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.
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.
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:
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.
Higher-Order Finite Elements for Computing Thermal Radiation
NASA Technical Reports Server (NTRS)
Gould, Dana C.
2004-01-01
Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higher-order finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times. One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications. In the basic form of the RSE method, each finite element selected for use in computing radiative heat transfer is considered to be a parent element and is divided into sub-elements for the purpose of solving the surface-to-surface radiation-exchange problem. The sub-elements are then treated as classical finite elements; that is, they are assumed to be isothermal, and their view factors and absorbed heat fluxes are calculated accordingly. The heat fluxes absorbed by the sub-elements are then transferred back to the parent element to obtain a radiative heat flux that varies spatially across the parent element. Variants of the RSE method involve the use of polynomials to interpolate and/or extrapolate to approximate spatial variations of physical quantities. The other variant of the finite-element method is termed the integration method (IM). Unlike in the RSE methods, the parent finite elements are not subdivided into smaller elements, and neither isothermality nor other
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.
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
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.
High-order finite element methods for cardiac monodomain simulations.
Vincent, Kevin P; Gonzales, Matthew J; Gillette, Andrew K; Villongco, Christopher T; Pezzuto, Simone; Omens, Jeffrey H; Holst, Michael J; McCulloch, Andrew D
2015-01-01
Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori. PMID:26300783
High-order finite element methods for cardiac monodomain simulations
Vincent, Kevin P.; Gonzales, Matthew J.; Gillette, Andrew K.; Villongco, Christopher T.; Pezzuto, Simone; Omens, Jeffrey H.; Holst, Michael J.; McCulloch, Andrew D.
2015-01-01
Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori. PMID:26300783
Higher order finite element analysis of thick composite laminates
NASA Technical Reports Server (NTRS)
Goering, J.; Kim, H. J.
1992-01-01
A higher order, sub-parametric, laminated, 3D solid finite element was used for the analysis of very thick laminated composite plates. The geometry of this element is defined by four nodes in the X-Y plane which define a prism of material through the thickness of the laminate. There are twenty-four degrees of freedom at each node; translations at the upper and lower surfaces of the laminate in each of the three coordinate directions, and the derivatives of these translations with respect to each coordinate. This choice of degrees of freedom leads to displacement and strain compatibility at the corners. Stacking sequence effects are accounted for by explicitly integrating the strain energy density through the thickness of the element. The laminated solid element was combined with a gap-contact element to analyze thick laminated composite lugs loaded through flexible pins. The resulting model accounts for pin bending effects that produce non-uniform bearing stresses through the thickness of the lug. A thick composite lug experimental test program was performed, and provided data that was used to validate the analytical model. Two lug geometries and three stacking sequences were tested.
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.
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)
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).
Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order Finite Elements
NASA Technical Reports Server (NTRS)
Gould, Dana C.
2000-01-01
This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version finite elements. The work was motivated by a thermal analysis of a High Speed Civil Transport (HSCT) wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining the finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Traditional methods for calculating surface-to-surface radiation are based on assumptions that are not appropriate for p-version finite elements. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version finite elements. In the first method, higher-order elements are divided into a number of sub-elements. Traditional methods are used to determine radiation heat flux along each sub-element and then mapped back to the parent element. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order element. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-element method. Comparison to results from traditional finite elements shows that significant reduction in the number of elements in the mesh is possible using higher-order (p-version) finite elements.
Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
NASA Astrophysics Data System (ADS)
Motamarri, P.; Nowak, M. R.; Leiter, K.; Knap, J.; Gavini, V.
2013-11-01
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss-Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100-200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn-Sham DFT problem. Our studies suggest that staggering computational savings-of the order of 1000-fold-relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn-Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using
Higher-order adaptive finite-element methods for Kohn–Sham density functional theory
Motamarri, P.; Nowak, M.R.; Leiter, K.; Knap, J.; Gavini, V.
2013-11-15
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688
NASA Astrophysics Data System (ADS)
Wang, Yajun; Liu, Yang; Li, Hong; Wang, Jinfeng
2016-03-01
In this article, a Galerkin finite element method combined with second-order time discrete scheme for finding the numerical solution of nonlinear time fractional Cable equation is studied and discussed. At time t_{k-α/2} , a second-order two step scheme with α -parameter is proposed to approximate the first-order derivative, and a weighted discrete scheme covering second-order approximation is used to approximate the Riemann-Liouville fractional derivative, where the approximate order is higher than the obtained results by the L1-approximation with order (2-α in the existing references. For the spatial direction, Galerkin finite element approximation is presented. The stability of scheme and the rate of convergence in L^2 -norm with O(Δ t^2+(1+Δ t^{-α})h^{m+1}) are derived in detail. Moreover, some numerical tests are shown to support our theoretical results.
NASA Technical Reports Server (NTRS)
Narayanaswami, R.
1973-01-01
A new higher order triangular plate-bending finite element is presented which possesses high accuracy for practical mesh subdivisions and which uses only translations and rotations as grid point degrees of freedom. The element has 18 degrees of freedom, the transverse displacement and two rotations at the vertices and mid-side grid points of the triangle. The transverse displacement within the element is approximated by a quintic polynomial; the bending strains thus vary cubically within the element. Transverse shear flexibility is taken into account in the stiffness formulation. Two examples of static and dynamic analysis are included to show the behavior of the element.
NASA Astrophysics Data System (ADS)
Carrera, E.; Miglioretti, F.; Petrolo, M.
2011-11-01
This paper compares and evaluates various plate finite elements to analyse the static response of thick and thin plates subjected to different loading and boundary conditions. Plate elements are based on different assumptions for the displacement distribution along the thickness direction. Classical (Kirchhoff and Reissner-Mindlin), refined (Reddy and Kant), and other higher-order displacement fields are implemented up to fourth-order expansion. The Unified Formulation UF by the first author is used to derive finite element matrices in terms of fundamental nuclei which consist of 3×3 arrays. The MITC4 shear-locking free type formulation is used for the FE approximation. Accuracy of a given plate element is established in terms of the error vs. thickness-to-length parameter. A significant number of finite elements for plates are implemented and compared using displacement and stress variables for various plate problems. Reduced models that are able to detect the 3D solution are built and a Best Plate Diagram (BPD) is introduced to give guidelines for the construction of plate theories based on a given accuracy and number of terms. It is concluded that the UF is a valuable tool to establish, for a given plate problem, the most accurate FE able to furnish results within a certain accuracy range. This allows us to obtain guidelines and recommendations in building refined elements in the bending analysis of plates for various geometries, loadings, and boundary conditions.
High order curvilinear finite elements for elastic–plastic Lagrangian dynamics
Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.
2014-01-15
This paper presents a high-order finite element method for calculating elastic–plastic flow on moving curvilinear meshes and is an extension of our general high-order curvilinear finite element approach for solving the Euler equations of gas dynamics in a Lagrangian frame [1,2]. In order to handle transition to plastic flow, we formulate the stress–strain relation in rate (or incremental) form and augment our semi-discrete equations for Lagrangian hydrodynamics with an additional evolution equation for the deviatoric stress which is valid for arbitrary order spatial discretizations of the kinematic and thermodynamic variables. The semi-discrete equation for the deviatoric stress rate is developed for 2D planar, 2D axisymmetric and full 3D geometries. For each case, the strain rate is approximated via a collocation method at zone quadrature points while the deviatoric stress is approximated using an L{sub 2} projection onto the thermodynamic basis. We apply high order, energy conserving, explicit time stepping methods to the semi-discrete equations to develop the fully discrete method. We conclude with numerical results from an extensive series of verification tests that demonstrate several practical advantages of using high-order finite elements for elastic–plastic flow.
Efficient simulation of cardiac electrical propagation using high order finite elements
NASA Astrophysics Data System (ADS)
Arthurs, Christopher J.; Bishop, Martin J.; Kay, David
2012-05-01
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.
A suitable low-order, eight-node tetrahedral finite element for solids
Key, S.W.; Heinstein, M.S.; Stone, C.M.; Mello, F.J.; Blanford, M.L.; Budge, K.G.
1998-03-01
To use the all-tetrahedral mesh generation existing today, the authors have explored the creation of a computationally efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping, and the element`s performance in applications are presented. In particular they examine the eight-node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hour-glass modes. In this regard it bears similarities to the eight-node, mean-quadrature hexahedral finite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, constant-strain tetrahedral finite element is a suitable replacement for the eight-node hexahedral finite element in those cases where mesh generation requires an inordinate amount of user intervention and direction to obtain acceptable mesh properties.
NASA Astrophysics Data System (ADS)
Banaś, Krzysztof; Krużel, Filip; Bielański, Jan
2016-06-01
The paper presents investigations on the implementation and performance of the finite element numerical integration algorithm for first order approximations and three processor architectures, popular in scientific computing, classical CPU, Intel Xeon Phi and NVIDIA Kepler GPU. A unifying programming model and portable OpenCL implementation is considered for all architectures. Variations of the algorithm due to different problems solved and different element types are investigated and several optimizations aimed at proper optimization and mapping of the algorithm to computer architectures are demonstrated. Performance models of execution are developed for different processors and tested in practical experiments. The results show the varying levels of performance for different architectures, but indicate that the algorithm can be effectively ported to all of them. The general conclusion is that the finite element numerical integration can achieve sufficient performance on different multi- and many-core architectures and should not become a performance bottleneck for finite element simulation codes. Specific observations lead to practical advises on how to optimize the kernels and what performance can be expected for the tested architectures.
Free-Vibration Analysis of Rotating Beams by a Variable-Order Finite-Element Method
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Rutkowski, Michael J.
1981-01-01
The free vibration of rotating beams is analyzed by means of a finite-element method of variable order. This method entails displacement functions that are a complete power series of a variable number of terms. The terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and, additionally, displacements at certain points within the element. The displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series. Numerical results are presented for uniform beams with zero and nonzero hub radii, tapered beams, and a nonuniform beam with discontinuities. Since the present method reduces to a conventional beam finite-element method for a cubic displacement function, the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom. Indeed, essentially exact eigenvalues and eigenvectors are obtained with this technique, which is far more rapidly convergent than other approaches in the literature.
Surya Mohan, P.; Tarvainen, Tanja; Schweiger, Martin; Pulkkinen, Aki; Arridge, Simon R.
2011-08-10
Highlights: {yields} We developed a variable order global basis scheme to solve light transport in 3D. {yields} Based on finite elements, the method can be applied to a wide class of geometries. {yields} It is computationally cheap when compared to the fixed order scheme. {yields} Comparisons with local basis method and other models demonstrate its accuracy. {yields} Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P{sub N} approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P{sub N} approximation is compared against Monte Carlo simulations and other state-of-the-art methods.
Modeling fragmentation with new high order finite element technology and node splitting
NASA Astrophysics Data System (ADS)
Olovsson, Lars; Limido, Jérôme; Lacome, Jean-Luc; Grønsund Hanssen, Arve; Petit, Jacques
2015-09-01
The modeling of fragmentation has historically been linked to the weapons industry where the main goal is to optimize a bomb or to design effective blast shields. Numerical modeling of fragmentation from dynamic loading has traditionally been modeled by legacy finite element solvers that rely on element erosion to model material failure. However this method results in the removal of too much material. This is not realistic as retaining the mass of the structure is critical to modeling the event correctly. We propose a new approach implemented in the IMPETUS AFEA SOLVER® based on the following: New High Order Finite Elements that can easily deal with very large deformations; Stochastic distribution of initial damage that allows for a non homogeneous distribution of fragments; and a Node Splitting Algorithm that allows for material fracture without element erosion that is mesh independent. The approach is evaluated for various materials and scenarios: -Titanium ring electromagnetic compression; Hard steel Taylor bar impact, Fused silica Taylor bar impact, Steel cylinder explosion, The results obtained from the simulations are representative of the failure mechanisms observed experimentally. The main benefit of this approach is good energy conservation (no loss of mass) and numerical robustness even in complex situations.
NASA Astrophysics Data System (ADS)
Suri, Manil
1990-01-01
We investigate the use of higher-order mixed methods for second-order elliptic problems by establishing refined stability and convergence estimates which take into account both the mesh size h and polynomial degree p. Our estimates yield asymptotic convergence rates for the p- and h - p-versions of the finite element method. They also describe more accurately than previously proved estimates the increased rate of convergence expected when the h-version is used with higher-order polynomials. For our analysis, we choose the Raviart-Thomas and the Brezzi-Douglas-Marini elements and establish optimal rates of convergence in both h and p (up to arbitrary \\varepsilon > 0 ).
A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models
Guerra, Jorge E.; Ullrich, Paul A.
2016-06-01
Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy alsomore » eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Lastly, our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.« less
A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models
NASA Astrophysics Data System (ADS)
Guerra, Jorge E.; Ullrich, Paul A.
2016-06-01
Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.
A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models
Guerra, Jorge E.; Ullrich, Paul A.
2016-06-01
Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy alsomore » eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.« less
MGGHAT: Elliptic PDE software with adaptive refinement, multigrid and high order finite elements
NASA Technical Reports Server (NTRS)
Mitchell, William F.
1993-01-01
MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations in two dimensional polygonal domains. This program is now available for public use. It is a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Window display, and a posteriori through output files that can be used as GNUPLOT input. In this paper, we describe the methods used by MGGHAT, define the problem domain for which it is appropriate, illustrate use of the program, show numerical and graphical examples, and explain how to obtain the software.
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. PMID:19773193
A high order accurate finite element algorithm for high Reynolds number flow prediction
NASA Technical Reports Server (NTRS)
Baker, A. J.
1978-01-01
A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.
Application of High Order Acoustic Finite Elements to Transmission Losses and Enclosure Problems
NASA Technical Reports Server (NTRS)
Craggs, A.; Stevenson, G.
1985-01-01
A family of acoustic finite elements was developed based on C continuity (acoustic pressure being the nodal variable) and the no-flow condition. The family include triangular, quadrilateral and hexahedral isoparametric elements with linear quadratic and cubic variation in modelling and distortion. Of greatest use in problems with irregular boundaries are the cubic isoparametric elements: the 32 node hexahedral element for three-dimensional systems; and the twelve node quadrilateral and ten node triangular elements for two-dimensional/axisymmetric applications. These elements were applied to problems involving cavity resonances, transmission loss in silencers and the study of end effects, using a Floating Point Systems 164 attached array processor accessed through an Amdahl 5860 mainframe. The elements are presently being used to study the end effects associated with duct terminations within finite enclosures. The transmission losses with various silencers and sidebranches in ducts is also being studied using the same elements.
NASA Astrophysics Data System (ADS)
Bause, Markus
2008-02-01
In this work we study mixed finite element approximations of Richards' equation for simulating variably saturated subsurface flow and simultaneous reactive solute transport. Whereas higher order schemes have proved their ability to approximate reliably reactive solute transport (cf., e.g. [Bause M, Knabner P. Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping. Comput Visual Sci 7;2004:61-78]), the Raviart- Thomas mixed finite element method ( RT0) with a first order accurate flux approximation is popular for computing the underlying water flow field (cf. [Bause M, Knabner P. Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods. Adv Water Resour 27;2004:565-581, Farthing MW, Kees CE, Miller CT. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv Water Resour 26;2003:373-394, Starke G. Least-squares mixed finite element solution of variably saturated subsurface flow problems. SIAM J Sci Comput 21;2000:1869-1885, Younes A, Mosé R, Ackerer P, Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J Comp Phys 149;1999:148-167, Woodward CS, Dawson CN. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media. SIAM J Numer Anal 37;2000:701-724]). This combination might be non-optimal. Higher order techniques could increase the accuracy of the flow field calculation and thereby improve the prediction of the solute transport. Here, we analyse the application of the Brezzi- Douglas- Marini element ( BDM1) with a second order accurate flux approximation to elliptic, parabolic and degenerate problems whose solutions lack the regularity that is assumed in optimal order error analyses. For the flow field calculation a superiority of the BDM1 approach to the RT0 one is
Leng, Wei; Ju, Lili; Gunzburger, Max; Price, Stephen; Ringler, Todd
2012-01-01
The numerical modeling of glacier and ice sheet evolution is a subject of growing interest, in part because of the potential for models to inform estimates of global sea level change. This paper focuses on the development of a numerical model that determines the velocity and pressure fields within an ice sheet. Our numerical model features a high-fidelity mathematical model involving the nonlinear Stokes system and combinations of no-sliding and sliding basal boundary conditions, high-order accurate finite element discretizations based on variable resolution grids, and highly scalable parallel solution strategies, all of which contribute to a numerical model that can achieve accurate velocity and pressure approximations in a highly efficient manner. We demonstrate the accuracy and efficiency of our model by analytical solution tests, established ice sheet benchmark experiments, and comparisons with other well-established ice sheet models.
