetry in layered formation. Numerical examples as well as a field case with water based mud as drilling fluid are given to demonstrate the validity and effectiveness of this method.
Generalized Potential Energy Finite Elements for Modeling Molecular Nanostructures.
Chatzieleftheriou, Stavros; Adendorff, Matthew R; Lagaros, Nikos D
2016-10-24
The potential energy of molecules and nanostructures is commonly calculated in the molecular mechanics formalism by superimposing bonded and nonbonded atomic energy terms, i.e. bonds between two atoms, bond angles involving three atoms, dihedral angles involving four atoms, nonbonded terms expressing the Coulomb and Lennard-Jones interactions, etc. In this work a new, generalized numerical simulation is presented for studying the mechanical behavior of three-dimensional nanostructures at the atomic scale. The energy gradient and Hessian matrix of such assemblies are usually computed numerically; a potential energy finite element model is proposed herein where these two components are expressed analytically. In particular, generalized finite elements are developed that express the interactions among atoms in a manner equivalent to that invoked in simulations performed based on the molecular dynamics method. Thus, the global tangent stiffness matrix for any nanostructure is formed as an assembly of the generalized finite elements and is directly equivalent to the Hessian matrix of the potential energy. The advantages of the proposed model are identified in terms of both accuracy and computational efficiency. In the case of popular force fields (e.g., CHARMM), the computation of the Hessian matrix by implementing the proposed method is of the same order as that of the gradient. This analysis can be used to minimize the potential energy of molecular systems under nodal loads in order to derive constitutive laws for molecular systems where the entropy and solvent effects are neglected and can be approximated as solids, such as double stranded DNA nanostructures. In this context, the sequence dependent stretch modulus for some typical base pairs step is calculated.
Discontinuous Galerkin finite element solution for poromechanics
NASA Astrophysics Data System (ADS)
Liu, Ruijie
This dissertation focuses on applying discontinuous Galerkin (DG) methods to poromechanics problems. A few challenges have been presented in traditional and popular continuous Galerkin (CG) finite element methods for solving complex coupled thermal, flow and solid mechanics. For example, nonphysical pore pressure oscillations often occur in CG solutions for poroelasticity problems with low permeability. A robust and practical numerical scheme for removing or alleviating the oscillation is not available. In modeling thermoporoelastoplasticity, CG methods require the use of very small time steps to obtain a convergent solution. The temperature profile predicted by CG methods in the fine mesh zones is often seriously polluted by large errors produced in coarse mesh zones in the case where the convection dominates the thermal process. The nonphysical oscillations in pore pressure and temperature solutions induced by CG methods at very early time stages seriously corrupt the solutions at longer time. We propose DG methods to handle these challenges because they are physics driven, provide local conservation of mass and momentum, have high stability and robustness, are locking-free, and because of their meshing and implementation capabilities. We first apply a family of DG methods, including Oden-Babuska-Baumann (OBB), Nonsymmetric Interior Penalty Galerkin (NIPG), Symmetric Interior Penalty Galerkin (SIPG) and Incomplete Interior Penalty Galerkin (IIPG), to 3D linear elasticity problems. This family of DG methods is tested and evaluated by using a cantilever beam problem with nearly incompressible materials. It is shown that DG methods are simple, robust and locking-free in dealing with nearly incompressible materials. Based on the success of DG methods in elasticity, we extend the DG theory into plasticity problems. A DG formulation has been implemented for solving 3D poroelasticity problems with low permeability. Numerical examples solved by DG methods demonstrate
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.
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
Three Dimensional Eddy Current Analysis by Multi-Order Vector Finite Elements
NASA Astrophysics Data System (ADS)
Hano, Mitsuo; Hotta, Masashi
In this paper, we propose new method based on multi-order vector finite elements in three dimensional eddy current analysis. Edges, faces, and volume of the multi-order element have orders of shape functions, respectively. In order to realize high efficiency of numerical calculation, high-order elements are assigned in the important area of the eddy current model, and low-order elements in the surrounding area, and multi-order elements in the middle area to bond two areas, respectively. The results obtained by multi-order elements are compared with those by full high-order elements and by full low-order elements.
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 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.
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.
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 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.
Quality assessment and control of finite element solutions
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Babuska, Ivo
1987-01-01
Status and some recent developments in the techniques for assessing the reliability of finite element solutions are summarized. Discussion focuses on a number of aspects including: the major types of errors in the finite element solutions; techniques used for a posteriori error estimation and the reliability of these estimators; the feedback and adaptive strategies for improving the finite element solutions; and postprocessing approaches used for improving the accuracy of stresses and other important engineering data. Also, future directions for research needed to make error estimation and adaptive movement practical are identified.
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 Anlaysis of Laminated Composite Plates
1988-09-01
4.2, results depicting maximum displacement obtained using 2 x 2 integration points, 3 x 3 integration points and ’ heterosis ’ [Ref. 4] elements are...thick and thin plates. This element gives better predictions for thick plates than heterosis ele- ment, however, for thin plates, heterosis element...results showing the normalized maximum displacements are shown in Figure 4.8. The heterosis element results in about ten percent error while the
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
Architecting the Finite Element Method Pipeline for the GPU.
Fu, Zhisong; Lewis, T James; Kirby, Robert M; Whitaker, Ross T
2014-02-01
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.
North Atlantic Finite Element Ocean Modeling
NASA Astrophysics Data System (ADS)
Veluthedathekuzhiyil, Praveen
This thesis presents a modified version of the Finite Element Ocean Model (FEOM) developed at Alfred Wegener Institute for Polar and Marine Research (AWI) for the North Atlantic Ocean. A reasonable North Atlantic Ocean simulation is obtained against the observational data sets in a Control simulation (CS) where the surface boundary conditions are relaxed to a climatology. The vertical mixing in the model was tuned to represent convection in the model, also the horizontal mixing and diffusion coefficients to represent the changes in the resolution of the model’s unstructured grid. In addition, the open boundaries in the model are treated with a sponge layer where tracers are relaxed to climatology. The model is then further modified to accept the atmospheric flux forcing at the surface boundary with an added net heat flux correction and freshwater forcing from major rivers that are flowing into the North Atlantic Ocean. The impact of this boundary condition on the simulation results is then analyzed and shows many improvements albeit the drift in tracer properties around the Gulf Stream region remains as that of the CS case. However a comparison of the vertical sections at Cape Desolation and Cape Farewell with the available observational data sets shows many improvements in this simulation compared to that of the CS case. But the freshwater content in the Labrador Sea interior shows a continued drift as that of the CS case with an improvement towards the 10th model year. A detailed analysis of the boundary currents around the Labrador Sea shows the weak offshore transport of freshwater from the West Greenland Current (WGC) as one of the causes. To further improve the model and reasonably represent the boundary currents and associated sub-grid scale eddies in the model, a modified sub-grid scale parameterization based on Gent and McWilliams, (1990) is adopted. The sensitivity of using various approaches in the thickness diffusion parameter ( Kgm) for this
Superconvergence in the Generalized Finite Element Method
2005-01-01
Galerkin method for elliptic equations based on tensor products of piecewise polynomials. RAIRO Anal. Numer., 8:61– 66, 1974. [19] M. Kř́ıžek...London, 1986. [22] P. Lesaint and M. Zlámal. Superconvergence of the gradient of finite ele- ment solutions. RAIRO Anal. Numer., 13:139–166, 1979. [23] Q
Application of Mass Lumped Higher Order Finite Elements
Chen, J.; Strauss, H. R.; Jardin, S. C.; Park, W.; Sugiyama, L. E.; G. Fu; Breslau, J.
2005-11-01
There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied.
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)
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.
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.
Finite element analysis to evaluate optical mirror deformations
NASA Astrophysics Data System (ADS)
Izazaga-Pérez, R.; Aguirre-Aguirre, D.; Villalobos-Mendoza, B.
2015-10-01
In this work we describe the use of Finite Element Analysis software to simulate the deformations of an optical mirror. We use Finite Element Method software as a tool to simulate the mirror deformations assuming that it is a thin plate that can be mechanically tensed or compressed; the Finite Element Analysis give us information about the displacements of the mirror from an initial position and the tensions that remains in the surface. The information obtained by means of Finite Element Analysis can be easily exported to a coordinate system and processed in a simulation environment. Finally, a ray-tracing subroutine is used in the obtained data giving us information in terms of aberration coefficients. We present some results of the simulations describing the followed procedure.
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.
The finite element machine: An experiment in parallel processing
NASA Technical Reports Server (NTRS)
Storaasli, O. O.; Peebles, S. W.; Crockett, T. W.; Knott, J. D.; Adams, L.
1982-01-01
The finite element machine is a prototype computer designed to support parallel solutions to structural analysis problems. The hardware architecture and support software for the machine, initial solution algorithms and test applications, and preliminary results are described.
Adaptive Finite-Element Computation In Fracture Mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1995-01-01
Report discusses recent progress in use of solution-adaptive finite-element computational methods to solve two-dimensional problems in linear elastic fracture mechanics. Method also shown extensible to three-dimensional problems.
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.
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 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.
Evaluation of a hybrid, anisotropic, multilayered, quadrilateral finite element
NASA Technical Reports Server (NTRS)
Robinson, J. C.; Blackburn, C. L.
1978-01-01
A multilayered finite element with bending-extensional coupling is evaluated for: (1) buckling of general laminated plates; (2) thermal stresses of laminated plates cured at elevated temperatures; (3) displacements of a bimetallic beam; and (4) displacement and stresses of a single-cell box beam with warped cover panels. Also, displacements and stresses for flat and spherical orthotropic and anisotropic segments are compared with results from higher order plate and shell finite-element analyses.
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.
Simple bounds on limit loads by elastic finite element analysis
Mackenzie, D.; Nadarajah, C.; Shi, J.; Boyle, J.T. . Dept. of Mechanical Engineering)
1993-02-01
A method for bounding limit loads by an iterative elastic continuum finite element analysis procedure, referred to as the elastic compensation method, is proposed. A number of sample problems are considered, based on both exact solutions and finite element analysis, and it is concluded that the method may be used to obtain limit-load bounds for pressure vessel design by analysis applications with useful accuracy.
Finite element analysis to model complex mitral valve repair.
Labrosse, Michel; Mesana, Thierry; Baxter, Ian; Chan, Vincent
2016-01-01
Although finite element analysis has been used to model simple mitral repair, it has not been used to model complex repair. A virtual mitral valve model was successful in simulating normal and abnormal valve function. Models were then developed to simulate an edge-to-edge repair and repair employing quadrangular resection. Stress contour plots demonstrated increased stresses along the mitral annulus, corresponding to the annuloplasty. The role of finite element analysis in guiding clinical practice remains undetermined.
FINITE ELEMENT 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.
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.
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.
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.
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.
Nonlinear finite element analysis: An alternative formulation
NASA Technical Reports Server (NTRS)
Merazzi, S.; Stehlin, P.
1980-01-01
A geometrical nonlinear analysis based on an alternative definition of strain is presented. Expressions for strain are obtained by computing the change in length of the base vectors in the curvilinear element coordinate system. The isoparametric element formulation is assumed in the global Cartesian coordinate system. The approach is based on the minimization of the strain energy, and the resulting nonlinear equations are solved by the modified Newton method. Integration of the first and second variation of the strain energy is performed numerically in the case of two and three dimensional elements. Application is made to a simple long cantilever beam.
