Improved finite element methodology for integrated thermal structural analysis

NASA Technical Reports Server (NTRS)

Dechaumphai, P.; Thornton, E. A.

1982-01-01

An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. New thermal finite elements which yield exact nodal and element temperatures for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.

Element-topology-independent preconditioners for parallel finite element computations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

Finite Element Barotropic Model for the Indian and Western Pacific OceanBasin: Tidal Model Data Comparisons and Sensitivities

DTIC Science & Technology

2018-01-11

From - To) 01/11/2018 Final Technical Report June 01 2016 - Dec 30 2017 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Finite - Element Barotropic Model...grid finite - element barotropic fully hydrodynamic model in order to understand the shallow-water dynamics of the Indian Ocean and Western Pacific Ocean...dissipative dissipative processes are explored. 15. SUBJECTTERMS finite - element , unstructured grid, barotropic tides, bathymetry, internal tide

Dispersion analysis of the Pn -Pn-1DG mixed finite element pair for atmospheric modelling

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2018-02-01

Mixed finite element methods provide a generalisation of staggered grid finite difference methods with a framework to extend the method to high orders. The ability to generate a high order method is appealing for applications on the kind of quasi-uniform grids that are popular for atmospheric modelling, so that the method retains an acceptable level of accuracy even around special points in the grid. The dispersion properties of such schemes are important to study as they provide insight into the numerical adjustment to imbalance that is an important component in atmospheric modelling. This paper extends the recent analysis of the P2 - P1DG pair, that is a quadratic continuous and linear discontinuous finite element pair, to higher polynomial orders and also spectral element type pairs. In common with the previously studied element pair, and also with other schemes such as the spectral element and discontinuous Galerkin methods, increasing the polynomial order is found to provide a more accurate dispersion relation for the well resolved part of the spectrum but at the cost of a number of unphysical spectral gaps. The effects of these spectral gaps are investigated and shown to have a varying impact depending upon the width of the gap. Finally, the tensor product nature of the finite element spaces is exploited to extend the dispersion analysis into two-dimensions.

Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

NASA Astrophysics Data System (ADS)

Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

2018-06-01

This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

NASA Astrophysics Data System (ADS)

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-05-01

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructs high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss-Lobatto-Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

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

Gao, Kai; Fu, Shubin; Chung, Eric T.

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructsmore » high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss–Lobatto–Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.« less

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

DOE PAGES

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-02-04

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructsmore » high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss–Lobatto–Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.« less

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

NASA Astrophysics Data System (ADS)

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

1999-05-01

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

Reissner-Mindlin Legendre Spectral Finite Elements with Mixed Reduced Quadrature

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

Brito, K. D.; Sprague, M. A.

2012-10-01

Legendre spectral finite elements (LSFEs) are examined through numerical experiments for static and dynamic Reissner-Mindlin plate bending and a mixed-quadrature scheme is proposed. LSFEs are high-order Lagrangian-interpolant finite elements with nodes located at the Gauss-Lobatto-Legendre quadrature points. Solutions on unstructured meshes are examined in terms of accuracy as a function of the number of model nodes and total operations. While nodal-quadrature LSFEs have been shown elsewhere to be free of shear locking on structured grids, locking is demonstrated here on unstructured grids. LSFEs with mixed quadrature are, however, locking free and are significantly more accurate than low-order finite-elements for amore » given model size or total computation time.« less

A new conformal absorbing boundary condition for finite element meshes and parallelization of FEMATS

NASA Technical Reports Server (NTRS)

Chatterjee, A.; Volakis, J. L.; Nguyen, J.; Nurnberger, M.; Ross, D.

1993-01-01

Some of the progress toward the development and parallelization of an improved version of the finite element code FEMATS is described. This is a finite element code for computing the scattering by arbitrarily shaped three dimensional surfaces composite scatterers. The following tasks were worked on during the report period: (1) new absorbing boundary conditions (ABC's) for truncating the finite element mesh; (2) mixed mesh termination schemes; (3) hierarchical elements and multigridding; (4) parallelization; and (5) various modeling enhancements (antenna feeds, anisotropy, and higher order GIBC).

A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

PubMed Central

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L 2(Ω))2 space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term w = −Δu and a priori error estimates in (L 2)2-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes. PMID:23864831

A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.

PubMed

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.

ICASE Semiannual Report, October 1, 1992 through March 31, 1993

DTIC Science & Technology

1993-06-01

NUMERICAL MATHEMATICS Saul Abarbanel Further results have been obtained regarding long time integration of high order compact finite difference schemes...overall accuracy. These problems are common to all numerical methods: finite differences , finite elements and spectral methods. It should be noted that...fourth order finite difference scheme. * In the same case, the D6 wavelets provide a sixth order finite difference , noncompact formula. * The wavelets

Interpolation Hermite Polynomials For Finite Element Method

NASA Astrophysics Data System (ADS)

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

2018-02-01

We describe a new algorithm for analytic calculation of high-order Hermite interpolation polynomials of the simplex and give their classification. A typical example of triangle element, to be built in high accuracy finite element schemes, is given.

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Application of finite element approach to transonic flow problems

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C., Jr.

1976-01-01

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions, and blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, nonrectangular elements, and discontinuous approximation of shock waves are also discussed.

Finite element modeling of hyper-viscoelasticity of peripheral nerve ultrastructures.

PubMed

Chang, Cheng-Tao; Chen, Yu-Hsing; Lin, Chou-Ching K; Ju, Ming-Shaung

2015-07-16

The mechanical characteristics of ultrastructures of rat sciatic nerves were investigated through animal experiments and finite element analyses. A custom-designed dynamic testing apparatus was used to conduct in vitro transverse compression experiments on the nerves. The optical coherence tomography (OCT) was utilized to record the cross-sectional images of nerve during the dynamic testing. Two-dimensional finite element models of the nerves were built based on their OCT images. A hyper-viscoelastic model was employed to describe the elastic and stress relaxation response of each ultrastructure of the nerve, namely the endoneurium, the perineurium and the epineurium. The first-order Ogden model was employed to describe the elasticity of each ultrastructure and a generalized Maxwell model for the relaxation. The inverse finite element analysis was used to estimate the material parameters of the ultrastructures. The results show the instantaneous shear modulus of the ultrastructures in decreasing order is perineurium, endoneurium, and epineurium. The FE model combined with the first-order Ogden model and the second-order Prony series is good enough for describing the compress-and-hold response of the nerve ultrastructures. The integration of OCT and the nonlinear finite element modeling may be applicable to study the viscoelasticity of peripheral nerve down to the ultrastructural level. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

The constraint method: A new finite element technique. [applied to static and dynamic loads on plates

NASA Technical Reports Server (NTRS)

Tsai, C.; Szabo, B. A.

1973-01-01

An approch to the finite element method which utilizes families of conforming finite elements based on complete polynomials is presented. Finite element approximations based on this method converge with respect to progressively reduced element sizes as well as with respect to progressively increasing orders of approximation. Numerical results of static and dynamic applications of plates are presented to demonstrate the efficiency of the method. Comparisons are made with plate elements in NASTRAN and the high-precision plate element developed by Cowper and his co-workers. Some considerations are given to implementation of the constraint method into general purpose computer programs such as NASTRAN.

Acceleration of low order finite element computation with GPUs (Invited)

NASA Astrophysics Data System (ADS)

Knepley, M. G.

2010-12-01

Considerable effort has been focused on the acceleration using GPUs of high order spectral element methods and discontinuous Galerkin finite element methods. However, these methods are not universally applicable, and much of the existing FEM software base employs low order methods. In this talk, we present a formulation of FEM, using the PETSc framework from ANL, which is amenable to GPU acceleration even at very low order. In addition, using the FEniCS system for FEM, we show that the relevant kernels can be automatically generated and optimized using a symbolic manipulation system.

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

Wiley, J.C.

The author describes a general `hp` finite element method with adaptive grids. The code was based on the work of Oden, et al. The term `hp` refers to the method of spatial refinement (h), in conjunction with the order of polynomials used as a part of the finite element discretization (p). This finite element code seems to handle well the different mesh grid sizes occuring between abuted grids with different resolutions.

A curvilinear, anisotropic, p-version, brick finite element based on geometric entities

NASA Technical Reports Server (NTRS)

Hinnant, Howard E.

1992-01-01

A 'brick' solid finite element is presently developed on the basis of the p-version analysis, and used to demonstrate the FEM concept of 'geometric entities'. This method eliminates interelement discontinuities between low- and high-order elements, allowing very fine control over the shape-function order in various parts of the model. Attention is given to the illustrative cases of a one-element model of an elliptic pipe, and a square cross-section cantilevered beam.

An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems

NASA Technical Reports Server (NTRS)

Deng, Qingping

1996-01-01

A multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.

Error analysis of finite element method for Poisson–Nernst–Planck equations

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

Sun, Yuzhou; Sun, Pengtao; Zheng, Bin

A priori error estimates of finite element method for time-dependent Poisson-Nernst-Planck equations are studied in this work. We obtain the optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm, with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semi- and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.

Arbitrary-Order Conservative and Consistent Remapping and a Theory of Linear Maps: Part II

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

Ullrich, Paul A.; Devendran, Dharshi; Johansen, Hans

2016-04-01

The focus on this series of articles is on the generation of accurate, conservative, consistent, and (optionally) monotone linear offline maps. This paper is the second in the series. It extends on the first part by describing four examples of 2D linear maps that can be constructed in accordance with the theory of the earlier work. The focus is again on spherical geometry, although these techniques can be readily extended to arbitrary manifolds. The four maps include conservative, consistent, and (optionally) monotone linear maps (i) between two finite-volume meshes, (ii) from finite-volume to finite-element meshes using a projection-type approach, (iii)more » from finite-volume to finite-element meshes using volumetric integration, and (iv) between two finite-element meshes. Arbitrary order of accuracy is supported for each of the described nonmonotone maps.« less

Supercomputer implementation of finite element algorithms for high speed compressible flows

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Ramakrishnan, R.

1986-01-01

Prediction of compressible flow phenomena using the finite element method is of recent origin and considerable interest. Two shock capturing finite element formulations for high speed compressible flows are described. A Taylor-Galerkin formulation uses a Taylor series expansion in time coupled with a Galerkin weighted residual statement. The Taylor-Galerkin algorithms use explicit artificial dissipation, and the performance of three dissipation models are compared. A Petrov-Galerkin algorithm has as its basis the concepts of streamline upwinding. Vectorization strategies are developed to implement the finite element formulations on the NASA Langley VPS-32. The vectorization scheme results in finite element programs that use vectors of length of the order of the number of nodes or elements. The use of the vectorization procedure speeds up processing rates by over two orders of magnitude. The Taylor-Galerkin and Petrov-Galerkin algorithms are evaluated for 2D inviscid flows on criteria such as solution accuracy, shock resolution, computational speed and storage requirements. The convergence rates for both algorithms are enhanced by local time-stepping schemes. Extension of the vectorization procedure for predicting 2D viscous and 3D inviscid flows are demonstrated. Conclusions are drawn regarding the applicability of the finite element procedures for realistic problems that require hundreds of thousands of nodes.

A simple finite element method for linear hyperbolic problems

DOE PAGES

Mu, Lin; Ye, Xiu

2017-09-14

Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

A simple finite element method for linear hyperbolic problems

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

Mu, Lin; Ye, Xiu

Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

Transport Modeling of Hydrogen in Metals for Application to Hydrogen Assisted Cracking of Metals.

DTIC Science & Technology

1995-04-04

34 consists of a Fortran "user element" subroutine for use with the ABAQUS 2 finite element program. Documentation of the 1-D user element subroutine is...trapping theory. The use of the ABAQUS finite element "User Element" subroutines for solving 1-D problems is then outlined in full detail. This is followed...reflect the new ordering given by Eq. (57). ABAOUS User Element Subroutines ABAQUS executes a Fortran subroutine named UEL for each "user defined" finite

Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

DOE PAGES

Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; ...

2015-09-15

Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinearmore » normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.« less

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.

The aggregated unfitted finite element method for elliptic problems

NASA Astrophysics Data System (ADS)

Badia, Santiago; Verdugo, Francesc; Martín, Alberto F.

2018-07-01

Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use of iterative Krylov methods and, in consequence, hinders the practical usage of unfitted methods for realistic large scale applications. In this work, we present a technique that addresses such conditioning problems by constructing enhanced finite element spaces based on a cell aggregation technique. The presented method, called aggregated unfitted finite element method, is easy to implement, and can be used, in contrast to previous works, in Galerkin approximations of coercive problems with conforming Lagrangian finite element spaces. The mathematical analysis of the new method states that the condition number of the resulting linear system matrix scales as in standard finite elements for body-fitted meshes, without being affected by small cut cells, and that the method leads to the optimal finite element convergence order. These theoretical results are confirmed with 2D and 3D numerical experiments.

Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method

NASA Astrophysics Data System (ADS)

Yang, Zailin; Wang, Yao; Hei, Baoping

2013-12-01

The dynamic inhomogeneous finite element method is studied for use in the transient analysis of onedimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.

New Multigrid Method Including Elimination Algolithm Based on High-Order Vector Finite Elements in Three Dimensional Magnetostatic Field Analysis

NASA Astrophysics Data System (ADS)

Hano, Mitsuo; Hotta, Masashi

A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.

Generalizing the TRAPRG and TRAPAX finite elements

NASA Technical Reports Server (NTRS)

Hurwitz, M. M.

1983-01-01

The NASTRAN TRAPRG and TRAPAX finite elements are very restrictive as to shape and grid point numbering. The elements must be trapezoidal with two sides parallel to the radial axis. In addition, the ordering of the grid points on the element connection card must follow strict rules. The paper describes the generalization of these elements so that these restrictions no longer apply.

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1996-01-01

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

Vertical discretization with finite elements for a global hydrostatic model on the cubed sphere

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong; Park, Ja-Rin

2017-06-01

A formulation of Galerkin finite element with basis-spline functions on a hybrid sigma-pressure coordinate is presented to discretize the vertical terms of global Eulerian hydrostatic equations employed in a numerical weather prediction system, which is horizontally discretized with high-order spectral elements on a cubed sphere grid. This replaces the vertical discretization of conventional central finite difference that is first-order accurate in non-uniform grids and causes numerical instability in advection-dominant flows. Therefore, a model remains in the framework of Galerkin finite elements for both the horizontal and vertical spatial terms. The basis-spline functions, obtained from the de-Boor algorithm, are employed to derive both the vertical derivative and integral operators, since Eulerian advection terms are involved. These operators are used to discretize the vertical terms of the prognostic and diagnostic equations. To verify the vertical discretization schemes and compare their performance, various two- and three-dimensional idealized cases and a hindcast case with full physics are performed in terms of accuracy and stability. It was shown that the vertical finite element with the cubic basis-spline function is more accurate and stable than that of the vertical finite difference, as indicated by faster residual convergence, fewer statistical errors, and reduction in computational mode. This leads to the general conclusion that the overall performance of a global hydrostatic model might be significantly improved with the vertical finite element.

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

NASA Technical Reports Server (NTRS)

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

1984-01-01

A mixed shear flexible finite element based on the Hencky-Mindlin type shear deformation theory of laminated plates is presented and their behavior in bending is investigated. The element consists of three displacements, two rotations, and three moments as the generalized degrees of freedom per node. The numerical convergence and accuracy characteristics of the element are investigated by comparing the finite element solutions with the exact solutions. The present study shows that reduced-order integration of the stiffness coefficients due to shear is necessary to obtain accurate results for thin plates.

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

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

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

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

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.

Using a multifrontal sparse solver in a high performance, finite element code

NASA Technical Reports Server (NTRS)

King, Scott D.; Lucas, Robert; Raefsky, Arthur

1990-01-01

We consider the performance of the finite element method on a vector supercomputer. The computationally intensive parts of the finite element method are typically the individual element forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a finite element code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a finite element application on one processor of a Cray X-MP.

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.

Geometric multigrid to accelerate the solution of the quasi-static electric field problem by tetrahedral finite elements.

PubMed

Hollaus, K; Weiss, B; Magele, Ch; Hutten, H

2004-02-01

The acceleration of the solution of the quasi-static electric field problem considering anisotropic complex conductivity simulated by tetrahedral finite elements of first order is investigated by geometric multigrid.

Stress Recovery and Error Estimation for 3-D Shell Structures

NASA Technical Reports Server (NTRS)

Riggs, H. R.

2000-01-01

The C1-continuous stress fields obtained from finite element analyses are in general lower- order accurate than are the corresponding displacement fields. Much effort has focussed on increasing their accuracy and/or their continuity, both for improved stress prediction and especially error estimation. A previous project developed a penalized, discrete least squares variational procedure that increases the accuracy and continuity of the stress field. The variational problem is solved by a post-processing, 'finite-element-type' analysis to recover a smooth, more accurate, C1-continuous stress field given the 'raw' finite element stresses. This analysis has been named the SEA/PDLS. The recovered stress field can be used in a posteriori error estimators, such as the Zienkiewicz-Zhu error estimator or equilibrium error estimators. The procedure was well-developed for the two-dimensional (plane) case involving low-order finite elements. It has been demonstrated that, if optimal finite element stresses are used for the post-processing, the recovered stress field is globally superconvergent. Extension of this work to three dimensional solids is straightforward. Attachment: Stress recovery and error estimation for shell structure (abstract only). A 4-node, shear-deformable flat shell element developed via explicit Kirchhoff constraints (abstract only). A novel four-node quadrilateral smoothing element for stress enhancement and error estimation (abstract only).

Vectorial finite elements for solving the radiative transfer equation

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Le Corre, S.; Digonnet, H.; Favennec, Y.

2018-06-01

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

Improving finite element results in modeling heart valve mechanics.

PubMed

Earl, Emily; Mohammadi, Hadi

2018-06-01

Finite element analysis is a well-established computational tool which can be used for the analysis of soft tissue mechanics. Due to the structural complexity of the leaflet tissue of the heart valve, the currently available finite element models do not adequately represent the leaflet tissue. A method of addressing this issue is to implement computationally expensive finite element models, characterized by precise constitutive models including high-order and high-density mesh techniques. In this study, we introduce a novel numerical technique that enhances the results obtained from coarse mesh finite element models to provide accuracy comparable to that of fine mesh finite element models while maintaining a relatively low computational cost. Introduced in this study is a method by which the computational expense required to solve linear and nonlinear constitutive models, commonly used in heart valve mechanics simulations, is reduced while continuing to account for large and infinitesimal deformations. This continuum model is developed based on the least square algorithm procedure coupled with the finite difference method adhering to the assumption that the components of the strain tensor are available at all nodes of the finite element mesh model. The suggested numerical technique is easy to implement, practically efficient, and requires less computational time compared to currently available commercial finite element packages such as ANSYS and/or ABAQUS.