NASA Technical Reports Server (NTRS)
Maliassov, Serguei
1996-01-01
In this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second order elliptic problems in 3D domains with a piecewise constant diffusion coefficient. Using a substructuring idea and a block Gauss elimination, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix does not depend on either the mesh step size or the jump of the coefficient. Finally, numerical experiments are presented to illustrate the theory being developed.
A High-order Eulerian-Lagrangian Finite Element Method for Coupled Electro-mechanical Systems
NASA Astrophysics Data System (ADS)
Brandstetter, Gerd
The main focus of this work is on the development of a high-order Eulerian-Lagrangian finite element method for the simulation of electro-mechanical systems. The coupled problem is solved by a staggered scheme, where the mechanical motion is discretized by standard Lagrangian finite elements, and the electrical field is solved on a fixed Eulerian grid with embedded boundary conditions. Traditional Lagrangian-Lagrangian or arbitrary Lagrangian-Eulerian (ALE) methods encounter deficiencies, for example, when dealing with mesh distortion due to large deformations, or topology changes due to contacting bodies. The presented Eulerian-Lagrangian approach addresses these issues in a natural way. Within this context we develop a high-order immersed boundary discontinuous-Galerkin (IB-DG) method, which is shown to be necessary for (i) the accurate representation of the electrical gradient along nonlinear boundary features such as singular corners, and (ii) to achieve full convergence during the iterative global solution. We develop an implicit scheme based on the mid-point rule, as well as an explicit scheme based on the centered-difference method, with the incorporation of energy conserving, frictionless contact algorithms for an elastic-to-rigid-surface contact. The performance of the proposed method is assessed for several benchmark tests: the electro-static force vector around a singular corner, the quasi-static pull-in of an electro-mechanically actuated switch, the excitation of a carbon nanotube at resonance, and the cyclic impact simulation of a micro-electro-mechanical resonant-switch. We report improved accuracy for the high-order method as compared to low-order methods, and linear convergence in the iterative solution of the staggered scheme. Additionally, we investigate a Newton-Krylov shooting scheme in order to directly find cyclic steady states of electro-mechanical devices excited at resonance-- as opposed to a naive time-stepping from zero initial
Maginot, P. G.; Ragusa, J. C.; Morel, J. E.
2013-07-01
We examine several possible methods of mass matrix lumping for discontinuous finite element discrete ordinates transport using a Lagrange interpolatory polynomial trial space. Though positive outflow angular flux is guaranteed with traditional mass matrix lumping in a purely absorbing 1-D slab cell for the linear discontinuous approximation, we show that when used with higher degree interpolatory polynomial trial spaces, traditional lumping does yield strictly positive outflows and does not increase in accuracy with an increase in trial space polynomial degree. As an alternative, we examine methods which are 'self-lumping'. Self-lumping methods yield diagonal mass matrices by using numerical quadrature restricted to the Lagrange interpolatory points. Using equally-spaced interpolatory points, self-lumping is achieved through the use of closed Newton-Cotes formulas, resulting in strictly positive outflows in pure absorbers for odd power polynomials in 1-D slab geometry. By changing interpolatory points from the traditional equally-spaced points to the quadrature points of the Gauss-Legendre or Lobatto-Gauss-Legendre quadratures, it is possible to generate solution representations with a diagonal mass matrix and a strictly positive outflow for any degree polynomial solution representation in a pure absorber medium in 1-D slab geometry. Further, there is no inherent limit to local truncation error order of accuracy when using interpolatory points that correspond to the quadrature points of high order accuracy numerical quadrature schemes. (authors)
Candel, A.; Kabel, A.; Lee, L.; Li, Z.; Limborg, C.; Ng, C.; Prudencio, E.; Schussman, G.; Uplenchwar, R.; Ko, K.; /SLAC
2009-06-19
Over the past years, SLAC's Advanced Computations Department (ACD), under SciDAC sponsorship, has developed a suite of 3D (2D) parallel higher-order finite element (FE) codes, T3P (T2P) and Pic3P (Pic2P), aimed at accurate, large-scale simulation of wakefields and particle-field interactions in radio-frequency (RF) cavities of complex shape. The codes are built on the FE infrastructure that supports SLAC's frequency domain codes, Omega3P and S3P, to utilize conformal tetrahedral (triangular)meshes, higher-order basis functions and quadratic geometry approximation. For time integration, they adopt an unconditionally stable implicit scheme. Pic3P (Pic2P) extends T3P (T2P) to treat charged-particle dynamics self-consistently using the PIC (particle-in-cell) approach, the first such implementation on a conformal, unstructured grid using Whitney basis functions. Examples from applications to the International Linear Collider (ILC), Positron Electron Project-II (PEP-II), Linac Coherent Light Source (LCLS) and other accelerators will be presented to compare the accuracy and computational efficiency of these codes versus their counterparts using structured grids.
A unidirectional approach for d-dimensional finite element methods for higher order on sparse grids
Bungartz, H.J.
1996-12-31
In the last years, sparse grids have turned out to be a very interesting approach for the efficient iterative numerical solution of elliptic boundary value problems. In comparison to standard (full grid) discretization schemes, the number of grid points can be reduced significantly from O(N{sup d}) to O(N(log{sub 2}(N)){sup d-1}) in the d-dimensional case, whereas the accuracy of the approximation to the finite element solution is only slightly deteriorated: For piecewise d-linear basis functions, e. g., an accuracy of the order O(N{sup - 2}(log{sub 2}(N)){sup d-1}) with respect to the L{sub 2}-norm and of the order O(N{sup -1}) with respect to the energy norm has been shown. Furthermore, regular sparse grids can be extended in a very simple and natural manner to adaptive ones, which makes the hierarchical sparse grid concept applicable to problems that require adaptive grid refinement, too. An approach is presented for the Laplacian on a uinit domain in this paper.
Estimation of Sonic Fatigue by Reduced-Order Finite Element Based Analyses
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Przekop, Adam
2006-01-01
A computationally efficient, reduced-order method is presented for prediction of sonic fatigue of structures exhibiting geometrically nonlinear response. A procedure to determine the nonlinear modal stiffness using commercial finite element codes allows the coupled nonlinear equations of motion in physical degrees of freedom to be transformed to a smaller coupled system of equations in modal coordinates. The nonlinear modal system is first solved using a computationally light equivalent linearization solution to determine if the structure responds to the applied loading in a nonlinear fashion. If so, a higher fidelity numerical simulation in modal coordinates is undertaken to more accurately determine the nonlinear response. Comparisons of displacement and stress response obtained from the reduced-order analyses are made with results obtained from numerical simulation in physical degrees-of-freedom. Fatigue life predictions from nonlinear modal and physical simulations are made using the rainflow cycle counting method in a linear cumulative damage analysis. Results computed for a simple beam structure under a random acoustic loading demonstrate the effectiveness of the approach and compare favorably with results obtained from the solution in physical degrees-of-freedom.
An assessment of four-noded plate finite elements based on a generalized third-order theory
NASA Technical Reports Server (NTRS)
Averill, R. C.; Reddy, J. N.
1992-01-01
Plate finite elements based on the generalized third-order theory of Reddy and the first-order shear deformation theory are analyzed and compared on the basis of thick and thin plate modeling behavior, distortion sensitivity, overall accuracy, reliability, and efficiency. In particular, several four-noded Reddy-type elements and the nine-noded Lagrangian and heterosis (Mindlin-type) plate elements are analyzed to assess their behavior in bending, vibration, and stability of isotropic and laminated composite plates. A four-noded Reddy-type element is identified which is free of all spurious stiffness and zero energy modes, computationally efficient, and suitable for use in any general-purpose finite element program.
Structural damage detection using higher-order finite elements and a scanning laser vibrometer
NASA Astrophysics Data System (ADS)
Jin, Si
In contrast to conventional non-destructive evaluation methods, dynamics-based damage detection methods are capable of rapid integrity evaluation of large structures and have received considerable attention from aerospace, mechanical, and civil engineering communities in recent years. However, the identifiable damage size using dynamics-based methods is determined by the number of sensors used, level of measurement noise, accuracy of structural models, and signal processing techniques. In this thesis we study dynamics of structures with damage and then derive and experimentally verify new model-independent structural damage detection methods that can locate small damage to structures. To find sensitive damage detection parameters we develop a higher-order beam element that enforces the continuity of displacements, slopes, bending moments, and shear forces at all nodes, and a higher-order rectangular plate element that enforces the continuity of displacements, slopes, and bending and twisting moments at all nodes. These two elements are used to study the dynamics of beams and plates. Results show that high-order spatial derivatives of high-frequency modes are important sensitive parameters that can locate small structural damage. Unfortunately the most powerful and popular structural modeling technique, the finite element method, is not accurate in predicting high-frequency responses. Hence, a model-independent method using dynamic responses obtained from high density measurements is concluded to be the best approach. To increase measurement density and reduce noise a Polytec PI PSV-200 scanning laser vibrometer is used to provide non-contact, dense, and accurate measurements of structural vibration velocities. To avoid the use of structural models and to extract sensitive detection parameters from experimental data, a brand-new structural damage detection method named BED (Boundary-Effect Detection) is developed for pinpointing damage locations using Operational
Rieben, R; White, D; Rodrigue, G
2004-01-13
In this paper we motivate the use of a novel high order time domain vector finite element method that is of arbitrary order accuracy in space and up to 5th order accurate in time; and in particular, we apply it to the case of photonic band-gap (PBG) structures. Such structures have been extensively studied in the literature with several practical applications; in particular, for the low loss transmission of electromagnetic energy around sharp 90 degree bends [1]. Typically, such structures are simulated via a numerical solution of Maxwell's equations either in the frequency domain or directly in the time domain over a computational grid. The majority of numerical simulations performed for such structures make use of the widely popular finite difference time domain (FDTD) method [2], where the time dependent electric and magnetic fields are discretized over a ''dual'' grid to second order accuracy in space and time. However, such methods do not generalize to unstructured, non-orthogonal grids or to higher order spatial discretization schemes. To simulate more complicated structures with curved boundaries, such as the structure of [3], a cell based finite element method with curvilinear elements is preferred over standard stair-stepped Cartesian meshes; and to more efficiently reduce the effects of numerical dispersion, a higher order method is highly desirable. In this paper, the high order basis functions of [5] are used in conjunction with the high order energy conserving symplectic time integration algorithms of [6] resulting in a high order, fully mimetic, mixed vector finite element method.
Finite element computational fluid mechanics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
NASA Astrophysics Data System (ADS)
Hasegawa, Kei; Geller, Robert J.; Hirabayashi, Nobuyasu
2016-02-01
We present a theoretical analysis of the error of synthetic seismograms computed by higher-order finite element methods (ho-FEMs). We show the existence of a previously unrecognized type of error due to degenerate coupling between waves with the same frequency but different wavenumbers. These results are confirmed by simple numerical experiments using the spectral element method (SEM) as an example of ho-FEMs. Errors of the type found by this study may occur generally in applications of ho-FEMs.
NASA Astrophysics Data System (ADS)
Brunner, Fabian; Radu, Florin A.; Bause, Markus; Knabner, Peter
2012-01-01
We present a mass conservative finite element approach of second order accuracy for the numerical approximation of reactive solute transport in porous media modeled by a coupled system of advection-diffusion-reaction equations. The lowest order Brezzi-Douglas-Marini ( BDM1) mixed finite element method is used. A modification based on the hybrid form of the approach is suggested for the discretization of the advective term. It is demonstrated numerically that this leads to optimal second order convergence of the flux variable. The modification improves the convergence behavior of the classical BDM1 scheme, which is known to be suboptimal of first order accuracy only for advection-diffusion problems; cf. [8]. Moreover, the new scheme shows more robustness for high Péclet numbers than the classical approach. A comparison with the Raviart-Thomas element ( RT1) of second order accuracy for the approximation of the flux variable is also presented. For the case of strongly advection-dominated problems we propose a full upwind scheme. Various numerical studies, including also a nonlinear test problem, are presented to illustrate the numerical performance properties of the considered numerical methods.
Quevedo González, Fernando José; Nuño, Natalia
2016-06-01
The mechanical properties of well-ordered porous materials are related to their geometrical parameters at the mesoscale. Finite element (FE) analysis is a powerful tool to design well-ordered porous materials by analysing the mechanical behaviour. However, FE models are often computationally expensive. This article aims to develop a cost-effective FE model to simulate well-ordered porous metallic materials for orthopaedic applications. Solid and beam FE modelling approaches are compared, using finite size and infinite media models considering cubic unit cell geometry. The model is then applied to compare two unit cell geometries: cubic and diamond. Models having finite size provide similar results than the infinite media model approach for large sample sizes. In addition, these finite size models also capture the influence of the boundary conditions on the mechanical response for small sample sizes. The beam FE modelling approach showed little computational cost and similar results to the solid FE modelling approach. Diamond unit cell geometry appeared to be more suitable for orthopaedic applications than the cubic unit cell geometry. PMID:26260268
Yaqi Wang; Jean C. Ragusa
2011-10-01
Diffusion synthetic acceleration (DSA) schemes compatible with adaptive mesh refinement (AMR) grids are derived for the SN transport equations discretized using high-order discontinuous finite elements. These schemes are directly obtained from the discretized transport equations by assuming a linear dependence in angle of the angular flux along with an exact Fick's law and, therefore, are categorized as partially consistent. These schemes are akin to the symmetric interior penalty technique applied to elliptic problems and are all based on a second-order discontinuous finite element discretization of a diffusion equation (as opposed to a mixed or P1 formulation). Therefore, they only have the scalar flux as unknowns. A Fourier analysis has been carried out to determine the convergence properties of the three proposed DSA schemes for various cell optical thicknesses and aspect ratios. Out of the three DSA schemes derived, the modified interior penalty (MIP) scheme is stable and effective for realistic problems, even with distorted elements, but loses effectiveness for some highly heterogeneous configurations. The MIP scheme is also symmetric positive definite and can be solved efficiently with a preconditioned conjugate gradient method. Its implementation in an AMR SN transport code has been performed for both source iteration and GMRes-based transport solves, with polynomial orders up to 4. Numerical results are provided and show good agreement with the Fourier analysis results. Results on AMR grids demonstrate that the cost of DSA can be kept low on locally refined meshes.
Automatic finite element generators
NASA Technical Reports Server (NTRS)
Wang, P. S.
1984-01-01
The design and implementation of a software system for generating finite elements and related computations are described. Exact symbolic computational techniques are employed to derive strain-displacement matrices and element stiffness matrices. Methods for dealing with the excessive growth of symbolic expressions are discussed. Automatic FORTRAN code generation is described with emphasis on improving the efficiency of the resultant code.
NASA Astrophysics Data System (ADS)
Moortgat, J.; Firoozabadi, A.
2013-12-01
Most problems of interest in hydrogeology and subsurface energy resources involve complex heterogeneous geological formations. Such domains are most naturally represented in numerical reservoir simulations by unstructured computational grids. Finite element methods are a natural choice to describe fluid flow on unstructured meshes, because the governing equations can be readily discretized for any grid-element geometry. In this work, we consider the challenging problem of fully compositional three-phase flow in 3D unstructured grids, discretized by tetrahedra, prisms, or hexahedra, and compare to simulations on 3D structured grids. We employ a combination of mixed hybrid finite element methods to solve for the pressure and flux fields in a fractional flow formulation, and higher-order discontinuous Galerkin methods for the mass transport equations. These methods are well suited to simulate flow in heterogeneous and fractured reservoirs, because they provide a globally continuous pressure and flux field, while allowing for sharp discontinuities in the phase properties, such as compositions and saturations. The increased accuracy from using higher-order methods improves the modeling of highly non-linear flow, such as gravitational and viscous fingering. We present several numerical examples to study convergence rates and the (lack of) sensitivity to gridding/mesh orientation, and mesh quality. These examples consider gravity depletion, water and gas injection in oil saturated subsurface reservoirs with species exchange between up to three fluid phases. The examples demonstrate the wide applicability of our chosen finite element methods in the study of challenging multiphase flow problems in porous, geometrically complex, subsurface media.