NASA Astrophysics Data System (ADS)
Conley, Rebecca; Delaney, Tristan J.; Jiao, Xiangmin
2016-11-01
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the Adaptive Extended Stencil Finite Element Method (AES-FEM) as a means for overcoming this dependence on element shape quality. Our method replaces the traditional basis functions with a set of generalized Lagrange polynomial (GLP) basis functions, which we construct using local weighted least-squares approximations. The method preserves the theoretical framework of FEM, and allows imposing essential boundary conditions and integrating the stiffness matrix in the same way as the classical FEM. In addition, AES-FEM can use higher-degree polynomial basis functions than the classical FEM, while virtually preserving the sparsity pattern of the stiffness matrix. We describe the formulation and implementation of AES-FEM, and analyze its consistency and stability. We present numerical experiments in both 2D and 3D for the Poison equation and a time-independent convection-diffusion equation. The numerical results demonstrate that AES-FEM is more accurate than linear FEM, is also more efficient than linear FEM in terms of error versus runtime, and enables much better stability and faster convergence of iterative solvers than linear FEM over poor-quality meshes
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.
Nonlinear Finite Element Analysis of Sandwich Composites.
1981-03-01
to the element midsurface z - z(x,y) at all points. An additional coordinate r is used to describe the distance away from the midsurface at any point...It is assumed that on the element level, the shell is shallow, so that z2 2 (56) ,y everywhere. The unit vector normal to the shell midsurface at a...relations above do not involve the orientation of the displaced midsurface normal, and, therefore, apply to arbitrarily large displacements and rotations
Recent developments in finite element analysis for transonic airfoils
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Murman, E. M.
1979-01-01
The prediction of aerodynamic forces in the transonic regime generally requires a flow field calculation to solve the governing non-linear mixed elliptic-hyperbolic partial differential equations. Finite difference techniques were developed to the point that design and analysis application are routine, and continual improvements are being made by various research groups. The principal limitation in extending finite difference methods to complex three-dimensional geometries is the construction of a suitable mesh system. Finite element techniques are attractive since their application to other problems have permitted irregular mesh elements to be employed. The purpose of this paper is to review the recent developments in the application of finite element methods to transonic flow problems and to report some recent results.
Dynamical observer for a flexible beam via finite element approximations
NASA Technical Reports Server (NTRS)
Manitius, Andre; Xia, Hong-Xing
1994-01-01
The purpose of this view-graph presentation is a computational investigation of the closed-loop output feedback control of a Euler-Bernoulli beam based on finite element approximation. The observer is part of the classical observer plus state feedback control, but it is finite-dimensional. In the theoretical work on the subject it is assumed (and sometimes proved) that increasing the number of finite elements will improve accuracy of the control. In applications, this may be difficult to achieve because of numerical problems. The main difficulty in computing the observer and simulating its work is the presence of high frequency eigenvalues in the finite-element model and poor numerical conditioning of some of the system matrices (e.g. poor observability properties) when the dimension of the approximating system increases. This work dealt with some of these difficulties.
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.
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)
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.
Radiosity algorithms using higher order finite element methods
Troutman, R.; Max, N.
1993-08-01
Many of the current radiosity algorithms create a piecewise constant approximation to the actual radiosity. Through interpolation and extrapolation, a continuous solution is obtained. An accurate solution is found by increasing the number of patches which describe the scene. This has the effect of increasing the computation time as well as the memory requirements. By using techniques found in the finite element method, we can incorporate an interpolation function directly into our form factor computation. We can then use less elements to achieve a more accurate solution. Two algorithms, derived from the finite element method, are described and analyzed.
Probabilistic finite elements for fatigue and fracture analysis
NASA Technical Reports Server (NTRS)
Belytschko, Ted; Liu, Wing Kam
1992-01-01
Attenuation is focused on the development of Probabilistic Finite Element Method (PFEM), which combines the finite element method with statistics and reliability methods, and its application to linear, nonlinear structural mechanics problems and fracture mechanics problems. The computational tool based on the Stochastic Boundary Element Method is also given for the reliability analysis of a curvilinear fatigue crack growth. The existing PFEM's have been applied to solve for two types of problems: (1) determination of the response uncertainty in terms of the means, variance and correlation coefficients; and (2) determination the probability of failure associated with prescribed limit states.
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.
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 Model Development For Aircraft Fuselage Structures
NASA Technical Reports Server (NTRS)
Buehrle, Ralph D.; Fleming, Gary A.; Pappa, Richard S.; Grosveld, Ferdinand W.
2000-01-01
The ability to extend the valid frequency range for finite element based structural dynamic predictions using detailed models of the structural components and attachment interfaces is examined for several stiffened aircraft fuselage structures. This extended dynamic prediction capability is needed for the integration of mid-frequency noise control technology. Beam, plate and solid element models of the stiffener components are evaluated. Attachment models between the stiffener and panel skin range from a line along the rivets of the physical structure to a constraint over the entire contact surface. The finite element models are validated using experimental modal analysis results.
Time domain finite element analysis of multimode microwave applicators
Dibben, D.C.; Metaxas, R.
1996-05-01
Analysis of multimode applicators in the frequency domain via the finite element technique produces a set of very ill-conditioned equations. This paper outlines a time domain finite element method (TDFE) for analyzing three dimensional microwave applicators where this ill-conditioning is avoided. Edge elements are used in order to handle sharp metal edges and to avoid spurious solutions. Analysis in the time domain allows field distributions at a range of different frequencies to be obtained with a single calculation. Lumping is investigated as a means of reducing the time taken for the calculation. The reflection coefficient is also obtained.
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.
A Successive Selection Method for finite element model updating
NASA Astrophysics Data System (ADS)
Gou, Baiyong; Zhang, Weijie; Lu, Qiuhai; Wang, Bo
2016-03-01
Finite Element (FE) model can be updated effectively and efficiently by using the Response Surface Method (RSM). However, it often involves performance trade-offs such as high computational cost for better accuracy or loss of efficiency for lots of design parameter updates. This paper proposes a Successive Selection Method (SSM), which is based on the linear Response Surface (RS) function and orthogonal design. SSM rewrites the linear RS function into a number of linear equations to adjust the Design of Experiment (DOE) after every FE calculation. SSM aims to interpret the implicit information provided by the FE analysis, to locate the Design of Experiment (DOE) points more quickly and accurately, and thereby to alleviate the computational burden. This paper introduces the SSM and its application, describes the solution steps of point selection for DOE in detail, and analyzes SSM's high efficiency and accuracy in the FE model updating. A numerical example of a simply supported beam and a practical example of a vehicle brake disc show that the SSM can provide higher speed and precision in FE model updating for engineering problems than traditional RSM.
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.
Finite element analysis for acoustic characteristics of a magnetostrictive transducer
NASA Astrophysics Data System (ADS)
Kim, Jaehwan; Jung, Eunmi
2005-12-01
This paper presents a finite element analysis for a magnetostrictive transducer by taking into account the nonlinear behavior of the magnetostrictive material and fluid interaction. A finite element formulation is derived for the coupling of magnetostrictive and elastic materials based upon a separated magnetic and displacement field calculation and a curve fitting technique of material properties. The fluid and structure coupled problem is taken into account based upon pressure and velocity potential fields formulation. Infinite wave envelope elements are introduced at an artificial boundary to deal with the infinite fluid domain. A finite element code for the analysis of a magnetostrictive transducer is developed. A magnetostrictive tonpilz transducer is taken as an example and verification for the developed program is made by comparing with a commercial code. The acoustic characteristics of the magnetostrictive tonpilz transducer are calculated in terms of radiation pattern and transmitted current response.
Footbridge between finite volumes and finite elements with applications to CFD
NASA Astrophysics Data System (ADS)
Pascal, Frédéric; Ghidaglia, Jean-Michel
2001-12-01
The aim of this paper is to introduce a new algorithm for the discretization of second-order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier-Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided. Copyright
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.
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.
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.
Effective Finite Elements for Shell Analysis.
1984-02-20
important mode of deformation , and when an element is not capable of representing inextensional bending, parasitic membrane energy is generated in many modes...of deformation . In the same manner that parasitic shear causes shear locking, this spurious membrane energy causes membrane locking. Membrane locking...dominant mode of deformation . (cont.) 20. OISTRIBUTION/AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION UNCLASSIFIEO/UNLIMITEO X SAME AS
The Mathematics of Finite Elements and Applications
1993-04-30
suitable geometrical mapping between the parametric u,v-plane and the physical xy- plane. In the u,v-plane the geometry of the elements is linear. In...the plate. For thin plates there may be a boundary layer, the existence and structure of which depends on the boundary conditions, the plate geometry ...exhibits a boundary layer except for very special data or plate geometry . The bending moment tensor and shear force vector have more pronounced boundary
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.
Stabilized plane and axisymmetric Lobatto finite element models
NASA Astrophysics Data System (ADS)
Hu, Y. C.; Sze, K. Y.; Zhou, Y. X.
2015-11-01
High order elements are renowned for their high accuracy and convergence. Among them, Lobatto spectral finite elements are commonly used in explicit dynamic analyses as their mass matrices when evaluated by the Lobatto integration rule are diagonal. While there are numerous advanced first and second order elements, advanced high order elements are rarely seen. In this paper, generic stabilization schemes are devised for the reduced integrated plane and axisymmetric elements. Static and explicit dynamic tests are considered for evaluating the relatively merits of the stabilized and conventional elements. The displacement errors of the stabilized elements are less than those of the conventional Lobatto elements. When the material is nearly incompressible, the stabilized elements are also more accurate in terms of the energy error norm. This advantage is of practical importance for bio-tissue and hydrated soil analyses.
NASA Technical Reports Server (NTRS)
Chulya, Abhisak; Mullen, Robert L.
1989-01-01
A linear finite strip plate element based on Mindlin-Reissner plate theory is developed. The analysis is suitable for both thin and thick plates. In the formulation, new transverse shear strains are introduced and assumed constant in each two-node linear strip. The element stiffness matrix is explicitly formulated for efficient computation and computer implementation. Numerical results showing the efficiency and predictive capability of the element for the analysis of plates are presented for different support and loading conditions and a wide range of thicknesses. No sign of shear locking is observed with the newly developed element.
The Constraint Method for Solid Finite Elements.
1982-11-30
Sciences 13 . NUMBER S Bolling Air Force Base, DC 20332 - -Jfi’ 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) IS. SECURITY CVASS...1- 4)Q2 (n) (’+C) Higher degree elements add edge modes, face modes and internal modes. More details are given in [12, 13 ]. triangular prism A...23) N2 (L2 , L3)(l-z) edge u (31) N2 (L3 ’ L)(1-z) nodes s u s (45). N2 (L1, L2 )z uso (56) N2 (L2, L3 )z K - 13 - nodal variable shape function u
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.
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.
Finite element methods on supercomputers - The scatter-problem
NASA Technical Reports Server (NTRS)
Loehner, R.; Morgan, K.
1985-01-01
Certain problems arise in connection with the use of supercomputers for the implementation of finite-element methods. These problems are related to the desirability of utilizing the power of the supercomputer as fully as possible for the rapid execution of the required computations, taking into account the gain in speed possible with the aid of pipelining operations. For the finite-element method, the time-consuming operations may be divided into three categories. The first two present no problems, while the third type of operation can be a reason for the inefficient performance of finite-element programs. Two possibilities for overcoming certain difficulties are proposed, giving attention to a scatter-process.
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.
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.
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
2011-01-15
An approach for efficient and accurate finite element analysis of harmonically excited soft solids using high-order spectral finite elements is presented and evaluated. The Helmholtz-type equations used to model such systems suffer from additional numerical error known as pollution when excitation frequency becomes high relative to stiffness (i.e. high wave number), which is the case, for example, for soft tissues subject to ultrasound excitations. The use of high-order polynomial elements allows for a reduction in this pollution error, but requires additional consideration to counteract Runge's phenomenon and/or poor linear system conditioning, which has led to the use of spectral element approaches. This work examines in detail the computational benefits and practical applicability of high-order spectral elements for such problems. The spectral elements examined are tensor product elements (i.e. quad or brick elements) of high-order Lagrangian polynomials with non-uniformly distributed Gauss-Lobatto-Legendre nodal points. A shear plane wave example is presented to show the dependence of the accuracy and computational expense of high-order elements on wave number. Then, a convergence study for a viscoelastic acoustic-structure interaction finite element model of an actual ultrasound driven vibroacoustic experiment is shown. The number of degrees of freedom required for a given accuracy level was found to consistently decrease with increasing element order. However, the computationally optimal element order was found to strongly depend on the wave number.