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.

Shear-flexible finite-element models of laminated composite plates and shells

NASA Technical Reports Server (NTRS)

Noor, A. K.; Mathers, M. D.

1975-01-01

Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters.

Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements

NASA Astrophysics Data System (ADS)

Lohmann, Christoph; Kuzmin, Dmitri; Shadid, John N.; Mabuza, Sibusiso

2017-09-01

This work extends the flux-corrected transport (FCT) methodology to arbitrary order continuous finite element discretizations of scalar conservation laws on simplex meshes. Using Bernstein polynomials as local basis functions, we constrain the total variation of the numerical solution by imposing local discrete maximum principles on the Bézier net. The design of accuracy-preserving FCT schemes for high order Bernstein-Bézier finite elements requires the development of new algorithms and/or generalization of limiting techniques tailored for linear and multilinear Lagrange elements. In this paper, we propose (i) a new discrete upwinding strategy leading to local extremum bounded low order approximations with compact stencils, (ii) high order variational stabilization based on the difference between two gradient approximations, and (iii) new localized limiting techniques for antidiffusive element contributions. The optional use of a smoothness indicator, based on a second derivative test, makes it possible to potentially avoid unnecessary limiting at smooth extrema and achieve optimal convergence rates for problems with smooth solutions. The accuracy of the proposed schemes is assessed in numerical studies for the linear transport equation in 1D and 2D.

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

A simple finite element method for non-divergence form elliptic equation

DOE PAGES

Mu, Lin; Ye, Xiu

2017-03-01

Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

Convergence rates for finite element problems with singularities. Part 1: Antiplane shear. [crack

NASA Technical Reports Server (NTRS)

Plunkett, R.

1980-01-01

The problem of a finite crack in an infinite medium under antiplane shear load is considered. It is shown that the nodal forces at the tip of the crack accurately gives the order of singularity, that n energy release methods can give the strength to better than 1 percent with element size 1/10 the crack length, and that nodal forces give a much better estimate of the stress field than do the elements themselves. The finite element formulation and the factoring of tridiagonal matrices are discussed.

A simple finite element method for non-divergence form elliptic equation

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

Mu, Lin; Ye, Xiu

Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

Periodic trim solutions with hp-version finite elements in time

NASA Technical Reports Server (NTRS)

Peters, David A.; Hou, Lin-Jun

1990-01-01

Finite elements in time as an alternative strategy for rotorcraft trim problems are studied. The research treats linear flap and linearized flap-lag response both for quasi-trim and trim cases. The connection between Fourier series analysis and hp-finite elements for periodic a problem is also examined. It is proved that Fourier series is a special case of space-time finite elements in which one element is used with a strong displacement formulation. Comparisons are made with respect to accuracy among Fourier analysis, displacement methods, and mixed methods over a variety parameters. The hp trade-off is studied for the periodic trim problem to provide an optimum step size and order of polynomial for a given error criteria. It is found that finite elements in time can outperform Fourier analysis for periodic problems, and for some given error criteria. The mixed method provides better results than does the displacement method.

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.

Development of an hp-version finite element method for computational optimal control

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Warner, Michael S.

1993-01-01

The purpose of this research effort is to develop a means to use, and to ultimately implement, hp-version finite elements in the numerical solution of optimal control problems. The hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element.

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.

1992-01-01

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

A point-value enhanced finite volume method based on approximate delta functions

NASA Astrophysics Data System (ADS)

Xuan, Li-Jun; Majdalani, Joseph

2018-02-01

We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.

A hybridized formulation for the weak Galerkin mixed finite element method

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

Mu, Lin; Wang, Junping; Ye, Xiu

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising frommore » the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.« less

A hybridized formulation for the weak Galerkin mixed finite element method

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2016-01-14

This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed in Wang and Ye (2014) for second order elliptic equations. The WG-MFEM method was designed by using discontinuous piecewise polynomials on finite element partitions consisting of polygonal or polyhedral elements of arbitrary shape. The key to WG-MFEM is the use of a discrete weak divergence operator which is defined and computed by solving inexpensive problems locally on each element. The hybridized formulation of this paper leads to a significantly reduced system of linear equations involving only the unknowns arising frommore » the Lagrange multiplier in hybridization. Optimal-order error estimates are derived for the hybridized WG-MFEM approximations. In conclusion, some numerical results are reported to confirm the theory and a superconvergence for the Lagrange multiplier.« less

Automated Seat Cushion for Pressure Ulcer Prevention Using Real-Time Mapping, Offloading, and Redistribution of Interface Pressure

DTIC Science & Technology

2016-10-01

testing as well as finite element simulation. Automation and control testing has been completed on a 5x5 array of bubble actuators to verify pressure...mechanical behavior at varying loads and internal pressures both by experimental testing as well as finite element simulation. Automation and control...A finite element (FE) model of the bubble actuator was developed in the commercial software ANSYS in order to determine the deformation of the

A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Hu, Changqing; Shu, Chi-Wang

1998-01-01

In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.

Wakefield Simulation of CLIC PETS Structure Using Parallel 3D Finite Element Time-Domain Solver T3P

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

Candel, A.; Kabel, A.; Lee, L.

In recent years, SLAC's Advanced Computations Department (ACD) has developed the parallel 3D Finite Element electromagnetic time-domain code T3P. Higher-order Finite Element methods on conformal unstructured meshes and massively parallel processing allow unprecedented simulation accuracy for wakefield computations and simulations of transient effects in realistic accelerator structures. Applications include simulation of wakefield damping in the Compact Linear Collider (CLIC) power extraction and transfer structure (PETS).

The p-version of the finite element method in incremental elasto-plastic analysis

NASA Technical Reports Server (NTRS)

Holzer, Stefan M.; Yosibash, Zohar

1993-01-01

Whereas the higher-order versions of the finite elements method (the p- and hp-version) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. Aspects of incremental elasto-plastic finite element analysis which are particularly amenable to improvements by the p-version is discussed. These theoretical considerations are supported by several numerical experiments. First, an example for which an analytical solution is available is studied. It is demonstrated that the p-version performs very well even in cycles of elasto-plastic loading and unloading, not only as compared to the traditional h-version but also in respect to the exact solution. Finally, an example of considerable practical importance - the analysis of a cold-worked lug - is presented which demonstrates how the modeling tools offered by higher-order finite element techniques can contribute to an improved approximation of practical problems.

On Finite Groups and Finite Fields.

ERIC Educational Resources Information Center

Reid, J. D.

1991-01-01

Given a multiplicative group of nonzero elements with order n, the explicit relationship between the number of cyclic subgroups of order d, which divides n, is used in the proof concerning the cyclic nature of that given multiplicative group. (JJK)

Higher Order Lagrange Finite Elements In M3D

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

J. Chen; H.R. Strauss; S.C. Jardin

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 schemesmore » 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.« less

BeamDyn: a high-fidelity wind turbine blade solver in the FAST modular framework

DOE PAGES

Wang, Qi; Sprague, Michael A.; Jonkman, Jason; ...

2017-03-14

Here, this paper presents a numerical implementation of the geometrically exact beam theory based on the Legendre-spectral-finite-element (LSFE) method. The displacement-based geometrically exact beam theory is presented, and the special treatment of three-dimensional rotation parameters is reviewed. An LSFE is a high-order finite element with nodes located at the Gauss-Legendre-Lobatto points. These elements can be an order of magnitude more computationally efficient than low-order finite elements for a given accuracy level. The new module, BeamDyn, is implemented in the FAST modularization framework for dynamic simulation of highly flexible composite-material wind turbine blades within the FAST aeroelastic engineering model. The frameworkmore » allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples are provided to validate BeamDyn and examine the LSFE performance as well as the coupling algorithm in the FAST modularization framework. BeamDyn can also be used as a stand-alone high-fidelity beam tool.« less

BeamDyn: a high-fidelity wind turbine blade solver in the FAST modular framework

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

Wang, Qi; Sprague, Michael A.; Jonkman, Jason

Here, this paper presents a numerical implementation of the geometrically exact beam theory based on the Legendre-spectral-finite-element (LSFE) method. The displacement-based geometrically exact beam theory is presented, and the special treatment of three-dimensional rotation parameters is reviewed. An LSFE is a high-order finite element with nodes located at the Gauss-Legendre-Lobatto points. These elements can be an order of magnitude more computationally efficient than low-order finite elements for a given accuracy level. The new module, BeamDyn, is implemented in the FAST modularization framework for dynamic simulation of highly flexible composite-material wind turbine blades within the FAST aeroelastic engineering model. The frameworkmore » allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples are provided to validate BeamDyn and examine the LSFE performance as well as the coupling algorithm in the FAST modularization framework. BeamDyn can also be used as a stand-alone high-fidelity beam tool.« less

Evaluation of the use of a singularity element in finite element analysis of center-cracked plates

NASA Technical Reports Server (NTRS)

Mendelson, A.; Gross, B.; Srawley, J., E.

1972-01-01

Two different methods are applied to the analyses of finite width linear elastic plates with central cracks. Both methods give displacements as a primary part of the solution. One method makes use of Fourier transforms. The second method employs a coarse mesh of triangular second-order finite elements in conjunction with a single singularity element subjected to appropriate additional constraints. The displacements obtained by these two methods are in very good agreement. The results suggest considerable potential for the use of a cracked element for related crack problems, particularly in connection with the extension to nonlinear material behavior.

Dynamic responses of graphite/epoxy laminated beam to impact of elastic spheres

NASA Technical Reports Server (NTRS)

Sun, C. T.; Wang, T.

1982-01-01

Wave propagation in 90/45/90/-45/902s and 0/45/0/-45/02s laminates of a graphite/epoxy composite due to impact of a steel ball was investigated experimentally and also by using a high order beam finite element. Dynamic strain responses at several locations were obtained using strain gages. The finite element program which incorporated statically determined contact laws was employed to calculate the contact force history as well as the target beam dynamic deformation. The comparison of the finite element solutions with the experimental data indicated that the static contact laws for loading and unloading (developed under this grant) are adequate for the dynamic impact analysis. It was found that for the 0/45/0/-45/02s laminate which has a much larger longitudinal bending rigidity, the use of beam finite elements is not suitable and plate finite element should be used instead.

An accurate nonlinear finite element analysis and test correlation of a stiffened composite wing panel

NASA Astrophysics Data System (ADS)

Davis, D. D., Jr.; Krishnamurthy, T.; Stroud, W. J.; McCleary, S. L.

1991-05-01

State-of-the-art nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain-displacement relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis.

An accurate nonlinear finite element analysis and test correlation of a stiffened composite wing panel

NASA Technical Reports Server (NTRS)

Davis, D. D., Jr.; Krishnamurthy, T.; Stroud, W. J.; Mccleary, S. L.

1991-01-01

State-of-the-art nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain-displacement relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis.

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

NASA Technical Reports Server (NTRS)

Cowsar, Lawrence C.

1993-01-01

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

Development library of finite elements for computer-aided design system of reed sensors

NASA Astrophysics Data System (ADS)

Kozlov, A. S.; Shmakov, N. A.; Tkalich, V. L.; Labkovskaia, R. I.; Kalinkina, M. E.; Pirozhnikova, O. I.

2018-05-01

The article is devoted to the development of a modern highly reliable element base of devices for security and fire alarm systems, in particular, to the improvement of the quality of contact cores (reed and membrane) of reed sensors. Modeling of elastic sensitive elements uses quadrangular elements of plates and shells, considered in the system of curvilinear orthogonal coordinates. The developed mathematical models and the formed finite element library are designed for systems of automated design of reed switch detectors to create competitive devices alarms. The finite element library is used for the automated system production of reed switch detectors both in series production and in the implementation of individual orders.

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES

PubMed Central

GILLETTE, ANDREW; RAND, ALEXANDER; BAJAJ, CHANDRAJIT

2016-01-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties. PMID:28077939

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES.

PubMed

Gillette, Andrew; Rand, Alexander; Bajaj, Chandrajit

2016-10-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties.

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

NASA Astrophysics Data System (ADS)

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

2011-11-01

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

Hybrid DG/FV schemes for magnetohydrodynamics and relativistic hydrodynamics

NASA Astrophysics Data System (ADS)

Núñez-de la Rosa, Jonatan; Munz, Claus-Dieter

2018-01-01

This paper presents a high order hybrid discontinuous Galerkin/finite volume scheme for solving the equations of the magnetohydrodynamics (MHD) and of the relativistic hydrodynamics (SRHD) on quadrilateral meshes. In this approach, for the spatial discretization, an arbitrary high order discontinuous Galerkin spectral element (DG) method is combined with a finite volume (FV) scheme in order to simulate complex flow problems involving strong shocks. Regarding the time discretization, a fourth order strong stability preserving Runge-Kutta method is used. In the proposed hybrid scheme, a shock indicator is computed at the beginning of each Runge-Kutta stage in order to flag those elements containing shock waves or discontinuities. Subsequently, the DG solution in these troubled elements and in the current time step is projected onto a subdomain composed of finite volume subcells. Right after, the DG operator is applied to those unflagged elements, which, in principle, are oscillation-free, meanwhile the troubled elements are evolved with a robust second/third order FV operator. With this approach we are able to numerically simulate very challenging problems in the context of MHD and SRHD in one, and two space dimensions and with very high order polynomials. We make convergence tests and show a comprehensive one- and two dimensional testbench for both equation systems, focusing in problems with strong shocks. The presented hybrid approach shows that numerical schemes of very high order of accuracy are able to simulate these complex flow problems in an efficient and robust manner.

Finite element modelling of aluminum alloy 2024-T3 under transverse impact loading

NASA Astrophysics Data System (ADS)

Abdullah, Ahmad Sufian; Kuntjoro, Wahyu; Yamin, A. F. M.

2017-12-01

Fiber metal laminate named GLARE is a new aerospace material which has great potential to be widely used in future lightweight aircraft. It consists of aluminum alloy 2024-T3 and glass-fiber reinforced laminate. In order to produce reliable finite element model of impact response or crashworthiness of structure made of GLARE, one can initially model and validate the finite element model of the impact response of its constituents separately. The objective of this study was to develop a reliable finite element model of aluminum alloy 2024-T3 under low velocity transverse impact loading using commercial software ABAQUS. Johnson-Cook plasticity and damage models were used to predict the alloy's material properties and impact behavior. The results of the finite element analysis were compared to the experiment that has similar material and impact conditions. Results showed good correlations in terms of impact forces, deformation and failure progressions which concluded that the finite element model of 2024-T3 aluminum alloy under low velocity transverse impact condition using Johnson-Cook plastic and damage models was reliable.

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S.; Rosen, I. G.

1988-01-01

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation

NASA Astrophysics Data System (ADS)

Anderson, R.; Dobrev, V.; Kolev, Tz.; Kuzmin, D.; Quezada de Luna, M.; Rieben, R.; Tomov, V.

2017-04-01

In this work we present a FCT-like Maximum-Principle Preserving (MPP) method to solve the transport equation. We use high-order polynomial spaces; in particular, we consider up to 5th order spaces in two and three dimensions and 23rd order spaces in one dimension. The method combines the concepts of positive basis functions for discontinuous Galerkin finite element spatial discretization, locally defined solution bounds, element-based flux correction, and non-linear local mass redistribution. We consider a simple 1D problem with non-smooth initial data to explain and understand the behavior of different parts of the method. Convergence tests in space indicate that high-order accuracy is achieved. Numerical results from several benchmarks in two and three dimensions are also reported.

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.

A weak Galerkin generalized multiscale finite element method

DOE PAGES

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.

A weak Galerkin generalized multiscale finite element method

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

Mu, Lin; Wang, Junping; Ye, Xiu

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.

Sensitivity Analysis for Multidisciplinary Systems (SAMS)

DTIC Science & Technology

2016-12-01

support both mode-based structural representations and time-dependent, nonlinear finite element structural dynamics. This interim report describes...Adaptation, & Sensitivity Toolkit • Elasticity, heat transfer, & compressible flow • Adjoint solver for sensitivity analysis • High-order finite elements ...PROGRAM ELEMENT NUMBER 62201F 6. AUTHOR(S) Richard D. Snyder 5d. PROJECT NUMBER 2401 5e. TASK NUMBER N/A 5f. WORK UNIT NUMBER Q1FS 7

A higher-order theory for geometrically nonlinear analysis of composite laminates

NASA Technical Reports Server (NTRS)

Reddy, J. N.; Liu, C. F.

1987-01-01

A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

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

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

A new family of stable elements for the Stokes problem based on a mixed Galerkin/least-squares finite element formulation

NASA Technical Reports Server (NTRS)

Franca, Leopoldo P.; Loula, Abimael F. D.; Hughes, Thomas J. R.; Miranda, Isidoro

1989-01-01

Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.

Development of an adaptive hp-version finite element method for computational optimal control

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Warner, Michael S.

1994-01-01

In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications.

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.

Analysis of frame structure of medium and small truck crane

NASA Astrophysics Data System (ADS)

Cao, Fuyi; Li, Jinlong; Cui, Mengkai

2018-03-01

Truck crane is an important part of hoisting machinery. Frame, as the support component of the quality of truck crane, determines the safety of crane jib load and the rationality of structural design. In this paper, the truck crane frame is a box structure, the three-dimensional model is established in CATIA software, and imported into Hyperworks software for finite element analysis. On the base of doing constraints and loads for the finite element model of the frame, the finite element static analysis is carried out. And the static stress test verifies whether the finite element model and the frame structure design are reasonable; then the free modal analysis of the frame and the analysis of the first 8 - order modal vibration deformation are carried out. The analysis results show that the maximum stress value of the frame is greater than the yield limit value of the material, and the low-order modal value is close to the excitation frequency value, which needs to be improved to provide theoretical reference for the structural design of the truck crane frame.