NASA Astrophysics Data System (ADS)
Li, Zhi-Hui; Ma, Qiang; Cui, Junzhi
2016-06-01
The new second-order two-scale (SOTS) finite element algorithm is developed for the dynamic thermo-mechanical coupling problems in axisymmetric and spherical symmetric structures made of composite materials. The axisymmetric structure considered is periodic in both radial and axial directions and homogeneous in circumferential direction. The spherical symmetric structure is only periodic in radial direction. The dynamic thermo-mechanical coupling model is presented and the equivalent compact form is derived. Then, the cell problems, effective material coefficients and the homogenized thermo-mechanical coupling problem are obtained successively by the second-order asymptotic expansion of the temperature increment and displacement. The homogenized material obtained is manifested with the anisotropic property in the circumferential direction. The explicit expressions of the homogenized coefficients in the plane axisymmetric and spherical symmetric cases are given and both the derivation of the analytical solutions of the cell functions and the quasi-static thermoelasticity problems are discussed. Based on the SOTS method, the corresponding finite-element procedure is presented and the unconditionally stable implicit algorithm is established. Some numerical examples are solved and the mutual interaction between the temperature and displacement field is studied under the condition of structural vibration. The computational results demonstrate that the second-order asymptotic analysis finite-element algorithm is feasible and effective in simulating and predicting the dynamic thermo-mechanical behaviors of the composite materials with small periodic configurations in axisymmetric and spherical symmetric structures. This may provide a vital computational tool for analyzing composite material internal temperature distribution and structural deformation induced by the dynamic thermo-mechanical coupling response under strong aerothermodynamic environment.
NASA Astrophysics Data System (ADS)
Eldred, Christopher; Dubos, Thomas; Kritsikis, Evaggelos
2016-04-01
There has been a great deal of work in the past decade on the development of mimetic and conservative numerical schemes for atmospheric dynamical cores using Hamiltonian methods, such as Dynamico (Dubos et. al 2015). This model conserves mass, potential vorticity and total energy; and posses properties such as a curl-free pressure gradient that does not produce spurious vorticity. Unfortunately, the underlying finite-difference discretization scheme used in Dynamico has been shown to be inconsistent on general grids. An alternative scheme based on mimetic finite elements has been developed for the rotating shallow water equations that solves these accuracy issues but retains the desirable mimetic and conservation properties. Preliminary results on the extension of this scheme to the hydrostatic primitive equations are shown. The compatible 2D finite elements spaces are extended to compatible 3D spaces using tensor products, in a way that preserves their properties. It is shown that use of the same prognostic variables as Dynamico combined with a Lorenz staggering leads to a relatively simple formulation that allows conservation of total energy along with high-order accuracy.
Rieben, R N; Rodrigue, G H; White, D A
2004-03-09
We present a mixed vector finite element method for solving the time dependent coupled Ampere and Faraday laws of Maxwell's equations on unstructured hexahedral grids that employs high order discretization in both space and time. The method is of arbitrary order accuracy in space and up to 5th order accurate in time, making it well suited for electrically large problems where grid anisotropy and numerical dispersion have plagued other methods. In addition, the method correctly models both the jump discontinuities and the divergence-free properties of the electric and magnetic fields, is charge and energy conserving, conditionally stable, and free of spurious modes. Several computational experiments are performed to demonstrate the accuracy, efficiency and benefits of the method.
High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster
Komatitsch, Dimitri; Erlebacher, Gordon; Goeddeke, Dominik; Michea, David
2010-10-01
We implement a high-order finite-element application, which performs the numerical simulation of seismic wave propagation resulting for instance from earthquakes at the scale of a continent or from active seismic acquisition experiments in the oil industry, on a large cluster of NVIDIA Tesla graphics cards using the CUDA programming environment and non-blocking message passing based on MPI. Contrary to many finite-element implementations, ours is implemented successfully in single precision, maximizing the performance of current generation GPUs. We discuss the implementation and optimization of the code and compare it to an existing very optimized implementation in C language and MPI on a classical cluster of CPU nodes. We use mesh coloring to efficiently handle summation operations over degrees of freedom on an unstructured mesh, and non-blocking MPI messages in order to overlap the communications across the network and the data transfer to and from the device via PCIe with calculations on the GPU. We perform a number of numerical tests to validate the single-precision CUDA and MPI implementation and assess its accuracy. We then analyze performance measurements and depending on how the problem is mapped to the reference CPU cluster, we obtain a speedup of 20x or 12x.
Efficient finite element modeling of laminated composite plates based on higher-order theory
NASA Technical Reports Server (NTRS)
Tessler, Alexander; Saether, Erik
1990-01-01
A simple and efficient three-node plate bending element for the analysis of composite laminates is developed from a variational principle. The deformations due to transverse shear and transverse normal effects are accounted for, allowing accurate predictions in the range of thin to thick plates. The methodology incorporates C(exp 0) and C(exp 1) continuous displacement approximations and yields accurate ply-by-ply predictions of all displacement, strain, and stress variables.
NASA Technical Reports Server (NTRS)
Liu, C.; Liu, Z.
1993-01-01
The high order finite difference and multigrid methods have been successfully applied to direct numerical simulation (DNS) for flow transition in 3D channels and 3D boundary layers with 2D and 3D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semicoarsening multigrid method associated with line distributive relaxation scheme, and a new treatment of the outflow boundary condition, which needs only a very short buffer domain to damp all wave reflection, are developed. These approaches make the multigrid DNS code very accurate and efficient. This makes us not only able to do spatial DNS for the 3D channel and flat plate at low computational costs, but also able to do spatial DNS for transition in the 3D boundary layer with 3D single and multiple roughness elements. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments.
Rieben, R N
2004-07-20
The goal of this dissertation is twofold. The first part concerns the development of a numerical method for solving Maxwell's equations on unstructured hexahedral grids that employs both high order spatial and high order temporal discretizations. The second part involves the use of this method as a computational tool to perform high fidelity simulations of various electromagnetic devices such as optical transmission lines and photonic crystal structures to yield a level of accuracy that has previously been computationally cost prohibitive. This work is based on the initial research of Daniel White who developed a provably stable, charge and energy conserving method for solving Maxwell's equations in the time domain that is second order accurate in both space and time. The research presented here has involved the generalization of this procedure to higher order methods. High order methods are capable of yielding far more accurate numerical results for certain problems when compared to corresponding h-refined first order methods , and often times at a significant reduction in total computational cost. The first half of this dissertation presents the method as well as the necessary mathematics required for its derivation. The second half addresses the implementation of the method in a parallel computational environment, its validation using benchmark problems, and finally its use in large scale numerical simulations of electromagnetic transmission devices.
Energy Science and Technology Software Center (ESTSC)
2006-03-08
MAPVAR-KD is designed to transfer solution results from one finite element mesh to another. MAPVAR-KD draws heavily from the structure and coding of MERLIN II, but it employs a new finite element data base, EXODUS II, and offers enhanced speed and new capabilities not available in MERLIN II. In keeping with the MERLIN II documentation, the computational algorithms used in MAPVAR-KD are described. User instructions are presented. Example problems are included to demonstrate the operationmore » of the code and the effects of various input options. MAPVAR-KD is a modification of MAPVAR in which the search algorithm was replaced by a kd-tree-based search for better performance on large problems.« less
A refined higher-order theory and its finite element method for thick laminated plates
NASA Astrophysics Data System (ADS)
Fu, Xiaohua; Chen, Haoran; Wang, Zhenming
1992-04-01
An improved higher-order theory developed to enhance the accuracy of the shear deformation theory of thick laminated plates is presented. The Legendre polynomials are introduced in the approximate displacement distributions across the plate thickness, and an FEM is suggested from the original equations. The accuracy of the present theory is examined by applying it to bending problems of laminate plates solved by Pagano. The results are compared with 3D elasticity solutions, the second order shear deformation theory, and some other higher-order shear deformation theory solutions. The present theory shows the deflections and stress more accurately than that obtained from previous works in the structural analysis of laminated plates with a small span with respect to thickness.
S.C. Jardin; J.A. Breslau
2004-12-17
Here we describe a technique for solving the four-field extended-magnetohydrodynamic (MHD) equations in two dimensions. The introduction of triangular high-order finite elements with continuous first derivatives (C{sup 1} continuity) leads to a compact representation compatible with direct inversion of the associated sparse matrices. The split semi-implicit method is introduced and used to integrate the equations in time, yielding unconditional stability for arbitrary time step. The method is applied to the cylindrical tilt mode problem with the result that a non-zero value of the collisionless ion skin depth will increase the growth rate of that mode. The effect of this parameter on the reconnection rate and geometry of a Harris equilibrium and on the Taylor reconnection problem is also demonstrated. This method forms the basis for a generalization to a full extended-MHD description of the plasma with six, eight, or more scalar fields.
NASA Technical Reports Server (NTRS)
Hou, Gene
1998-01-01
Sensitivity analysis is a technique for determining derivatives of system responses with respect to design parameters. Among many methods available for sensitivity analysis, automatic differentiation has been proven through many applications in fluid dynamics and structural mechanics to be an accurate and easy method for obtaining derivatives. Nevertheless, the method can be computational expensive and can require a high memory space. This project will apply an automatic differentiation tool, ADIFOR, to a p-version finite element code to obtain first- and second- order then-nal derivatives, respectively. The focus of the study is on the implementation process and the performance of the ADIFOR-enhanced codes for sensitivity analysis in terms of memory requirement, computational efficiency, and accuracy.
NASA Astrophysics Data System (ADS)
White, J. A.; Borja, R. I.
2007-12-01
In fluid-saturated sediments and sedimentary rocks, we recognize that the presence of the pore-fluid can serve to impose an incompressibilty constraint on the solid matrix in the limit of undrained conditions or fast loading rates. While such situations are commonly encountered in practice, they pose a challenge for the numerical analyst. From a finite element point of view, incompressibility constraints will often lead to non-physical oscillations in the pressure field unless special care is taken to use stable combinations of pressure and displacement interpolations. Unfortunately, many seemingly natural combinations of mixed interpolations---e.g. linear interpolations for both displacements and pressure---are unstable. The relatively high computational burden associated with standard stable elements has limited the widespread adoption of fully-coupled geomechanical models, especially for large three-dimensional simulations. In this work we explore a stabilizing modification of the coupled balance equations that allows for the use of low-order mixed elements while avoiding non-physical pressure oscillations. The improved efficiency of this technique is a step toward making large-scale, fully-coupled three-dimensional simulations feasible. We demonstrate the efficacy of the technique for simulating coupled solid deformation and fluid flow in fault zones.
Banks, H T; Birch, Malcolm J; Brewin, Mark P; Greenwald, Stephen E; Hu, Shuhua; Kenz, Zackary R; Kruse, Carola; Maischak, Matthias; Shaw, Simon; Whiteman, John R
2014-01-01
We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685–6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension (r + 1)D and is usually regarded as being too large when r > 1. Werder et al. found that the space-time coupling matrices are diagonalizable over for r ⩽100, and this means that the time-coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin–Voigt and Maxwell–Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high-order (up to degree 7) temporal and spatio-temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd. PMID:25834284
High-order Finite-Element Seismic Wave Propagation Modeling with MPI on a large GPU Cluster
NASA Astrophysics Data System (ADS)
Göddeke, D.; Komatitsch, D.; Erlebacher, G.; Michéa, D.
2011-12-01
We develop a hybrid multi-GPU and CPU version of an algorithm to model seismic wave propagation based on the spectral-element method. We implement an open-source high-order finite-element application, called SPECFEM3D that performs the numerical simulation of seismic wave propagation resulting for instance from earthquakes at the scale of a continent or from active seismic acquisition experiments in the oil industry, on a large cluster of NVIDIA graphics cards using the CUDA programming environment and non-blocking message passing based on MPI. This allows users to handle large numerical grids and simulate a large number of time steps for each geophysical model under study. Contrary to many other numerical techniques, ours is implemented successfully in single precision, maximizing the performance of current generation GPUs. Our GPU code can handle models of the Earth containing both fluid and solid layers (which is the case for instance at the scale of the full Earth, whose outer core is fluid). We will discuss the implementation and optimization of the code and compare it to an existing very optimized implementation in C language and MPI on a classical cluster of CPU nodes. We remove dependencies between neighboring mesh elements, which cannot easily be handled in parallel, based upon a mesh coloring technique to create subsets of independent elements. Thus, we efficiently handle summation operations over degrees of freedom on an unstructured mesh. Non-blocking MPI messages allow overlap between communications across the network and the data transfer to and from the device via the PCI-Express bus with calculations on the GPU. We perform a number of numerical tests to validate the single-precision CUDA and MPI implementation and assess its accuracy. We then analyze performance measurements and depending on how the problem is mapped to the reference CPU cluster, we obtain a speedup of 20x or 12x. Thanks to the overlapping of communications and computation, we
Energy Science and Technology Software Center (ESTSC)
2005-05-07
CONEX is a code for joining sequentially in time multiple exodusll database files which all represent the same base mesh topology and geometry. It is used to create a single results or restart file from multiple results or restart files which typically arise as the result of multiple restarted analyses. CONEX is used to postprocess the results from a series of finite element analyses. It can join sequentially the data from multiple results databases intomore » a single database which makes it easier to postprocess the results data.« less
Energy Science and Technology Software Center (ESTSC)
2005-06-26
Exotxt is an analysis code that reads finite element results data stored in an exodusII file and generates a file in a structured text format. The text file can be edited or modified via a number of text formatting tools. Exotxt is used by analysis to translate data from the binary exodusII format into a structured text format which can then be edited or modified and then either translated back to exodusII format or tomore » another format.« less
NASA Astrophysics Data System (ADS)
Kanellopoulos, V. N.; Webb, J. P.
1993-03-01
A 3D vector analysis of plane wave scattering by a metallic sphere using finite elements and Absorbing Boundary Conditions (ABCs) is presented. The ABCs are applied on the outer surface that truncates the infinitely extending domain. Mixed order curvilinear covariantprojection elements are used to avoid spurious corruptions. The second order ABC is superior to the first at no extra computational cost. The errors due to incomplete absorption decrease as the outer surface is moved further away from the scatterer. An error of about 1% in near-field values was obtained with the second order ABC, when the outer surface was less than half a wavelength from the scatterer. Une analyse tridimensionnelle vectorielle de la diffusion d'onde plane sur une sphère métallique utilisant des éléments finis et des Conditions aux Limites Absorbantes (CLA) est présentée. Les CLA sont appliquées sur la surface exteme tronquant le domaine s'étendant à l'infini. Des éléments curvilignes mixtes utilisant des projections covariantes sont utilisés pour éviter des solutions parasites. La CLA de second ordre est supérieure à celle de premier ordre sans effort de calcul additionnel. Les erreurs dues à l'absorption incomplète décroissent à mesure que l'on déplace la surface externe à une distance croissante du diffuseur. Un taux d'erreur d'environ 1 % dans les valeurs du champ proche a été obtenu avec les CLA de second ordre lorsque la surface externe était placée à une distance inférieure à une demi-longueur de la source de diffusion.
NASA Astrophysics Data System (ADS)
Wang, Shuai; Wang, Yu; Zi, Yanyang; Li, Bing; He, Zhengjia
2015-10-01
A novel reduced-order modeling method is presented in this paper for dynamics analysis of rotating impeller-shaft-bearing assembly with cracked impellers. Based on three-dimensional finite element model, the complex component mode synthesis (CMS) method is employed to generate an efficient reduced-order model (ROM) for studying the effects of crack on the global vibration of the rotating assembly. First, a modeling framework for impeller-shaft-bearing systems in rotating frame is presented. Rotational effects, including Coriolis matrix and centrifugal softening, have been taken into account. Then, the governing equation of motion of the damped gyroscopic system is reduced by the complex CMS method. Finally, the obtained ROM is employed to study the effects of crack on assembly's vibration. During the steady-state response analysis, external excitations on the impeller due to rotor-stator interactions have been taken into account, which was however neglected in previous investigations on rotordynamics. Numerical results show that the lower-order eigenvalues and the unbalance response of the assembly are not sensitive to the local crack on impeller. Nevertheless, the flexible coupling between impeller and shaft becomes more complex when the air flow-induced excitations are considered. Under EO1 traveling wave excitations, a crack leads to slight changes in the assembly's response. In contrast, the effect of crack becomes significant when the assembly is excited by EO2 and higher EO excitations. Moreover, the nonlinear crack breathing effects affect the assembly's response obviously. Finally, a potential technique for detecting the crack on impeller during operation is discussed.
NASA Astrophysics Data System (ADS)
Brown, J.; Ahmadia, A.; Knepley, M. G.; Smith, B.