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
Life assessment of structural components using inelastic finite element analyses
NASA Technical Reports Server (NTRS)
Arya, Vinod K.; Halford, Gary R.
1993-01-01
The need for enhanced and improved performance of structural components subject to severe cyclic thermal/mechanical loadings, such as in the aerospace industry, requires development of appropriate solution technologies involving time-dependent inelastic analyses. Such analyses are mandatory to predict local stress-strain response and to assess more accurately the cyclic life time of structural components. The NASA-Lewis Research Center is cognizant of this need. As a result of concerted efforts at Lewis during the last few years, several such finite element solution technologies (in conjunction with the finite element program MARC) were developed and successfully applied to numerous uniaxial and multiaxial problems. These solution technologies, although developed for use with MARC program, are general in nature and can easily be extended for adaptation with other finite element programs such as ABAQUS, ANSYS, etc. The description and results obtained from two such inelastic finite element solution technologies are presented. The first employs a classical (non-unified) creep-plasticity model. An application of this technology is presented for a hypersonic inlet cowl-lip problem. The second of these technologies uses a unified creep-plasticity model put forth by Freed. The structural component for which this finite element solution technology is illustrated, is a cylindrical rocket engine thrust chamber. The advantages of employing a viscoplastic model for nonlinear time-dependent structural analyses are demonstrated. The life analyses for cowl-lip and cylindrical thrust chambers are presented. These analyses are conducted by using the stress-strain response of these components obtained from the corresponding finite element analyses.
Life assessment of structural components using inelastic finite element analyses
NASA Astrophysics Data System (ADS)
Arya, Vinod K.; Halford, Gary R.
1993-10-01
The need for enhanced and improved performance of structural components subject to severe cyclic thermal/mechanical loadings, such as in the aerospace industry, requires development of appropriate solution technologies involving time-dependent inelastic analyses. Such analyses are mandatory to predict local stress-strain response and to assess more accurately the cyclic life time of structural components. The NASA-Lewis Research Center is cognizant of this need. As a result of concerted efforts at Lewis during the last few years, several such finite element solution technologies (in conjunction with the finite element program MARC) were developed and successfully applied to numerous uniaxial and multiaxial problems. These solution technologies, although developed for use with MARC program, are general in nature and can easily be extended for adaptation with other finite element programs such as ABAQUS, ANSYS, etc. The description and results obtained from two such inelastic finite element solution technologies are presented. The first employs a classical (non-unified) creep-plasticity model. An application of this technology is presented for a hypersonic inlet cowl-lip problem. The second of these technologies uses a unified creep-plasticity model put forth by Freed. The structural component for which this finite element solution technology is illustrated, is a cylindrical rocket engine thrust chamber. The advantages of employing a viscoplastic model for nonlinear time-dependent structural analyses are demonstrated. The life analyses for cowl-lip and cylindrical thrust chambers are presented. These analyses are conducted by using the stress-strain response of these components obtained from the corresponding finite element analyses.
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.
Convergence of finite element approximations of large eddy motion.
Iliescu, T.; John, V.; Layton, W. J.; Mathematics and Computer Science; Otto-von-Guericke Univ.; Univ. of Pittsburgh
2002-11-01
This report considers 'numerical errors' in LES. Specifically, for one family of space filtered flow models, we show convergence of the finite element approximation of the model and give an estimate of the error. Keywords: Navier Stokes equations, large eddy simulation, finite element method I. INTRODUCTION Consider the (turbulent) flow of an incompressible fluid. One promising and common approach to the simulation of the motion of the large fluid structures is Large Eddy Simulation (LES). Various models are used in LES; a common one is to find (w, q), where w : {Omega}
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.
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.
Analysis of the Performance of Mixed Finite Element Methods.
1986-10-01
October 1986 SUMMARY The initial goal of this project is to analyze various mixed methods based on the p- and h-p versions of the finite element methods...The convergence of mixed methods depends on two factors: (1) Approximability of polynomial spaces used (2) Stability. In the past year, the question...significant portion of the research is geared towards the investigation of mixed methods based on the ’p’ and ’h-p’ versions of the finite element method
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.
Predicting Rediated Noise With Power Flow Finite Element Analysis
2007-02-01
Defence R&D Canada – Atlantic DEFENCE DÉFENSE & Predicting Rediated Noise With Power Flow Finite Element Analysis D. Brennan T.S. Koko L. Jiang J...PREDICTING RADIATED NOISE WITH POWER FLOW FINITE ELEMENT ANALYSIS D.P. Brennan T.S. Koko L. Jiang J.C. Wallace Martec Limited Martec Limited...model- or full-scale data before it is available for general use. Brennan, D.P., Koko , T.S., Jiang, L., Wallace, J.C. 2007. Predicting Radiated
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.
Differentiating a Finite Element Biodegradation Simulation Model for Optimal Control
NASA Astrophysics Data System (ADS)
Minsker, Barbara S.; Shoemaker, Christine A.
1996-01-01
An optimal control model for improving the design of in situ bioremediation of groundwater has been developed. The model uses a finite element biodegradation simulation model called Bio2D to find optimal pumping strategies. Analytical derivatives of the bioremediation finite element model are derived; these derivatives must be computed for the optimal control algorithm. The derivatives are complex and nonlinear; the bulk of the computational effort in solving the optimal control problem is required to calculate the derivatives. An overview of the optimal control and simulation model formulations is also given.
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.
Engineering and Design: Geotechnical Analysis by the Finite Element Method
2007-11-02
used it to determine stresses and movements in embank- ments, and Reyes and Deer described its application to analysis of underground openings in rock...36 Hughes, T. J. R. (1987). The Finite Element Reyes , S. F., and Deene, D. K. (1966). “Elastic Method, Linear Static and Dynamic Finite Element...SM4), 1,435-1,457. Fernando Dams During the Earthquakes of February Davis, E. H., and Poulos, H. G. (1972). “Rate of Report EERC-73-2, Berkeley, CA
Experimentally validated finite element model of electrocaloric multilayer ceramic structures
NASA Astrophysics Data System (ADS)
Smith, N. A. S.; Rokosz, M. K.; Correia, T. M.
2014-07-01
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.
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.
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.
Using Finite-Element Analysis In Estimating Reliability
NASA Technical Reports Server (NTRS)
Zaretsky, Erwin V.; August, Richard
1994-01-01
Method of estimating design survivability of structural component incorporates finite-element and probabilistic properties of materials. Involves evaluation of design parameters through direct comparisons of survivability of component expressed in terms of percentages of like components that survive at various lifetimes. Probabilistic properties of materials, given in terms of Weibull parameters, coupled with stress field computed by finite-element analysis to determine fatigue life based on initiation of cracks. Method applied to rotating disk containing bolt holes, representative of disks used in aerospace propulsion turbines. Also used in early stages of design process to optimize life-based designs, reducing testing of full-sized components needed to validate designs.
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.
NASA Technical Reports Server (NTRS)
1976-01-01
A survey of research efforts in the area of geometrically nonlinear finite elements is presented. The survey is intended to serve as a guide in the choice of nonlinear elements for specific problems, and as background to provide directions for new element developments. The elements are presented in a handbook format and are separated by type as beams, plates (or shallow shells), shells, and other elements. Within a given type, the elements are identified by the assumed displacement shapes and the forms of the nonlinear strain equations. Solution procedures are not discussed except when a particular element formulation poses special problems or capabilities in this regard. The main goal of the format is to provide quick access to a wide variety of element types, in a consistent presentation format, and to facilitate comparison and evaluation of different elements with regard to features, probable accuracy, and complexity.
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.
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
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.
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.
Finite element approach for transient analysis of multibody systems
NASA Technical Reports Server (NTRS)
Wu, Shih-Chin; Chang, Che-Wei; Housner, Jerrold M.
1992-01-01
A three-dimensional, finite element based formulation for the transient dynamics of constrained multibody systems with trusslike configurations is presented. A convected coordinate system is used to define the rigid-body motion of individual elements in the system. Deformation of each element is defined relative to its convected coordinate system. The formulation is oriented toward joint-dominated structures. Through a series of sequential transformations, the joint degree of freedom is built into the equations of motion of the element to reduce geometric constraints. Based on the derivation, a general-purpose code has been developed. Two examples are presented to illustrate the application of the code.
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.
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 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.
Finite Element Modeling of the Buckling Response of Sandwich Panels
NASA Technical Reports Server (NTRS)
Rose, Cheryl A.; Moore, David F.; Knight, Norman F., Jr.; Rankin, Charles C.
2002-01-01
A comparative study of different modeling approaches for predicting sandwich panel buckling response is described. The study considers sandwich panels with anisotropic face sheets and a very thick core. Results from conventional analytical solutions for sandwich panel overall buckling and face-sheet-wrinkling type modes are compared with solutions obtained using different finite element modeling approaches. Finite element solutions are obtained using layered shell element models, with and without transverse shear flexibility, layered shell/solid element models, with shell elements for the face sheets and solid elements for the core, and sandwich models using a recently developed specialty sandwich element. Convergence characteristics of the shell/solid and sandwich element modeling approaches with respect to in-plane and through-the-thickness discretization, are demonstrated. Results of the study indicate that the specialty sandwich element provides an accurate and effective modeling approach for predicting both overall and localized sandwich panel buckling response. Furthermore, results indicate that anisotropy of the face sheets, along with the ratio of principle elastic moduli, affect the buckling response and these effects may not be represented accurately by analytical solutions. Modeling recommendations are also provided.
A 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.
Finite element modeling of the deformation of magnetoelastic film
Barham, Matthew I.; White, Daniel A.; Steigmann, David J.
2010-09-01
Recently a new class of biocompatible elastic polymers loaded with small ferrous particles, a magnetoelastic polymer, has been developed. This engineered material is formed into a thin film using spin casting. An applied magnetic field will deform the film. The magnetic deformation of this film has many possible applications, particularly in microfluidic pumps and pressure regulators. In this paper a finite element method suitable for the transient simulation of arbitrarily shaped three-dimensional magnetoelastic polymers subjected to time-varying magnetic fields is developed. The approach is similar to that employed in finite elment magnetohydrodynamic simulations, the key difference is a more complex hyperelastic material model. In order to confirm the validity of the approach, finite element solutions for an axially symmetric thin film are compared to an analytical solution based on the membrane (infinitely thin) approximation. For this particular problem the two approaches give qualitatively similar results and converge as the film thickness approaches zero.
Dedicated finite elements for electrode thin films on quartz resonators.
Srivastava, Sonal A; Yong, Yook-Kong; Tanaka, Masako; Imai, Tsutomu
2008-08-01
The accuracy of the finite element analysis for thickness shear quartz resonators is a function of the mesh resolution; the finer the mesh resolution, the more accurate the finite element solution. A certain minimum number of elements are required in each direction for the solution to converge. This places a high demand on memory for computation, and often the available memory is insufficient. Typically the thickness of the electrode films is very small compared with the thickness of the resonator itself; as a result, electrode elements have very poor aspect ratios, and this is detrimental to the accuracy of the result. In this paper, we propose special methods to model the electrodes at the crystal interface of an AT cut crystal. This reduces the overall problem size and eliminates electrode elements having poor aspect ratios. First, experimental data are presented to demonstrate the effects of electrode film boundary conditions on the frequency-temperature curves of an AT cut plate. Finite element analysis is performed on a mesh representing the resonator, and the results are compared for testing the accuracy of the analysis itself and thus validating the results of analysis. Approximations such as lumping and Guyan reduction are then used to model the electrode thin films at the electrode interface and their results are studied. In addition, a new approximation called merging is proposed to model electrodes at the electrode interface.