Crack Turning and Arrest Mechanisms for Integral Structure

NASA Technical Reports Server (NTRS)

Pettit, Richard; Ingraffea, Anthony

1999-01-01

In the course of several years of research efforts to predict crack turning and flapping in aircraft fuselage structures and other problems related to crack turning, the 2nd order maximum tangential stress theory has been identified as the theory most capable of predicting the observed test results. This theory requires knowledge of a material specific characteristic length, and also a computation of the stress intensity factors and the T-stress, or second order term in the asymptotic stress field in the vicinity of the crack tip. A characteristic length, r(sub c), is proposed for ductile materials pertaining to the onset of plastic instability, as opposed to the void spacing theories espoused by previous investigators. For the plane stress case, an approximate estimate of r(sub c), is obtained from the asymptotic field for strain hardening materials given by Hutchinson, Rice and Rosengren (HRR). A previous study using of high order finite element methods to calculate T-stresses by contour integrals resulted in extremely high accuracy values obtained for selected test specimen geometries, and a theoretical error estimation parameter was defined. In the present study, it is shown that a large portion of the error in finite element computations of both K and T are systematic, and can be corrected after the initial solution if the finite element implementation utilizes a similar crack tip discretization scheme for all problems. This scheme is applied for two-dimensional problems to a both a p-version finite element code, showing that sufficiently accurate values of both K(sub I) and T can be obtained with fairly low order elements if correction is used. T-stress correction coefficients are also developed for the singular crack tip rosette utilized in the adaptive mesh finite element code FRANC2D, and shown to reduce the error in the computed T-stress significantly. Stress intensity factor correction was not attempted for FRANC2D because it employs a highly accurate quarter-point scheme to obtain stress intensity factors.

Three-Dimensional Finite Element Analysis of Sheet-Pile Cellular Cofferdams

DTIC Science & Technology

1992-04-01

requirements were in selecting the shell element for this study: * Nodes only at the midsurface of the element. * Higher-order shape functions to...on orthogonal curvilinear coordinate (shell coordinates) system with the ref- erence surface of the element midsurface (Figure 4.13). The formulation...element was selected which allows for: * Nodes at the midsurface of the element only. 150 CHAPTER 4. ADDITIONS TO THE ELEMENT LIBRARY " Higher-order

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

NASA Astrophysics Data System (ADS)

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

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

Application of finite-element methods to dynamic analysis of flexible spatial and co-planar linkage systems, part 2

NASA Technical Reports Server (NTRS)

Dubowsky, Steven

1989-01-01

An approach is described to modeling the flexibility effects in spatial mechanisms and manipulator systems. The method is based on finite element representations of the individual links in the system. However, it should be noted that conventional finite element methods and software packages will not handle the highly nonlinear dynamic behavior of these systems which results form their changing geometry. In order to design high-performance lightweight systems and their control systems, good models of their dynamic behavior which include the effects of flexibility are required.

Finite element methods for the biomechanics of soft hydrated tissues: nonlinear analysis and adaptive control of meshes.

PubMed

Spilker, R L; de Almeida, E S; Donzelli, P S

1992-01-01

This chapter addresses computationally demanding numerical formulations in the biomechanics of soft tissues. The theory of mixtures can be used to represent soft hydrated tissues in the human musculoskeletal system as a two-phase continuum consisting of an incompressible solid phase (collagen and proteoglycan) and an incompressible fluid phase (interstitial water). We first consider the finite deformation of soft hydrated tissues in which the solid phase is represented as hyperelastic. A finite element formulation of the governing nonlinear biphasic equations is presented based on a mixed-penalty approach and derived using the weighted residual method. Fluid and solid phase deformation, velocity, and pressure are interpolated within each element, and the pressure variables within each element are eliminated at the element level. A system of nonlinear, first-order differential equations in the fluid and solid phase deformation and velocity is obtained. In order to solve these equations, the contributions of the hyperelastic solid phase are incrementally linearized, a finite difference rule is introduced for temporal discretization, and an iterative scheme is adopted to achieve equilibrium at the end of each time increment. We demonstrate the accuracy and adequacy of the procedure using a six-node, isoparametric axisymmetric element, and we present an example problem for which independent numerical solution is available. Next, we present an automated, adaptive environment for the simulation of soft tissue continua in which the finite element analysis is coupled with automatic mesh generation, error indicators, and projection methods. Mesh generation and updating, including both refinement and coarsening, for the two-dimensional examples examined in this study are performed using the finite quadtree approach. The adaptive analysis is based on an error indicator which is the L2 norm of the difference between the finite element solution and a projected finite element solution. Total stress, calculated as the sum of the solid and fluid phase stresses, is used in the error indicator. To allow the finite difference algorithm to proceed in time using an updated mesh, solution values must be transferred to the new nodal locations. This rezoning is accomplished using a projected field for the primary variables. The accuracy and effectiveness of this adaptive finite element analysis is demonstrated using a linear, two-dimensional, axisymmetric problem corresponding to the indentation of a thin sheet of soft tissue. The method is shown to effectively capture the steep gradients and to produce solutions in good agreement with independent, converged, numerical solutions.

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

PubMed

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

2013-09-15

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

A finite element analysis of viscoelastically damped sandwich plates

NASA Astrophysics Data System (ADS)

Ma, B.-A.; He, J.-F.

1992-01-01

A finite element analysis associated with an asymptotic solution method for the harmonic flexural vibration of viscoelastically damped unsymmetrical sandwich plates is given. The element formulation is based on generalization of the discrete Kirchhoff theory (DKT) element formulation. The results obtained with the first order approximation of the asymptotic solution presented here are the same as those obtained by means of the modal strain energy (MSE) method. By taking more terms of the asymptotic solution, with successive calculations and use of the Padé approximants method, accuracy can be improved. The finite element computation has been verified by comparison with an analytical exact solution for rectangular plates with simply supported edges. Results for the same plates with clamped edges are also presented.

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

PubMed

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

2015-12-24

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

Finite element probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes

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

Bacvarov, D.C.

1981-01-01

A new method for probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes is presented. The utilized approach of applying the finite element method for probabilistic risk assessment is demonstrated to be very powerful. The reasons for this are two. First, the finite element method is inherently suitable for analysis of three dimensional spaces where the parameters, such as three variate probability densities of the lightning currents, are non-uniformly distributed. Second, the finite element method permits non-uniform discretization of the three dimensional probability spaces thus yielding high accuracy in critical regions, such as the area of themore » low probability events, while at the same time maintaining coarse discretization in the non-critical areas to keep the number of grid points and the size of the problem to a manageable low level. The finite element probabilistic risk assessment method presented here is based on a new multidimensional search algorithm. It utilizes an efficient iterative technique for finite element interpolation of the transmission line insulation flashover criteria computed with an electro-magnetic transients program. Compared to other available methods the new finite element probabilistic risk assessment method is significantly more accurate and approximately two orders of magnitude computationally more efficient. The method is especially suited for accurate assessment of rare, very low probability events.« less

A projection hybrid high order finite volume/finite element method for incompressible turbulent flows

NASA Astrophysics Data System (ADS)

Busto, S.; Ferrín, J. L.; Toro, E. F.; Vázquez-Cendón, M. E.

2018-01-01

In this paper the projection hybrid FV/FE method presented in [1] is extended to account for species transport equations. Furthermore, turbulent regimes are also considered thanks to the k-ε model. Regarding the transport diffusion stage new schemes of high order of accuracy are developed. The CVC Kolgan-type scheme and ADER methodology are extended to 3D. The latter is modified in order to profit from the dual mesh employed by the projection algorithm and the derivatives involved in the diffusion term are discretized using a Galerkin approach. The accuracy and stability analysis of the new method are carried out for the advection-diffusion-reaction equation. Within the projection stage the pressure correction is computed by a piecewise linear finite element method. Numerical results are presented, aimed at verifying the formal order of accuracy of the scheme and to assess the performance of the method on several realistic test problems.

Finite element normal mode analysis of resistance welding jointed of dissimilar plate hat structure

NASA Astrophysics Data System (ADS)

Nazri, N. A.; Sani, M. S. M.

2017-10-01

Structural joints offer connection between structural element (beam, plate, solid etc.) in order to build a whole assembled structure. The complex behaviour of connecting elements plays a valuable role in characteristics of dynamic such as natural frequencies and mode shapes. In automotive structures, the trustworthiness arrangement of the structure extremely depends on joints. In this paper, top hat structure is modelled and designed with spot welding joint using dissimilar materials which is mild steel 1010 and stainless steel 304, using finite element software. Different types of connector elements such as rigid body element (RBE2), welding joint element (CWELD), and bar element (CBAR) are applied to represent real connection between two dissimilar plates. Normal mode analysis is simulated with different types of joining element in order to determine modal properties. Natural frequencies using RBE2, CBAR and CWELD are compared to equivalent rigid body method. Connection that gives the lowest percentage error among these three will be selected as the most reliable joining for resistance spot weld. From the analysis, it is shown that CWELD is better compared to others in term of weld joining among dissimilar plate materials. It is expected that joint modelling of finite element plays significant role in structural dynamics.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Finite element analysis of low speed viscous and inviscid aerodynamic flows

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

Coupled porohyperelastic mass transport (PHEXPT) finite element models for soft tissues using ABAQUS.

PubMed

Vande Geest, Jonathan P; Simon, B R; Rigby, Paul H; Newberg, Tyler P

2011-04-01

Finite element models (FEMs) including characteristic large deformations in highly nonlinear materials (hyperelasticity and coupled diffusive/convective transport of neutral mobile species) will allow quantitative study of in vivo tissues. Such FEMs will provide basic understanding of normal and pathological tissue responses and lead to optimization of local drug delivery strategies. We present a coupled porohyperelastic mass transport (PHEXPT) finite element approach developed using a commercially available ABAQUS finite element software. The PHEXPT transient simulations are based on sequential solution of the porohyperelastic (PHE) and mass transport (XPT) problems where an Eulerian PHE FEM is coupled to a Lagrangian XPT FEM using a custom-written FORTRAN program. The PHEXPT theoretical background is derived in the context of porous media transport theory and extended to ABAQUS finite element formulations. The essential assumptions needed in order to use ABAQUS are clearly identified in the derivation. Representative benchmark finite element simulations are provided along with analytical solutions (when appropriate). These simulations demonstrate the differences in transient and steady state responses including finite deformations, total stress, fluid pressure, relative fluid, and mobile species flux. A detailed description of important model considerations (e.g., material property functions and jump discontinuities at material interfaces) is also presented in the context of finite deformations. The ABAQUS-based PHEXPT approach enables the use of the available ABAQUS capabilities (interactive FEM mesh generation, finite element libraries, nonlinear material laws, pre- and postprocessing, etc.). PHEXPT FEMs can be used to simulate the transport of a relatively large neutral species (negligible osmotic fluid flux) in highly deformable hydrated soft tissues and tissue-engineered materials.

Binary tree eigen solver in finite element analysis

NASA Technical Reports Server (NTRS)

Akl, F. A.; Janetzke, D. C.; Kiraly, L. J.

1993-01-01

This paper presents a transputer-based binary tree eigensolver for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on the method of recursive doubling, which parallel implementation of a number of associative operations on an arbitrary set having N elements is of the order of o(log2N), compared to (N-1) steps if implemented sequentially. The hardware used in the implementation of the binary tree consists of 32 transputers. The algorithm is written in OCCAM which is a high-level language developed with the transputers to address parallel programming constructs and to provide the communications between processors. The algorithm can be replicated to match the size of the binary tree transputer network. Parallel and sequential finite element analysis programs have been developed to solve for the set of the least-order eigenpairs using the modified subspace method. The speed-up obtained for a typical analysis problem indicates close agreement with the theoretical prediction given by the method of recursive doubling.

Parallel eigenanalysis of finite element models in a completely connected architecture

NASA Technical Reports Server (NTRS)

Akl, F. A.; Morel, M. R.

1989-01-01

A parallel algorithm is presented for the solution of the generalized eigenproblem in linear elastic finite element analysis, (K)(phi) = (M)(phi)(omega), where (K) and (M) are of order N, and (omega) is order of q. The concurrent solution of the eigenproblem is based on the multifrontal/modified subspace method and is achieved in a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm was successfully implemented on a tightly coupled multiple-instruction multiple-data parallel processing machine, Cray X-MP. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor or to a logical processor (task) if the number of domains exceeds the number of physical processors. The macrotasking library routines are used in mapping each domain to a user task. Computational speed-up and efficiency are used to determine the effectiveness of the algorithm. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts and the dimension of the subspace on the performance of the algorithm are investigated. A parallel finite element dynamic analysis program, p-feda, is documented and the performance of its subroutines in parallel environment is analyzed.

A finite element study of the EIDI system. [Electro-Impulse De-Icing System

NASA Technical Reports Server (NTRS)

Khatkhate, A. A.; Scavuzzo, R. J.; Chu, M. L.

1988-01-01

This paper presents a method for modeling the structural dynamics of an Electro-Impulse De-Icing System, using finite element analyses procedures. A guideline for building a representative finite element model is discussed. Modeling was done initially using four noded cubic elements, four noded isoparametric plate elements and eight noded isoparametric shell elements. Due to the size of the problem and due to the underestimation of shear stress results when compared to previous analytical work an approximate model was created to predict possible areas of shedding of ice. There appears to be good agreement with the test data provided by The Boeing Commercial Airplane Company. Thus these initial results of this method were found to be encouraging. Additional analytical work and comparison with experiment is needed in order to completely evaluate this approach.

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

Giunta, G.; Belouettar, S.

In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements’ stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigationsmore » show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements’ family.« less

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.

Certified dual-corrected radiation patterns of phased antenna arrays by offline–online order reduction of finite-element models

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

Sommer, A., E-mail: a.sommer@lte.uni-saarland.de; Farle, O., E-mail: o.farle@lte.uni-saarland.de; Dyczij-Edlinger, R., E-mail: edlinger@lte.uni-saarland.de

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.

Analysis of warping deformation modes using higher order ANCF beam element

NASA Astrophysics Data System (ADS)

Orzechowski, Grzegorz; Shabana, Ahmed A.

2016-02-01

Most classical beam theories assume that the beam cross section remains a rigid surface under an arbitrary loading condition. However, in the absolute nodal coordinate formulation (ANCF) continuum-based beams, this assumption can be relaxed allowing for capturing deformation modes that couple the cross-section deformation and beam bending, torsion, and/or elongation. The deformation modes captured by ANCF finite elements depend on the interpolating polynomials used. The most widely used spatial ANCF beam element employs linear approximation in the transverse direction, thereby restricting the cross section deformation and leading to locking problems. The objective of this investigation is to examine the behavior of a higher order ANCF beam element that includes quadratic interpolation in the transverse directions. This higher order element allows capturing warping and non-uniform stretching distribution. Furthermore, this higher order element allows for increasing the degree of continuity at the element interface. It is shown in this paper that the higher order ANCF beam element can be used effectively to capture warping and eliminate Poisson locking that characterizes lower order ANCF finite elements. It is also shown that increasing the degree of continuity requires a special attention in order to have acceptable results. Because higher order elements can be more computationally expensive than the lower order elements, the use of reduced integration for evaluating the stress forces and the use of explicit and implicit numerical integrations to solve the nonlinear dynamic equations of motion are investigated in this paper. It is shown that the use of some of these integration methods can be very effective in reducing the CPU time without adversely affecting the solution accuracy.

Evaluation of the finite element software ABAQUS for biomechanical modelling of biphasic tissues.

PubMed

Wu, J Z; Herzog, W; Epstein, M

1998-02-01

The biphasic cartilage model proposed by Mow et al. (1980) has proven successful to capture the essential mechanical features of articular cartilage. In order to analyse the joint contact mechanics in real, anatomical joints, the cartilage model needs to be implemented into a suitable finite element code to approximate the irregular surface geometries of such joints. However, systematic and extensive evaluation of the capacity of commercial software for modelling the contact mechanics with biphasic cartilage layers has not been made. This research was aimed at evaluating the commercial finite element software ABAQUS for analysing biphasic soft tissues. The solutions obtained using ABAQUS were compared with those obtained using other finite element models and analytical solutions for three numerical tests: an unconfined indentation test, a test with the contact of a spherical cartilage surface with a rigid plate, and an axi-symmetric joint contact test. It was concluded that the biphasic cartilage model can be implemented into the commercial finite element software ABAQUS to analyse practical joint contact problems with biphasic articular cartilage layers.

Reduced-order modeling of piezoelectric energy harvesters with nonlinear circuits under complex conditions

NASA Astrophysics Data System (ADS)

Xiang, Hong-Jun; Zhang, Zhi-Wei; Shi, Zhi-Fei; Li, Hong

2018-04-01

A fully coupled modeling approach is developed for piezoelectric energy harvesters in this work based on the use of available robust finite element packages and efficient reducing order modeling techniques. At first, the harvester is modeled using finite element packages. The dynamic equilibrium equations of harvesters are rebuilt by extracting system matrices from the finite element model using built-in commands without any additional tools. A Krylov subspace-based scheme is then applied to obtain a reduced-order model for improving simulation efficiency but preserving the key features of harvesters. Co-simulation of the reduced-order model with nonlinear energy harvesting circuits is achieved in a system level. Several examples in both cases of harmonic response and transient response analysis are conducted to validate the present approach. The proposed approach allows to improve the simulation efficiency by several orders of magnitude. Moreover, the parameters used in the equivalent circuit model can be conveniently obtained by the proposed eigenvector-based model order reduction technique. More importantly, this work establishes a methodology for modeling of piezoelectric energy harvesters with any complicated mechanical geometries and nonlinear circuits. The input load may be more complex also. The method can be employed by harvester designers to optimal mechanical structures or by circuit designers to develop novel energy harvesting circuits.

Thermal Transport Model for Heat Sink Design

NASA Technical Reports Server (NTRS)

Chervenak, James A.; Kelley, Richard L.; Brown, Ari D.; Smith, Stephen J.; Kilbourne, Caroline a.