2011-12-01
The cost of memory, especially memory bandwidth, is becoming increasingly expensive on modern high performance computing architectures including GPUs and multi-core systems. In contrast, floating point operations are relatively inexpensive when they can be vectorized (e.g. thread blocks on a GPU or vector registers on a CPU). This relative cost of memory to flops will continue to become even more pronounced due to fundamental issues of power utilization, therefore it is important to rethink algorithms to effectively utilize hardware. Commonly used methods for implicit solves with finite element methods involve assembly of a sparse matrix. Unfortunately, sparse matrix kernels have an arithmetic intensity (ratio of flops to bytes of memory movement) that is orders of magnitude less than that delivered by modern hardware, causing the floating point units to be massively under-utilized. The ``free flops'' can be effectively utilized by higher order methods which deliver improved accuracy for the same number of degrees of freedom. Effective use of high order methods require eschewing assembled data structures for matrix storage in exchange for unassembled representations. The resulting computation reduces to small dense tensor-product operations and indepedent ``physics'' kernels at each quadrature point, both of which are amenable to vectorization and capable of delivering a high fraction of peak performance. To reduce the effort required to implement new physics (e.g. constitutive relations and additional fields), retain code verifiability, and experiment with different vectorization strategies and solver algorithms, we express the continuum equations in Python and use automatic differentiation, symbolic methods, and code generation techniques to create vectorized kernels for residual evaluation, Jacobian storage, Jacobian application, and adjoints for each block of the system. The performance and effectiveness of these methods is demonstrated for free-surface Stokes
Probabilistic fracture finite elements
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.; Lua, Y. J.
1991-01-01
The Probabilistic Fracture Mechanics (PFM) is a promising method for estimating the fatigue life and inspection cycles for mechanical and structural components. The Probability Finite Element Method (PFEM), which is based on second moment analysis, has proved to be a promising, practical approach to handle problems with uncertainties. As the PFEM provides a powerful computational tool to determine first and second moment of random parameters, the second moment reliability method can be easily combined with PFEM to obtain measures of the reliability of the structural system. The method is also being applied to fatigue crack growth. Uncertainties in the material properties of advanced materials such as polycrystalline alloys, ceramics, and composites are commonly observed from experimental tests. This is mainly attributed to intrinsic microcracks, which are randomly distributed as a result of the applied load and the residual stress.
NASA Astrophysics Data System (ADS)
Li, Xikui; Liang, Yuanbo; Duan, Qinglin; Schrefler, B. A.; Du, Youyao
2014-11-01
A mixed finite element (FE) procedure of the gradient Cosserat continuum for the second-order computational homogenisation of granular materials is presented. The proposed mixed FE is developed based on the Hu-Washizu variational principle. Translational displacements, microrotations, and displacement gradients with Lagrange multipliers are taken as the independent nodal variables. The tangent stiffness matrix of the mixed FE is formulated. The advantage of the gradient Cosserat continuum model in capturing the meso-structural size effect is numerically demonstrated. Patch tests are specially designed and performed to validate the mixed FE formulations. A numerical example is presented to demonstrate the performance of the mixed FE procedure in the simulation of strain softening and localisation phenomena, while without the need to specify the macroscopic phenomenological constitutive relationship and material failure model. The meso-structural mechanisms of the macroscopic failure of granular materials are detected, i.e. significant development of dissipative sliding and rolling frictions among particles in contacts, resulting in the loss of contacts.
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.
Toward automatic finite element analysis
NASA Technical Reports Server (NTRS)
Kela, Ajay; Perucchio, Renato; Voelcker, Herbert
1987-01-01
Two problems must be solved if the finite element method is to become a reliable and affordable blackbox engineering tool. Finite element meshes must be generated automatically from computer aided design databases and mesh analysis must be made self-adaptive. The experimental system described solves both problems in 2-D through spatial and analytical substructuring techniques that are now being extended into 3-D.
NASA Astrophysics Data System (ADS)
Hasegawa, Kei; Geller, Robert J.; Hirabayashi, Nobuyasu
2016-06-01
We present a theoretical analysis of the error of synthetic seismograms computed by higher-order finite-element methods (ho-FEMs). We show the existence of a previously unrecognized type of error due to degenerate coupling between waves with the same frequency but different wavenumbers. These results are confirmed by simple numerical experiments using the spectral element method as an example of ho-FEMs. Errors of the type found by this study may occur generally in applications of ho-FEMs.
Probabilistic Finite Element: Variational Theory
NASA Technical Reports Server (NTRS)
Belytschko, T.; Liu, W. K.
1985-01-01
The goal of this research is to provide techniques which are cost-effective and enable the engineer to evaluate the effect of uncertainties in complex finite element models. Embedding the probabilistic aspects in a variational formulation is a natural approach. In addition, a variational approach to probabilistic finite elements enables it to be incorporated within standard finite element methodologies. Therefore, once the procedures are developed, they can easily be adapted to existing general purpose programs. Furthermore, the variational basis for these methods enables them to be adapted to a wide variety of structural elements and to provide a consistent basis for incorporating probabilistic features in many aspects of the structural problem. Tasks concluded include the theoretical development of probabilistic variational equations for structural dynamics, the development of efficient numerical algorithms for probabilistic sensitivity displacement and stress analysis, and integration of methodologies into a pilot computer code.
Pingenot, J; Rieben, R; White, D
2004-12-06
We present a computational study of signal propagation and attenuation of a 200 MHz dipole antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The simulation is performed for a series of random meshes in order to generate statistical data for the propagation and attenuation properties of the cave environment. Results for the power spectral density and phase of the electric field vector components are presented and discussed.
Sommer, A. Farle, O. Dyczij-Edlinger, R.
2015-10-15
This paper presents a fast numerical method for computing certified far-field patterns of phased antenna arrays over broad frequency bands as well as wide ranges of steering and look angles. The proposed scheme combines finite-element analysis, dual-corrected model-order reduction, and empirical interpolation. To assure the reliability of the results, improved a posteriori error bounds for the radiated power and directive gain are derived. Both the reduced-order model and the error-bounds algorithm feature offline–online decomposition. A real-world example is provided to demonstrate the efficiency and accuracy of the suggested approach.
The NESSUS finite element code
NASA Technical Reports Server (NTRS)
Dias, J. B.; Nagiegaal, J. C.; Nakazawa, S.
1987-01-01
The objective of this development is to provide a new analysis tool which integrates the structural modeling versatility of a modern finite element code with the latest advances in the area of probabilistic modeling and structural reliability. Version 2.0 of the NESSUS finite element code was released last February, and is currently being exercised on a set of problems which are representative of typical Space Shuttle Main Engine (SSME) applications. NESSUS 2.0 allows linear elastostatic and eigenvalue analysis of structures with uncertain geometry, material properties and boundary conditions, which are subjected to a random mechanical and thermal loading environment. The NESSUS finite element code is a key component in a broader software system consisting of five major modules. NESSUS/EXPERT is an expert system under development at Southwest Research Institute, with the objective of centralizing all component-specific knowledge useful for conducting probabilistic analysis of typical Space Shuttle Main Engine (SSME) components. NESSUS/FEM contains the finite element code used for the structural analysis and parameter sensitivity evaluation of these components. The task of parametrizing a finite element mesh in terms of the random variables present is facilitated with the use of the probabilistic data preprocessor in NESSUS/PRE. An external database file is used for managing the bulk of the data generated by NESSUS/FEM.
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.
Yaqi Wang; Cristian Rabiti; Giuseppe Palmiotti
2011-06-01
The Red-Black algorithm has been successfully applied on solving the second-order parity transport equation with the PN approximation in angle and the Hybrid Finite Element Method (HFEM) in space, i.e., the Variational Nodal Method (VNM) [1,2,3,4,5]. Any transport solving techniques, including the Red-Black algorithm, need to be parallelized in order to take the advantage of the development of supercomputers with multiple processors for the advanced modeling and simulation. To our knowledge, an attempt [6] was done to parallelize it, but it was devoted only to the z axis plans in three-dimensional calculations. General parallelization of the Red-Black algorithm with the spatial domain decomposition has not been reported in the literature. In this summary, we present our implementation of the parallelization of the Red-Black algorithm and its efficiency results.
Pingenot, J; Rieben, R; White, D; Dudley, D
2005-10-31
We present a computational study of signal propagation and attenuation of a 200 MHz planar loop antenna in a cave environment. The cave is modeled as a straight and lossy random rough wall. To simulate a broad frequency band, the full wave Maxwell equations are solved directly in the time domain via a high order vector finite element discretization using the massively parallel CEM code EMSolve. The numerical technique is first verified against theoretical results for a planar loop antenna in a smooth lossy cave. The simulation is then performed for a series of random rough surface meshes in order to generate statistical data for the propagation and attenuation properties of the antenna in a cave environment. Results for the mean and variance of the power spectral density of the electric field are presented and discussed.
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.
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)
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.
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
NASA Astrophysics Data System (ADS)
Moortgat, Joachim; Li, Zhidong; Firoozabadi, Abbas
2012-12-01
Most simulators for subsurface flow of water, gas, and oil phases use empirical correlations, such as Henry's law, for the CO2 composition in the aqueous phase, and equations of state (EOS) that do not represent the polar interactions between CO2and water. Widely used simulators are also based on lowest-order finite difference methods and suffer from numerical dispersion and grid sensitivity. They may not capture the viscous and gravitational fingering that can negatively affect hydrocarbon (HC) recovery, or aid carbon sequestration in aquifers. We present a three-phase compositional model based on higher-order finite element methods and incorporate rigorous and efficient three-phase-split computations for either three HC phases or water-oil-gas systems. For HC phases, we use the Peng-Robinson EOS. We allow solubility of CO2in water and adopt a new cubic-plus-association (CPA) EOS, which accounts for cross association between H2O and CO2 molecules, and association between H2O molecules. The CPA-EOS is highly accurate over a broad range of pressures and temperatures. The main novelty of this work is the formulation of a reservoir simulator with new EOS-based unique three-phase-split computations, which satisfy both the equalities of fugacities in all three phases and the global minimum of Gibbs free energy. We provide five examples that demonstrate twice the convergence rate of our method compared with a finite difference approach, and compare with experimental data and other simulators. The examples consider gravitational fingering during CO2sequestration in aquifers, viscous fingering in water-alternating-gas injection, and full compositional modeling of three HC phases.
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.
Revolution in Orthodontics: Finite element analysis
Singh, Johar Rajvinder; Kambalyal, Prabhuraj; Jain, Megha; Khandelwal, Piyush
2016-01-01
Engineering has not only developed in the field of medicine but has also become quite established in the field of dentistry, especially Orthodontics. Finite element analysis (FEA) is a computational procedure to calculate the stress in an element, which performs a model solution. This structural analysis allows the determination of stress resulting from external force, pressure, thermal change, and other factors. This method is extremely useful for indicating mechanical aspects of biomaterials and human tissues that can hardly be measured in vivo. The results obtained can then be studied using visualization software within the finite element method (FEM) to view a variety of parameters, and to fully identify implications of the analysis. This is a review to show the applications of FEM in Orthodontics. It is extremely important to verify what the purpose of the study is in order to correctly apply FEM. PMID:27114948
Finite element methods in numerical relativity.
NASA Astrophysics Data System (ADS)
Mann, P. J.
The finite element method is very successful in Newtonian fluid simulations, and can be extended to relativitstic fluid flows. This paper describes the general method, and then outlines some preliminary results for spherically symmetric geometries. The mixed finite element - finite difference scheme is introduced, and used for the description of spherically symmetric collapse. Baker's (Newtonian) shock modelling method and Miller's moving finite element method are also mentioned. Collapse in double-null coordinates requires non-constant time slicing, so the full finite element method in space and time is described.
Diagonal multisoliton matrix elements in finite volume
NASA Astrophysics Data System (ADS)
Pálmai, T.; Takács, G.
2013-02-01
We consider diagonal matrix elements of local operators between multisoliton states in finite volume in the sine-Gordon model and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential in the volume. This conjecture extends the results of Pozsgay and Takács which were only valid for diagonal scattering. In order to test the conjecture, we implement a numerical renormalization group improved truncated conformal space approach. The numerical comparisons confirm the conjecture, which is expected to be valid for general integrable field theories. The conjectured formula can be used to evaluate finite temperature one-point and two-point functions using recently developed methods.
Finite element and finite difference methods in electromagnetic scattering
NASA Astrophysics Data System (ADS)
Morgan, Michael A.
Finite-difference and finite-element methods for the computational analysis of EM scattering phenomena are examined in chapters contributed by leading experts. Topics addressed include an FEM for composite scatterers, coupled finite- and boundary-element methods for EM scattering, absorbing boundary conditions for the direct solution PDEs arising in EM scattering problems, application of the control-region approximation to two-dimensional EM scattering, coupled potentials for EM fields in inhomogeneous media, the method of conforming boundary elements for transient electromagnetics, and the finite-difference time-domain method for numerical modeling of EM wave interactions with arbitrary structures. Extensive diagrams and graphs of typical results are provided.
Probabilistic finite element analysis of a craniofacial finite element model.
Berthaume, Michael A; Dechow, Paul C; Iriarte-Diaz, Jose; Ross, Callum F; Strait, David S; Wang, Qian; Grosse, Ian R
2012-05-01
We employed a probabilistic finite element analysis (FEA) method to determine how variability in material property values affects stress and strain values in a finite model of a Macaca fascicularis cranium. The material behavior of cortical bone varied in three ways: isotropic homogeneous, isotropic non-homogeneous, and orthotropic non-homogeneous. The material behavior of the trabecular bone and teeth was always treated as isotropic and homogeneous. All material property values for the cranium were randomized with a Gaussian distribution with either coefficients of variation (CVs) of 0.2 or with CVs calculated from empirical data. Latin hypercube sampling was used to determine the values of the material properties used in the finite element models. In total, four hundred and twenty six separate deterministic FE simulations were executed. We tested four hypotheses in this study: (1) uncertainty in material property values will have an insignificant effect on high stresses and a significant effect on high strains for homogeneous isotropic models; (2) the effect of variability in material property values on the stress state will increase as non-homogeneity and anisotropy increase; (3) variation in the in vivo shear strain values reported by Strait et al. (2005) and Ross et al. (2011) is not only due to variations in muscle forces and cranial morphology, but also due to variation in material property values; (4) the assumption of a uniform coefficient of variation for the material property values will result in the same trend in how moderate-to-high stresses and moderate-to-high strains vary with respect to the degree of non-homogeneity and anisotropy as the trend found when the coefficients of variation for material property values are calculated from empirical data. Our results supported the first three hypotheses and falsified the fourth. When material properties were varied with a constant CV, as non-homogeneity and anisotropy increased the level of variability in
Dynamic analysis of mechanisms by finite elements
Botsali, F.M.; Uenuevar, A.
1996-11-01
The need to increase productivity in order to decrease manufacturing costs lead to an increase in the working speeds of machines and mechanical systems used in manufacturing. A method is presented for investigating the dynamics of mechanisms with elastic links. Finite element method is used in the formulation of the dynamic problem. Modal transformation is used in order to reduce the number of equations of motion. Using the presented technique, elastic and rigid body motions of mechanism links are solved simultaneously. The presented method may be applied to spatial and open loop mechanisms including robot manipulators as well.
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.
NASA Astrophysics Data System (ADS)
Wang, Shuai; Wang, Yu; Zi, Yanyang; He, Zhengjia
2015-12-01
A generalized and efficient model for rotating anisotropic rotor-bearing systems is presented in this paper with full considerations of the system's anisotropy in stiffness, inertia and damping. Based on the 3D finite element model and the model order reduction method, the effects of anisotropy in shaft and bearings on the forced response and whirling of anisotropic rotor-bearing systems are systematically investigated. First, the coefficients of journal bearings are transformed from the fixed frame to the rotating one. Due to the anisotropy in shaft and bearings, the motion is governed by differential equations with periodically time-variant coefficients. Then, a free-interface complex component mode synthesis (CMS) method is employed to generate efficient reduced-order models (ROM) for the periodically time-variant systems. In order to solve the obtained equations, a variant of Hill's method for systems with multiple harmonic excitations is developed. Four dimensionless parameters are defined to quantify the types and levels of anisotropy of bearings. Finally, the effects of the four types of anisotropy on the forced response and whirl orbits are studied. Numerical results show that the anisotropy of bearings in stiffness splits the sole resonant peak into two isolated ones, but the anisotropy of bearings in damping coefficients mainly affect the response amplitudes. Moreover, the whirl orbits become much more complex when the shaft and bearings are both anisotropic. In addition, the cross-coupling stiffness coefficients of bearings significantly affect the dynamic behaviors of the systems and cannot be neglected, though they are often much smaller than the principle stiffness terms.
NASA Astrophysics Data System (ADS)
Leibs, Christopher A.