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.
2-D Finite Element Cable and Box IEMP Analysis
Scivner, G.J.; Turner, C.D.
1998-12-17
A 2-D finite element code has been developed for the solution of arbitrary geometry cable SGEMP and box IEMP problems. The quasi- static electric field equations with radiation- induced charge deposition and radiation-induced conductivity y are numerically solved on a triangular mesh. Multiple regions of different dielectric materials and multiple conductors are permitted.
Finite-element analysis of an epoxy-curing process
Gartling, D K; Hickox, C E; Nunziato, J W
1983-01-01
A finite element numerical procedure is used to study the curing of an epoxy compound. The problem involves the gelation of an incompressible liquid due to an exothermic chemical reaction. Nonuniform temperature fields produce buoyancy-driven fluid motions that interact with the solidifying material. The numerical simulations provide temperature histories and the progression of the gel front that are compared with experimental data.
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.
Coupling finite element and spectral methods: First results
NASA Technical Reports Server (NTRS)
Bernardi, Christine; Debit, Naima; Maday, Yvon
1987-01-01
A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.
Design, development and use of the finite element machine
NASA Technical Reports Server (NTRS)
Adams, L. M.; Voigt, R. C.
1983-01-01
Some of the considerations that went into the design of the Finite Element Machine, a research asynchronous parallel computer are described. The present status of the system is also discussed along with some indication of the type of results that were obtained.
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.
Finite-Element Fracture Analysis of Pins and Bolts
NASA Technical Reports Server (NTRS)
Nord, K. J.
1986-01-01
Stress intensities calculated in bending and tension. Finite-element stress-analysis method gives stress-intensity estimates for surface flaws on smooth and threaded round bars. Calculations done for purely tensile and purely bending loads. Results, presented in dimensionless form, useful for determining fatigue lives of bolts and pins.
Coupling of Peridynamics and Finite Element Formulation for Multiscale Simulations
2012-10-16
state-based peridynamic method, Warren et al. [46] studied the elastic deformation and fracture of a bar. Littlewood [47] presented fragmentation of an...Journal of Solids and Structures 46 (2009) 1186-1195. [47] D. J. Littlewood , Simulation of dynamic fracture using peridynamics, finite element modeling
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.
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.
Inversion of Robin coefficient by a spectral stochastic finite element approach
Jin Bangti Zou Jun
2008-03-01
This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.
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 code development for modeling detonation of HMX composites
NASA Astrophysics Data System (ADS)
Duran, Adam V.; Sundararaghavan, Veera
2017-01-01
In this work, 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. Benchmark problems are presented for geometries in which a single HMX crystal is subjected to a shock condition.
Beyond first-order finite element schemes in micromagnetics
Kritsikis, E.; Vaysset, A.; Buda-Prejbeanu, L.D.; Toussaint, J.-C.
2014-01-01
Magnetization dynamics in ferromagnetic materials is ruled by the Landau–Lifshitz–Gilbert equation (LLG). Reliable schemes must conserve the magnetization norm, which is a nonconvex constraint, and be energy-decreasing unless there is pumping. Some of the authors previously devised a convergent finite element scheme that, by choice of an appropriate test space – the tangent plane to the magnetization – reduces to a linear problem at each time step. The scheme was however first-order in time. We claim it is not an intrinsic limitation, and the same approach can lead to efficient micromagnetic simulation. We show how the scheme order can be increased, and the nonlocal (magnetostatic) interactions be tackled in logarithmic time, by the fast multipole method or the non-uniform fast Fourier transform. Our implementation is called feeLLGood. A test-case of the National Institute of Standards and Technology is presented, then another one relevant to spin-transfer effects (the spin-torque oscillator)
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.
Beyond first-order finite element schemes in micromagnetics
NASA Astrophysics Data System (ADS)
Kritsikis, E.; Vaysset, A.; Buda-Prejbeanu, L. D.; Alouges, F.; Toussaint, J.-C.
2014-01-01
Magnetization dynamics in ferromagnetic materials is ruled by the Landau-Lifshitz-Gilbert equation (LLG). Reliable schemes must conserve the magnetization norm, which is a nonconvex constraint, and be energy-decreasing unless there is pumping. Some of the authors previously devised a convergent finite element scheme that, by choice of an appropriate test space - the tangent plane to the magnetization - reduces to a linear problem at each time step. The scheme was however first-order in time. We claim it is not an intrinsic limitation, and the same approach can lead to efficient micromagnetic simulation. We show how the scheme order can be increased, and the nonlocal (magnetostatic) interactions be tackled in logarithmic time, by the fast multipole method or the non-uniform fast Fourier transform. Our implementation is called feeLLGood. A test-case of the National Institute of Standards and Technology is presented, then another one relevant to spin-transfer effects (the spin-torque oscillator).
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.
Modelling of orbital deformation using finite-element analysis
Al-Sukhun, Jehad; Lindqvist, Christian; Kontio, Risto
2005-01-01
The purpose of this study was to develop a three-dimensional finite-element model (FEM) of the human orbit, containing the globe, to predict orbital deformation in subjects following a blunt injury. This study investigated the hypothesis that such deformation could be modelled using finite-element techniques. One patient who had CT-scan examination to the maxillofacial skeleton including the orbits, as part of her treatment, was selected for this study. A FEM of one of the orbits containing the globe was constructed, based on CT-scan images. Simulations were performed with a computer using the finite-element software NISA (EMRC, Troy, USA). The orbit was subjected to a blunt injury of a 0.5 kg missile with 30 m s−1 velocity. The FEM was then used to predict principal and shear stresses or strains at each node position. Two types of orbital deformation were predicted during different impact simulations: (i) horizontal distortion and (ii) rotational distortion. Stress values ranged from 213.4 to 363.3 MPa for the maximum principal stress, from −327.8 to −653.1 MPa for the minimum principal stress, and from 212.3 to 444.3 MPa for the maximum shear stress. This is the first finite-element study, which demonstrates different and concurrent patterns of orbital deformation in a subject following a blunt injury. Finite element modelling is a powerful and invaluable tool to study the multifaceted phenomenon of orbital deformation. PMID:16849235
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.
Adaptive implicit-explicit finite element algorithms for fluid mechanics problems
NASA Technical Reports Server (NTRS)
Tezduyar, T. E.; Liou, J.
1988-01-01
The adaptive implicit-explicit (AIE) approach is presented for the finite-element solution of various problems in computational fluid mechanics. In the AIE approach, the elements are dynamically (adaptively) arranged into differently treated groups. The differences in treatment could be based on considerations such as the cost efficiency, the type of spatial or temporal discretization employed, the choice of field equations, etc. Several numerical tests are performed to demonstrate that this approach can achieve substantial savings in CPU time and memory.
Finite element 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
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.
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 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.
Nitsche Extended Finite Element Methods for Earthquake Simulation
NASA Astrophysics Data System (ADS)
Coon, Ethan T.
Modeling earthquakes and geologically short-time-scale events on fault networks is a difficult problem with important implications for human safety and design. These problems demonstrate a. rich physical behavior, in which distributed loading localizes both spatially and temporally into earthquakes on fault systems. This localization is governed by two aspects: friction and fault geometry. Computationally, these problems provide a stern challenge for modelers --- static and dynamic equations must be solved on domains with discontinuities on complex fault systems, and frictional boundary conditions must be applied on these discontinuities. The most difficult aspect of modeling physics on complicated domains is the mesh. Most numerical methods involve meshing the geometry; nodes are placed on the discontinuities, and edges are chosen to coincide with faults. The resulting mesh is highly unstructured, making the derivation of finite difference discretizations difficult. Therefore, most models use the finite element method. Standard finite element methods place requirements on the mesh for the sake of stability, accuracy, and efficiency. The formation of a mesh which both conforms to fault geometry and satisfies these requirements is an open problem, especially for three dimensional, physically realistic fault. geometries. In addition, if the fault system evolves over the course of a dynamic simulation (i.e. in the case of growing cracks or breaking new faults), the geometry must he re-meshed at each time step. This can be expensive computationally. The fault-conforming approach is undesirable when complicated meshes are required, and impossible to implement when the geometry is evolving. Therefore, meshless and hybrid finite element methods that handle discontinuities without placing them on element boundaries are a desirable and natural way to discretize these problems. Several such methods are being actively developed for use in engineering mechanics involving crack
Mohammadi, Hadi; Bahramian, Fereshteh; Wan, Wankei
2009-11-01
Modeling soft tissue using the finite element method is one of the most challenging areas in the field of biomechanical engineering. To date, many models have been developed to describe heart valve leaflet tissue mechanics, which are accurate to some extent. Nevertheless, there is no comprehensive method to modeling soft tissue mechanics, This is because (1) the degree of anisotropy in the heart valve leaflet changes layer by layer due to a variety of collagen fiber densities and orientations that cannot be taken into account in the model and also (2) a constitutive material model fully describing the mechanical properties of the leaflet structure is not available in the literature. In this framework, we develop a new high-order element using p-type finite element formulation to create anisotropic material properties similar to those of the heart valve leaflet tissue in only one single element. This element also takes the nonlinearity of the leaflet tissue into consideration using a bilinear material model. This new element is composed a two-dimensional finite element in the principal directions of leaflet tissue and a p-type finite element in the direction of thickness. The proposed element is easy to implement, much more efficient than standard elements available in commercial finite element packages. This study is one step towards the modeling of soft tissue mechanics using a meshless finite element approach to be applied in real-time haptic feedback of soft-tissue models in virtual reality simulation.
Finite-size scaling for quantum criticality using the finite-element method.
Antillon, Edwin; Wehefritz-Kaufmann, Birgit; Kais, Sabre
2012-03-01
Finite size scaling for the Schrödinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite-element method was shown to be a powerful numerical method for ab initio electronic-structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite-element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, local density approximation, and an "exact" formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.
NASA Technical Reports Server (NTRS)
Hughes, T. J. R.; Winget, J.; Levit, I.; Tezduyar, T. E.
1983-01-01
Element-by-element approximate factorization procedures are proposed for solving the large finite element equation systems which arise in computational mechanics. A variety of techniques are compared on problems of structural mechanics, heat conduction and fluid mechanics. The results obtained suggest considerable potential for the methods described.
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.
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.
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.
Compatibility conditions of structural mechanics for finite element analysis
NASA Technical Reports Server (NTRS)
Patnaik, S. N.; Berke, L.; Gallagher, R. H.
1991-01-01
The equilibrium equations and the compatibility conditions are fundamental to the analyses of structures. However, anyone who undertakes even a cursory generic study of the compatibility conditions can discover, with little effort, that historically this facet of structural mechanics had not been adequately researched by the profession. Now the compatibility conditions (CC's) have been researched and are understood to a great extent. For finite element discretizations, the CC's are banded and can be divided into three distinct categories: (1) the interface CC's; (2) the cluster or field CC's; and (3) the external CC's. The generation of CC's requires the separating of a local region, then writing the deformation displacement relation (ddr) for the region, and finally, the eliminating of the displacements from the ddr. The procedure to generate all three types of CC's is presented and illustrated through examples of finite element models. The uniqueness of the CC's thus generated is shown.
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.
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 Analysis of Extrusion of Multifilamentary Superconductor Precursor
Peng, X.; Sumption, M.D.; Collings, E.W.