2009-01-01

A document discusses the development of a finite element model for describing thermal transport through microcalorimeter arrays in order to assist in heat-sinking design. A fabricated multi-absorber transition edge sensor (PoST) was designed in order to reduce device wiring density by a factor of four. The finite element model consists of breaking the microcalorimeter array into separate elements, including the transition edge sensor (TES) and the silicon substrate on which the sensor is deposited. Each element is then broken up into subelements, whose surface area subtends 10 10 microns. The heat capacity per unit temperature, thermal conductance, and thermal diffusivity of each subelement are the model inputs, as are the temperatures of each subelement. Numerical integration using the Finite in Time Centered in Space algorithm of the thermal diffusion equation is then performed in order to obtain a temporal evolution of the subelement temperature. Thermal transport across interfaces is modeled using a thermal boundary resistance obtained using the acoustic mismatch model. The document concludes with a discussion of the PoST fabrication. PoSTs are novel because they enable incident x-ray position sensitivity with good energy resolution and low wiring density.

Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)

2002-01-01

Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

Adaptive mixed finite element methods for Darcy flow in fractured porous media

NASA Astrophysics Data System (ADS)

Chen, Huangxin; Salama, Amgad; Sun, Shuyu

2016-10-01

In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

PubMed Central

Wang, Wansheng; Chen, Long; Zhou, Jie

2015-01-01

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Greene, William H.

1989-01-01

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models.

A combined experimental and finite element study to predict the failure mechanisms in SiC coated carbon/carbon composites at room and elevated temperatures under flexural loading

NASA Technical Reports Server (NTRS)

Mahfuz, Hassan; Das, Partha S.; Xue, Dongwei; Krishnagopalan, Jaya; Jeelani, Shaik

1993-01-01

Response of quasi-isotropic laminates of SiC coated Carbon/Carbon (C/C) composites have been investigated under flexural loading at various temperatures. Variation of load-deflection behavior with temperatures are studied. Increase in flexural strength and stiffness are observed with the rise in temperature. Extensive analyses through Optical Microscope (OM) and Non-Destructive Evaluation (NDE) have been performed to understand the failure mechanisms. Damage zone is found only within the neighborhood of the loading plane. Isoparametric layered shell elements developed on the basis of the first order shear deformation theory have been used to model the thin laminates of C/C under flexural loading. Large deformation behavior has been considered in the finite element analysis to account for the non-linearities encountered during the actual test. Data generated using finite element analysis are presented to corroborate the experimental findings, and a comparison in respect of displacement and stress-strain behavior are given to check the accuracy of the finite element analysis. Reasonable correlation between the experimental and finite element results have been established.

Verification of a non-hydrostatic dynamical core using horizontally spectral element vertically finite difference method: 2-D aspects

NASA Astrophysics Data System (ADS)

Choi, S.-J.; Giraldo, F. X.; Kim, J.; Shin, S.

2014-06-01

The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative terms and quadrature. The Euler equations used here are in a flux form based on the hydrostatic pressure vertical coordinate, which are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate is implemented in this model. We verified the model by conducting widely used standard benchmark tests: the inertia-gravity wave, rising thermal bubble, density current wave, and linear hydrostatic mountain wave. The results from those tests demonstrate that the horizontally spectral element vertically finite difference model is accurate and robust. By using the 2-D slice model, we effectively show that the combined spatial discretization method of the spectral element and finite difference method in the horizontal and vertical directions, respectively, offers a viable method for the development of a NH dynamical core.

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.

Simulation-aided constitutive law development - Assessment of low triaxiality void nucleation models via extended finite element method

NASA Astrophysics Data System (ADS)

Zhao, Jifeng; Kontsevoi, Oleg Y.; Xiong, Wei; Smith, Jacob

2017-05-01

In this work, a multi-scale computational framework has been established in order to investigate, refine and validate constitutive behaviors in the context of the Gurson-Tvergaard-Needleman (GTN) void mechanics model. The eXtended Finite Element Method (XFEM) has been implemented in order to (1) develop statistical volume elements (SVE) of a matrix material with subscale inclusions and (2) to simulate the multi-void nucleation process due to interface debonding between the matrix and particle phases. Our analyses strongly suggest that under low stress triaxiality the nucleation rate of the voids f˙ can be well described by a normal distribution function with respect to the matrix equivalent stress (σe), as opposed to that proposed (σbar + 1 / 3σkk) in the original form of the single void GTN model. The modified form of the multi-void nucleation model has been validated based on a series of numerical experiments with different loading conditions, material properties, particle shape/size and spatial distributions. The utilization of XFEM allows for an invariant finite element mesh to represent varying microstructures, which implies suitability for drastically reducing complexity in generating the finite element discretizations for large stochastic arrays of microstructure configurations. The modified form of the multi-void nucleation model is further applied to study high strength steels by incorporating first principles calculations. The necessity of using a phenomenological interface separation law has been fully eliminated and replaced by the physics-based cohesive relationship obtained from Density Functional Theory (DFT) calculations in order to provide an accurate macroscopic material response.

Finite element formulation of viscoelastic sandwich beams using fractional derivative operators

NASA Astrophysics Data System (ADS)

Galucio, A. C.; Deü, J.-F.; Ohayon, R.

This paper presents a finite element formulation for transient dynamic analysis of sandwich beams with embedded viscoelastic material using fractional derivative constitutive equations. The sandwich configuration is composed of a viscoelastic core (based on Timoshenko theory) sandwiched between elastic faces (based on Euler-Bernoulli assumptions). The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. Concerning the parameter identification, a strategy to estimate the fractional order of the time derivative and the relaxation time is outlined. Curve-fitting aspects are focused, showing a good agreement with experimental data. In order to implement the viscoelastic model into the finite element formulation, the Grünwald definition of the fractional operator is employed. To solve the equation of motion, a direct time integration method based on the implicit Newmark scheme is used. One of the particularities of the proposed algorithm lies in the storage of displacement history only, reducing considerably the numerical efforts related to the non-locality of fractional operators. After validations, numerical applications are presented in order to analyze truncation effects (fading memory phenomena) and solution convergence aspects.

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.

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.

CosmosDG: An hp -adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

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

Anninos, Peter; Lau, Cheuk; Bryant, Colton

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performedmore » separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.« less

CosmosDG: An hp-adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

NASA Astrophysics Data System (ADS)

Anninos, Peter; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Lau, Cheuk; Nemergut, Daniel

2017-08-01

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge-Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.

A comparison of matrix methods for calculating eigenvalues in acoustically lined ducts

NASA Technical Reports Server (NTRS)

Watson, W.; Lansing, D. L.

1976-01-01

Three approximate methods - finite differences, weighted residuals, and finite elements - were used to solve the eigenvalue problem which arises in finding the acoustic modes and propagation constants in an absorptively lined two-dimensional duct without airflow. The matrix equations derived for each of these methods were solved for the eigenvalues corresponding to various values of wall impedance. Two matrix orders, 20 x 20 and 40 x 40, were used. The cases considered included values of wall admittance for which exact eigenvalues were known and for which several nearly equal roots were present. Ten of the lower order eigenvalues obtained from the three approximate methods were compared with solutions calculated from the exact characteristic equation in order to make an assessment of the relative accuracy and reliability of the three methods. The best results were given by the finite element method using a cubic polynomial. Excellent accuracy was consistently obtained, even for nearly equal eigenvalues, by using a 20 x 20 order matrix.

A Semi-Analytical Method for Determining the Energy Release Rate of Cracks in Adhesively-Bonded Single-Lap Composite Joints

NASA Technical Reports Server (NTRS)

Yang, Charles; Sun, Wenjun; Tomblin, John S.; Smeltzer, Stanley S., III

2007-01-01

A semi-analytical method for determining the strain energy release rate due to a prescribed interface crack in an adhesively-bonded, single-lap composite joint subjected to axial tension is presented. The field equations in terms of displacements within the joint are formulated by using first-order shear deformable, laminated plate theory together with kinematic relations and force equilibrium conditions. The stress distributions for the adherends and adhesive are determined after the appropriate boundary and loading conditions are applied and the equations for the field displacements are solved. Based on the adhesive stress distributions, the forces at the crack tip are obtained and the strain energy release rate of the crack is determined by using the virtual crack closure technique (VCCT). Additionally, the test specimen geometry from both the ASTM D3165 and D1002 test standards are utilized during the derivation of the field equations in order to correlate analytical models with future test results. The system of second-order differential field equations is solved to provide the adherend and adhesive stress response using the symbolic computation tool, Maple 9. Finite element analyses using J-integral as well as VCCT were performed to verify the developed analytical model. The finite element analyses were conducted using the commercial finite element analysis software ABAQUS. The results determined using the analytical method correlated well with the results from the finite element analyses.

Finite-element simulation of ceramic drying processes

NASA Astrophysics Data System (ADS)

Keum, Y. T.; Jeong, J. H.; Auh, K. H.

2000-07-01

A finite-element simulation for the drying process of ceramics is performed. The heat and moisture movements in green ceramics caused by the temperature gradient, moisture gradient, conduction, convection and evaporation are considered. The finite-element formulation for solving the temperature and moisture distributions, which not only change the volume but also induce the hygro-thermal stress, is carried out. Employing the internally discontinuous interface elements, the numerical divergence problem arising from sudden changes in heat capacity in the phase zone is solved. In order to verify the reliability of the formulation, the drying process of a coal and the wetting process of a graphite epoxy are simulated and the results are compared with the analytical solution and another investigator's result. Finally, the drying process of a ceramic electric insulator is simulated.

Finite Element Peen Forming Simulation

NASA Astrophysics Data System (ADS)

Gariépy, Alexandre; Larose, Simon; Perron, Claude; Bocher, Philippe; Lévesque, Martin

Shot peening consists of projecting multiple small particles onto a ductile part in order to induce compressive residual stresses near the surface. Peen forming, a derivative of shot peening, is a process that creates an unbalanced stress state which in turn leads to a deformation to shape thin parts. This versatile and cost-effective process is commonly used to manufacture aluminum wing skins and rocket panels. This paper presents the finite element modelling approach that was developed by the authors to simulate the process. The method relies on shell elements and calculated stress profiles and uses an approximation equation to take into account the incremental nature of the process. Finite element predictions were in good agreement with experimental results for small-scale tests. The method was extended to a hypothetical wing skin model to show its potential applications.

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2004-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

An evaluation of a coupled microstructural approach for the analysis of functionally graded composites via the finite-element method

NASA Technical Reports Server (NTRS)

Pindera, Marek-Jerzy; Dunn, Patrick

1995-01-01

A comparison is presented between the predictions of the finite-element analysis and a recently developed higher-order theory for functionally graded materials subjected to a thorough-thickness temperature gradient. In contrast to existing micromechanical theories that utilize classical (i.e., uncoupled) homogenization schemes to calculate micro-level and macro-level stress and displacement fields in materials with uniform or nonuniform fiber spacing (i.e., functionally graded materials), the new theory explicitly couples the microstructural details with the macrostructure of the composite. Previous thermo-elastic analysis has demonstrated that such coupling is necessary when: the temperature gradient is large with respect to the dimension of the reinforcement; the characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing fibers or inclusions is small. In these circumstances, the standard micromechanical analyses based on the concept of the representative volume element used to determine average composite properties produce questionable results. The comparison between the predictions of the finite-element method and the higher-order theory presented herein establish the theory's accuracy in predicting thermal and stress fields within composites with a finite number of fibers in the thickness direction subjected to a thorough-thickness thermal gradient.

A compact finite element method for elastic bodies

NASA Technical Reports Server (NTRS)

Rose, M. E.

1984-01-01

A nonconforming finite method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose is examined. A condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenization.

[Application of finite element method in spinal biomechanics].

PubMed

Liu, Qiang; Zhang, Jun; Sun, Shu-Chun; Wang, Fei

2017-02-25

The finite element model is one of the most important methods in study of modern spinal biomechanics, according to the needs to simulate the various states of the spine, calculate the stress force and strain distribution of the different groups in the state, and explore its principle of mechanics, mechanism of injury, and treatment effectiveness. In addition, in the study of the pathological state of the spine, the finite element is mainly used in the understanding the mechanism of lesion location, evaluating the effects of different therapeutic tool, assisting and completing the selection and improvement of therapeutic tool, in order to provide a theoretical basis for the rehabilitation of spinal lesions. Finite element method can be more provide the service for the patients suffering from spinal correction, operation and individual implant design. Among the design and performance evaluation of the implant need to pay attention to the individual difference and perfect the evaluation system. At present, how to establish a model which is more close to the real situation has been the focus and difficulty of the study of human body's finite element.Although finite element method can better simulate complex working condition, it is necessary to improve the authenticity of the model and the sharing of the group by using many kinds of methods, such as image science, statistics, kinematics and so on. Copyright© 2017 by the China Journal of Orthopaedics and Traumatology Press.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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.

A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

DOE PAGES

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 (2Δ x) modes. Furthermore, high-order accuracymore » 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. 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

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

Guerra, Jorge E.; Ullrich, Paul A.

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 (2Δ x) modes. Furthermore, high-order accuracymore » 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. 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 Discontinuous Galerkin Method for 2D Incompressible Flows

NASA Technical Reports Server (NTRS)

Liu, Jia-Guo; Shu, Chi-Wang

1999-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

1989-03-01

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

Modeling 3D PCMI using the Extended Finite Element Method with higher order elements

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

Jiang, W.; Spencer, Benjamin W.

2017-03-31

This report documents the recent development to enable XFEM to work with higher order elements. It also demonstrates the application of higher order (quadratic) elements to both 2D and 3D models of PCMI problems, where discrete fractures in the fuel are represented using XFEM. The modeling results demonstrate the ability of the higher order XFEM to accurately capture the effects of a crack on the response in the vicinity of the intersecting surfaces of cracked fuel and cladding, as well as represent smooth responses in the regions away from the crack.

Anisotropic constitutive model for nickel base single crystal alloys: Development and finite element implementation

NASA Technical Reports Server (NTRS)

Dame, L. T.; Stouffer, D. C.

1986-01-01

A tool for the mechanical analysis of nickel base single crystal superalloys, specifically Rene N4, used in gas turbine engine components is developed. This is achieved by a rate dependent anisotropic constitutive model implemented in a nonlinear three dimensional finite element code. The constitutive model is developed from metallurigical concepts utilizing a crystallographic approach. A non Schmid's law formulation is used to model the tension/compression asymmetry and orientation dependence in octahedral slip. Schmid's law is a good approximation to the inelastic response of the material in cube slip. The constitutive equations model the tensile behavior, creep response, and strain rate sensitivity of these alloys. Methods for deriving the material constants from standard tests are presented. The finite element implementation utilizes an initial strain method and twenty noded isoparametric solid elements. The ability to model piecewise linear load histories is included in the finite element code. The constitutive equations are accurately and economically integrated using a second order Adams-Moulton predictor-corrector method with a dynamic time incrementing procedure. Computed results from the finite element code are compared with experimental data for tensile, creep and cyclic tests at 760 deg C. The strain rate sensitivity and stress relaxation capabilities of the model are evaluated.

Evaluation of Transverse Thermal Stresses in Composite Plates Based on First-Order Shear Deformation Theory

NASA Technical Reports Server (NTRS)

Rolfes, R.; Noor, A. K.; Sparr, H.

1998-01-01

A postprocessing procedure is presented for the evaluation of the transverse thermal stresses in laminated plates. The analytical formulation is based on the first-order shear deformation theory and the plate is discretized by using a single-field displacement finite element model. The procedure is based on neglecting the derivatives of the in-plane forces and the twisting moments, as well as the mixed derivatives of the bending moments, with respect to the in-plane coordinates. The calculated transverse shear stiffnesses reflect the actual stacking sequence of the composite plate. The distributions of the transverse stresses through-the-thickness are evaluated by using only the transverse shear forces and the thermal effects resulting from the finite element analysis. The procedure is implemented into a postprocessing routine which can be easily incorporated into existing commercial finite element codes. Numerical results are presented for four- and ten-layer cross-ply laminates subjected to mechanical and thermal loads.

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.

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

NASA Technical Reports Server (NTRS)

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

1987-01-01

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

Development and Application of the p-Version of the Finite Element Method.

DTIC Science & Technology

1987-12-30

element method has been the subject of intensive study since the early 1950’s and perhaps even earlier. Study of the p-version of the finite element...method, on the other hand, began at *Washington University in St. Louis in the early 1970’s and led to a more recent study of the h-p version. Research...infinite strip to a bounded domain. 3.3 A Numerical Argument Principle In order to assure that all roots have indeed been obtained, we have studied the

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

GEMPIC: geometric electromagnetic particle-in-cell methods

NASA Astrophysics Data System (ADS)

Kraus, Michael; Kormann, Katharina; Morrison, Philip J.; Sonnendrücker, Eric

2017-08-01

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

Definition of NASTRAN sets by use of parametric geometry

NASA Technical Reports Server (NTRS)

Baughn, Terry V.; Tiv, Mehran

1989-01-01

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

A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael

2014-10-01

In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with stiff relaxation source terms.

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.

An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems

NASA Technical Reports Server (NTRS)

Farhat, C.; Park, K. C.; Dubois-Pelerin, Y.

1991-01-01

An unconditionally stable second order accurate implicit-implicit staggered procedure for the finite element solution of fully coupled thermoelasticity transient problems is proposed. The procedure is stabilized with a semi-algebraic augmentation technique. A comparative cost analysis reveals the superiority of the proposed computational strategy to other conventional staggered procedures. Numerical examples of one and two-dimensional thermomechanical coupled problems demonstrate the accuracy of the proposed numerical solution algorithm.

The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes

NASA Astrophysics Data System (ADS)

Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran

2018-04-01

This paper investigates the lowest-order weak Galerkin finite element method for solving the Darcy equation on quadrilateral and hybrid meshes consisting of quadrilaterals and triangles. In this approach, the pressure is approximated by constants in element interiors and on edges. The discrete weak gradients of these constant basis functions are specified in local Raviart-Thomas spaces, specifically RT0 for triangles and unmapped RT[0] for quadrilaterals. These discrete weak gradients are used to approximate the classical gradient when solving the Darcy equation. The method produces continuous normal fluxes and is locally mass-conservative, regardless of mesh quality, and has optimal order convergence in pressure, velocity, and normal flux, when the quadrilaterals are asymptotically parallelograms. Implementation is straightforward and results in symmetric positive-definite discrete linear systems. We present numerical experiments and comparisons with other existing methods.