Efforts are currently being directed towards a fully implicit, electromagnetic, JFNK-based solver, motivating the necessity of developing a fluid-based, electromag- netic, preconditioning strategy. The two-fluid plasma (TFP) model is an ideal approximation to the kinetic Jacobian. The TFP model couples both an ion and an electron fluid with Maxwell's equations. The fluid equations consist of the conservation of momentum and number density. A Darwin approximation of Maxwell is used to eliminate light waves from the model in order to facilitate coupling to non-relativistic particle models. We analyze the TFP-Darwin system in the context of a stand-alone solver with consideration of preconditioning a kinetic-JFNK approach. The TFP-Darwin system is addressed numerically by use of nested iteration (NI) and a First-Order Systems Least Squares (FOSLS) discretization. An important goal of NI is to produce an approximation that is within the basis of attraction for Newton's method on a relatively coarse mesh and, thus, on all subsequent meshes. After scaling and modification, the TFP-Darwin model yields a nonlinear, first-order system of equa- tions whose Frechet derivative is shown to be uniformly H1-elliptic in a neighborhood of the exact solution. H1 ellipticity yields optimal finite element performance and lin- ear systems amenable to solution with Algebraic Multigrid (AMG). To efficiently focus computational resources, an adaptive mesh refinement scheme, based on the accuracy per computational cost, is leveraged. Numerical tests demonstrate the efficacy of the approach, yielding an approximate solution within discretization error in a relatively small number of computational work units.
NASA Astrophysics Data System (ADS)
Tezaur, I. K.; Perego, M.; Salinger, A. G.; Tuminaro, R. S.; Price, S. F.
2015-04-01
This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, along with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.
Tezaur, I. K.; Perego, M.; Salinger, A. G.; Tuminaro, R. S.; Price, S. F.
2015-04-27
This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, alongmore » with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.« less
Tezaur, I. K.; Perego, M.; Salinger, A. G.; Tuminaro, R. S.; Price, S. F.
2015-04-27
This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, along with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.
Enhancements to modal testing using finite elements
NASA Astrophysics Data System (ADS)
Jarvis, Brian
In calculating the natural frequencies and mode shapes from a finite element analysis, there are generally many more degrees of freedom than can be handled for the eigensolution. A reduction process is employed to reduce the number to a master set and chosen so that the modes of interest are well defined. By choosing those freedoms where the inertia terms are high or the stiffness terms are low then an automatic procedure for selecting the best freedoms can be defined. For modal testing, these master freedoms also indicate the best transducer locations for optimum low order mode identification. Having carried out the modal test, the mode shapes obtained can be forced onto the finite element model giving greatly enhanced results. By examining terms in all mode shapes from the finite element model in the frequency range of interest, the best reference or excitation position can be found. An example of the use of this technique to study the modal properties of an aero-engine compressor blade is given.
FEBio: finite elements for biomechanics.
Maas, Steve A; Ellis, Benjamin J; Ateshian, Gerard A; Weiss, Jeffrey A
2012-01-01
In the field of computational biomechanics, investigators have primarily used commercial software that is neither geared toward biological applications nor sufficiently flexible to follow the latest developments in the field. This lack of a tailored software environment has hampered research progress, as well as dissemination of models and results. To address these issues, we developed the FEBio software suite (http://mrl.sci.utah.edu/software/febio), a nonlinear implicit finite element (FE) framework, designed specifically for analysis in computational solid biomechanics. This paper provides an overview of the theoretical basis of FEBio and its main features. FEBio offers modeling scenarios, constitutive models, and boundary conditions, which are relevant to numerous applications in biomechanics. The open-source FEBio software is written in C++, with particular attention to scalar and parallel performance on modern computer architectures. Software verification is a large part of the development and maintenance of FEBio, and to demonstrate the general approach, the description and results of several problems from the FEBio Verification Suite are presented and compared to analytical solutions or results from other established and verified FE codes. An additional simulation is described that illustrates the application of FEBio to a research problem in biomechanics. Together with the pre- and postprocessing software PREVIEW and POSTVIEW, FEBio provides a tailored solution for research and development in computational biomechanics. PMID:22482660
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.
Graphics for Finite-Element Analysis
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Sawyer, L. M.
1982-01-01
ELPLOT program is a passive computer graphics system that could be utilized for display of models and responses of general finite-element analyses. Program includes: Wide range of view-orientation selections, number of alternative data-input formats, extensive family of finite-element types, and capabilities for both static and dynamic-response displays.
3-D Finite Element Code Postprocessor
Energy Science and Technology Software Center (ESTSC)
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.
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.
Finite element solutions of free surface flows
NASA Technical Reports Server (NTRS)
Zarda, P. R.; Marcus, M. S.
1977-01-01
A procedure is presented for using NASTRAN to determine the flow field about arbitrarily shaped bodies in the presence of a free surface. The fundamental unknown of the problem is the velocity potential which must satisfy Laplace's equation in the fluid region. Boundary conditions on the free surface may involve second order derivatives in space and time. In cases involving infinite domains either a tractable radiation condition is applied at a truncated boundary or a series expansion is used and matched to the local finite elements. Solutions are presented for harmonic, transient, and steady state problems and compared to either exact solutions or other numerical solutions.
Finite element methods in probabilistic mechanics
NASA Technical Reports Server (NTRS)
Liu, Wing Kam; Mani, A.; Belytschko, Ted
1987-01-01
Probabilistic methods, synthesizing the power of finite element methods with second-order perturbation techniques, are formulated for linear and nonlinear problems. Random material, geometric properties and loads can be incorporated in these methods, in terms of their fundamental statistics. By construction, these methods are applicable when the scale of randomness is not too large and when the probabilistic density functions have decaying tails. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. Applications showing the effects of combined random fields and cyclic loading/stress reversal are studied and compared with Monte Carlo simulation results.
Advances in 3D electromagnetic finite element modeling
Nelson, E.M.
1997-08-01
Numerous advances in electromagnetic finite element analysis (FEA) have been made in recent years. The maturity of frequency domain and eigenmode calculations, and the growth of time domain applications is briefly reviewed. A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will also be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis is also discussed.
Overcoming element erosion limitations within Lagrangian finite element codes
NASA Astrophysics Data System (ADS)
Vignjevic, Rade; Hughes, Kevin; Walker, Andrew; Taylor, Emma A.
2001-10-01
Lagrangian finite element methods have been used extensively in the past to study the non-linear transient behaviour of materials, ranging from crash test of cars to simulating bird strikes on planes.... However, as this type of space discretization does not allow for motion of the material through the mesh when modelling extremely large deformations, the mesh becomes highly distorted. This paper describes some limitations and applicability of this type of analysis for high velocity impacts. A method for dealing with this problem is by the erosion of elements is proposed where the main issue is the deformation of element failure strains. Results were compared with empirical perforation results and were found to be in good agreement. The results were then used to simulate high velocity impacts upon a multi-layered aluminium target, in order to predict a ballistic limit curve. LS-DYNA3D was used as the FE solver for all simulations. Meshes were generated with Truegrid.
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
Will Finite Elements Replace Structural Mechanics?
NASA Astrophysics Data System (ADS)
Ojalvo, I. U.
1984-01-01
This paper presents a personal view regarding the need for a continued interest and activity in structural methods in general, while viewing finite elements and the computer as simply two specific tools for assisting in this endeavor. An attempt is made to provide some insight as to why finite element methods seem to have "won the war," and to give examples of their more (and less) intelligent use. Items addressed include a highlight of unnecessary limitations of many existing standard finite element codes and where it is felt that further development work is needed.
The finite element method in thermomechanics
Hsu, T.
1986-01-01
Thermal stress analysis is critical in the design and operation of energy-efficient power plant components and engines as well as in nuclear and aerospace systems. The Finite Element Method in Thermomechanics attempts to embrace a wide range of topics in the nonlinear thermomechanical analysis. The book covers the basic principles of the finite element method: the formulations for the base thermomechanical analysis, including thermoelastic-plastic-creep stress analysis; the use of Fourier series for nonaxisymmetric loadings, and stress waves in solids in thermal environments; and the base finite element code called TEPSAC.
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.
P-Finite-Element Program For Analysis Of Plates
NASA Technical Reports Server (NTRS)
Smith, James P.
1995-01-01
BUCKY is p-finite-element computer program for highly accurate analysis of structures. Used to analyze buckling, bending, and in-plane stress-and-strain behaviors of plates. Provides elastic-plastic solutions for isotropic plates in states of plane stress, and axisymmetric solution sequence used to treat three-dimensional problems. Computes response of plate to variety of loading and boundary conditions by use of higher-order displacement function in p-finite-element method. Enables user to obtain results more accurate than obtained by use of traditional h-finite elements. Written in FORTRAN 77.
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 survey of mixed finite element methods
NASA Technical Reports Server (NTRS)
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
Finite element modeling of the human pelvis
Carlson, B.
1995-11-01
A finite element model of the human pelvis was created using a commercial wire frame image as a template. To test the final mesh, the model`s mechanical behavior was analyzed through finite element analysis and the results were displayed graphically as stress concentrations. In the future, this grid of the pelvis will be integrated with a full leg model and used in side-impact car collision simulations.
Finite-Element Modeling For Structural Analysis
NASA Technical Reports Server (NTRS)
Min, J. B.; Androlake, S. G.
1995-01-01
Report presents study of finite-element mathematical modeling as used in analyzing stresses and strains at joints between thin, shell-like components (e.g., ducts) and thicker components (e.g., flanges or engine blocks). First approach uses global/local model to evaluate system. Provides correct total response and correct representation of stresses away from any discontinuities. Second approach involves development of special transition finite elements to model transitions between shells and thicker structural components.
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.
Finite element analysis of flexible, rotating blades
NASA Technical Reports Server (NTRS)
Mcgee, Oliver G.
1987-01-01
A reference guide that can be used when using the finite element method to approximate the static and dynamic behavior of flexible, rotating blades is given. Important parameters such as twist, sweep, camber, co-planar shell elements, centrifugal loads, and inertia properties are studied. Comparisons are made between NASTRAN elements through published benchmark tests. The main purpose is to summarize blade modeling strategies and to document capabilities and limitations (for flexible, rotating blades) of various NASTRAN elements.
Finite Element Interface to Linear Solvers
Williams, Alan
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on the problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.
Fuzzy finite element analysis of smart structures
NASA Astrophysics Data System (ADS)
Akpan, Unyime O.; Koko, Tamunoiyala S.; Orisamolu, Irewole R.; Gallant, B. Keith
2000-06-01
A fuzzy finite element based approach is developed for modelling smart structures with vague or imprecise uncertainties. Fuzzy sets are used to represent the uncertainties present in the piezoelectric, mechanical, thermal, and physical properties of the smart structure. In order to facilitate efficient computation, a sensitivity analysis procedure is used to streamline the number of input fuzzy variables, and the vertex fuzzy analysis technique is then used to compute the possibility distributions of the responses of the smart structural system. The methodology has been developed within the framework of the SMARTCOM computational tool for the design/analysis of smart composite structures. The methodology developed is found to be accurate and computationally efficient for solution of practical problems.
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.
Azimuthally-dependent Finite Element Solution to the Cylindrical Resonator
NASA Technical Reports Server (NTRS)
Osegueda, R.; Pierluissi, J.; Gil, L.; Revilla, A.; Villalva, G.; Dick, G.; Wang, D. SantiagoR.
1994-01-01
The cylindrical cavity resonator loaded with an anisotropic dielectric is analyzed as a two-dimensional problem using a finite element approach that assumes sinusoidal dependence in azimuth. This methodology allows the first finite element treatment of the technically important case of a resonator containing a sapphire element with a cylindrically aligned c axis. Second order trial functions together with quadrilateral elements are adopted in the calculations. The method was validated through comparisons with the analytical solutions for the hollow metal cavity and a coaxial cavity, as well as through measurements on a shielded sapphire resonator.
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.
A Viscoelastic Hybrid Shell Finite Element
NASA Technical Reports Server (NTRS)
Johnson, Arthur
1999-01-01
An elastic large displacement thick-shell hybrid finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at he element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses in included in the mixed variational functional. Nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to numerically simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.
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.
Error analysis of finite element solutions for postbuckled cylinders
NASA Technical Reports Server (NTRS)
Sistla, Rajaram; Thurston, Gaylen A.
1989-01-01
A general method of error analysis and correction is investigated for the discrete finite-element results for cylindrical shell structures. The method for error analysis is an adaptation of the method of successive approximation. When applied to the equilibrium equations of shell theory, successive approximations derive an approximate continuous solution from the discrete finite-element results. The advantage of this continuous solution is that it contains continuous partial derivatives of an order higher than the basis functions of the finite-element solution. Preliminary numerical results are presented in this paper for the error analysis of finite-element results for a postbuckled stiffened cylindrical panel modeled by a general purpose shell code. Numerical results from the method have previously been reported for postbuckled stiffened plates. A procedure for correcting the continuous approximate solution by Newton's method is outlined.
Generalized multiscale finite element method. Symmetric interior penalty coupling
NASA Astrophysics Data System (ADS)
Efendiev, Y.; Galvis, J.; Lazarov, R.; Moon, M.; Sarkis, M.
2013-12-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the “mass” matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples.
Finite element analyses of CCAT preliminary design
NASA Astrophysics Data System (ADS)
Sarawit, Andrew T.; Kan, Frank W.
2014-07-01
This paper describes the development of the CCAT telescope finite element model (FEM) and the analyses performed to support the preliminary design work. CCAT will be a 25 m diameter telescope operating in the 0.2 to 2 mm wavelength range. It will be located at an elevation of 5600 m on Cerro Chajnantor in Northern Chile, near ALMA. The telescope will be equipped with wide-field cameras and spectrometers mounted at the two Nasmyth foci. The telescope will be inside an enclosure to protect it from wind buffeting, direct solar heating, and bad weather. The main structures of the telescope include a steel Mount and a carbon-fiber-reinforced-plastic (CFRP) primary truss. The finite element model developed in this study was used to perform modal, frequency response, seismic response spectrum, stress, and deflection analyses of telescope. Modal analyses of telescope were performed to compute the structure natural frequencies and mode shapes and to obtain reduced order modal output at selected locations in the telescope structure to support the design of the Mount control system. Modal frequency response analyses were also performed to compute transfer functions at these selected locations. Seismic response spectrum analyses of the telescope subject to the Maximum Likely Earthquake were performed to compute peak accelerations and seismic demand stresses. Stress analyses were performed for gravity load to obtain gravity demand stresses. Deflection analyses for gravity load, thermal load, and differential elevation drive torque were performed so that the CCAT Observatory can verify that the structures meet the stringent telescope surface and pointing error requirements.
Verification of Orthogrid Finite Element Modeling Techniques
NASA Technical Reports Server (NTRS)
Steeve, B. E.
1996-01-01
The stress analysis of orthogrid structures, specifically with I-beam sections, is regularly performed using finite elements. Various modeling techniques are often used to simplify the modeling process but still adequately capture the actual hardware behavior. The accuracy of such 'Oshort cutso' is sometimes in question. This report compares three modeling techniques to actual test results from a loaded orthogrid panel. The finite element models include a beam, shell, and mixed beam and shell element model. Results show that the shell element model performs the best, but that the simpler beam and beam and shell element models provide reasonable to conservative results for a stress analysis. When deflection and stiffness is critical, it is important to capture the effect of the orthogrid nodes in the model.
Finite elements based on consistently assumed stresses and displacements
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1985-01-01
Finite element stiffness matrices are derived using an extended Hellinger-Reissner principle in which internal displacements are added to serve as Lagrange multipliers to introduce the equilibrium constraint in each element. In a consistent formulation the assumed stresses are initially unconstrained and complete polynomials and the total displacements are also complete such that the corresponding strains are complete in the same order as the stresses. Several examples indicate that resulting properties for elements constructed by this consistent formulation are ideal and are less sensitive to distortions of element geometries. The method has been used to find the optimal stress terms for plane elements, 3-D solids, axisymmetric solids, and plate bending elements.
Finite element radiation transport in one dimension
Painter, J.F.
1997-05-09
A new physics package solves radiation transport equations in one space dimension, multiple energy groups and directions. A discontinuous finite element method discretizes radiation intensity with respect to space and angle, and a continuous finite element method discretizes electron temperature `in space. A splitting method solves the resulting linear equations. This is a one-dimensional analog of Kershaw and Harte`s two-dimensional package. This package has been installed in a two-dimensional inertial confinement fusion code, and has given excellent results for both thermal waves and highly directional radiation. In contrast, the traditional discrete ordinate and spherical harmonic methods show less accurate results in both cases.