2004-06-28
The extrusion of multifilamentary superconductor precursor billets has been modeled using finite element analysis. The billet configuration was 6 around 1, with the subelement consisting of Nb rods, and the outer can or sleeve was Cu. Two general cases were investigated, those in which the re-stack rods were initially; (i) round, and (ii) hexed. A thermo-mechanical, elasto-plastic, finite-element method was used to analyze the extrusion process. In this 3D FEM model, the initial state of the billet was assumed to be absent of bonding. A typical die angle (2{alpha}=45 deg.) and a series of extrusion ratios were selected to perform the simulation and the corresponding stress and strain distributions of the two billet variants processed were compared. Based on the stress and deformation created at the rod/rod and rod/sleeve interfaces, the bonding conditions generated through the extrusion were investigated.
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.
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.
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.
Cyclic creep analysis from elastic finite-element solutions
NASA Technical Reports Server (NTRS)
Kaufman, A.; Hwang, S. Y.
1986-01-01
A uniaxial approach was developed for calculating cyclic creep and stress relaxation at the critical location of a structure subjected to cyclic thermomechanical loading. This approach was incorporated into a simplified analytical procedure for predicting the stress-strain history at a crack initiation site for life prediction purposes. An elastic finite-element solution for the problem was used as input for the simplified procedure. The creep analysis includes a self-adaptive time incrementing scheme. Cumulative creep is the sum of the initial creep, the recovery from the stress relaxation and the incremental creep. The simplified analysis was exercised for four cases involving a benchmark notched plate problem. Comparisons were made with elastic-plastic-creep solutions for these cases using the MARC nonlinear finite-element computer code.
Finite element methods for integrated aerodynamic heating analysis
NASA Technical Reports Server (NTRS)
Peraire, J.
1990-01-01
Over the past few years finite element based procedures for the solution of high speed viscous compressible flows were developed. The objective of this research is to build upon the finite element concepts which have already been demonstrated and to develop these ideas to produce a method which is applicable to the solution of large scale practical problems. The problems of interest range from three dimensional full vehicle Euler simulations to local analysis of three-dimensional viscous laminar flow. Transient Euler flow simulations involving moving bodies are also to be included. An important feature of the research is to be the coupling of the flow solution methods with thermal/structural modeling techniques to provide an integrated fluid/thermal/structural modeling capability. The progress made towards achieving these goals during the first twelve month period of the research is presented.
Pavement nondestructive evaluation using finite-element dynamic simulation
NASA Astrophysics Data System (ADS)
Uddin, W.; Hackett, R. M.
1996-11-01
This paper describes the nondestructive evaluation devices, visual distress survey and coring used to investigate jointed concrete pavement performance in northern Mississippi. 3D finite-element models were developed to simulate in-service conditions and to characterize in-situ material properties. Reasonable good agreement is found between in-situ moduli backcalculated from the dynamic analysis of falling weight deflectometer (FWD) deflections measured on selected pavements and laboratory moduli. Effects of load pulse shape, cracking, and discontinuities on the surface deflection response of pavements subjected to FWD load wee also investigated. It is shown that 3D analysis of temperature distribution and resulting thermal stresses play a significant role int he performance of concrete pavements. The study results demonstrated the extensive usefulness of the finite-element dynamic analysis and limitations of the static multilayered analysis and other pavement analysis programs which do not allow for crack modeling and dynamic analysis.
Finite Element Analysis of Electrically Excited Quartz Tuning Fork Devices
Oria, Roger; Otero, Jorge; González, Laura; Botaya, Luis; Carmona, Manuel; Puig-Vidal, Manel
2013-01-01
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. PMID:23722828
FEHM: finite element heat and mass transfer code
Zyvoloski, G.; Dash, Z.; Kelkar, S.
1988-03-01
The finite element heat and mass (FEHM) transfer code is a computer code developed to simulate geothermal and hot dry rock reservoirs. It is also applicable to natural-state studies of geothermal systems and ground-water flow. It solves the equations of heat and mass transfer for multiphase flow in porous and permeable media using the finite element method. The code also has provisions for a noncoupled tracer; that is, the tracer solutions do not affect the heat and mass transfer solutions. It can simulate two-dimensional, two-dimensional radial, or three-dimensional geometries. A summary of the equations in the model, the numerical solution procedure, and model verification and validation are provided in this report. A user's guide and sample problems are included in the appendices. 17 refs., 10 figs., 4 tabs.
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 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.
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.
Compatibility conditions of structural mechanics for finite element analysis
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Berke, Laszlo; Gallagher, Richard H.
1990-01-01
The equilibrium equations and the compatibility conditions are fundamental to the analyses of structures. However, anyone who undertakes even a cursory generic study of the compatibility conditions can discover, with little effort, that historically this facet of structural mechanics had not been adequately researched by the profession. Now the compatibility conditions (CC's) have been researched and are understood to a great extent. For finite element discretizations, the CC's are banded and can be divided into three distinct categories: (1) the interface CC's; (2) the cluster or field CC's; and (3) the external CC's. The generation of CC's requires the separating of a local region, then writing the deformation displacement relation (ddr) for the region, and finally, the eliminating of the displacements from the ddr. The procedure to generate all three types of CC's is presented and illustrated through examples of finite element models. The uniqueness of the CC's thus generated is shown.
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.
Recent finite element studies in plasticity and fracture mechanics
NASA Technical Reports Server (NTRS)
Rice, J. R.; Mcmeeking, R. M.; Parks, D. M.; Sorensen, E. P.
1979-01-01
The paper reviews recent work on fundamentals of elastic-plastic finite-element analysis and its applications to the mechanics of crack opening and growth in ductile solids. The presentation begins with a precise formulation of incremental equilibrium equations and their finite-element forms in a manner valid for deformations of arbitrary magnitude. Special features of computational procedures are outlined for accuracy in view of the near-incompressibility of elastic-plastic response. Applications to crack mechanics include the analysis of large plastic deformations at a progressively opening crack tip, the determination of J integral values and of limitations to J characterizations of the intensity of the crack tip field, and the determination of crack tip fields in stable crack growth.
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.
An hybrid finite volume finite element method for variable density incompressible flows
NASA Astrophysics Data System (ADS)
Calgaro, Caterina; Creusé, Emmanuel; Goudon, Thierry
2008-04-01
This paper is devoted to the numerical simulation of variable density incompressible flows, modeled by the Navier-Stokes system. We introduce an hybrid scheme which combines a finite volume approach for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint. The breakthrough relies on the definition of a suitable footbridge between the two methods, through the design of compatibility condition. In turn, the method is very flexible and allows to deal with unstructured meshes. Several numerical tests are performed to show the scheme capabilities. In particular, the viscous Rayleigh-Taylor instability evolution is carefully investigated.
Elastoplastic notch root strains - Measurements versus finite-element predictions
NASA Technical Reports Server (NTRS)
Tregoning, R. L.
1992-01-01
A study intended to experimentally and computationally probe the nature of the elastoplastic strain fields created by notches with various levels of constraint is presented. An interferometric strain/displacement gage is used to measure both the axial and lateral strain at the center of a machined and polished notch. The monotonic response of various notches is determined using 3D finite-element calculations.
Finite Element Modeling of Intermuscular Interactions and Myofascial Force Transmission
2001-10-25
obtained explain force differences at the distal and proximal tendons of muscles that have mechanical interaction. This is in agreement with experimental...consequence is that active force generated within one muscle may be exerted at the tendon of another muscle. Keywords- Finite element method...7]. Therefore, in vivo there is an additional route for force transmission out off the muscle, which completely bypasses the tendon of the muscle
Quality Assessment and Control of Finite Element Solutions.
1986-05-01
Extensions," to be published in the Proceedings of the NATO Advanced Study Institute on Computer Aided Optimal Design, Portugal, Springer-Verlag, June 1986...FINITE ELEMENT SOLUTIONS by I. Babuska Institute f’or Physical Science and Technology University of Maryland College Park, Maryland 2C742 and Ahmed K...PROJECT. TASK AREA & WORK UNIT NUMBERS Institute for Physical Science and Technology University of Maryland College Park, MD 20742 II. CONTROLLING OFFICE
Finite Element Modeling and Exploration of Double Hearing Protection Systems
2006-02-10
broad frequency range were determined from this method. The elastomeric rubber material was cut into small wafers of 2 to 5mm thickness. A mass was... material (being 0.1 for soft elastomeric foams), G and E are the shear and elastic moduli of the material , respectively, D is the diameter of the...and to investigate the behavior of the modeled system. The foam earplug material properties for the finite element model are required in the same shear
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.
Faster, Easier Finite-Element Modeling Of Weld Offsets
NASA Technical Reports Server (NTRS)
Hong, C. Chen; Lichwala, Bradley E.
1993-01-01
In faster, easier technique, material in weld zone fictitiously softened to negligibly low modulus of elasticity, and material considered deformed to specified offset. Displacements caused by deformation computed by analysis of static stresses and strains in fictitiously deformed material, using specified offset as displacement boundary condition. Resulting displacements added to coordinates of corresponding nodes of original (nonoffset) mathematical model of welded part. Technique used to modify large finite-element mathematical model to any desired weld offset configuration in short time.
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.
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.
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.
Finite Element Modeling of Tire-Terrain Interaction
2001-11-01
cent advancements in the contact formulations of general-purpose finite element codes (e.g. ABAQUS , HKS 1998) and increases in computer processing...are based on the models as implemented in ABAQUS (HKS 1998). Additional information on soil plasticity and critical state soil mechanics is given...snow interaction, however, the model must simulate snow deformation in a three-dimensional stress field. Initial simulations using the ABAQUS
Building Finite Element Models to Investigate Zebrafish Jaw Biomechanics
Brunt, Lucy H.; Roddy, Karen A.; Rayfield, Emily J.; Hammond, Chrissy L.
2016-01-01
Skeletal morphogenesis occurs through tightly regulated cell behaviors during development; many cell types alter their behavior in response to mechanical strain. Skeletal joints are subjected to dynamic mechanical loading. Finite element analysis (FEA) is a computational method, frequently used in engineering that can predict how a material or structure will respond to mechanical input. By dividing a whole system (in this case the zebrafish jaw skeleton) into a mesh of smaller 'finite elements', FEA can be used to calculate the mechanical response of the structure to external loads. The results can be visualized in many ways including as a 'heat map' showing the position of maximum and minimum principal strains (a positive principal strain indicates tension while a negative indicates compression. The maximum and minimum refer the largest and smallest strain). These can be used to identify which regions of the jaw and therefore which cells are likely to be under particularly high tensional or compressional loads during jaw movement and can therefore be used to identify relationships between mechanical strain and cell behavior. This protocol describes the steps to generate Finite Element models from confocal image data on the musculoskeletal system, using the zebrafish lower jaw as a practical example. The protocol leads the reader through a series of steps: 1) staining of the musculoskeletal components, 2) imaging the musculoskeletal components, 3) building a 3 dimensional (3D) surface, 4) generating a mesh of Finite Elements, 5) solving the FEA and finally 6) validating the results by comparison to real displacements seen in movements of the fish jaw. PMID:28060270
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.
Finite element analysis of a deployable space structure
NASA Technical Reports Server (NTRS)
Hutton, D. V.
1982-01-01
To assess the dynamic characteristics of a deployable space truss, a finite element model of the Scientific Applications Space Platform (SASP) truss has been formulated. The model incorporates all additional degrees of freedom associated with the pin-jointed members. Comparison of results with SPAR models of the truss show that the joints of the deployable truss significantly affect the vibrational modes of the structure only if the truss is relatively short.
Better Finite-Element Analysis of Composite Shell Structures
NASA Technical Reports Server (NTRS)
Clarke, Gregory
2007-01-01
A computer program implements a finite-element-based method of predicting the deformations of thin aerospace structures made of isotropic materials or anisotropic fiber-reinforced composite materials. The technique and corresponding software are applicable to thin shell structures in general and are particularly useful for analysis of thin beamlike members having open cross-sections (e.g. I-beams and C-channels) in which significant warping can occur.