Development of an hp-version finite element method for computational optimal control

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Warner, Michael S.

1993-01-01

The purpose of this research effort was to begin the study of the application of hp-version finite elements to the numerical solution of optimal control problems. Under NAG-939, the hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element. One possible drawback is the increased computational effort within each element required in implementing hp-version finite elements. We are trying to determine whether this computational effort is sufficiently offset by the reduction in the number of time elements used and improved Newton-Raphson convergence so as to be useful in solving optimal control problems in real time. Because certain of the element interior unknowns can be eliminated at the element level by solving a small set of nonlinear algebraic equations in which the nodal values are taken as given, the scheme may turn out to be especially powerful in a parallel computing environment. A different processor could be assigned to each element. The number of processors, strictly speaking, is not required to be any larger than the number of sub-regions which are free of discontinuities of any kind.

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.

Full Wave Analysis of RF Signal Attenuation in a Lossy Cave using a High Order Time Domain Vector Finite Element Method

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

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 ofmore » the electric field vector components are presented and discussed.« less

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.

Application of the Finite Element Method in Atomic and Molecular Physics

NASA Technical Reports Server (NTRS)

Shertzer, Janine

2007-01-01

The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.

Fuzzy interval Finite Element/Statistical Energy Analysis for mid-frequency analysis of built-up systems with mixed fuzzy and interval parameters

NASA Astrophysics Data System (ADS)

Yin, Hui; Yu, Dejie; Yin, Shengwen; Xia, Baizhan

2016-10-01

This paper introduces mixed fuzzy and interval parametric uncertainties into the FE components of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) model for mid-frequency analysis of built-up systems, thus an uncertain ensemble combining non-parametric with mixed fuzzy and interval parametric uncertainties comes into being. A fuzzy interval Finite Element/Statistical Energy Analysis (FIFE/SEA) framework is proposed to obtain the uncertain responses of built-up systems, which are described as intervals with fuzzy bounds, termed as fuzzy-bounded intervals (FBIs) in this paper. Based on the level-cut technique, a first-order fuzzy interval perturbation FE/SEA (FFIPFE/SEA) and a second-order fuzzy interval perturbation FE/SEA method (SFIPFE/SEA) are developed to handle the mixed parametric uncertainties efficiently. FFIPFE/SEA approximates the response functions by the first-order Taylor series, while SFIPFE/SEA improves the accuracy by considering the second-order items of Taylor series, in which all the mixed second-order items are neglected. To further improve the accuracy, a Chebyshev fuzzy interval method (CFIM) is proposed, in which the Chebyshev polynomials is used to approximate the response functions. The FBIs are eventually reconstructed by assembling the extrema solutions at all cut levels. Numerical results on two built-up systems verify the effectiveness of the proposed methods.

Dynamic Shape Reconstruction of Three-Dimensional Frame Structures Using the Inverse Finite Element Method

NASA Technical Reports Server (NTRS)

Gherlone, Marco; Cerracchio, Priscilla; Mattone, Massimiliano; Di Sciuva, Marco; Tessler, Alexander

2011-01-01

A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.

A partially penalty immersed Crouzeix-Raviart finite element method for interface problems.

PubMed

An, Na; Yu, Xijun; Chen, Huanzhen; Huang, Chaobao; Liu, Zhongyan

2017-01-01

The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matrix. The standard linear Crouzeix-Raviart type finite element space is used on non-interface elements and the piecewise linear Crouzeix-Raviart type immersed finite element (IFE) space is constructed on interface elements. The piecewise linear functions satisfying the interface jump conditions are uniquely determined by the integral averages on the edges as degrees of freedom. The PIFE scheme is given based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. The solvability of the method is proved and the optimal error estimates in the energy norm are obtained. Numerical experiments are presented to confirm our theoretical analysis and show that the newly developed PIFE method has optimal-order convergence in the [Formula: see text] norm as well. In addition, numerical examples also indicate that this method is valid for both the isotropic and the anisotropic elliptic interface problems.

Lower- and higher-order aberrations predicted by an optomechanical model of arcuate keratotomy for astigmatism.

PubMed

Navarro, Rafael; Palos, Fernando; Lanchares, Elena; Calvo, Begoña; Cristóbal, José A

2009-01-01

To develop a realistic model of the optomechanical behavior of the cornea after curved relaxing incisions to simulate the induced astigmatic change and predict the optical aberrations produced by the incisions. ICMA Consejo Superior de Investigaciones Científicas and Universidad de Zaragoza, Zaragoza, Spain. A 3-dimensional finite element model of the anterior hemisphere of the ocular surface was used. The corneal tissue was modeled as a quasi-incompressible, anisotropic hyperelastic constitutive behavior strongly dependent on the physiological collagen fibril distribution. Similar behaviors were assigned to the limbus and sclera. With this model, some corneal incisions were computer simulated after the Lindstrom nomogram. The resulting geometry of the biomechanical simulation was analyzed in the optical zone, and finite ray tracing was performed to compute refractive power and higher-order aberrations (HOAs). The finite-element simulation provided new geometry of the corneal surfaces, from which elevation topographies were obtained. The surgically induced astigmatism (SIA) of the simulated incisions according to the Lindstrom nomogram was computed by finite ray tracing. However, paraxial computations would yield slightly different results (undercorrection of astigmatism). In addition, arcuate incisions would induce significant amounts of HOAs. Finite-element models, together with finite ray-tracing computations, yielded realistic simulations of the biomechanical and optical changes induced by relaxing incisions. The model reproduced the SIA indicated by the Lindstrom nomogram for the simulated incisions and predicted a significant increase in optical aberrations induced by arcuate keratotomy.

Anisotropic Resistivity Forward Modelling Using Automatic Generated Higher-order Finite Element Codes

NASA Astrophysics Data System (ADS)

Wang, W.; Liu, J.

2016-12-01

Forward modelling is the general way to obtain responses of geoelectrical structures. Field investigators might find it useful for planning surveys and choosing optimal electrode configurations with respect to their targets. During the past few decades much effort has been put into the development of numerical forward codes, such as integral equation method, finite difference method and finite element method. Nowadays, most researchers prefer the finite element method (FEM) for its flexible meshing scheme, which can handle models with complex geometry. Resistivity Modelling with commercial sofewares such as ANSYS and COMSOL is convenient, but like working with a black box. Modifying the existed codes or developing new codes is somehow a long period. We present a new way to obtain resistivity forward modelling codes quickly, which is based on the commercial sofeware FEPG (Finite element Program Generator). Just with several demanding scripts, FEPG could generate FORTRAN program framework which can easily be altered to adjust our targets. By supposing the electric potential is quadratic in each element of a two-layer model, we obtain quite accurate results with errors less than 1%, while more than 5% errors could appear by linear FE codes. The anisotropic half-space model is supposed to concern vertical distributed fractures. The measured apparent resistivities along the fractures are bigger than results from its orthogonal direction, which are opposite of the true resistivities. Interpretation could be misunderstood if this anisotropic paradox is ignored. The technique we used can obtain scientific codes in a short time. The generated powerful FORTRAN codes could reach accurate results by higher-order assumption and can handle anisotropy to make better interpretations. The method we used could be expand easily to other domain where FE codes are needed.

Deformation of two-phase aggregates using standard numerical methods

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

A Runge-Kutta discontinuous finite element method for high speed flows

NASA Technical Reports Server (NTRS)

Bey, Kim S.; Oden, J. T.

1991-01-01

A Runge-Kutta discontinuous finite element method is developed for hyperbolic systems of conservation laws in two space variables. The discontinuous Galerkin spatial approximation to the conservation laws results in a system of ordinary differential equations which are marched in time using Runge-Kutta methods. Numerical results for the two-dimensional Burger's equation show that the method is (p+1)-order accurate in time and space, where p is the degree of the polynomial approximation of the solution within an element and is capable of capturing shocks over a single element without oscillations. Results for this problem also show that the accuracy of the solution in smooth regions is unaffected by the local projection and that the accuracy in smooth regions increases as p increases. Numerical results for the Euler equations show that the method captures shocks without oscillations and with higher resolution than a first-order scheme.

A least-squares finite element method for 3D incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.

1993-01-01

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.

Error associated with a reduced order linear model of a spur gear pair

NASA Technical Reports Server (NTRS)

Kahraman, A.; Singh, R.

1991-01-01

The paper proposes a reduced-order analytical model of a spur gear pair which consists of two identical spur gears, two identical flexible shafts, and four identical rolling element bearings of a given radial stiffness. The error associated with the undamped eigensolution is estimated by a comparison with a benchmark finite element model.

Nonlinear Finite Element Analysis of Shells with Large Aspect Ratio

NASA Technical Reports Server (NTRS)

Chang, T. Y.; Sawamiphakdi, K.

1984-01-01

A higher order degenerated shell element with nine nodes was selected for large deformation and post-buckling analysis of thick or thin shells. Elastic-plastic material properties are also included. The post-buckling analysis algorithm is given. Using a square plate, it was demonstrated that the none-node element does not have shear locking effect even if its aspect ratio was increased to the order 10 to the 8th power. Two sample problems are given to illustrate the analysis capability of the shell element.

The Reverse Time Migration technique coupled with Interior Penalty Discontinuous Galerkin method.

NASA Astrophysics Data System (ADS)

Baldassari, C.; Barucq, H.; Calandra, H.; Denel, B.; Diaz, J.

2009-04-01

Seismic imaging is based on the seismic reflection method which produces an image of the subsurface from reflected waves recordings by using a tomography process and seismic migration is the industrial standard to improve the quality of the images. The migration process consists in replacing the recorded wavefields at their actual place by using various mathematical and numerical methods but each of them follows the same schedule, according to the pioneering idea of Claerbout: numerical propagation of the source function (propagation) and of the recorded wavefields (retropropagation) and next, construction of the image by applying an imaging condition. The retropropagation step can be realized accouting for the time reversibility of the wave equation and the resulting algorithm is currently called Reverse Time Migration (RTM). To be efficient, especially in three dimensional domain, the RTM requires the solution of the full wave equation by fast numerical methods. Finite element methods are considered as the best discretization method for solving the wave equation, even if they lead to the solution of huge systems with several millions of degrees of freedom, since they use meshes adapted to the domain topography and the boundary conditions are naturally taken into account in the variational formulation. Among the different finite element families, the spectral element one (SEM) is very interesting because it leads to a diagonal mass matrix which dramatically reduces the cost of the numerical computation. Moreover this method is very accurate since it allows the use of high order finite elements. However, SEM uses meshes of the domain made of quadrangles in 2D or hexaedra in 3D which are difficult to compute and not always suitable for complex topographies. Recently, Grote et al. applied the IPDG (Interior Penalty Discontinuous Galerkin) method to the wave equation. This approach is very interesting since it relies on meshes with triangles in 2D or tetrahedra in 3D, which allows to handle the topography of the domain very accurately. Moreover, the fact that the resulting mass matrix is block-diagonal and that IPDG is compatible with the use of high-order finite element may let us suppose that its performances are similar to the ones of the SEM. In this presentation, we study the performances of IDPG through numerical comparisons with the SEM in 1D and 2D. We compare in particular the accuracy of the solutions obtained by the two methods with various order of approximation and the computational burden of the algorithms. The conclusion is IPDG and SEM perform similarly when considering low order finite elements while IPDG outperforms SEM in case of high order finite elements. Next we illustrate the impact of IPDG on the RTM, first through a simple configuration test (two-layered medium), then through realistic industrial applications in 2D.

A three-dimensional FEM-DEM technique for predicting the evolution of fracture in geomaterials and concrete

NASA Astrophysics Data System (ADS)

Zárate, Francisco; Cornejo, Alejandro; Oñate, Eugenio

2018-07-01

This paper extends to three dimensions (3D), the computational technique developed by the authors in 2D for predicting the onset and evolution of fracture in a finite element mesh in a simple manner based on combining the finite element method and the discrete element method (DEM) approach (Zárate and Oñate in Comput Part Mech 2(3):301-314, 2015). Once a crack is detected at an element edge, discrete elements are generated at the adjacent element vertexes and a simple DEM mechanism is considered in order to follow the evolution of the crack. The combination of the DEM with simple four-noded linear tetrahedron elements correctly captures the onset of fracture and its evolution, as shown in several 3D examples of application.

Assessment of the performance of rigid pavement back-calculation through finite element modeling

NASA Astrophysics Data System (ADS)

Shoukry, Samir N.; William, Gergis W.; Martinelli, David R.

1999-02-01

This study focuses on examining the behavior of rigid pavement layers during the Falling Weight Deflectometer (FWD) test. Factors affecting the design of a concrete slab, such as whether the joints are doweled or undoweled and the spacing between the transverse joints, were considered in this study. Explicit finite element analysis was employed to investigate pavement layers' responses to the action of the impulse of the FWD test. Models of various dimensions were developed to satisfy the factors under consideration. The accuracy of the finite element models developed in this investigation was verified by comparing the finite element- generated deflection basin with that experimentally measured during an actual test. The results showed that the measured deflection basin can be reproduced through finite element modeling of the pavement structure. The resulting deflection basins from the use FE modeling was processed in order to backcalculate pavement layer moduli. This approach provides a method for the evaluation of the performance of existing backcalculation programs which are based on static elastic layer analysis. Based upon the previous studies conducted for the selection of software, three different backcalculation programs were chosen for the evaluation: MODULUS5.0, EVERCALC4.0, and MODCOMP3. The results indicate that ignoring the dynamic nature of the load may lead to crude results, especially during backcalculation procedures.

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

NASA Technical Reports Server (NTRS)

Barth, Timothy (Editor); Deconinck, Herman (Editor)

1999-01-01

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Spectral/ hp element methods: Recent developments, applications, and perspectives

NASA Astrophysics Data System (ADS)

Xu, Hui; Cantwell, Chris D.; Monteserin, Carlos; Eskilsson, Claes; Engsig-Karup, Allan P.; Sherwin, Spencer J.

2018-02-01

The spectral/ hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/ hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/ hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/ hp element method in more complex science and engineering applications are discussed.

Very high order discontinuous Galerkin method in elliptic problems

NASA Astrophysics Data System (ADS)

Jaśkowiec, Jan

2017-09-01

The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

Very high order discontinuous Galerkin method in elliptic problems

NASA Astrophysics Data System (ADS)

Jaśkowiec, Jan

2018-07-01

The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

Eigensolution of finite element problems in a completely connected parallel architecture

NASA Technical Reports Server (NTRS)

Akl, Fred A.; Morel, Michael R.

1989-01-01

A parallel algorithm for the solution of the generalized eigenproblem in linear elastic finite element analysis, (K)(phi)=(M)(phi)(omega), where (K) and (M) are of order N, and (omega) is of order q is presented. The parallel algorithm is based on a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm has been successfully implemented on a tightly coupled multiple-instruction-multiple-data (MIMD) parallel processing computer, Cray X-MP. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor, or to a logical processor (task) if the number of domains exceeds the number of physical processors. The macro-tasking library routines are used in mapping each domain to a user task. Computational speed-up and efficiency are used to determine the effectiveness of the algorithm. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts and the dimension of the subspace on the performance of the algorithm are investigated. For a 64-element rectangular plate, speed-ups of 1.86, 3.13, 3.18 and 3.61 are achieved on two, four, six and eight processors, respectively.

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

NASA Astrophysics Data System (ADS)

Heumann, Holger; Rapetti, Francesca

2017-04-01

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

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2015-12-21

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

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

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

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

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

NASA Astrophysics Data System (ADS)

Chróścielewski, Jacek; Schmidt, Rüdiger; Eremeyev, Victor A.

2018-05-01

This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

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

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.

1992-01-01

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

Simulation of surface hardening in the deep rolling process by means of an axial symmetric nodal averaged finite element

NASA Astrophysics Data System (ADS)

Morrev, P. G.; Gordon, V. A.

2018-03-01

Surface hardening by deep rolling can be considered as the axial symmetric problem in some special events (namely, when large R and small r radii of the deforming roller meet the requirement R>> r). An axisymmetric nodal averaged stabilized finite element is formulated. The formulation is based on a variational principle with a penalty (stabilizing) item in order to involve large elastic-plastic strain and near to incompressible materials. The deep rolling process for a steel rod is analyzed. Axial residual stress, yield stress, and Odkvist’s parameter are calculated. The residual stress is compared with the data obtained by other authors using a three-dimensional statement of the problem. The results obtained demonstrate essential advantages of the newly developed finite element.

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

PubMed

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

2014-01-01

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

Modeling and Design of a Full-Scale Rotor Blade with Embedded Piezocomposite Actuators

NASA Astrophysics Data System (ADS)

Kovalovs, A.; Barkanov, E.; Ruchevskis, S.; Wesolowski, M.

2017-05-01

An optimization methodology for the design of a full-scale rotor blade with an active twist in order to enhance its ability to reduce vibrations and noise is presented. It is based on a 3D finite-element model, the planning of experiments, and the response surface technique to obtain high piezoelectric actuation forces and displacements with a minimum actuator weight and energy applied. To investigate an active twist of the helicopter rotor blade, a structural static analysis using a 3D finite-element model was carried out. Optimum results were obtained at two possible applications of macrofiber composite actuators. The torsion angle found from the finite-element simulation of helicopter rotor blades was successfully validated by its experimental values, which confirmed the modeling accuracy.

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-Order Entropy Stable Formulations for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Fisher, Travis C.

2013-01-01

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

On the Exploitation of Sensitivity Derivatives for Improving Sampling Methods

NASA Technical Reports Server (NTRS)

Cao, Yanzhao; Hussaini, M. Yousuff; Zang, Thomas A.

2003-01-01

Many application codes, such as finite-element structural analyses and computational fluid dynamics codes, are capable of producing many sensitivity derivatives at a small fraction of the cost of the underlying analysis. This paper describes a simple variance reduction method that exploits such inexpensive sensitivity derivatives to increase the accuracy of sampling methods. Three examples, including a finite-element structural analysis of an aircraft wing, are provided that illustrate an order of magnitude improvement in accuracy for both Monte Carlo and stratified sampling schemes.

A p-version finite element method for steady incompressible fluid flow and convective heat transfer

NASA Technical Reports Server (NTRS)

Winterscheidt, Daniel L.