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.
Slave finite elements: The temporal element approach to nonlinear analysis
NASA Technical Reports Server (NTRS)
Gellin, S.
1984-01-01
A formulation method for finite elements in space and time incorporating nonlinear geometric and material behavior is presented. The method uses interpolation polynomials for approximating the behavior of various quantities over the element domain, and only explicit integration over space and time. While applications are general, the plate and shell elements that are currently being programmed are appropriate to model turbine blades, vanes, and combustor liners.
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.
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.
Evolution of assumed stress hybrid finite element
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1984-01-01
Early versions of the assumed stress hybrid finite elements were based on the a priori satisifaction of stress equilibrium conditions. In the new version such conditions are relaxed but are introduced through additional internal displacement functions as Lagrange multipliers. A rational procedure is to choose the displacement terms such that the resulting strains are now of complete polynomials up to the same degree as that of the assumed stresses. Several example problems indicate that optimal element properties are resulted by this method.
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.
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 Simulation of Smart Structures
NASA Technical Reports Server (NTRS)
Cui, Y. Lawrence; Panahandeh, M.
1996-01-01
Finite element equations representing the behavior of piezoelectric materials when bounded to a typical structure and used as sensors and actuators were developed. Emphasis was placed on generating sensor output equations of piezoelectric sensors and responses of a typical structure bonded with piezoelectric sensors and actuators on the basis of finite element formulation. The model can predict not only structural responses due to both mechanical and electrical loading but also electrical potential due to mechanical or thermal effects. The resulted finite element equations were then used for simple control design and performance evaluation. In the control algorithm, voltages coming out from piezoelectric sensors, which are proportional to strains at sensing locations, are taken as input. The voltages applied to the piezoelectric actuators are used as output. The feasibility of integrating control algorithm with the element routine developed herein and FEAP was demonstrated. In particular, optimal independent modal space control was implemented in a software package on the basis of finite element formulation. A rudimentary finite element-control algorithm package was also developed to evaluate the performance of candidate control laws. A few numerical simulations using the software package developed herein were given. The integrated software package will provide a design tool to address issues such as how adaptive smart systems will scale to a full size aircraft, the amount of piezoelectric materials and the powers needed to actuate it for desired performance. It will also provide a viable new structural control design concept for practical applications in large flexible structures such as aerospace vehicles and aircraft.
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.
Animation of finite element models and results
NASA Technical Reports Server (NTRS)
Lipman, Robert R.
1992-01-01
This is not intended as a complete review of computer hardware and software that can be used for animation of finite element models and results, but is instead a demonstration of the benefits of visualization using selected hardware and software. The role of raw computational power, graphics speed, and the use of videotape are discussed.
On Hybrid and mixed finite element methods
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1981-01-01
Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.
Finite element computation with parallel VLSI
NASA Technical Reports Server (NTRS)
Mcgregor, J.; Salama, M.
1983-01-01
This paper describes a parallel processing computer consisting of a 16-bit microcomputer as a master processor which controls and coordinates the activities of 8086/8087 VLSI chip set slave processors working in parallel. The hardware is inexpensive and can be flexibly configured and programmed to perform various functions. This makes it a useful research tool for the development of, and experimentation with parallel mathematical algorithms. Application of the hardware to computational tasks involved in the finite element analysis method is demonstrated by the generation and assembly of beam finite element stiffness matrices. A number of possible schemes for the implementation of N-elements on N- or n-processors (N is greater than n) are described, and the speedup factors of their time consumption are determined as a function of the number of available parallel processors.
Finite Element Interface to Linear Solvers
Energy Science and Technology Software Center (ESTSC)
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on themore » problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.« less
Finite element modeling of retinal prosthesis mechanics
NASA Astrophysics Data System (ADS)
Basinger, B. C.; Rowley, A. P.; Chen, K.; Humayun, M. S.; Weiland, J. D.
2009-10-01
Epiretinal prostheses used to treat degenerative retina diseases apply stimulus via an electrode array fixed to the ganglion cell side of the retina. Mechanical pressure applied by these arrays to the retina, both during initial insertion and throughout chronic use, could cause sufficient retinal damage to reduce the device's effectiveness. In order to understand and minimize potential mechanical damage, we have used finite element analysis to model mechanical interactions between an electrode array and the retina in both acute and chronic loading configurations. Modeling indicates that an acute tacking force distributes stress primarily underneath the tack site and heel edge of the array, while more moderate chronic stresses are distributed more evenly underneath the array. Retinal damage in a canine model chronically implanted with a similar array occurred in correlating locations, and model predictions correlate well with benchtop eyewall compression tests. This model provides retinal prosthesis researchers with a tool to optimize the mechanical electrode array design, but the techniques used here represent a unique effort to combine a modifiable device and soft biological tissues in the same model and those techniques could be extended to other devices that come into mechanical contact with soft neural tissues.
Finite Element Heat & Mass Transfer Code
Energy Science and Technology Software Center (ESTSC)
1996-10-10
FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; andmore » double porosity and double porosity/double permeability capabilities.« less
Probabilistic nonlinear finite element analysis of composite structures
NASA Technical Reports Server (NTRS)
Engelstad, S. P.; Reddy, J. N.
1993-01-01
A probabilistic finite element analysis procedure for laminated composite shells is developed. A total Lagrangian finite element formulation, employing a degenerated three-dimensional laminated composite shell element with the full Green-Lagrange strains and first-order shear deformable kinematics, is used. 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. Reliability calculations are made by using the first-order reliability method combined with sensitivity derivatives from the finite element analysis. Both ply-level and micromechanics-level random variables are incorporated, the latter by means of the Aboudi micromechanics model. Two sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. In general, the procedure is quite effective in determining the response statistics and reliability for linear and geometric nonlinear behavior of laminated composite shells.
Experiences in interfacing NASTRAN with another finite element program
NASA Technical Reports Server (NTRS)
Schwerzler, D. D.; Leverenz, R. K.
1972-01-01
The coupling of NASTRAN to another finite element program developed for the static analysis of automotive structures is discussed. The two programs were coupled together to use the substructuring capability of the in-house program and the normal mode analysis capability of NASTRAN. Modifications were made to the NASTRAN program in order to make the coupling feasible.
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.
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.
Adaptive finite-element method for diffraction gratings
NASA Astrophysics Data System (ADS)
Bao, Gang; Chen, Zhiming; Wu, Haijun
2005-06-01
A second-order finite-element adaptive strategy with error control for one-dimensional grating problems is developed. The unbounded computational domain is truncated to a bounded one by a perfectly-matched-layer (PML) technique. The PML parameters, such as the thickness of the layer and the medium properties, are determined through sharp a posteriori error estimates. The adaptive finite-element method is expected to increase significantly the accuracy and efficiency of the discretization as well as reduce the computation cost. Numerical experiments are included to illustrate the competitiveness of the proposed adaptive method.
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, J M
2004-08-12
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.
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 Analysis of Honeycomb Impact Attenuator
NASA Astrophysics Data System (ADS)
Yang, Seung-Yong; Choi, Seung-Kyu; Kim, Nohyu
To participate in Student Formula Society of Automotive Engineers (SAE) competitions, it is necessary to build an impact attenuator that would give an average deceleration not to exceed 20g when it runs into a rigid wall. Students can use numerical simulations or experimental test data to show that their car satisfies this safety requirement. A student group to study formula cars at the Korea University of Technology and Education has designed a vehicle to take part in a SAE competition, and a honeycomb structure was adopted as the impact attenuator. In this paper, finite element calculations were carried out to investigate the dynamic behavior of the honeycomb attenuator. Deceleration and deformation behaviors were studied. Effect of the yield strength was checked by comparing the numerical results. ABAQUS/Explicit finite element code was used.
Plasticity - Theory and finite element applications.
NASA Technical Reports Server (NTRS)
Armen, H., Jr.; Levine, H. S.
1972-01-01
A unified presentation is given of the development and distinctions associated with various incremental solution procedures used to solve the equations governing the nonlinear behavior of structures, and this is discussed within the framework of the finite-element method. Although the primary emphasis here is on material nonlinearities, consideration is also given to geometric nonlinearities acting separately or in combination with nonlinear material behavior. The methods discussed here are applicable to a broad spectrum of structures, ranging from simple beams to general three-dimensional bodies. The finite-element analysis methods for material nonlinearity are general in the sense that any of the available plasticity theories can be incorporated to treat strain hardening or ideally plastic behavior.
2-d Finite Element Code Postprocessor
Energy Science and Technology Software Center (ESTSC)
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forcesmore » along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.« less
Finite element analysis of human joints
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.
Finite element 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 Analysis of Reverberation Chambers
NASA Technical Reports Server (NTRS)
Bunting, Charles F.; Nguyen, Duc T.
2000-01-01
The primary motivating factor behind the initiation of this work was to provide a deterministic means of establishing the validity of the statistical methods that are recommended for the determination of fields that interact in -an avionics system. The application of finite element analysis to reverberation chambers is the initial step required to establish a reasonable course of inquiry in this particularly data-intensive study. The use of computational electromagnetics provides a high degree of control of the "experimental" parameters that can be utilized in a simulation of reverberating structures. As the work evolved there were four primary focus areas they are: 1. The eigenvalue problem for the source free problem. 2. The development of a complex efficient eigensolver. 3. The application of a source for the TE and TM fields for statistical characterization. 4. The examination of shielding effectiveness in a reverberating environment. One early purpose of this work was to establish the utility of finite element techniques in the development of an extended low frequency statistical model for reverberation phenomena. By employing finite element techniques, structures of arbitrary complexity can be analyzed due to the use of triangular shape functions in the spatial discretization. The effects of both frequency stirring and mechanical stirring are presented. It is suggested that for the low frequency operation the typical tuner size is inadequate to provide a sufficiently random field and that frequency stirring should be used. The results of the finite element analysis of the reverberation chamber illustrate io-W the potential utility of a 2D representation for enhancing the basic statistical characteristics of the chamber when operating in a low frequency regime. The basic field statistics are verified for frequency stirring over a wide range of frequencies. Mechanical stirring is shown to provide an effective frequency deviation.
Finite element 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.
ExodusII Finite Element Data Model
Energy Science and Technology Software Center (ESTSC)
2005-05-14
EXODUS II is a model developed to store and retrieve data for finite element analyses. It is used for preprocessing (problem definition), postprocessing (results visualization), as well as code to code data transfer. An EXODUS II data file is a random access, machine independent, binary file that is written and read via C, C++, or Fortran library routines which comprise the Application Programming Interface. (exodus II is based on netcdf)
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.
Finite element model of needle electrode sensitivity
NASA Astrophysics Data System (ADS)
Høyum, P.; Kalvøy, H.; Martinsen, Ø. G.; Grimnes, S.
2010-04-01
We used the Finite Element (FE) Method to estimate the sensitivity of a needle electrode for bioimpedance measurement. This current conducting needle with insulated shaft was inserted in a saline solution and current was measured at the neutral electrode. FE model resistance and reactance were calculated and successfully compared with measurements on a laboratory model. The sensitivity field was described graphically based on these FE simulations.
NASA Technical Reports Server (NTRS)
Fulton, R. E.
1986-01-01
The requirements of complex aerospace vehicles combined with the age of structural analysis systems enhance the need to advance technology toward a new generation of structural analysis capability. Recent and impeding advances in parallel and supercomputers provide the opportunity to significantly improve these structural analysis capabilities for large order finite element problems. Long-term research in parallel computing, associated with the NASA Finite Element Machine project, is discussed. The results show the potential of parallel computers to provide substantial increases in computation speed over sequential computers. Results are given for sample problems in the areas of eigenvalue analysis and transient response.
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.
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.
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.
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.
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.
The finite element method for calculating the marine structural design
NASA Astrophysics Data System (ADS)
Ion, A.; Ticu, I.
2015-11-01
The aim of this paper is to optimally design and dimension marine structures in order for them to fulfil both functional and safety requirements. A master level of structural mechanics is vital in order to check tests and analysis and to develop new structures. This study can improve the calculation and estimation of the effects of hydrodynamics and of other loads; movements, strains and internal forces in fixed and floating platforms and ships. The finite element method (FEM) ensures basic understanding of the finite element model as applied on static cases including beam and plate elements, experience with static analysis of marine structures like platforms and ships, along with the basic understanding of dynamic response of systems with one degree of freedom and simple continuous beams, and also how analysis models can be established for real structures by the use of generalized coordinates and superposition.
Finite element modelling for materials with size effect
NASA Astrophysics Data System (ADS)
Swaddiwudhipong, S.; Hua, J.; Tho, K. K.; Liu, Z. S.
2006-10-01
This paper involves the formulation of the C0 finite elements incorporating the conventional mechanism-based strain gradient plasticity theory. Higher-order variables and consequently higher-order continuity conditions are not required allowing the direct applications of conventional plasticity algorithms in the existing finite element package. Implementation of the model whether analytically or computationally is efficient and straightforward as the strain gradient effect is confined in the material constitutive relation. The accuracy of the proposed elements in simulating the response of materials with strong size effect is verified through several numerical examples. The approach is applicable and valid to any materials with non-uniform plastic deformation larger than about 100 nm onwards. The proposed model becomes imperative when the deformation is less than 10 µm as classical plasticity is unable to describe the phenomenon comprehensively at this low level of deformation.
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.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2016-02-01
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less
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
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).
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.
Iterative methods for mixed finite element equations
NASA Technical Reports Server (NTRS)
Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.
1985-01-01
Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.
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.
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.
Shape optimization including finite element grid adaptation
NASA Technical Reports Server (NTRS)
Kikuchi, N.; Taylor, J. E.
1984-01-01
The prediction of optimal shape design for structures depends on having a sufficient level of precision in the computation of structural response. These requirements become critical in situations where the region to be designed includes stress concentrations or unilateral contact surfaces, for example. In the approach to shape optimization discussed here, a means to obtain grid adaptation is incorporated into the finite element procedures. This facility makes it possible to maintain a level of quality in the computational estimate of response that is surely adequate for the shape design problem.
2-D Finite Element Heat Conduction
Energy Science and Technology Software Center (ESTSC)
1989-10-30
AYER is a finite element program which implicitly solves the general two-dimensional equation of thermal conduction for plane or axisymmetric bodies. AYER takes into account the effects of time (transient problems), in-plane anisotropic thermal conductivity, a three-dimensional velocity distribution, and interface thermal contact resistance. Geometry and material distributions are arbitrary, and input is via subroutines provided by the user. As a result, boundary conditions, material properties, velocity distributions, and internal power generation may be mademore » functions of, e.g., time, temperature, location, and heat flux.« less
Adaptive Finite Element Methods in Geodynamics
NASA Astrophysics Data System (ADS)
Davies, R.; Davies, H.; Hassan, O.; Morgan, K.; Nithiarasu, P.
2006-12-01
Adaptive finite element methods are presented for improving the quality of solutions to two-dimensional (2D) and three-dimensional (3D) convection dominated problems in geodynamics. The methods demonstrate the application of existing technology in the engineering community to problems within the `solid' Earth sciences. Two-Dimensional `Adaptive Remeshing': The `remeshing' strategy introduced in 2D adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver and an error estimator. In this study, the procedure is implemented in conjunction with the well-known geodynamical finite element code `ConMan'. An unstructured quadrilateral mesh generator is utilised, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermo-chemical problems with known benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy whilst increasing computational efficiency. For thermo-chemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies. Three-Dimensional Adaptive Multigrid: We extend the ideas from our 2D work into the 3D realm in the context of a pre-existing 3D-spherical mantle dynamics code, `TERRA'. In its original format, `TERRA' is computationally highly efficient since it employs a multigrid solver that depends upon a grid utilizing a clever
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.
NASA Technical Reports Server (NTRS)
Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.
1983-01-01
The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.
Advance finite element modeling of rotor blade aeroelasticity
NASA Technical Reports Server (NTRS)
Straub, F. K.; Sangha, K. B.; Panda, B.
1994-01-01
An advanced beam finite element has been developed for modeling rotor blade dynamics and aeroelasticity. This element is part of the Element Library of the Second Generation Comprehensive Helicopter Analysis System (2GCHAS). The element allows modeling of arbitrary rotor systems, including bearingless rotors. It accounts for moderately large elastic deflections, anisotropic properties, large frame motion for maneuver simulation, and allows for variable order shape functions. The effects of gravity, mechanically applied and aerodynamic loads are included. All kinematic quantities required to compute airloads are provided. In this paper, the fundamental assumptions and derivation of the element matrices are presented. Numerical results are shown to verify the formulation and illustrate several features of the element.