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.
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.
GRIZ. Finite Element Results Visualization for Unstructured Grids
Dovey, D.; Spelce, T.E.; Christon, M.A.
1996-03-01
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.
Nonlinear finite element analysis of mechanical characteristics on CFRP composite pressure vessels
NASA Astrophysics Data System (ADS)
Liu, Dong-xia; Liang, Li; Li, Ming
2010-06-01
CFRP(Carbon Fibre Reinforced Plastic) composite pressure vessel was calculated using finite element program of ANSYS for their mechanical characteristics in this paper. The elastic-plastic model and elements of Solid95 were selected for aluminium alloys of gas cylinder. Also liner-elastic model and layer elements of Shell99 were adopted for carbon fibre/epoxy resin. The stress state of CFRP composite pressure vessel was calculated under different internal pressures include pre-stressing pressures, working pressures, test hydraulic pressures, minimum destructive pressures etcetera to determine the size of gas cylinder and layer parameter of carbon fibre. The mechanical characteristics CFRP composite vessel could were using to design and test of gas cylinder. Numerical results showed that finite element model and calculating method were efficient for study of CFRP gas cylinder and useful for engineering design.
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.
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.
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.
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.
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.
Finite element model for brittle fracture and fragmentation
Li, Wei; Delaney, Tristan J.; Jiao, Xiangmin; ...
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.
PC Windows finite element modeling of landfill gas flow
Mull, S.R.; Lang, R.J.; Vigil, S.A.; Cota, H.
1996-09-01
A two dimensional demonstration program, GAS, has been developed for the solution of landfill gas (LFG) flow problems on a personal computer (PC). The program combines a Windows{trademark} graphical user interface, object oriented programming (OOP) techniques, and finite element modeling (FEM) to demonstrate the practicality of performing LFG flow modeling on the PC. GAS is demonstrated on a sample LFG problem consisting of a landfill, one gas extraction well, the landfill liner, cap, and surrounding soil. Analyses of the program results are performed for successively finer grid resolutions. Element flux imbalance, execution time, and required memory are characterized as a function of grid resolution.
Acceleration of low order finite element computation with GPUs (Invited)
NASA Astrophysics Data System (ADS)
Knepley, M. G.
2010-12-01
Considerable effort has been focused on the acceleration using GPUs of high order spectral element methods and discontinuous Galerkin finite element methods. However, these methods are not universally applicable, and much of the existing FEM software base employs low order methods. In this talk, we present a formulation of FEM, using the PETSc framework from ANL, which is amenable to GPU acceleration even at very low order. In addition, using the FEniCS system for FEM, we show that the relevant kernels can be automatically generated and optimized using a symbolic manipulation system.
3-D Finite Element Analyses of the Egan Cavern Field
Klamerus, E.W.; Ehgartner, B.L.
1999-02-01
Three-dimensional finite element analyses were performed for the two gas-filled storage caverns at the Egan field, Jennings dome, Louisiana. The effects of cavern enlargement on surface subsidence, storage loss, and cavern stability were investigated. The finite element model simulated the leaching of caverns to 6 and 8 billion cubic feet (BCF) and examined their performance at various operating conditions. Operating pressures varied from 0.15 psi/ft to 0.9 psi/ft at the bottom of the lowest cemented casing. The analysis also examined the stability of the web or pillar of salt between the caverns under differential pressure loadings. The 50-year simulations were performed using JAC3D, a three dimensional finite element analysis code for nonlinear quasistatic solids. A damage criterion based on onset of dilatancy was used to evaluate cavern instability. Dilation results from the development of microfractures in salt and, hence, potential increases in permeability onset occurs well before large scale failure. The analyses predicted stable caverns throughout the 50-year period for the range of pressures investigated. Some localized salt damage was predicted near the bottom walls of the caverns if the caverns are operated at minimum pressure for long periods of time. Volumetric cavern closures over time due to creep were moderate to excessive depending on the salt creep properties and operating pressures. However, subsidence above the cavern field was small and should pose no problem, to surface facilities.
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.
Process control of large-scale finite element simulation software
Spence, P.A.; Weingarten, L.I.; Schroder, K.; Tung, D.M.; Sheaffer, D.A.
1996-02-01
We have developed a methodology for coupling large-scale numerical codes with process control algorithms. Closed-loop simulations were demonstrated using the Sandia-developed finite element thermal code TACO and the commercially available finite element thermal-mechanical code ABAQUS. This new capability enables us to use computational simulations for designing and prototyping advanced process-control systems. By testing control algorithms on simulators before building and testing hardware, enormous time and cost savings can be realized. The need for a closed-loop simulation capability was demonstrated in a detailed design study of a rapid-thermal-processing reactor under development by CVC Products Inc. Using a thermal model of the RTP system as a surrogate for the actual hardware, we were able to generate response data needed for controller design. We then evaluated the performance of both the controller design and the hardware design by using the controller to drive the finite element model. The controlled simulations provided data on wafer temperature uniformity as a function of ramp rate, temperature sensor locations, and controller gain. This information, which is critical to reactor design, cannot be obtained from typical open-loop simulations.
Massively parallel finite element computation of three dimensional flow problems
NASA Astrophysics Data System (ADS)
Tezduyar, T.; Aliabadi, S.; Behr, M.; Johnson, A.; Mittal, S.
1992-12-01
The parallel finite element computation of three-dimensional compressible, and incompressible flows, with emphasis on the space-time formulations, mesh moving schemes and implementations on the Connection Machines CM-200 and CM-5 are presented. For computation of unsteady compressible and incompressible flows involving moving boundaries and interfaces, the Deformable-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation that previously developed are employed. In this approach, the stabilized finite element formulations of the governing equations are written over the space-time domain of the problem; therefore, the deformation of the spatial domain with respect to time is taken into account automatically. This approach gives the capability to solve a large class of problems involving free surfaces, moving interfaces, and fluid-structure and fluid-particle interactions. By using special mesh moving schemes, the frequency of remeshing is minimized to reduce the projection errors involved in remeshing and also to increase the parallelization ease of the computations. The implicit equation systems arising from the finite element discretizations are solved iteratively by using the GMRES update technique with the diagonal and nodal-block-diagonal preconditioners. These formulations have all been implemented on the CM-200 and CM-5, and have been applied to several large-scale problems. The three-dimensional problems in this report were all computed on the CM-200 and CM-5.
Finite Element Modeling, Simulation, Tools, and Capabilities at Superform
NASA Astrophysics Data System (ADS)
Raman, Hari; Barnes, A. J.
2010-06-01
Over the past thirty years Superform has been a pioneer in the SPF arena, having developed a keen understanding of the process and a range of unique forming techniques to meet varying market needs. Superform’s high-profile list of customers includes Boeing, Airbus, Aston Martin, Ford, and Rolls Royce. One of the more recent additions to Superform’s technical know-how is finite element modeling and simulation. Finite element modeling is a powerful numerical technique which when applied to SPF provides a host of benefits including accurate prediction of strain levels in a part, presence of wrinkles and predicting pressure cycles optimized for time and part thickness. This paper outlines a brief history of finite element modeling applied to SPF and then reviews some of the modeling tools and techniques that Superform have applied and continue to do so to successfully superplastically form complex-shaped parts. The advantages of employing modeling at the design stage are discussed and illustrated with real-world examples.
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 methods for the nonlinear motion of flexible aircraft
NASA Astrophysics Data System (ADS)
Yang, Victor P.
Conventional strategies in aeroelasticity and flight dynamics for studying aircraft involve making broad assumptions based more on analytical or computational convenience rather than on physical reality. Typically in aeroelastic analyses, the study of the interaction between aircraft flexibility and aerodynamic forces, the aircraft or structural component in question is constrained in a way that is not representative of realistic flight conditions. In flight dynamics, the study of the maneuvering of aircraft, it is common to consider the vehicle as perfectly rigid. In both disciplines it is well known that such contrivances can produce incorrect results. To address these shortcomings, a finite element formulation is developed for analyzing the dynamics of flexible aircraft undergoing arbitrarily large rotation and translation. The formulation is derived in a set of body-attached axes, a frame of reference conducive to analyzing the motion and control of aircraft, and considers the structure as a whole. Several implementation issues are addressed and mitigated, including finite element interpolating functions, the use of eigenvectors as the basis for nonlinear deformation, inclusion of geometrically nonlinear effects in the strain energy, and enforcement of kinematic constraints. Numerical examples illustrate the capabilities of the latter two aspects, and a free-flying aeroelastic model problem demonstrates the overall potential of the proposed formulation. The development is approached in a general way so that the methodology can be applied to any structure that may be modeled by finite elements.
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.
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
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.
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.
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.
Evaluation of MHOST analysis capabilities for a plate element. [finite element modeling
NASA Technical Reports Server (NTRS)
Lee, Ho-Jun; Abumeri, Galib H.; Brown, Helen C.
1992-01-01
Results of the evaluation of the static, buckling, and free vibration analyses capabilities of MHOST for the plate elements are presented. Two large scale, general purpose finite element codes (MARC and MSC/NASTRAN) are used to validate MHOST. Comparisons of MHOST results with those from MARC and MSC/NASTRAN show good agreement and indicate that MHOST can be used with confidence to perform the aforementioned analyses using the plate element.
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.
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.
Most Efficient Quantum Thermoelectric at Finite Power Output
NASA Astrophysics Data System (ADS)
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.
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.
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.
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.
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
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.
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.
Shear deformable finite beam elements for composite box beams
NASA Astrophysics Data System (ADS)
Kim, Nam-Il; Choi, Dong-Ho
2014-04-01
The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study, numerical solutions are presented and compared with the results obtained by other researchers and the detailed three-dimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress-strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated. [Figure not available: see fulltext.
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.
Discontinuous finite element method for vector radiative transfer
NASA Astrophysics Data System (ADS)
Wang, Cun-Hai; Yi, Hong-Liang; Tan, He-Ping
2017-03-01
The discontinuous finite element method (DFEM) is applied to solve the vector radiative transfer in participating media. The derivation in a discrete form of the vector radiation governing equations is presented, in which the angular space is discretized by the discrete-ordinates approach with a local refined modification, and the spatial domain is discretized into finite non-overlapped discontinuous elements. The elements in the whole solution domain are connected by modelling the boundary numerical flux between adjacent elements, which makes the DFEM numerically stable for solving radiative transfer equations. Several various problems of vector radiative transfer are tested to verify the performance of the developed DFEM, including vector radiative transfer in a one-dimensional parallel slab containing a Mie/Rayleigh/strong forward scattering medium and a two-dimensional square medium. The fact that DFEM results agree very well with the benchmark solutions in published references shows that the developed DFEM in this paper is accurate and effective for solving vector radiative transfer problems.
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.
Finite element modeling of the higher harmonic controlled OH-6A helicopter airframe
NASA Technical Reports Server (NTRS)
Ferg, Douglas; Toossi, Mostafa
1990-01-01
An MSC/NASTRAN finite element model of the higher harmonic control configured OH-6A helicopter fuselage was developed. This finite element model was verified by performing various model checkouts and correlation with results from a ground vibration test.
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)
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.
Multiphase poroelastic finite element models for soft tissue structures
Simon, B.R.