1993-01-01

A new p-version finite element formulation for steady, incompressible fluid flow and convective heat transfer problems is presented. The steady-state residual equations are obtained by considering a limiting case of the least-squares formulation for the transient problem. The method circumvents the Babuska-Brezzi condition, permitting the use of equal-order interpolation for velocity and pressure, without requiring the use of arbitrary parameters. Numerical results are presented to demonstrate the accuracy and generality of the method.

An error analysis of least-squares finite element method of velocity-pressure-vorticity formulation for Stokes problem

NASA Technical Reports Server (NTRS)

Chang, Ching L.; Jiang, Bo-Nan

1990-01-01

A theoretical proof of the optimal rate of convergence for the least-squares method is developed for the Stokes problem based on the velocity-pressure-vorticity formula. The 2D Stokes problem is analyzed to define the product space and its inner product, and the a priori estimates are derived to give the finite-element approximation. The least-squares method is found to converge at the optimal rate for equal-order interpolation.

Arbitrary-level hanging nodes for adaptive hphp-FEM approximations in 3D

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

Pavel Kus; Pavel Solin; David Andrs

2014-11-01

In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods (hphp-FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the finite element mesh. The technique makes it possible to design efficient adaptive algorithms for purely hexahedral meshes. We present a detailed mathematical description of the method and illustrate it with numerical examples.

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2007-09-01

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

3D FE simulation of semi-finishing machining of Ti6Al4V additively manufactured by direct metal laser sintering

NASA Astrophysics Data System (ADS)

Imbrogno, Stano; Rinaldi, Sergio; Raso, Antonio; Bordin, Alberto; Bruschi, Stefania; Umbrello, Domenico

2018-05-01

The Additive Manufacturing techniques are gaining more and more interest in various industrial fields due to the possibility of drastically reduce the material waste during the production processes, revolutionizing the standard scheme and strategies of the manufacturing processes. However, the metal parts shape produced, frequently do not satisfy the tolerances as well as the surface quality requirements. During the design phase, the finite element simulation results a fundamental tool to help the engineers in the correct decision of the most suitable process parameters, especially in manufacturing processes, in order to produce products of high quality. The aim of this work is to develop a 3D finite element model of semi-finishing turning operation of Ti6Al4V, produced via Direct Metal Laser Sintering (DMLS). A customized user sub-routine was built-up in order to model the mechanical behavior of the material under machining operations to predict the main fundamental variables as cutting forces and temperature. Moreover, the machining induced alterations are also studied by the finite element model developed.

A Unique Finite Element Modeling of the Periodic Wave Transformation over Sloping and Barred Beaches by Beji and Nadaoka's Extended Boussinesq Equations

PubMed Central

Jabbari, Mohammad Hadi; Sayehbani, Mesbah; Reisinezhad, Arsham

2013-01-01

This paper presents a numerical model based on one-dimensional Beji and Nadaoka's Extended Boussinesq equations for simulation of periodic wave shoaling and its decomposition over morphological beaches. A unique Galerkin finite element and Adams-Bashforth-Moulton predictor-corrector methods are employed for spatial and temporal discretization, respectively. For direct application of linear finite element method in spatial discretization, an auxiliary variable is hereby introduced, and a particular numerical scheme is offered to rewrite the equations in lower-order form. Stability of the suggested numerical method is also analyzed. Subsequently, in order to display the ability of the presented model, four different test cases are considered. In these test cases, dispersive and nonlinearity effects of the periodic waves over sloping beaches and barred beaches, which are the common coastal profiles, are investigated. Outputs are compared with other existing numerical and experimental data. Finally, it is concluded that the current model can be further developed to model any morphological development of coastal profiles. PMID:23853534

Reduced-order modeling approach for frictional stick-slip behaviors of joint interface

NASA Astrophysics Data System (ADS)

Wang, Dong; Xu, Chao; Fan, Xuanhua; Wan, Qiang

2018-03-01

The complex frictional stick-slip behaviors of mechanical joint interface have a great effect on the dynamic properties of assembled structures. In this paper, a reduced-order modeling approach based on the constitutive Iwan model is proposed to describe the stick-slip behaviors of joint interface. An improved Iwan model is developed to describe the non-zero residual stiffness at macro-slip regime and smooth transition of joint stiffness from micro-slip to macro-slip regime, and the power-law relationship of energy dissipation during the micro-slip regime. In allusion to these nonlinear behaviors, the finite element method is used to calculate the recycle force under monolithic loading and the energy dissipation per cycle under oscillatory loading. The proposed model is then used to predict the nonlinear stick-slip behaviors of joint interface by curve-fitting to the results of finite element analysis, and the results show good agreements with the finite element analysis. A comparison with the experiment results in literature is also made. The proposed model agrees very well with the experiment results.

On mixed and displacement finite element models of a refined shear deformation theory for laminated anisotropic plates

NASA Technical Reports Server (NTRS)

Reddy, J. N.

1986-01-01

An improved plate theory that accounts for the transverse shear deformation is presented, and mixed and displacement finite element models of the theory are developed. The theory is based on an assumed displacement field in which the inplane displacements are expanded in terms of the thickness coordinate up to the cubic term and the transverse deflection is assumed to be independent of the thickness coordinate. The governing equations of motion for the theory are derived from the Hamilton's principle. The theory eliminates the need for shear correction factors because the transverse shear stresses are represented parabolically. A mixed finite element model that uses independent approximations of the displacements and moments, and a displacement model that uses only displacements as degrees of freedom are developed. A comparison of the numerical results for bending with the exact solutions of the new theory and the three-dimensional elasticity theory shows that the present theory (and hence the finite element models) is more accurate than other plate-theories of the same order.

Probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, Ted; Wing, Kam Liu

1987-01-01

In the Probabilistic Finite Element Method (PFEM), finite element methods have been efficiently combined with second-order perturbation techniques to provide an effective method for informing the designer of the range of response which is likely in a given problem. The designer must provide as input the statistical character of the input variables, such as yield strength, load magnitude, and Young's modulus, by specifying their mean values and their variances. The output then consists of the mean response and the variance in the response. Thus the designer is given a much broader picture of the predicted performance than with simply a single response curve. These methods are applicable to a wide class of problems, provided that the scale of randomness is not too large and the probabilistic density functions possess decaying tails. By incorporating the computational techniques we have developed in the past 3 years for efficiency, the probabilistic finite element methods are capable of handling large systems with many sources of uncertainties. Sample results for an elastic-plastic ten-bar structure and an elastic-plastic plane continuum with a circular hole subject to cyclic loadings with the yield stress on the random field are given.

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

PubMed

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

2018-01-01

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

Modeling the effect of shroud contact and friction dampers on the mistuned response of turbopumps

NASA Technical Reports Server (NTRS)

Griffin, Jerry H.; Yang, M.-T.

1994-01-01

The contract has been revised. Under the revised scope of work a reduced order model has been developed that can be used to predict the steady-state response of mistuned bladed disks. The approach has been implemented in a computer code, LMCC. It is concluded that: the reduced order model displays structural fidelity comparable to that of a finite element model of an entire bladed disk system with significantly improved computational efficiency; and, when the disk is stiff, both the finite element model and LMCC predict significantly more amplitude variation than was predicted by earlier models. This second result may have important practical ramifications, especially in the case of integrally bladed disks.

Adaptation of a program for nonlinear finite element analysis to the CDC STAR 100 computer

NASA Technical Reports Server (NTRS)

Pifko, A. B.; Ogilvie, P. L.

1978-01-01

The conversion of a nonlinear finite element program to the CDC STAR 100 pipeline computer is discussed. The program called DYCAST was developed for the crash simulation of structures. Initial results with the STAR 100 computer indicated that significant gains in computation time are possible for operations on gloval arrays. However, for element level computations that do not lend themselves easily to long vector processing, the STAR 100 was slower than comparable scalar computers. On this basis it is concluded that in order for pipeline computers to impact the economic feasibility of large nonlinear analyses it is absolutely essential that algorithms be devised to improve the efficiency of element level computations.

Analytical and Numerical Results for an Adhesively Bonded Joint Subjected to Pure Bending

NASA Technical Reports Server (NTRS)

Smeltzer, Stanley S., III; Lundgren, Eric

2006-01-01

A one-dimensional, semi-analytical methodology that was previously developed for evaluating adhesively bonded joints composed of anisotropic adherends and adhesives that exhibit inelastic material behavior is further verified in the present paper. A summary of the first-order differential equations and applied joint loading used to determine the adhesive response from the methodology are also presented. The method was previously verified against a variety of single-lap joint configurations from the literature that subjected the joints to cases of axial tension and pure bending. Using the same joint configuration and applied bending load presented in a study by Yang, the finite element analysis software ABAQUS was used to further verify the semi-analytical method. Linear static ABAQUS results are presented for two models, one with a coarse and one with a fine element meshing, that were used to verify convergence of the finite element analyses. Close agreement between the finite element results and the semi-analytical methodology were determined for both the shear and normal stress responses of the adhesive bondline. Thus, the semi-analytical methodology was successfully verified using the ABAQUS finite element software and a single-lap joint configuration subjected to pure bending.

Copper Tube Compression in Z-Current Geometry, Numerical Simulations and Comparison with Cyclope Experiments

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

Lefrancois, A.; L'Eplattenier, P.; Burger, M.

2006-02-13

Metallic tubes compressions in Z-current geometry were performed at the Cyclope facility from Gramat Research Center in order to study the behavior of metals under large strain at high strain rate. 3D configurations of cylinder compressions have been calculated here to benchmark the new beta version of the electromagnetism package coupled with the dynamics in Ls-Dyna and compared with the Cyclope experiments. The electromagnetism module is being developed in the general-purpose explicit and implicit finite element program LS-DYNA{reg_sign} in order to perform coupled mechanical/thermal/electromagnetism simulations. The Maxwell equations are solved using a Finite Element Method (FEM) for the solid conductorsmore » coupled with a Boundary Element Method (BEM) for the surrounding air (or vacuum). More details can be read in the references.« less

Multigrid finite element method in stress analysis of three-dimensional elastic bodies of heterogeneous structure

NASA Astrophysics Data System (ADS)

Matveev, A. D.

2016-11-01

To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.

Non-integer viscoelastic constitutive law to model soft biological tissues to in-vivo indentation.

PubMed

Demirci, Nagehan; Tönük, Ergin

2014-01-01

During the last decades, derivatives and integrals of non-integer orders are being more commonly used for the description of constitutive behavior of various viscoelastic materials including soft biological tissues. Compared to integer order constitutive relations, non-integer order viscoelastic material models of soft biological tissues are capable of capturing a wider range of viscoelastic behavior obtained from experiments. Although integer order models may yield comparably accurate results, non-integer order material models have less number of parameters to be identified in addition to description of an intermediate material that can monotonically and continuously be adjusted in between an ideal elastic solid and an ideal viscous fluid. In this work, starting with some preliminaries on non-integer (fractional) calculus, the "spring-pot", (intermediate mechanical element between a solid and a fluid), non-integer order three element (Zener) solid model, finally a user-defined large strain non-integer order viscoelastic constitutive model was constructed to be used in finite element simulations. Using the constitutive equation developed, by utilizing inverse finite element method and in vivo indentation experiments, soft tissue material identification was performed. The results indicate that material coefficients obtained from relaxation experiments, when optimized with creep experimental data could simulate relaxation, creep and cyclic loading and unloading experiments accurately. Non-integer calculus viscoelastic constitutive models, having physical interpretation and modeling experimental data accurately is a good alternative to classical phenomenological viscoelastic constitutive equations.

Hybrid Evidence Theory-based Finite Element/Statistical Energy Analysis method for mid-frequency analysis of built-up systems with epistemic uncertainties

NASA Astrophysics Data System (ADS)

Yin, Shengwen; Yu, Dejie; Yin, Hui; Lü, Hui; Xia, Baizhan

2017-09-01

Considering the epistemic uncertainties within the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) model when it is used for the response analysis of built-up systems in the mid-frequency range, the hybrid Evidence Theory-based Finite Element/Statistical Energy Analysis (ETFE/SEA) model is established by introducing the evidence theory. Based on the hybrid ETFE/SEA model and the sub-interval perturbation technique, the hybrid Sub-interval Perturbation and Evidence Theory-based Finite Element/Statistical Energy Analysis (SIP-ETFE/SEA) approach is proposed. In the hybrid ETFE/SEA model, the uncertainty in the SEA subsystem is modeled by a non-parametric ensemble, while the uncertainty in the FE subsystem is described by the focal element and basic probability assignment (BPA), and dealt with evidence theory. Within the hybrid SIP-ETFE/SEA approach, the mid-frequency response of interest, such as the ensemble average of the energy response and the cross-spectrum response, is calculated analytically by using the conventional hybrid FE/SEA method. Inspired by the probability theory, the intervals of the mean value, variance and cumulative distribution are used to describe the distribution characteristics of mid-frequency responses of built-up systems with epistemic uncertainties. In order to alleviate the computational burdens for the extreme value analysis, the sub-interval perturbation technique based on the first-order Taylor series expansion is used in ETFE/SEA model to acquire the lower and upper bounds of the mid-frequency responses over each focal element. Three numerical examples are given to illustrate the feasibility and effectiveness of the proposed method.

A study of the response of nonlinear springs

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Knott, T. W.; Johnson, E. R.

1991-01-01

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

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.

Finite Element Analysis of a Copper Single Crystal Shape Memory Alloy-Based Endodontic Instruments

NASA Astrophysics Data System (ADS)

Vincent, Marin; Thiebaud, Frédéric; Bel Haj Khalifa, Saifeddine; Engels-Deutsch, Marc; Ben Zineb, Tarak

2015-10-01

The aim of the present paper is the development of endodontic Cu-based single crystal Shape Memory Alloy (SMA) instruments in order to eliminate the antimicrobial and mechanical deficiencies observed with the conventional Nickel-Titane (NiTi) SMA files. A thermomechanical constitutive law, already developed and implemented in a finite element code by our research group, is adopted for the simulation of the single crystal SMA behavior. The corresponding material parameters were identified starting from experimental results for a tensile test at room temperature. A computer-aided design geometry has been achieved and considered for a finite element structural analysis of the endodontic Cu-based single crystal SMA files. They are meshed with tetrahedral continuum elements to improve the computation time and the accuracy of results. The geometric parameters tested in this study are the length of the active blade, the rod length, the pitch, the taper, the tip diameter, and the rod diameter. For each set of adopted parameters, a finite element model is built and tested in a combined bending-torsion loading in accordance with ISO 3630-1 norm. The numerical analysis based on finite element procedure allowed purposing an optimal geometry suitable for Cu-based single crystal SMA endodontic files. The same analysis was carried out for the classical NiTi SMA files and a comparison was made between the two kinds of files. It showed that Cu-based single crystal SMA files are less stiff than the NiTi files. The Cu-based endodontic files could be used to improve the root canal treatments. However, the finite element analysis brought out the need for further investigation based on experiments.

Well-Balanced Second-Order Approximation of the Shallow Water Equations With Friction via Continuous Galerkin Finite Elements

NASA Astrophysics Data System (ADS)

Quezada de Luna, M.; Farthing, M.; Guermond, J. L.; Kees, C. E.; Popov, B.

2017-12-01

The Shallow Water Equations (SWEs) are popular for modeling non-dispersive incompressible water waves where the horizontal wavelength is much larger than the vertical scales. They can be derived from the incompressible Navier-Stokes equations assuming a constant vertical velocity. The SWEs are important in Geophysical Fluid Dynamics for modeling surface gravity waves in shallow regimes; e.g., in the deep ocean. Some common geophysical applications are the evolution of tsunamis, river flooding and dam breaks, storm surge simulations, atmospheric flows and others. This work is concerned with the approximation of the time-dependent Shallow Water Equations with friction using explicit time stepping and continuous finite elements. The objective is to construct a method that is at least second-order accurate in space and third or higher-order accurate in time, positivity preserving, well-balanced with respect to rest states, well-balanced with respect to steady sliding solutions on inclined planes and robust with respect to dry states. Methods fulfilling the desired goals are common within the finite volume literature. However, to the best of our knowledge, schemes with the above properties are not well developed in the context of continuous finite elements. We start this work based on a finite element method that is second-order accurate in space, positivity preserving and well-balanced with respect to rest states. We extend it by: modifying the artificial viscosity (via the entropy viscosity method) to deal with issues of loss of accuracy around local extrema, considering a singular Manning friction term handled via an explicit discretization under the usual CFL condition, considering a water height regularization that depends on the mesh size and is consistent with the polynomial approximation, reducing dispersive errors introduced by lumping the mass matrix and others. After presenting the details of the method we show numerical tests that demonstrate the well-balanced nature of the scheme and its convergence properties. We conclude with well-known benchmark problems including the Malpasset dam break (see the attached figure). All numerical experiments are performed and available in the Proteus toolkit, which is an open source python package for modeling continuum mechanical processes and fluid flow.

75 FR 733 - Implementation of the Executive Order, ``Classified National Security Information''

Federal Register 2010, 2011, 2012, 2013, 2014

2010-01-05

... 5.4 of the order as a key element in planning oversight of agencies. Each senior agency official... utilization of finite resources available for declassification, further referrals of these records are not...

Tempest: Mesoscale test case suite results and the effect of order-of-accuracy on pressure gradient force errors

NASA Astrophysics Data System (ADS)

Guerra, J. E.; Ullrich, P. A.

2014-12-01

Tempest is a new non-hydrostatic atmospheric modeling framework that allows for investigation and intercomparison of high-order numerical methods. It is composed of a dynamical core based on a finite-element formulation of arbitrary order operating on cubed-sphere and Cartesian meshes with topography. The underlying technology is briefly discussed, including a novel Hybrid Finite Element Method (HFEM) vertical coordinate coupled with high-order Implicit/Explicit (IMEX) time integration to control vertically propagating sound waves. Here, we show results from a suite of Mesoscale testing cases from the literature that demonstrate the accuracy, performance, and properties of Tempest on regular Cartesian meshes. The test cases include wave propagation behavior, Kelvin-Helmholtz instabilities, and flow interaction with topography. Comparisons are made to existing results highlighting improvements made in resolving atmospheric dynamics in the vertical direction where many existing methods are deficient.

Finite element dynamic analysis of soft tissues using state-space model.