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 modeling of piezoelectric elements with complex electrode configuration
NASA Astrophysics Data System (ADS)
Paradies, R.; Schläpfer, B.
2009-02-01
It is well known that the material properties of piezoelectric materials strongly depend on the state of polarization of the individual element. While an unpolarized material exhibits mechanically isotropic material properties in the absence of global piezoelectric capabilities, the piezoelectric material properties become transversally isotropic with respect to the polarization direction after polarization. Therefore, for evaluating piezoelectric elements the material properties, including the coupling between the mechanical and the electromechanical behavior, should be addressed correctly. This is of special importance for the micromechanical description of piezoelectric elements with interdigitated electrodes (IDEs). The best known representatives of this group are active fiber composites (AFCs), macro fiber composites (MFCs) and the radial field diaphragm (RFD), respectively. While the material properties are available for a piezoelectric wafer with a homogeneous polarization perpendicular to its plane as postulated in the so-called uniform field model (UFM), the same information is missing for piezoelectric elements with more complex electrode configurations like the above-mentioned ones with IDEs. This is due to the inhomogeneous field distribution which does not automatically allow for the correct assignment of the material, i.e. orientation and property. A variation of the material orientation as well as the material properties can be accomplished by including the polarization process of the piezoelectric transducer in the finite element (FE) simulation prior to the actual load case to be investigated. A corresponding procedure is presented which automatically assigns the piezoelectric material properties, e.g. elasticity matrix, permittivity, and charge vector, for finite element models (FEMs) describing piezoelectric transducers according to the electric field distribution (field orientation and strength) in the structure. A corresponding code has been
Quantum algorithms and the finite element method
NASA Astrophysics Data System (ADS)
Montanaro, Ashley; Pallister, Sam
2016-03-01
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretizes the parameter space and finds an approximate solution by solving a large system of linear equations. Here we investigate the extent to which the finite element method can be accelerated using an efficient quantum algorithm for solving linear equations. We consider the representative general question of approximately computing a linear functional of the solution to a boundary value problem and compare the quantum algorithm's theoretical performance with that of a standard classical algorithm—the conjugate gradient method. Prior work claimed that the quantum algorithm could be exponentially faster but did not determine the overall classical and quantum run times required to achieve a predetermined solution accuracy. Taking this into account, we find that the quantum algorithm can achieve a polynomial speedup, the extent of which grows with the dimension of the partial differential equation. In addition, we give evidence that no improvement of the quantum algorithm can lead to a superpolynomial speedup when the dimension is fixed and the solution satisfies certain smoothness properties.
Impeller deflection and modal finite element analysis.
Spencer, Nathan A.
2013-10-01
Deflections of an impeller due to centripetal forces are calculated using finite element analysis. The lateral, or out of plane, deflections are an important design consideration for this particular impeller because it incorporates an air bearing with critical gap tolerances. The target gap distance is approximately 10 microns at a rotational velocity of 2500 rpm. The centripetal forces acting on the impeller cause it deflect in a concave fashion, decreasing the initial gap distance as a function of radial position. This deflection is characterized for a previous and updated impeller design for comparative purposes. The impact of design options such as material selection, geometry dimensions, and operating rotational velocity are also explored, followed by a sensitivity study with these parameters bounded by specific design values. A modal analysis is also performed to calculate the impeller's natural frequencies which are desired to be avoided during operation. The finite element modeling techniques continue to be exercised by the impeller design team to address specific questions and evaluate conceptual designs, some of which are included in the Appendix.
Finite element analysis of 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.
A finite element model for ultrasonic cutting.
Lucas, Margaret; MacBeath, Alan; McCulloch, Euan; Cardoni, Andrea
2006-12-22
Using a single-blade ultrasonic cutting device, a study of ultrasonic cutting of three very different materials is conducted using specimens of cheese, polyurethane foam and epoxy resin. Initial finite element models are created, based on the assumption that the ultrasonic blade causes a crack to propagate in a controlled mode 1 opening, and these are validated against experimental data from three point bend fracture tests and ultrasonic cutting experiments on the materials. Subsequently, the finite element model is developed to represent ultrasonic cutting of a multi-layered material. Materials are chosen whose properties allow a model to be developed that could represent a multi-layer food product or biological structure, to enable ultrasonic cutting systems to be designed for applications both in the field of food processing and surgical procedures. The model incorporates an estimation of the friction condition between the cutting blade and the material to be cut and allows adjustment of the frequency, cutting amplitude and cutting speed. PMID:16814351
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Borovkov, Alexei I.; Avdeev, Ilya V.; Artemyev, A.
1999-05-01
In present work, the stress, vibration and buckling finite element analysis of laminated beams is performed. Review of the equivalent single-layer (ESL) laminate theories is done. Finite element algorithms and procedures integrated into the original FEA program system and based on the classical laminated plate theory (CLPT), first-order shear deformation theory (FSDT), third-order theory of Reddy (TSDT-R) and third- order theory of Kant (TSDT-K) with the use of the Lanczos method for solving of the eigenproblem are developed. Several numerical tests and examples of bending, free vibration and buckling of multilayered and sandwich beams with various material, geometry properties and boundary conditions are solved. New effective higher-order hierarchical element for the accurate calculation of transverse shear stress is proposed. The comparative analysis of results obtained by the considered models and solutions of 2D problems of the heterogeneous anisotropic elasticity is fulfilled.
Elbow stress indices using finite element analysis
NASA Astrophysics Data System (ADS)
Yu, Lixin
Section III of the ASME Boiler and Pressure Vessel Code (the Code) specifies rules for the design of nuclear power plant components. NB-3600 of the Code presents a simplified design method using stress indices---Scalar Coefficients used the modify straight pipe stress equations so that they can be applied to elbows, tees and other piping components. The stress indices of piping components are allowed to be determined both analytically and experimentally. This study concentrates on the determination of B2 stress indices for elbow components using finite element analysis (FEA). First, the previous theoretical, numerical and experimental investigations on elbow behavior were comprehensively reviewed, as was the philosophy behind the use of stress indices. The areas of further research was defined. Then, a comprehensive investigation was carried out to determine how the finite element method should be used to correctly simulate an elbow's structural behavior. This investigation included choice of element type, convergence of mesh density, use of boundary restraint and a reconciliation study between FEA and laboratory experiments or other theoretical formulations in both elastic and elasto-plastic domain. Results from different computer programs were also compared. Reasonably good reconciliation was obtained. Appendix II of the Code describes the experimental method to determine B2 stress indices based on load-deflection curves. This procedure was used to compute the B2 stress indices for various loading modes on one particular elbow configuration. The B2 stress indices thus determined were found to be about half of the value calculated from the Code equation. Then the effect on B2 stress indices of those factors such as internal pressure and flange attachments were studied. Finally, the investigation was extended to other configurations of elbow components. A parametric study was conducted on different elbow sizes and schedules. Regression analysis was then used to
NASA Astrophysics Data System (ADS)
Beilina, Larisa
2016-08-01
We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the computational domain: finite difference method is used on the structured part of the computational domain and finite elements on the unstructured part of the domain. Explicit discretizations for both methods are constructed such that the finite element and the finite difference schemes coincide on the common structured overlapping layer between computational subdomains. Then the resulting approach can be considered as a pure finite element scheme which avoids instabilities at the interfaces. We derive an energy estimate for the underlying hyperbolic equation with absorbing boundary conditions and illustrate efficiency of the domain decomposition method on the reconstruction of the conductivity function in three dimensions.
Asymmetric quadrilateral shell elements for finite strains
NASA Astrophysics Data System (ADS)
Areias, P.; Dias-da-Costa, D.; Pires, E. B.; Van Goethem, N.
2013-07-01
Very good results in infinitesimal and finite strain analysis of shells are achieved by combining either the enhanced-metric technique or the selective-reduced integration for the in-plane shear energy and an assumed natural strain technique (ANS) in a non-symmetric Petrov-Galerkin arrangement which complies with the patch-test. A recovery of the original Wilson incompatible mode element is shown for the trial functions in the in-plane components. As a beneficial side-effect, Newton-Raphson convergence behavior for non-linear problems is improved with respect to symmetric formulations. Transverse-shear and in-plane patch tests are satisfied while distorted-mesh accuracy is higher than with symmetric formulations. Classical test functions with assumed-metric components are required for compatibility reasons. Verification tests are performed with advantageous comparisons being observed in all of them. Applications to large displacement elasticity and finite strain plasticity are shown with both low sensitivity to mesh distortion and (relatively) high accuracy. A equilibrium-consistent (and consistently linearized) updated-Lagrangian algorithm is proposed and tested. Concerning the time-step dependency, it was found that the consistent updated-Lagrangian algorithm is nearly time-step independent and can replace the multiplicative plasticity approach if only moderate elastic strains are present, as is the case of most metals.
Finite element or Galerkin type semidiscrete schemes
NASA Technical Reports Server (NTRS)
Durgun, K.
1983-01-01
A finite element of Galerkin type semidiscrete method is proposed for numerical solution of a linear hyperbolic partial differential equation. The question of stability is reduced to the stability of a system of ordinary differential equations for which Dahlquist theory applied. Results of separating the part of numerical solution which causes the spurious oscillation near shock-like response of semidiscrete scheme to a step function initial condition are presented. In general all methods produce such oscillatory overshoots on either side of shocks. This overshoot pathology, which displays a behavior similar to Gibb's phenomena of Fourier series, is explained on the basis of dispersion of separated Fourier components which relies on linearized theory to be satisfactory. Expository results represented.
Finite-element modeling of nanoindentation
Knapp, J.A.; Follstaedt, D.M.; Myers, S.M.; Barbour, J.C.; Friedmann, T.A.
1999-02-01
Procedures have been developed based on finite-element modeling of nanoindentation data to obtain the mechanical properties of thin films and ion-beam-modified layers independently of the properties of the underlying substrates. These procedures accurately deduce the yield strength, Young{close_quote}s elastic modulus, and layer hardness from indentations as deep as 50{percent} of the layer thickness or more. We have used these procedures to evaluate materials ranging from ion implanted metals to deposited, diamond-like carbon layers. The technique increases the applicability of indentation testing to very thin layers, composite layers, and modulated compositions. This article presents an overview of the procedures involved and illustrates them with selected examples. {copyright} {ital 1999 American Institute of Physics.}
Continuation finite element analysis of viscoelastic fluids
NASA Astrophysics Data System (ADS)
Chow, Tai-Whang
A finite element procedure using a mixed formulation and a predictor-corrector type continuation algorithm for the analysis of two dimensional steady state flows of viscoelastic fluids is described. As a simple but nontrivial test example, radial flow immenating from a line by the numerical discretization and believed to be the cause for previous numerical failures, are shown and branch solution paths are followed by step length adjustment and by convergent tolerance relaxation. A technique for jumping over bifurcation points is presented and used to increase the Weissenberg number with no apparent limit for the radial flow problem. A second example related to extrusion of viscoelastic material is also analyzed. Steady state velocity fields, deviatoric stress distributions and pressure distributions for several different Weissenberg numbers are presented with bifurcation points and turning points noted.
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.
Optimizing electroslag cladding with finite element modeling
Li, M.V.; Atteridge, D.G.; Meekisho, L.
1996-12-31
Electroslag cladding of nickel alloys onto carbon steel propeller shafts was optimized in terms of interpass temperatures. A two dimensional finite element model was used in this study to analyze the heat transfer induced by multipass electroslag cladding. Changes of interpass temperatures during a cladding experiment with uniform initial temperature distribution on a section of shaft were first simulated. It was concluded that uniform initial temperature distribution would lead to interpass temperatures out of the optimal range if continuous cladding is expected. The difference in the cooling conditions among experimental and full size shafts and its impact on interpass temperatures during the cladding were discussed. Electroslag cladding onto a much longer shaft, virtually an semi infinite long shaft, was analyzed with specific reference to the practical applications of electroslag cladding. Optimal initial preheating temperature distribution was obtained for continuous cladding on full size shafts which would keep the interpass temperatures within the required range.
Finite element simulation of pipe dynamic response
Slagis, G.C.; Litton, R.W.
1996-12-01
Nonlinear finite element dynamic analyses of the response of a pipe span to controlled-displacement, sinusoidal vibration have been performed. The objective of this preliminary study is to compare strain and acceleration response data to those generated by Beaney in the Berkeley Nuclear Laboratories experiments. Results for an unpressurized, 5 Hz, carbon steel pipe are in good agreement with the experiments. Hence, it appears that analytical simulation will be useful to assess seismic margins. Recommendations for additional studies are provided. The analyses confirm the test results--dynamic response is greatly attenuated by material plasticity. Analytical strains and accelerations are about 30% higher than test data. There are several possible explanations for the differences. To assess the effect of frequency on response, the length of the pipe span was increased. Analysis of the longer, 2 Hz, pipe span shows significantly greater cyclic strains than the 5 Hz span at the same input excitation levels.
3-D Finite Element Heat Transfer
Energy Science and Technology Software Center (ESTSC)
1992-02-01
TOPAZ3D is a three-dimensional implicit finite element computer code for heat transfer analysis. TOPAZ3D can be used to solve for the steady-state or transient temperature field on three-dimensional geometries. Material properties may be temperature-dependent and either isotropic or orthotropic. A variety of time-dependent and temperature-dependent boundary conditions can be specified including temperature, flux, convection, and radiation. By implementing the user subroutine feature, users can model chemical reaction kinetics and allow for any type of functionalmore » representation of boundary conditions and internal heat generation. TOPAZ3D can solve problems of diffuse and specular band radiation in an enclosure coupled with conduction in the material surrounding the enclosure. Additional features include thermal contact resistance across an interface, bulk fluids, phase change, and energy balances.« less
Finite element analysis: A boon to dentistry
Trivedi, Shilpa
2014-01-01
The finite element analysis (FEA) is an upcoming and significant research tool for biomechanical analyses in biological research. It is an ultimate method for modeling complex structures and analyzing their mechanical properties. In Implantology, FEA has been used to study the stress patterns in various implant components and also in the peri-implant bone. It is also useful for studying the biomechanical properties of implants as well as for predicting the success of implants in clinical condition. FEA of simulated traumatic loads can be used to understand the biomechanics of fracture. FEA has various advantages compared with studies on real models. The experiments are repeatable, there are no ethical considerations and the study designs may be modified and changed as per the requirement. There are certain limitations of FEA too. It is a computerized in vitro study in which clinical condition may not be completely replicated. So, further FEA research should be supplemented with clinical evaluation. PMID:25737944
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.
Boundary element and finite element coupling for aeroacoustics simulations
NASA Astrophysics Data System (ADS)
Balin, Nolwenn; Casenave, Fabien; Dubois, François; Duceau, Eric; Duprey, Stefan; Terrasse, Isabelle
2015-08-01
We consider the scattering of acoustic perturbations in the presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert transformation to recover the Helmholtz equation. The well-known setting of boundary element method for the Helmholtz equation is available. In the second zone, the flow quantities are space dependent, we have to consider a local resolution, namely the finite element method. Herein, we carry out the coupling of these two methods and present various applications and validation test cases. The source term is given through the decomposition of an incident acoustic field on a section of the computational domain's boundary. Validations against analytic, another numerical method and measurements on different test cases are presented.
Global-Local Finite Element Analysis of Bonded Single-Lap Joints
NASA Technical Reports Server (NTRS)
Kilic, Bahattin; Madenci, Erdogan; Ambur, Damodar R.
2004-01-01
Adhesively bonded lap joints involve dissimilar material junctions and sharp changes in geometry, possibly leading to premature failure. Although the finite element method is well suited to model the bonded lap joints, traditional finite elements are incapable of correctly resolving the stress state at junctions of dissimilar materials because of the unbounded nature of the stresses. In order to facilitate the use of bonded lap joints in future structures, this study presents a finite element technique utilizing a global (special) element coupled with traditional elements. The global element includes the singular behavior at the junction of dissimilar materials with or without traction-free surfaces.
A tensor artificial viscosity using a finite element approach
NASA Astrophysics Data System (ADS)
Kolev, Tz. V.; Rieben, R. N.