1992-12-01
During the last two decades, biological structures with soft tissue components have been modeled using poroelastic or mixture-based constitutive laws, i.e., the material is viewed as a deformable (porous) solid matrix that is saturated by mobile tissue fluid. These structures exhibit a highly nonlinear, history-dependent material behavior; undergo finite strains; and may swell or shrink when tissue ionic concentrations are altered. Give the geometric and material complexity of soft tissue structures and that they are subjected to complicated initial and boundary conditions, finite element models (FEMs) have been very useful for quantitative structural analyses. This paper surveys recent applications of poroelastic and mixture-based theories and the associated FEMs for the study of the biomechanics of soft tissues, and indicates future directions for research in this area. Equivalent finite-strain poroelastic and mixture continuum biomechanical models are presented. Special attention is given to the identification of material properties using a porohyperelastic constitutive law ans a total Lagrangian view for the formulation. The associated FEMs are then formulated to include this porohyperelastic material response and finite strains. Extensions of the theory are suggested in order to include inherent viscoelasticity, transport phenomena, and swelling in soft tissue structures. A number of biomechanical research areas are identified, and possible applications of the porohyperelastic and mixture-based FEMs are suggested. 62 refs., 11 figs., 3 tabs.
Multiphase poroelastic finite element models for soft tissue structure
Simon, B.R.
1992-06-01
During the last two decades. biological structures with soft tissue components have been modeled using poroelastic or mixture-based constitutive laws, i.e., the material is viewed as a deformable (porous) solid matrix that is saturated by mobile tissue fluid. These structures exhibit a highly nonlinear, history-dependent material behavior; undergo finite strains-, and may swell or shrink when tissue ionic concentrations are altered. Given the geometric and material complexity of soft tissue structures and that they are subjected to complicated initial and boundary conditions, finite element models (FEMs) have been very useful for quantitative structural analyses. This paper surveys recent applications of poroelastic and mixture-based theories and the associated FEMs for the study of the biomechanics of soft tissues, and indicates future directions for research in this area. Equivalent finite-strain poroelastic and mixture continuum biomechanical models are presented. Special attention is given to the identification of material properties using a porohyperelastic constitutive law and a total Lagrangian view for the formulation. The associated FEMS are then formulated to include this porohyperelastic material response and finite strains. Extensions of the theory are suggested in order to include inherent viscoelasticity, transport phenomena, and swelling in soft tissue structures. A number of biomechanical research areas are identified, and possible applications of the porohyperelastic and mixture-based FEMs are suggested.
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.
Probabilistic finite elements for fracture and fatigue analysis
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.; Lawrence, M.; Besterfield, G. H.
1989-01-01
The fusion of the probabilistic finite element method (PFEM) and reliability analysis for probabilistic fracture mechanics (PFM) is presented. A comprehensive method for determining the probability of fatigue failure for curved crack growth was developed. The criterion for failure or performance function is stated as: the fatigue life of a component must exceed the service life of the component; otherwise failure will occur. An enriched element that has the near-crack-tip singular strain field embedded in the element is used to formulate the equilibrium equation and solve for the stress intensity factors at the crack-tip. Performance and accuracy of the method is demonstrated on a classical mode 1 fatigue problem.
3D finite element simulations of high velocity projectile impact
NASA Astrophysics Data System (ADS)
Ožbolt, Joško; İrhan, Barış; Ruta, Daniela
2015-09-01
An explicit three-dimensional (3D) finite element (FE) code is developed for the simulation of high velocity impact and fragmentation events. The rate sensitive microplane material model, which accounts for large deformations and rate effects, is used as a constitutive law. In the code large deformation frictional contact is treated by forward incremental Lagrange multiplier method. To handle highly distorted and damaged elements the approach based on the element deletion is employed. The code is then used in 3D FE simulations of high velocity projectile impact. The results of the numerical simulations are evaluated and compared with experimental results. It is shown that it realistically predicts failure mode and exit velocities for different geometries of plain concrete slab. Moreover, the importance of some relevant parameters, such as contact friction, rate sensitivity, bulk viscosity and deletion criteria are addressed.
Magnetic Elements at Finite Temperature and Large Deviation Theory
NASA Astrophysics Data System (ADS)
Kohn, R. V.; Reznikoff, M. G.; vanden-Eijnden, E.
2005-08-01
We investigate thermally activated phenomena in micromagnetics using large deviation theory and concepts from stochastic resonance. We give a natural mathematical definition of finite-temperature astroids, finite-temperature hysteresis loops, etc. Generically, these objects emerge when the (generalized) Arrhenius timescale governing the thermally activated barrier crossing event of magnetic switching matches the timescale at which the magnetic element is pulsed or ramped by an external field; in the special and physically relevant case of multiple-pulse experiments, on the other hand, short-time switching can lead to non-Arrhenius behavior. We show how large deviation theory can be used to explain some properties of the astroids, like their shrinking and sharpening as the number of applied pulses is increased. We also investigate the influence of the dynamics, in particular the relative importance of the gyromagnetic and the damping terms. Finally, we discuss some issues and open questions regarding spatially nonuniform magnetization.
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.
A triangular thin shell finite element: Nonlinear analysis. [structural analysis
NASA Technical Reports Server (NTRS)
Thomas, G. R.; Gallagher, R. H.
1975-01-01
Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.
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.
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.
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.
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)
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.
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.
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 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.
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.
Linear and nonlinear finite element analysis of laminated composite structures at high temperatures
NASA Astrophysics Data System (ADS)
Wilt, Thomas Edmund
The use of composite materials in aerospace applications, particularly engine components, is becoming more prevalent due to the materials high strength, yet low weight. In addition to thermomechanical deformation response, life prediction and damage modeling analysis is also required to assess the component's service life. These complex and computationally intensive analyses require the development of simple, efficient and robust finite element analysis capabilities. A simple robust finite element which can effectively model the multi-layer composite material is developed. This will include thermal gradient capabilities necessary for a complete thermomechanical analysis. In order to integrate the numerically stiff rate dependent viscoplastic equations, efficient, stable numerical algorithms are developed. In addition, consistent viscoplastic/plastic tangent matrices will also be formulated. The finite element is formulated based upon a generalized mixed variational principle with independently assumed displacements and layer number independent strains. A unique scheme utilizing nodal temperatures is used to model a linear thermal gradient through the thickness of the composite. The numerical integration algorithms are formulated in the context of a fully implicit backward Euler scheme. The consistent tangent matrices arise directly from the formulation. The multi-layer composite finite element demonstrates good performance in terms of static displacement and stress predictions, and dynamic response. Also, the element appears to be relatively insensitive to mesh distortions. The robustness and efficiency of the fully implicit integration algorithms is effectively demonstrated in the numerical results. That is, large time steps and a significant reduction in global iterations, as a direct result of utilizing the consistent tangent matrices, is shown.
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.
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.
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).
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.
A viscoelastic higher-order beam finite element
NASA Technical Reports Server (NTRS)
Johnson, Arthur R.; Tressler, Alexander
1996-01-01
A viscoelastic internal variable constitutive theory is applied to a higher-order elastic beam theory and finite element formulation. The behavior of the viscous material in the beam is approximately modeled as a Maxwell solid. The finite element formulation requires additional sets of nodal variables for each relaxation time constant needed by the Maxwell solid. Recent developments in modeling viscoelastic material behavior with strain variables that are conjugate to the elastic strain measures are combined with advances in modeling through-the-thickness stresses and strains in thick beams. The result is a viscous thick-beam finite element that possesses superior characteristics for transient analysis since its nodal viscous forces are not linearly dependent an the nodal velocities, which is the case when damping matrices are used. Instead, the nodal viscous forces are directly dependent on the material's relaxation spectrum and the history of the nodal variables through a differential form of the constitutive law for a Maxwell solid. The thick beam quasistatic analysis is explored herein as a first step towards developing more complex viscoelastic models for thick plates and shells, and for dynamic analyses. The internal variable constitutive theory is derived directly from the Boltzmann superposition theorem. The mechanical strains and the conjugate internal strains are shown to be related through a system of first-order, ordinary differential equations. The total time-dependent stress is the superposition of its elastic and viscous components. Equations of motion for the solid are derived from the virtual work principle using the total time-dependent stress. Numerical examples for the problems of relaxation, creep, and cyclic creep are carried out for a beam made from an orthotropic Maxwell solid.
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 panels with surface cracks
NASA Astrophysics Data System (ADS)
Glushkov, S. V.; Skvortsov, Yu. V.; Perov, S. N.; Chernyakin, S. A.
2017-01-01
With the aid of the ANSYS® FEM-packet, solution is offered with regard to the fracture mechanics for cylindrical panels with blind surface cracks of semi-elliptical shape. Obtained was distribution of the J-integral lengthwise the defect front, the values of which are calculated via the integration technique by area. Application of the cellular mesh with major number finite elements lengthwise the front line enables detection of the boundary effect near the crack front penetration to the surface. Offered are universal equations for estimating values of the stress intensify factor in the front characteristic points.
Nonlinear structural finite element model updating and uncertainty quantification
NASA Astrophysics Data System (ADS)
Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.
2015-04-01
This paper presents a framework for nonlinear finite element (FE) model updating, in which state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with the maximum likelihood estimation method (MLE) to estimate time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure. The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem. A proof-of-concept example, consisting of a cantilever steel column representing a bridge pier, is provided to verify the proposed nonlinear FE model updating framework.
Finite Element Simulation of Diametral Strength Test of Hydroxyapatite
Ozturk, Fahrettin; Toros, Serkan; Evis, Zafer
2011-01-17
In this study, the diametral strength test of sintered hydroxyapatite was simulated by the finite element software, ABAQUS/Standard. Stress distributions on diametral test sample were determined. The effect of sintering temperature on stress distribution of hydroxyapatite was studied. It was concluded that high sintering temperatures did not reduce the stress on hydroxyapatite. It had a negative effect on stress distribution of hydroxyapatite after 1300 deg. C. In addition to the porosity, other factors (sintering temperature, presence of phases and the degree of crystallinity) affect the diametral strength of the hydroxyapatite.
Modeling of coal stockpiles using a finite elements method
Ozdeniz, A.H.; Sensogut, C.
2008-07-01
In the case of coal stockpiles finding suitable environmental conditions, spontaneous combustion phenomenon will be unavoidable. In this study, an industrial-sized stockpile having a shape of triangle prism was constituted in a coal stockyard of Western Lignite Corporation (WLC), Turkey. The parameters of time, humidity and temperature of air, atmospheric pressure, velocity and direction of wind values that are effective on coal stockpile were measured in a continuous manner. These experimental works were transferred into a computer media in order to obtain similar outcomes by carrying out 2-dimensional analysis of the stockpile with Finite Elements Method (FEM). The performed experimental studies and obtained results were then compared.
Methods and framework for visualizing higher-order finite elements.
Schroeder, William J; Bertel, François; Malaterre, Mathieu; Thompson, David; Pébay, Philippe P; O'Bara, Robert; Tendulkar, Saurabh
2006-01-01
The finite element method is an important, widely used numerical technique for solving partial differential equations. This technique utilizes basis functions for approximating the geometry and the variation of the solution field over finite regions, or elements, of the domain. These basis functions are generally formed by combinations of polynomials. In the past, the polynomial order of the basis has been low-typically of linear and quadratic order. However, in recent years so-called p and hp methods have been developed, which may elevate the order of the basis to arbitrary levels with the aim of accelerating the convergence of the numerical solution. The increasing complexity of numerical basis functions poses a significant challenge to visualization systems. In the past, such systems have been loosely coupled to simulation packages, exchanging data via file transfer, and internally reimplementing the basis functions in order to perform interpolation and implement visualization algorithms. However, as the basis functions become more complex and, in some cases, proprietary in nature, it becomes increasingly difficult if not impossible to reimplement them within the visualization system. Further, most visualization systems typically process linear primitives, in part to take advantage of graphics hardware and, in part, due to the inherent simplicity of the resulting algorithms. Thus, visualization of higher-order finite elements requires tessellating the basis to produce data compatible with existing visualization systems. In this paper, we describe adaptive methods that automatically tessellate complex finite element basis functions using a flexible and extensible software framework. These methods employ a recursive, edge-based subdivision algorithm driven by a set of error metrics including geometric error, solution error, and error in image space. Further, we describe advanced pretessellation techniques that guarantees capture of the critical points of the
[Finite Element Analysis of Intravascular Stent Based on ANSYS Software].