PubMed

Iorga, Lucian N; Shan, Baoxiang; Pelegri, Assimina A

2009-04-01

A finite element (FE) model is employed to investigate the dynamic response of soft tissues under external excitations, particularly corresponding to the case of harmonic motion imaging. A solid 3D mixed 'u-p' element S8P0 is implemented to capture the near-incompressibility inherent in soft tissues. Two important aspects in structural modelling of these tissues are studied; these are the influence of viscous damping on the dynamic response and, following FE-modelling, a developed state-space formulation that valuates the efficiency of several order reduction methods. It is illustrated that the order of the mathematical model can be significantly reduced, while preserving the accuracy of the observed system dynamics. Thus, the reduced-order state-space representation of soft tissues for general dynamic analysis significantly reduces the computational cost and provides a unitary framework for the 'forward' simulation and 'inverse' estimation of soft tissues. Moreover, the results suggest that damping in soft-tissue is significant, effectively cancelling the contribution of all but the first few vibration modes.

Sandia Higher Order Elements (SHOE) v 0.5 alpha

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

2013-09-24

SHOE is research code for characterizing and visualizing higher-order finite elements; it contains a framework for defining classes of interpolation techniques and element shapes; methods for interpolating triangular, quadrilateral, tetrahedral, and hexahedral cells using Lagrange and Legendre polynomial bases of arbitrary order; methods to decompose each element into domains of constant gradient flow (using a polynomial solver to identify critical points); and an isocontouring technique that uses this decomposition to guarantee topological correctness. Please note that this is an alpha release of research software and that some time has passed since it was actively developed; build- and run-time issues likelymore » exist.« less

Loading-unloading response of circular GLARE fiber-metal laminates under lateral indentation

NASA Astrophysics Data System (ADS)

Tsamasphyros, George J.; Bikakis, George S.

2015-01-01

GLARE is a Fiber-Metal laminated material used in aerospace structures which are frequently subjected to various impact damages. Hence, the response of GLARE plates subjected to lateral indentation is very important. In this paper, analytical expressions are derived and a non-linear finite element modeling procedure is proposed in order to predict the static load-indentation curves of circular GLARE plates during loading and unloading by a hemispherical indentor. We have recently published analytical formulas and a finite element procedure for the static indentation of circular GLARE plates which are now used during the loading stage. Here, considering that aluminum layers are in a state of membrane yield and employing energy balance during unloading, the unloading path is determined. Using this unloading path, an algebraic equation is derived for calculating the permanent dent depth of the GLARE plate after the indentor's withdrawal. Furthermore, our finite element procedure is modified in order to simulate the unloading stage as well. The derived formulas and the proposed finite element modeling procedure are applied successfully to GLARE 2-2/1-0.3 and to GLARE 3-3/2-0.4 circular plates. The analytical results are compared with corresponding FEM results and a good agreement is found. The analytically calculated permanent dent depth is within 6 % for the GLARE 2 plate, and within 7 % for the GLARE 3 plate, of the corresponding numerically calculated result. No other solution of this problem is known to the authors.

Elasto-Plastic Analysis of Tee Joints Using HOT-SMAC

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

MHOST: An efficient finite element program for inelastic analysis of solids and structures

NASA Technical Reports Server (NTRS)

Nakazawa, S.

1988-01-01

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Finite element design procedure for correcting the coining die profiles

NASA Astrophysics Data System (ADS)

Alexandrino, Paulo; Leitão, Paulo J.; Alves, Luis M.; Martins, Paulo A. F.

2018-05-01

This paper presents a new finite element based design procedure for correcting the coining die profiles in order to optimize the distribution of pressure and the alignment of the resultant vertical force at the end of the die stroke. The procedure avoids time consuming and costly try-outs, does not interfere with the creative process of the sculptors and extends the service life of the coining dies by significantly decreasing the applied pressure and bending moments. The numerical simulations were carried out in a computer program based on the finite element flow formulation that is currently being developed by the authors in collaboration with the Portuguese Mint. A new experimental procedure based on the stack compression test is also proposed for determining the stress-strain curve of the materials directly from the coin blanks.

Finite element analysis of fretting contact for nonhomogenous materials

NASA Astrophysics Data System (ADS)

Korkmaz, Y. M.; Coker, D.

2018-01-01

Fretting problem arises in the case of relatively small sliding motion between contacting surfaces. Fatigue life of the components that are in contact with each other, especially in rotorcraft may be significantly reduced due to fretting. The purpose of this study is to investigate material inhomogeneity near the contact region on the fretting problem in a cylindrical on flat contact configuration. A finite element (FE) model was constructed by using commercial finite element package ABAQUSTMto study partial sliding and stress concentrations. In order to investigate the effect of material inhomogeneity, the fretting contact is analyzed by introducing voids near the contact region. The void size and an array of voids is introduced into the substrate. The results are compared in terms of pressure, shear traction, tangential stress magnitudes and relative slip between the contacting materials.

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

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

Stamping of Thin-Walled Structural Components with Magnesium Alloy AZ31 Sheets

NASA Astrophysics Data System (ADS)

Chen, Fuh-Kuo; Chang, Chih-Kun

2005-08-01

In the present study, the stamping process for manufacturing cell phone cases with magnesium alloy AZ31 sheets was studied using both the experimental approach and the finite element analysis. In order to determine the proper forming temperature and set up a fracture criterion, tensile tests and forming limit tests were first conducted to obtain the mechanical behaviors of AZ31 sheets at various elevated temperatures. The mechanical properties of Z31 sheets obtained from the experiments were then adopted in the finite element analysis to investigate the effects of the process parameters on the formability of the stamping process of cell phone cases. The finite element simulation results revealed that both the fracture and wrinkle defects could not be eliminated at the same time by adjusting blank-holder force or blank size. A drawbead design was then performed using the finite element simulations to determine the size and the location of drawbead required to suppress the wrinkle defect. An optimum stamping process, including die geometry, forming temperature, and blank dimension, was then determined for manufacturing the cell phone cases. The finite element analysis was validated by the good agreement between the simulation results and the experimental data. It confirms that the cell phone cases can be produced with magnesium alloy AZ31 sheet by the stamping process at elevated temperatures.

A 3D finite element ALE method using an approximate Riemann solution

DOE PAGES

Chiravalle, V. P.; Morgan, N. R.

2016-08-09

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

A 3D finite element ALE method using an approximate Riemann solution

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

Chiravalle, V. P.; Morgan, N. R.

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

A finite-element method for large-amplitude, two-dimensional panel flutter at hypersonic speeds

NASA Technical Reports Server (NTRS)

Mei, Chuh; Gray, Carl E.

1989-01-01

The nonlinear flutter behavior of a two-dimensional panel in hypersonic flow is investigated analytically. An FEM formulation based unsteady third-order piston theory (Ashley and Zartarian, 1956; McIntosh, 1970) and taking nonlinear structural and aerodynamic phenomena into account is derived; the solution procedure is outlined; and typical results are presented in extensive tables and graphs. A 12-element finite-element solution obtained using an alternative method for linearizing the assumed limit-cycle time function is shown to give predictions in good agreement with classical analytical results for large-amplitude vibration in a vacuum and large-amplitude panel flutter, using linear aerodynamics.

Co-simulation coupling spectral/finite elements for 3D soil/structure interaction problems

NASA Astrophysics Data System (ADS)

Zuchowski, Loïc; Brun, Michael; De Martin, Florent

2018-05-01

The coupling between an implicit finite elements (FE) code and an explicit spectral elements (SE) code has been explored for solving the elastic wave propagation in the case of soil/structure interaction problem. The coupling approach is based on domain decomposition methods in transient dynamics. The spatial coupling at the interface is managed by a standard coupling mortar approach, whereas the time integration is dealt with an hybrid asynchronous time integrator. An external coupling software, handling the interface problem, has been set up in order to couple the FE software Code_Aster with the SE software EFISPEC3D.

A three-dimensional finite element model of human atrial anatomy: New methods for cubic Hermite meshes with extraordinary vertices

PubMed Central

Gonzales, Matthew J.; Sturgeon, Gregory; Krishnamurthy, Adarsh; Hake, Johan; Jonas, René; Stark, Paul; Rappel, Wouter-Jan; Narayan, Sanjiv M.; Zhang, Yongjie; Segars, W. Paul; McCulloch, Andrew D.

2013-01-01

High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the “local-to-global” derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 millimeters, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology. PMID:23602918

3 CFR - Implementation of the Executive Order, “Classified National Security Information”

Code of Federal Regulations, 2010 CFR

2010-01-01

... requirements of section 5.4 of the order as a key element in planning oversight of agencies. Each senior agency... utilization of finite resources available for declassification, further referrals of these records are not...

Numerical Analysis of an H 1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

PubMed Central

Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

2014-01-01

We discuss and analyze an H 1-Galerkin mixed finite element (H 1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H 1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H 1-GMFE method. Based on the discussion on the theoretical error analysis in L 2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H 1-norm. Moreover, we derive and analyze the stability of H 1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

Optimization of the sources in local hyperthermia using a combined finite element-genetic algorithm method.

PubMed

Siauve, N; Nicolas, L; Vollaire, C; Marchal, C

2004-12-01

This article describes an optimization process specially designed for local and regional hyperthermia in order to achieve the desired specific absorption rate in the patient. It is based on a genetic algorithm coupled to a finite element formulation. The optimization method is applied to real human organs meshes assembled from computerized tomography scans. A 3D finite element formulation is used to calculate the electromagnetic field in the patient, achieved by radiofrequency or microwave sources. Space discretization is performed using incomplete first order edge elements. The sparse complex symmetric matrix equation is solved using a conjugate gradient solver with potential projection pre-conditionning. The formulation is validated by comparison of calculated specific absorption rate distributions in a phantom to temperature measurements. A genetic algorithm is used to optimize the specific absorption rate distribution to predict the phases and amplitudes of the sources leading to the best focalization. The objective function is defined as the specific absorption rate ratio in the tumour and healthy tissues. Several constraints, regarding the specific absorption rate in tumour and the total power in the patient, may be prescribed. Results obtained with two types of applicators (waveguides and annular phased array) are presented and show the faculties of the developed optimization process.

Finite element solution to passive scalar transport behind line sources under neutral and unstable stratification

NASA Astrophysics Data System (ADS)

Liu, Chun-Ho; Leung, Dennis Y. C.

2006-02-01

This study employed a direct numerical simulation (DNS) technique to contrast the plume behaviours and mixing of passive scalar emitted from line sources (aligned with the spanwise direction) in neutrally and unstably stratified open-channel flows. The DNS model was developed using the Galerkin finite element method (FEM) employing trilinear brick elements with equal-order interpolating polynomials that solved the momentum and continuity equations, together with conservation of energy and mass equations in incompressible flow. The second-order accurate fractional-step method was used to handle the implicit velocity-pressure coupling in incompressible flow. It also segregated the solution to the advection and diffusion terms, which were then integrated in time, respectively, by the explicit third-order accurate Runge-Kutta method and the implicit second-order accurate Crank-Nicolson method. The buoyancy term under unstable stratification was integrated in time explicitly by the first-order accurate Euler method. The DNS FEM model calculated the scalar-plume development and the mean plume path. In particular, it calculated the plume meandering in the wall-normal direction under unstable stratification that agreed well with the laboratory and field measurements, as well as previous modelling results available in literature.

A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields.

PubMed

Yang, R; Zelyak, O; Fallone, B G; St-Aubin, J

2018-01-30

Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.

A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields

NASA Astrophysics Data System (ADS)

Yang, R.; Zelyak, O.; Fallone, B. G.; St-Aubin, J.

2018-02-01

Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.

The spectral cell method in nonlinear earthquake modeling

NASA Astrophysics Data System (ADS)

Giraldo, Daniel; Restrepo, Doriam

2017-12-01

This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.

Isentropic Compression with a Rectangular Configuration for Tungstene and Tantalum, Computations and Comparison with Experiments

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

Lefrancois, A.; Reisman, D. B.; Bastea, M.

2006-02-13

Isentropic compression experiments and numerical simulations on metals are performed at Z accelerator facility from Sandia National Laboratory and at Lawrence Livermore National Laboratory in order to study the isentrope, associated Hugoniot and phase changes of these metals. 3D configurations have been calculated here to benchmark the new beta version of the electromagnetism package coupled with the dynamics in Ls-Dyna and compared with the ICE Z shots 1511 and 1555. The electromagnetism module is being developed in the general-purpose explicit and implicit finite element program LS-DYNA{reg_sign} in order to perform coupled mechanical/thermal/electromagnetism simulations. The Maxwell equations are solved using amore » Finite Element Method (FEM) for the solid conductors coupled with a Boundary Element Method (BEM) for the surrounding air (or vacuum). More details can be read in the references.« less

Isentropic Compression up to 200 KBars for LX 04, Numerical Simulations and Comparison with Experiments

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

Lefrancois, A.; Hare, D.; L'Eplattenier, P.

2006-02-13

Isentropic compression experiments and numerical simulations on LX-04 (HMX / Viton 85/15) were performed respectively at Z accelerator facility from Sandia National Laboratory and at Lawrence Livermore National Laboratory in order to study the isentrope and associated Hugoniot of this HE. 2D and 3D configurations have been calculated here to test the new beta version of the electromagnetism package coupled with the dynamics in Ls-Dyna and compared with the ICE Z shot 1067 on LX 04. The electromagnetism module is being developed in the general-purpose explicit and implicit finite element program LS-DYNA{reg_sign} in order to perform coupled mechanical/thermal/electromagnetism simulations. Themore » Maxwell equations are solved using a Finite Element Method (FEM) for the solid conductors coupled with a Boundary Element Method (BEM) for the surrounding air (or vacuum). More details can be read in the references.« less

First- and Second-Order Sensitivity Analysis of a P-Version Finite Element Equation Via Automatic Differentiation

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.

Critical temperatures of hybrid laminates using finite elements

NASA Astrophysics Data System (ADS)

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

1992-06-01

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

A least-squares finite element method for incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1992-01-01

A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.

Three-dimensional finite element analysis of acoustic instability of solid propellant rocket motors

NASA Technical Reports Server (NTRS)

Hackett, R. M.; Juruf, R. S.

1976-01-01

A three dimensional finite element solution of the acoustic vibration problem in a solid propellant rocket motor is presented. The solution yields the natural circular frequencies of vibration and the corresponding acoustic pressure mode shapes, considering the coupled response of the propellant grain to the acoustic oscillations occurring in the motor cavity. The near incompressibility of the solid propellant is taken into account in the formulation. A relatively simple example problem is solved in order to illustrate the applicability of the analysis and the developed computer code.

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method.

PubMed

Deng, Yongbo; Korvink, Jan G

2016-05-01

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method

PubMed Central

Korvink, Jan G.

2016-01-01

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable. PMID:27279766

Influence of local meshing size on stress intensity factor of orthopedic lag screw

NASA Astrophysics Data System (ADS)

Husain, M. N.; Daud, R.; Basaruddin, K. S.; Mat, F.; Bajuri, M. Y.; Arifin, A. K.

2017-09-01

Linear elastic fracture mechanics (LEFM) concept is generally used to study the influence of crack on the performance of structures. In order to study the LEFM concept on damaged structure, the usage of finite element analysis software is implemented to do the simulation of the structure. Mesh generation is one of the most crucial procedures in finite element method. For the structure that crack or damaged, it is very important to determine the accurate local meshing size at the crack tip of the crack itself in order to get the accurate value of stress intensity factor, KI. Pre crack will be introduced to the lag screw based on the von mises' stress result that had been performed in previous research. This paper shows the influence of local mesh arrangement on numerical value of the stress intensity factor, KI obtained by the displacement method. This study aims to simulate the effect of local meshing which is the singularity region on stress intensity factor, KI to the critical point of failure in screw. Five different set of wedges meshing size are introduced during the simulation of finite element analysis. The number of wedges used to simulate this research is 8, 10, 14, 16 and 20. There are three set of numerical equations used to validate the results which are brown and srawley, gross and brown and Tada equation. The result obtained from the finite element software (ANSYS APDL) has a positive agreement with the numerical analysis which is Brown and Srawley compared to other numerical formula. Radius of first row size of 0.014 and singularity element with 14 numbers of wedges is proved to be the best local meshing for this study.

Thermal History and Mantle Dynamics of Venus

NASA Technical Reports Server (NTRS)

Hsui, Albert T.

1997-01-01

One objective of this research proposal is to develop a 3-D thermal history model for Venus. The basis of our study is a finite-element computer model to simulate thermal convection of fluids with highly temperature- and pressure-dependent viscosities in a three-dimensional spherical shell. A three-dimensional model for thermal history studies is necessary for the following reasons. To study planetary thermal evolution, one needs to consider global heat budgets of a planet throughout its evolution history. Hence, three-dimensional models are necessary. This is in contrasts to studies of some local phenomena or local structures where models of lower dimensions may be sufficient. There are different approaches to treat three-dimensional thermal convection problems. Each approach has its own advantages and disadvantages. Therefore, the choice of the various approaches is subjective and dependent on the problem addressed. In our case, we are interested in the effects of viscosities that are highly temperature dependent and that their magnitudes within the computing domain can vary over many orders of magnitude. In order to resolve the rapid change of viscosities, small grid spacings are often necessary. To optimize the amount of computing, variable grids become desirable. Thus, the finite-element numerical approach is chosen for its ability to place grid elements of different sizes over the complete computational domain. For this research proposal, we did not start from scratch and develop the finite element codes from the beginning. Instead, we adopted a finite-element model developed by Baumgardner, a collaborator of this research proposal, for three-dimensional thermal convection with constant viscosity. Over the duration supported by this research proposal, a significant amount of advancements have been accomplished.

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

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

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2017-03-29

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Creating physically-based three-dimensional microstructures: Bridging phase-field and crystal plasticity models.

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

Lim, Hojun; Owen, Steven J.; Abdeljawad, Fadi F.