2009-12-01
We derive a tensor artificial viscosity suitable for use in a 2D or 3D unstructured arbitrary Lagrangian-Eulerian (ALE) hydrodynamics code. This work is similar in nature to that of Campbell and Shashkov [1]; however, our approach is based on a finite element discretization that is fundamentally different from the mimetic finite difference framework. The finite element point of view leads to novel insights as well as improved numerical results. We begin with a generalized tensor version of the Von Neumann-Richtmyer artificial viscosity, then convert it to a variational formulation and apply a Galerkin discretization process using high order Gaussian quadrature to obtain a generalized nodal force term and corresponding zonal heating (or shock entropy) term. This technique is modular and is therefore suitable for coupling to a traditional staggered grid discretization of the momentum and energy conservation laws; however, we motivate the use of such finite element approaches for discretizing each term in the Euler equations. We review the key properties that any artificial viscosity must possess and use these to formulate specific constraints on the total artificial viscosity force term as well as the artificial viscosity coefficient. We also show, that under certain simplifying assumptions, the two-dimensional scheme from [1] can be viewed as an under-integrated version of our finite element method. This equivalence holds on general distorted quadrilateral grids. Finally, we present computational results on some standard shock hydro test problems, as well as some more challenging problems, indicating the advantages of the new approach with respect to symmetry preservation for shock wave propagation over general grids.
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.
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.
Phased array antenna analysis using hybrid finite element methods
NASA Astrophysics Data System (ADS)
McGrath, Daniel T.
1993-06-01
This research in computational electromagnetics developed a new method for predicting the near-field mutual coupling effects in phased array antennas, using the finite element method (FEM) in combination with integral equations. Accurate feed modeling is accomplished by enforcing continuity between the FEM solution and an arbitrary number of wave guide models across a ground plane aperture. A periodic integral equation is imposed above the antenna's physical structure in order to enforce the radiation condition and to confine the analysis to an array unit cell. The electric field is expanded in terms of vector finite elements, and Galerkin's method is used to write the problem as a matrix equation. A general-purpose computer code was developed and validated by comparing its results to published data for several array types. Its versatility was demonstrated with predictions of the scanning properties of arrays of printed dipoles and printed flared notches.
Finite element solution theory for three-dimensional boundary flows
NASA Technical Reports Server (NTRS)
Baker, A. J.
1974-01-01
A finite element algorithm is derived for the numerical solution of a three-dimensional flow field described by a system of initial-valued, elliptic boundary value partial differential equations. The familiar three-dimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.
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.
Finite-element time evolution operator for the anharmonic oscillator
NASA Technical Reports Server (NTRS)
Milton, Kimball A.
1995-01-01
The finite-element approach to lattice field theory is both highly accurate (relative errors approximately 1/N(exp 2), where N is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is H = p(exp 2)/2 + lambda q(exp 4)/4. Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a results for the anharmonic oscillator ground state energy accurate to better than 1 percent, while a two-state approximation reduces the error to less than 0.1 percent.
A hybrid-stress finite element for linear anisotropic elasticity
NASA Technical Reports Server (NTRS)
Fly, Gerald W.; Oden, J. Tinsley; Pearson, Mark L.
1988-01-01
Standard assumed displacement finite elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased.
Finite element mesh refinement criteria for stress analysis
NASA Technical Reports Server (NTRS)
Kittur, Madan G.; Huston, Ronald L.
1990-01-01
This paper discusses procedures for finite-element mesh selection and refinement. The objective is to improve accuracy. The procedures are based on (1) the minimization of the stiffness matrix race (optimizing node location); (2) the use of h-version refinement (rezoning, element size reduction, and increasing the number of elements); and (3) the use of p-version refinement (increasing the order of polynomial approximation of the elements). A step-by-step procedure of mesh selection, improvement, and refinement is presented. The criteria for 'goodness' of a mesh are based on strain energy, displacement, and stress values at selected critical points of a structure. An analysis of an aircraft lug problem is presented as an example.
Effect of grid system on finite element calculation
NASA Technical Reports Server (NTRS)
Lee, K. D.; Yen, S. M.
1980-01-01
Detailed parametric studies of the effect of grid system on finite element calculation for potential flows were made. These studies led to the formulation of a design criteria for optimum mesh system and the development of two methods to generate the optimum mesh system. The guidelines for optimum mesh system are: (1) the mesh structure should be regular; (2) the element should be as regular and equilateral as possible; (3) the distribution of size of element should be consistent with that of flow variables to insure maximum uniformity in error distribution; (4) for non-Dirichlet boundary conditions, smaller boundary elements or higher order interpolation functions should be used; and (5) the mesh should accommodate the boundary geometry as accurately as possible. The results of the parametric studies are presented.
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.
Improved finite-element methods for rotorcraft structures
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1991-01-01
An overview of the research directed at improving finite-element methods for rotorcraft airframes is presented. The development of a modification to the finite element method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick finite element program.
Impact of new computing systems on finite element computations
NASA Technical Reports Server (NTRS)
Noor, A. K.; Storassili, O. O.; Fulton, R. E.
1983-01-01
Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified.
NASA Technical Reports Server (NTRS)
Fix, G. J.; Rose, M. E.
1983-01-01
A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.
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 analysis in a minicomputer/mainframe environment
NASA Technical Reports Server (NTRS)
Storaasli, O. O.; Murphy, R. C.
1978-01-01
Design considerations were evaluated for general purpose finite element systems to maximize performance when installed on distributed computer hardware/software systems. It is shown how the features of current minicomputers complement those of a modular implementation of the finite element method for increasing the control, speed, and visibility (interactive graphics) in solving structural problems at reduced cost. The approach used is to implement a finite element system in a distributed computer environment to solve structural problems and to explore alternatives in distributing finite element computations.
A multi-microprocessor system for finite element structural analysis
NASA Technical Reports Server (NTRS)
Jordan, H. F.; Sawyer, P. L.
1978-01-01
During the last few years, advances in microprocessor technology have spurred a renewed interest in special-purpose computers. The microprocessor has become small, inexpensive, and powerful enough to be considered as a building block for special-purpose hardware. A description is presented of the architecture of a prototype 'finite element machine' currently being built. Attention is given to details regarding the finite element analysis problem, the arrangement of the processors as finite element nodes in the structural model, the influence of the architecture on the solution algorithm, interprocessor communication primitives, and the performance of the finite element machine.
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.
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.
A phenomenological finite element model of stereolithography processing
Chambers, R.S.; Guess, T.R.; Hinnerichs, T.D.
1996-03-01
In the stereolithography process, three dimensional parts are built layer by layer using a laser to selectively cure slices of a photocurable resin, one on top of another. As the laser spot passes over the surface of the resin, the ensuing chemical reaction causes the resin to shrink and stiffen during solidification. When laser paths cross or when new layers are cured on top of existing layers, residual stresses are generated as the cure shrinkage of the freshly gelled resin is constrained by the adjoining previously-cured material. These internal stresses can cause curling in the compliant material. A capability for performing finite element analyses of the stereolithography process has been developed. Although no attempt has been made to incorporate all the physics of the process, a numerical platform suitable for such development has been established. A methodology and code architecture have been structured to allow finite elements to be birthed (activated) according to a prescribed order mimicking the procedure by which a laser is used to cure and build-up surface layers of resin to construct a three dimensional geometry. In its present form, the finite element code incorporates a simple phenomenological viscoelastic material model of solidification that is based on the shrinkage and relaxation observed following isolated, uncoupled laser exposures. The phenomenological material model has been used to analyze the curl in a simple cantilever beam and to make qualitative distinctions between two contrived build styles.
Finite element analysis of SMA beam bending using COMSOL
NASA Astrophysics Data System (ADS)
Yang, Shibin; Seelecke, Stefan S.; Li, Qifu
2009-03-01
Shape memory alloys (SMAs) represent a class of smart materials that has been extensively used in many engineering applications due to their unique material properties. To facilitate these new developments, an efficient computational tool like the finite element method has to be used in order to simulate the highly nonlinear, load-history and temperature dependent responses of SMA materials. The particular focus of this paper is on the aspects of modeling and simulation of the inhomogeneous beam bending problem. Based on small deformation Euler-Bernoulli beam theory, the SMA beam is treated as consisting of several layers. Each governed by a 1-D free energy SMA model. The SMA beam is implemented in the finite element software COMSOL using its general PDE form. The ordinary differential equations describing the kinetics of the phase transformations are treated as degenerated PDEs without a flux term and coupled with the mechanical equilibrium equation and the heat transfer equation. In this paper, we study the quasiplastic and superelastic isothermal behavior of an SMA cantilever beam at constant low and high temperature, respectively. Keywords: finite element analysis, shape memory alloy, COMSOL
Numerical algorithms for finite element computations on arrays of microprocessors
NASA Technical Reports Server (NTRS)
Ortega, J. M.
1981-01-01
The development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization.
Integrated finite element model of composite materials
NASA Astrophysics Data System (ADS)
Teply, Jan L.; Herbein, William C.
1989-05-01
Two problems traditionally addressed in the area of micromechanics of composite materials can be briefly summarized as follows: (1) for a macroscopically uniform volume of composite material, which is subjected to macroscopically uniform boundary tractions, displacements or heat influx, find overall thermomechanical properties in terms of the thermomechanical properties of the individual constituents; and (2) for the same material volume and boundary conditions as above, find the local stress, strain, and temperature fields in the constituents and on the interfaces. Two different types of micromechanical models are usually applied to the solutions of these two types of problems. For linear elastic materials, the micromechanical models to solve problem (1) offer simple solutions of overall thermomechanical properties either in terms of bound which are derived from periodic or random microstructures, or in terms of single estimates, which are derived from a solution of an isolated inclusion. The finite element variational approaches are applied to integrate the solutions of problems (1) and (2) into one model. The application of displacement and equilibrium variational approaches to the calculation of overall elastic-plastic properties, are extended to the solution of the second problem. The integrated model is then applied to calculate the overall properties and local stress and strain fields of boron-aluminum composites subjected to transverse tension, in-plane shear and bending.
Laterally displaced pipelines: Finite element analysis
Altaee, A.; Boivin, R.
1995-12-31
The rate effect of lateral soil movement against buried pipes in clay soils is investigated in finite element analyzes using two different computer programs, AGAC and CRISP. Rapid and slow ground movements are considered in ideal undrained and ideal drained analysis, respectively, which represent the two extreme boundaries with respect to rate of loading (rate of ground movement). The analyses address a typical full-scale buried pipe as described by Rizkalla et al. (1992). The pipe considered for the analysis has a diameter of 0.914 m and is placed in a backfilled 2.0 m wide and 1.8 m deep excavation. Results from both AGAC and CRISP analyzes are similar in terms of total lateral force versus lateral pipe movement. For example, both programs indicate the same clear difference in the resulting pipe movement for cases of rapid and slow ground movement, especially at large movement. When the ground movement is rapid, the pipe moves both laterally and upward. One the other hand, when the ground movement is slow, the pipe experiences only lateral movement and no noticeable vertical movement. The total force acting on the pipe (and stresses and strains within the pipe) is larger for the slow rate of loading. The results of analyzes presented herein agree with results of tests on a 5.5 m beam centrifuge performed by the Center for Cold Oceans Resources Engineering.
Finite Element Modeling of Human Placental Tissue
Yu, Mao; Manoogian, Sarah; Duma, Stefan M.; Stitzel, Joel D.
2009-01-01
Motor vehicle crashes account for a large portion of placental abruption and fetal losses. To better understand the material properties of the human placenta, a Finite Element (FE) model of human placenta tissue was created and verified using data from uniaxial tension tests. Sixty-four tensile tests at three different strain rates of 7% strain/s, 70% strain/s, and 700% strain/s from six whole human placentas were used for model development. Nominal stresses were calculated by dividing forces at the grips by the original cross-sectional area. Nominal strains were calculated by dividing cross-head displacement by the original gauge length. A detailed methodology for interpreting experimental data for application to material model development is presented. A model of the tension coupon was created in LS-DYNA and stretched in the same manner as the uniaxial tension tests. The behavior of the material was optimized to the uniaxial tension test using a multi-island genetic algorithm. The results demonstrate good correlation between experiments and the model, with an average difference of 2% between the optimized FE and experimental first principal stress at the termination state. The material parameters found in this study can be utilized in FE models of placental tissues for behavior under dynamic loading. PMID:20184849
TACO: a finite element heat transfer code
Mason, W.E. Jr.
1980-02-01
TACO is a two-dimensional implicit finite element code for heat transfer analysis. It can perform both linear and nonlinear analyses and can be used to solve either transient or steady state problems. Either plane or axisymmetric geometries can be analyzed. TACO has the capability to handle time or temperature dependent material properties and materials may be either isotropic or orthotropic. A variety of time and temperature dependent loadings and boundary conditions are available including temperature, flux, convection, and radiation boundary conditions and internal heat generation. Additionally, TACO has some specialized features such as internal surface conditions (e.g., contact resistance), bulk nodes, enclosure radiation with view factor calculations, and chemical reactive kinetics. A user subprogram feature allows for any type of functional representation of any independent variable. A bandwidth and profile minimization option is also available in the code. Graphical representation of data generated by TACO is provided by a companion post-processor named POSTACO. The theory on which TACO is based is outlined, the capabilities of the code are explained, the input data required to perform an analysis with TACO are described. Some simple examples are provided to illustrate the use of the code.
NASA Astrophysics Data System (ADS)
Stupkiewicz, Stanisław
2009-10-01
Soft elastohydrodynamic lubrication (EHL) problem is studied for a reciprocating elastomeric seal with full account of finite configuration changes. The fluid part is described by the Reynolds equation which is formulated on the deformed boundary of the seal treated as a hyperelastic body. The paper is concerned with the finite element (FE) treatment of this soft EHL problem. Displacement-based FE discretization is applied for the solid part. The Reynolds equation is discretized using the FE method or, alternatively, the discontinuous Galerkin method, both employing higher-order interpolation of pressure. The performance of both methods is assessed by studying convergence and stability of the solution for a benchmark problem of an O-ring seal. It is shown that the solution may exhibit spurious oscillations which occur in severe lubrication conditions. Mesh refinement results in reduction of these oscillations, while increasing the pressure interpolation order or application of the discontinuous Galerkin method does not help significantly.
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)
Automation Tools for Finite Element Analysis of Adhesively Bonded Joints
NASA Technical Reports Server (NTRS)
Tahmasebi, Farhad; Brodeur, Stephen J. (Technical Monitor)
2002-01-01
This article presents two new automation creation tools that obtain stresses and strains (Shear and peel) in adhesively bonded joints. For a given adhesively bonded joint Finite Element model, in which the adhesive is characterised using springs, these automation tools read the corresponding input and output files, use the spring forces and deformations to obtain the adhesive stresses and strains, sort the stresses and strains in descending order, and generate plot files for 3D visualisation of the stress and strain fields. Grids (nodes) and elements can be numbered in any order that is convenient for the user. Using the automation tools, trade-off studies, which are needed for design of adhesively bonded joints, can be performed very quickly.
Regularised finite element model updating using measured incomplete modal data
NASA Astrophysics Data System (ADS)
Chen, Hua-Peng; Maung, Than Soe
2014-10-01
This paper presents an effective approach for directly updating finite element model from measured incomplete vibration modal data with regularised algorithms. The proposed method is based on the relationship between the perturbation of structural parameters such as stiffness change and the modal data measurements of the tested structure such as measured mode shape readings. In order to adjust structural parameters at detailed locations, structural updating parameters will be selected at critical point level to reflect the modelling errors at the connections of structural elements. These updating parameters are then evaluated by an iterative or a direct solution procedure, which gives optimised solutions in the least squares sense without requiring an optimisation technique. In order to reduce the influence of modal measurement uncertainty, the Tikhonov regularisation method incorporating the L-curve criterion is employed to produce reliable solutions for the chosen updating parameters. Numerical simulation investigations and experimental studies for the laboratory tested space steel frame structure are undertaken to verify the accuracy and effectiveness of the proposed methods for adjusting the stiffness at the joints of structural members. The results demonstrate that the proposed methods provide reliable estimates of finite element model updating using the measured incomplete modal data.
Binary tree eigen solver in finite element analysis
Akl, F.A.; Janetzke, D.C.; Kiraly, L.J.
1993-01-01
This paper presents a transputer-based binary tree eigensolver for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on the method of recursive doubling, which parallel implementation of a number of associative operations on an arbitrary set having N elements is of the order of o(log2N), compared to (N-1) steps if implemented sequentially. The hardware used in the implementation of the binary tree consists of 32 transputers. The algorithm is written in OCCAM which is a high-level language developed with the transputers to address parallel programming constructs and to provide the communications between processors. The algorithm can be replicated to match the size of the binary tree transputer network. Parallel and sequential finite element analysis programs have been developed to solve for the set of the least-order eigenpairs using the modified subspace method. The speed-up obtained for a typical analysis problem indicates close agreement with the theoretical prediction given by the method of recursive doubling. 5 refs.