Shi, Gengqiang; Song, Xiaobing
2015-10-01
This paper adopted UG8.0 to bulid the stent and blood vessel models. The models were then imported into the finite element analysis software ANSYS. The simulation results of ANSYS software showed that after endothelial stent implantation, the velocity of the blood was slow and the fluctuation of velocity was small, which meant the flow was relatively stable. When blood flowed through the endothelial stent, the pressure gradually became smaller, and the range of the pressure was not wide. The endothelial shear stress basically unchanged. In general, it can be concluded that the endothelial stents have little impact on the flow of blood and can fully realize its function.
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.
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.
Galvanic Corrosion in Silicon Microsystems: Finite Element Simulation Tool Development
2009-08-28
marine vessels, but has previously not been miniaturized for microscale corrosion diagnostics. The resistive probes consist of four‐point “ Van der Pauw ” structures...used for boundary conditions in a finite element model for four‐point “ Van der Pauw ” resistive probe microscale devices. The modeling
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
Finite element modeling and experimentation of bone drilling forces
NASA Astrophysics Data System (ADS)
Lughmani, W. A.; Bouazza-Marouf, K.; Ashcroft, I.
2013-07-01
Bone drilling is an essential part of many orthopaedic surgery procedures, including those for internal fixation and for attaching prosthetics. Estimation and control of bone drilling forces are critical to prevent drill breakthrough, excessive heat generation, and mechanical damage to the bone. This paper presents a 3D finite element (FE) model for prediction of thrust forces experienced during bone drilling. The model incorporates the dynamic characteristics involved in the process along with the accurate geometrical considerations. The average critical thrust forces and torques obtained using FE analysis, for set of machining parameters are found to be in good agreement with the experimental results.
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 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.
The sensitivity method in finite element model updating: A tutorial
NASA Astrophysics Data System (ADS)
Mottershead, John E.; Link, Michael; Friswell, Michael I.
2011-10-01
The sensitivity method is probably the most successful of the many approaches to the problem of updating finite element models of engineering structures based on vibration test data. It has been applied successfully to large-scale industrial problems and proprietary codes are available based on the techniques explained in simple terms in this article. A basic introduction to the most important procedures of computational model updating is provided, including tutorial examples to reinforce the reader's understanding and a large scale model updating example of a helicopter airframe.
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.
Recent experiences using finite-element-based structural optimization
NASA Technical Reports Server (NTRS)
Paul, B. K.; Mcconnell, J. C.; Love, Mike H.
1989-01-01
Structural optimization has been available to the structural analysis community as a tool for many years. The popular use of displacement method finite-element techniques to analyze linearly elastic structures has resulted in an ability to calculate the weight and constraint gradients inexpensively for numerical optimization of structures. Here, recent experiences in the investigation and use of structural optimization are discussed. In particular, experience with the commercially available ADS/NASOPT code is addressed. An overview of the ADS/NASOPT procedure and how it was implemented is given. Two example problems are also discussed.
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 model for phase-change recording
NASA Astrophysics Data System (ADS)
Brusche, J. H.; Segal, A.; Urbach, H. P.
2005-04-01
The finite-element method is applied to model phase-change recording in a grooved recording stack. A rigorous model for the scattering of a three-dimensional focused spot by a one-dimensional periodic grating is used to determine the absorbed light in a three-dimensional region inside the phase-change layer. The optical model is combined with a three-dimensional thermal model to compute the temperature distribution. Land and groove recording and polarization dependence are studied, and the model is applied to the Blu-ray Disc.
Analysis of anelastic flow and numerical treatment via finite elements
Martinez, M.J.
1994-05-01
In this report, we reconsider the various approximations made to the full equations of motion and energy transport for treating low-speed flows with significant temperature induced property variations. This entails assessment of the development of so-called anelastic for low-Mach number flows outside the range of validity of the Boussinesq equations. An integral part of this assessment is the development of a finite element-based numerical scheme for obtaining approximate numerical solutions to this class of problems. Several formulations were attempted and are compared.
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.
Space-time formulation for finite element modeling of superconductors
Ashworth, Stephen P; Grilli, Francesco; Sirois, Frederic; Laforest, Marc
2008-01-01
In this paper we present a new model for computing the current density and field distributions in superconductors by means of a periodic space-time formulation for finite elements (FE). By considering a space dimension as time, we can use a static model to solve a time dependent problem. This allows overcoming one of the major problems of FE modeling of superconductors: the length of simulations, even for relatively simple cases. We present our first results and compare them to those obtained with a 'standard' time-dependent method and with analytical solutions.
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.
On finite element stress analysis of spur gears
NASA Technical Reports Server (NTRS)
Chang, S. H.; Huston, R. L.
1982-01-01
Spur gear stress analysis results are presented for a variety of loading conditions, support conditions, root radii, and rime thicknesses. These results are obtained using the SAP-IV finite element code. The maximum stresses, occurring at the root surface, substantially increase with decreasing rim thickness for partially supported rims (that is, with loose fitting hubs). For fully supported rims (that is, with tight fitting hubs), the root surface stresses slightly decrease with decreasing rim thickness. The fillet radius has a significant effect upon the maximum stesses at the root surface. These stresses increase with decreasing fillet radius. Finally, the fillet radius has little effect upon the internal root section stresses.
Edge-based finite element method for shallow water equations
NASA Astrophysics Data System (ADS)
Ribeiro, F. L. B.; Galeão, A. C.; Landau, L.
2001-07-01
This paper describes an edge-based implementation of the generalized residual minimum (GMRES) solver for the fully coupled solution of non-linear systems arising from finite element discretization of shallow water equations (SWEs). The gain in terms of memory, floating point operations and indirect addressing is quantified for semi-discrete and space-time analyses. Stabilized formulations, including Petrov-Galerkin models and discontinuity-capturing operators, are also discussed for both types of discretization. Results illustrating the quality of the stabilized solutions and the advantages of using the edge-based approach are presented at the end of the paper. Copyright
Lamb mode conversion at edges. A hybrid boundary element-finite-element solution.
Galán, José M; Abascal, Ramón
2005-04-01
Two general and flexible numerical techniques based on the finite-element and boundary element methods developed by the authors in a previous paper are applied to study Lamb wave propagation in multilayered plates and Lamb mode conversion at free edges for frequencies beyond the first cutoff frequency. Both techniques are supported by a meshing criterion which guarantees the accuracy of the results when a condition is fulfilled. A finite-element formulation is directly applicable to study Lamb wave propagation and reflection by simple obstacles such as a flat edge. In order to tackle Lamb wave diffraction problems by defects with more complex geometries, a hybrid boundary element-finite-element formulation is used. This technique provides a major improvement with respect to the only previous boundary element application on Lamb waves: the connecting boundary might be placed as close to the reflector as desired, reducing greatly the requirement on mesh size. Two main application problems on practical metallic plates are studied and compared with reported numerical, theoretical, and experimental results: (1) Lamb wave propagation in degraded titanium diffusion bonds, and (2) Lamb mode conversion at inclined or perpendicular free edges of steel plates for frequencies beyond the first cutoff frequency.
Finite element modeling of bending failure at HPFRC plates using 2-dimensional isoparametric element
NASA Astrophysics Data System (ADS)
Krisnamurti, Soehardjono, Agoes; Zacoeb, Achfas; Wibowo, Ari
2017-03-01
This paper presents finite element modeling of the bending failure on High-Performance Fiber-Reinforced Concrete (HPFRC) plate subjected to monotonic loading. Plate analysis is commonly used approach to plate bending theory. The results are sometimes less in accordance with laboratory tests. The aim of this study is to analyze the behavior of bending until failure which occurred at HPFRC plate, and load-displacement relation caused by variations of plate depth. Analysis carried out by 2-D isoparametric finite element method, with the approach of plane strain condition. The analysis was done by decreasing the stiffness of plate elements layer gradually in accordance with the development of maximum stress in the element due to workload. The rigidity of plate elements layer will be close to zero when maximum stress reaches a maximum tensile strength of HPFRC. Validation testing program conducted on plate specimen with a span length of 600 mm, width 300 mm and thickness variation of 40 mm, 50 mm and 60 mm. HPFRC compressive strength is 93.045 MPa, and splitting tensile strength is 6.018 MPa. Test performed with four points bending pattern at a distance of 1/3 span length. Comparison between the calculation by the finite element method and laboratory testing showed very consistent results.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Clark, J. H.; Kalinowski, A. J.; Wagner, C. A.
1983-01-01
An analysis is given using finite element techniques which addresses the propagaton of a uniform incident pressure wave through a finite diameter axisymmetric tapered plate immersed in a fluid. The approach utilized in developing a finite element solution to this problem is based upon a technique for axisymmetric fluid structure interaction problems. The problem addressed is that of a 10 inch diameter axisymmetric fixed plate totally immersed in a fluid. The plate increases in thickness from approximately 0.01 inches thick at the center to 0.421 inches thick at a radius of 5 inches. Against each face of the tapered plate a cylindrical fluid volume was represented extending five wavelengths off the plate in the axial direction. The outer boundary of the fluid and plate regions were represented as a rigid encasement cylinder as was nearly the case in the physical problem. The primary objective of the analysis is to determine the form of the transmitted pressure distribution on the downstream side of the plate.
Finite-element model of the active organ of Corti
Elliott, Stephen J.; Baumgart, Johannes
2016-01-01
The cochlear amplifier that provides our hearing with its extraordinary sensitivity and selectivity is thought to be the result of an active biomechanical process within the sensory auditory organ, the organ of Corti. Although imaging techniques are developing rapidly, it is not currently possible, in a fully active cochlea, to obtain detailed measurements of the motion of individual elements within a cross section of the organ of Corti. This motion is predicted using a two-dimensional finite-element model. The various solid components are modelled using elastic elements, the outer hair cells (OHCs) as piezoelectric elements and the perilymph and endolymph as viscous and nearly incompressible fluid elements. The model is validated by comparison with existing measurements of the motions within the passive organ of Corti, calculated when it is driven either acoustically, by the fluid pressure or electrically, by excitation of the OHCs. The transverse basilar membrane (BM) motion and the shearing motion between the tectorial membrane and the reticular lamina are calculated for these two excitation modes. The fully active response of the BM to acoustic excitation is predicted using a linear superposition of the calculated responses and an assumed frequency response for the OHC feedback. PMID:26888950
A finite element musculoskeletal model of the shoulder mechanism.
van der Helm, F C
1994-05-01
The finite element method described in this study provides an easy method to simulate the kinetics of multibody mechanisms. It is used in order to develop a musculoskeletal model of the shoulder mechanism. Each relevant morphological structure has been represented by an appropriate element. For the shoulder mechanism two special-purpose elements have been developed: a SURFACE element representing the scapulothoracic gliding plane and a CURVED-TRUSS element to represent muscles which are wrapped around bony contours. The model contains four bones, three joints, three extracapsular ligaments, the scapulothoracic gliding plane and 20 muscles and muscle parts. In the model, input variables are the positions of the shoulder girdle and humerus and the external load on the humerus. Output variables are muscles forces subject to an optimization procedure in which the mechanical stability of the glenohumeral joint is one of the constraints. Four different optimization criteria are compared. For 12 muscles, surface EMG is used to verify the model. Since the optimum muscle length and force-length relationship are unknown, and since maximal EMG amplitude is length dependent, verification is only possible in a qualitative sense. Nevertheless, it is concluded that a detailed model of the shoulder mechanism has been developed which provides good insight into the function of morphological structures.
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.