In order to better incorporate microstructures in continuum scale models, we use a novel finite element (FE) meshing technique to generate three-dimensional polycrystalline aggregates from a phase field grain growth model of grain microstructures. The proposed meshing technique creates hexahedral FE meshes that capture smooth interfaces between adjacent grains. Three dimensional realizations of grain microstructures from the phase field model are used in crystal plasticity-finite element (CP-FE) simulations of polycrystalline a -iron. We show that the interface conformal meshes significantly reduce artificial stress localizations in voxelated meshes that exhibit the so-called "wedding cake" interfaces. This framework provides a direct linkmore » between two mesoscale models - phase field and crystal plasticity - and for the first time allows mechanics simulations of polycrystalline materials using three-dimensional hexahedral finite element meshes with realistic topological features.« less

Finite element computation on nearest neighbor connected machines

NASA Technical Reports Server (NTRS)

Mcaulay, A. D.

1984-01-01

Research aimed at faster, more cost effective parallel machines and algorithms for improving designer productivity with finite element computations is discussed. A set of 8 boards, containing 4 nearest neighbor connected arrays of commercially available floating point chips and substantial memory, are inserted into a commercially available machine. One-tenth Mflop (64 bit operation) processors provide an 89% efficiency when solving the equations arising in a finite element problem for a single variable regular grid of size 40 by 40 by 40. This is approximately 15 to 20 times faster than a much more expensive machine such as a VAX 11/780 used in double precision. The efficiency falls off as faster or more processors are envisaged because communication times become dominant. A novel successive overrelaxation algorithm which uses cyclic reduction in order to permit data transfer and computation to overlap in time is proposed.

Generation of segmental chips in metal cutting modeled with the PFEM

NASA Astrophysics Data System (ADS)

Rodriguez Prieto, J. M.; Carbonell, J. M.; Cante, J. C.; Oliver, J.; Jonsén, P.

2018-06-01

The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is presented. The adaptive insertion and removal of particles are developed and employed in order to sidestep the difficulties associated with mesh distortion, shear localization as well as for resolving the fine-scale features of the solution. The performance of PFEM is studied with a set of different two-dimensional orthogonal cutting tests. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation metal cutting problems with continuous chip and serrated chip formation.

Generation of segmental chips in metal cutting modeled with the PFEM

NASA Astrophysics Data System (ADS)

Rodriguez Prieto, J. M.; Carbonell, J. M.; Cante, J. C.; Oliver, J.; Jonsén, P.

2017-09-01

The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is presented. The adaptive insertion and removal of particles are developed and employed in order to sidestep the difficulties associated with mesh distortion, shear localization as well as for resolving the fine-scale features of the solution. The performance of PFEM is studied with a set of different two-dimensional orthogonal cutting tests. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation metal cutting problems with continuous chip and serrated chip formation.

Finite Element Analysis of Absorbable Sheath to Prevent Stress Shielding of Tibial Interlocking Intramedullary Nail

NASA Astrophysics Data System (ADS)

Dong, Yansheng; Wang, Yongqing; Dong, Limin; Jia, Peng; Lu, Fengcheng

2017-07-01

The nail with absorbable sheath (AS nail) is designed to reduce the stress shielding effect of internal fixation with interlocking intramedullary nail. In order to verify its feasibility, two types of the finite element models of internal fixation of tibia with the AS nail and the common metal nail (CM nail) are established using the Softwares of Mimics, Geomagic, SolidWorks and ANSYS according to the CT scanning data of tibia. The result of the finite element analysis shows that the AS nail has great advantages compared with the CM nail in reducing the stress shielding effect in different periods of fracture healing. The conclusion is that the AS nail can realize the static fixation to the dynamic fixation from the early to the later automatically to shorten the time of fracture healing, which also provides a new technique to the interlocking intramedullary nail.

The Effect of Scale Dependent Discretization on the Progressive Failure of Composite Materials Using Multiscale Analyses

NASA Technical Reports Server (NTRS)

Ricks, Trenton M.; Lacy, Thomas E., Jr.; Pineda, Evan J.; Bednarcyk, Brett A.; Arnold, Steven M.

2013-01-01

A multiscale modeling methodology, which incorporates a statistical distribution of fiber strengths into coupled micromechanics/ finite element analyses, is applied to unidirectional polymer matrix composites (PMCs) to analyze the effect of mesh discretization both at the micro- and macroscales on the predicted ultimate tensile (UTS) strength and failure behavior. The NASA code FEAMAC and the ABAQUS finite element solver were used to analyze the progressive failure of a PMC tensile specimen that initiates at the repeating unit cell (RUC) level. Three different finite element mesh densities were employed and each coupled with an appropriate RUC. Multiple simulations were performed in order to assess the effect of a statistical distribution of fiber strengths on the bulk composite failure and predicted strength. The coupled effects of both the micro- and macroscale discretizations were found to have a noticeable effect on the predicted UTS and computational efficiency of the simulations.

The Finite Element Modelling and Dynamic Characteristics Analysis about One Kind of Armoured Vehicles’ Fuel Tanks

NASA Astrophysics Data System (ADS)

Gao, Yang; Ge, Zhishang; Zhai, Weihao; Tan, Shiwang; Zhang, Feng

2018-01-01

The static and dynamic characteristics of fuel tank are studied for the armoured vehicle in this paper. The CATIA software is applied to build the CAD model of the armoured vehicles’ fuel tank, and the finite element model is established in ANSYS Workbench. The finite element method is carried out to analyze the static and dynamic mechanical properties of the fuel tank, and the first six orders of mode shapes and their frequencies are also computed and given in the paper, then the stress distribution diagram and the high stress areas are obtained. The results of the research provide some references to the fuel tanks’ design improvement, and give some guidance for the installation of the fuel tanks on armoured vehicles, and help to improve the properties and the service life of this kind of armoured vehicles’ fuel tanks.

Finite element analysis on a medical implant.

PubMed

Semenescu, Augustin; Radu-Ioniță, Florentina; Mateș, Ileana Mariana; Bădică, Petre; Batalu, Nicolae Dan; Negoita, Olivia Doina; Purcarea, Victor Lorin

2016-01-01

Several studies have shown a tight connection between several ocular pathologies and an increased risk of hip fractures due to falling, especially among elderly patients. The total replacement of the hip joint is a major surgical intervention that aims to restore the function of the affected hip by various factors, such as arthritis, injures, and others. A corkscrew-like femoral stem was designed in order to preserve the bone stock and to prevent the occurrence of iatrogenic fractures during the hammering of the implant. In this paper, the finite element analysis for the proposed design was applied, considering different loads and three types of materials. A finite element analysis is a powerful tool to simulate, optimize, design, and select suitable materials for new medical implants. The results showed that the best scenario was for Ti6Al4V alloy, although Ti and 316L stainless steel had a reasonable high safety factor.

Developments in the Gung Ho dynamical core

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2017-04-01

Gung Ho is the new dynamical core being developed for the next generation Met Office weather and climate model, suitable for meeting the exascale challenge on emerging computer architectures. It builds upon the earlier collaborative project between the Met Office, NERC and STFC Daresbury of the same name to investigate suitable numerical methods for dynamical cores. A mixed-finite element approach is used, where different finite element spaces are used to represent various fields. This method provides a number of beneficial improvements over the current model, such a compatibility and inherent conservation on quasi-uniform unstructured meshes, whilst maintaining the accuracy and good dispersion properties of the staggered grid currently used. Furthermore, the mixed finite element approach allows a large degree of flexibility in the type of mesh, order of approximation and discretisation, providing a simple way to test alternative options to obtain the best model possible.

Finite element modeling of trolling-mode AFM.

PubMed

Sajjadi, Mohammadreza; Pishkenari, Hossein Nejat; Vossoughi, Gholamreza

2018-06-01

Trolling mode atomic force microscopy (TR-AFM) has overcome many imaging problems in liquid environments by considerably reducing the liquid-resonator interaction forces. The finite element model of the TR-AFM resonator considering the effects of fluid and nanoneedle flexibility is presented in this research, for the first time. The model is verified by ABAQUS software. The effect of installation angle of the microbeam relative to the horizon and the effect of fluid on the system behavior are investigated. Using the finite element model, frequency response curve of the system is obtained and validated around the frequency of the operating mode by the available experimental results, in air and liquid. The changes in the natural frequencies in the presence of liquid are studied. The effects of tip-sample interaction on the excitation of higher order modes of the system are also investigated in air and liquid environments. Copyright © 2018 Elsevier B.V. All rights reserved.

Fast calculation of the sensitivity matrix in magnetic induction tomography by tetrahedral edge finite elements and the reciprocity theorem.

PubMed

Hollaus, K; Magele, C; Merwa, R; Scharfetter, H

2004-02-01

Magnetic induction tomography of biological tissue is used to reconstruct the changes in the complex conductivity distribution by measuring the perturbation of an alternating primary magnetic field. To facilitate the sensitivity analysis and the solution of the inverse problem a fast calculation of the sensitivity matrix, i.e. the Jacobian matrix, which maps the changes of the conductivity distribution onto the changes of the voltage induced in a receiver coil, is needed. The use of finite differences to determine the entries of the sensitivity matrix does not represent a feasible solution because of the high computational costs of the basic eddy current problem. Therefore, the reciprocity theorem was exploited. The basic eddy current problem was simulated by the finite element method using symmetric tetrahedral edge elements of second order. To test the method various simulations were carried out and discussed.

The decline of soil due to the pile of highway project Medan-Kualanamu (STA 35 + 901) with the finite element method

NASA Astrophysics Data System (ADS)

Hastuty, I. P.; Roesyanto; Sihite, A. B.

2018-02-01

Consolidation is the process of discharge of water from the ground through the pore cavity. Consolidation occurs in soft soil or unstable soil that allows an improvement in order to make the soil more stable. The method of using Prefabricated Vertical Drain (PVD) is one way to improve unstable soils. PVD works like a sand column that can drain water vertically. This study aims to determine the decrease, pore water pressure and soil consolidation rate with Prefabricated Vertical Drain (PVD) and without PVD analytically and using finite element method that affect the duration of soil decline to reach 90% consolidation or in other words soil does not decline anymore. Based on the analytical calculation, the decrease obtained is equal to 0.47 m meanwhile the result of calculation using finite element method is 0.45 m. The consolidation rate obtained from analytical calculation is 19 days with PVD and 115 days without PVD. The consolidation rate obtained from finite element method is 63 days with PVD and 110 days without PVD. And the pore water pressure is 0.92 KN/m2.

A new multipartite plate system for anterior cervical spine surgery; finite element analysis.

PubMed

Şimşek, Hakan; Zorlu, Emre; Kaya, Serdar; Baydoğan, Murat; Atabey, Cem; Çolak, Ahmet

2017-12-19

There are numerous available plates, almost all of which are compact one-piece plates. During the placement of relatively long plates in the treatment of multi-level cervical pathologies, instrument related complications might appear. In order to overcome this potential problem, a novel 'articulated plate system' is designed. We aimed to delineate finite element analysis and mechanical evaluations. A new plate system consisting of multi partite structure for anterior cervical stabilization was designed. Segmental plates were designed for application onto the ventral surface of the vertebral body. Plates differed from 9 to13 mm in length. There are rods at one end and hooks at the other end. Terminal points consisted of either hooks or rods at one end but the other ends are blind. Finite element and mechanical tests of the construct were performed applying bending, axial loading, and distraction forces. Finite element and mechanical testing results yielded the cut off values for functional failure and breakage of the system. The articulated system proved to be mechanically safe and it lets extension of the system on either side as needed. Ease of application needs further verification via a cadaveric study.

Updating the Finite Element Model of the Aerostructures Test Wing Using Ground Vibration Test Data

NASA Technical Reports Server (NTRS)

Lung, Shun-Fat; Pak, Chan-Gi

2009-01-01

Improved and/or accelerated decision making is a crucial step during flutter certification processes. Unfortunately, most finite element structural dynamics models have uncertainties associated with model validity. Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. The model tuning process requires not only satisfactory correlations between analytical and experimental results, but also the retention of the mass and stiffness properties of the structures. Minimizing the difference between analytical and experimental results is a type of optimization problem. By utilizing the multidisciplinary design, analysis, and optimization (MDAO) tool in order to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes can be matched to the target data to retain the mass matrix orthogonality. This approach has been applied to minimize the model uncertainties for the structural dynamics model of the aerostructures test wing (ATW), which was designed and tested at the National Aeronautics and Space Administration Dryden Flight Research Center (Edwards, California). This study has shown that natural frequencies and corresponding mode shapes from the updated finite element model have excellent agreement with corresponding measured data.

Updating the Finite Element Model of the Aerostructures Test Wing using Ground Vibration Test Data

NASA Technical Reports Server (NTRS)

Lung, Shun-fat; Pak, Chan-gi

2009-01-01

Improved and/or accelerated decision making is a crucial step during flutter certification processes. Unfortunately, most finite element structural dynamics models have uncertainties associated with model validity. Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. The model tuning process requires not only satisfactory correlations between analytical and experimental results, but also the retention of the mass and stiffness properties of the structures. Minimizing the difference between analytical and experimental results is a type of optimization problem. By utilizing the multidisciplinary design, analysis, and optimization (MDAO) tool in order to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes can be matched to the target data to retain the mass matrix orthogonality. This approach has been applied to minimize the model uncertainties for the structural dynamics model of the Aerostructures Test Wing (ATW), which was designed and tested at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center (DFRC) (Edwards, California). This study has shown that natural frequencies and corresponding mode shapes from the updated finite element model have excellent agreement with corresponding measured data.

Adaptive finite element modelling of three-dimensional magnetotelluric fields in general anisotropic media

NASA Astrophysics Data System (ADS)

Liu, Ying; Xu, Zhenhuan; Li, Yuguo

2018-04-01

We present a goal-oriented adaptive finite element (FE) modelling algorithm for 3-D magnetotelluric fields in generally anisotropic conductivity media. The model consists of a background layered structure, containing anisotropic blocks. Each block and layer might be anisotropic by assigning to them 3 × 3 conductivity tensors. The second-order partial differential equations are solved using the adaptive finite element method (FEM). The computational domain is subdivided into unstructured tetrahedral elements, which allow for complex geometries including bathymetry and dipping interfaces. The grid refinement process is guided by a global posteriori error estimator and is performed iteratively. The system of linear FE equations for electric field E is solved with a direct solver MUMPS. Then the magnetic field H can be found, in which the required derivatives are computed numerically using cubic spline interpolation. The 3-D FE algorithm has been validated by comparisons with both the 3-D finite-difference solution and 2-D FE results. Two model types are used to demonstrate the effects of anisotropy upon 3-D magnetotelluric responses: horizontal and dipping anisotropy. Finally, a 3D sea hill model is modelled to study the effect of oblique interfaces and the dipping anisotropy.

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

PubMed Central

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

2017-01-01

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

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

PubMed

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

2017-10-13

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

Efficient combination of a 3D Quasi-Newton inversion algorithm and a vector dual-primal finite element tearing and interconnecting method

NASA Astrophysics Data System (ADS)

Voznyuk, I.; Litman, A.; Tortel, H.

2015-08-01

A Quasi-Newton method for reconstructing the constitutive parameters of three-dimensional (3D) penetrable scatterers from scattered field measurements is presented. This method is adapted for handling large-scale electromagnetic problems while keeping the memory requirement and the time flexibility as low as possible. The forward scattering problem is solved by applying the finite-element tearing and interconnecting full-dual-primal (FETI-FDP2) method which shares the same spirit as the domain decomposition methods for finite element methods. The idea is to split the computational domain into smaller non-overlapping sub-domains in order to simultaneously solve local sub-problems. Various strategies are proposed in order to efficiently couple the inversion algorithm with the FETI-FDP2 method: a separation into permanent and non-permanent subdomains is performed, iterative solvers are favorized for resolving the interface problem and a marching-on-in-anything initial guess selection further accelerates the process. The computational burden is also reduced by applying the adjoint state vector methodology. Finally, the inversion algorithm is confronted to measurements extracted from the 3D Fresnel database.

Large-scale computation of incompressible viscous flow by least-squares finite element method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, T. L.; Povinelli, Louis A.

1993-01-01

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

Computing Gravitational Fields of Finite-Sized Bodies

NASA Technical Reports Server (NTRS)

Quadrelli, Marco

2005-01-01

A computer program utilizes the classical theory of gravitation, implemented by means of the finite-element method, to calculate the near gravitational fields of bodies of arbitrary size, shape, and mass distribution. The program was developed for application to a spacecraft and to floating proof masses and associated equipment carried by the spacecraft for detecting gravitational waves. The program can calculate steady or time-dependent gravitational forces, moments, and gradients thereof. Bodies external to a proof mass can be moving around the proof mass and/or deformed under thermoelastic loads. An arbitrarily shaped proof mass is represented by a collection of parallelepiped elements. The gravitational force and moment acting on each parallelepiped element of a proof mass, including those attributable to the self-gravitational field of the proof mass, are computed exactly from the closed-form equation for the gravitational potential of a parallelepiped. The gravitational field of an arbitrary distribution of mass external to a proof mass can be calculated either by summing the fields of suitably many point masses or by higher-order Gauss-Legendre integration over all elements surrounding the proof mass that are part of a finite-element mesh. This computer program is compatible with more general finite-element codes, such as NASTRAN, because it is configured to read a generic input data file, containing the detailed description of the finiteelement mesh.

Finite-element numerical modeling of atmospheric turbulent boundary layer

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

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

DOE PAGES

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

2018-01-26

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

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

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

Bunting, Gregory; Prakash, Arun; Walsh, Timothy

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

An Efficient Finite Element Framework to Assess Flexibility Performances of SMA Self-Expandable Carotid Artery Stents

PubMed Central

Ferraro, Mauro; Auricchio, Ferdinando; Boatti, Elisa; Scalet, Giulia; Conti, Michele; Morganti, Simone; Reali, Alessandro

2015-01-01

Computer-based simulations are nowadays widely exploited for the prediction of the mechanical behavior of different biomedical devices. In this aspect, structural finite element analyses (FEA) are currently the preferred computational tool to evaluate the stent response under bending. This work aims at developing a computational framework based on linear and higher order FEA to evaluate the flexibility of self-expandable carotid artery stents. In particular, numerical simulations involving large deformations and inelastic shape memory alloy constitutive modeling are performed, and the results suggest that the employment of higher order FEA allows accurately representing the computational domain and getting a better approximation of the solution with a widely-reduced number of degrees of freedom with respect to linear FEA. Moreover, when buckling phenomena occur, higher order FEA presents a superior capability of reproducing the nonlinear local effects related to buckling phenomena. PMID:26184329

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Ultimate Load Behaviour of Reinforced Concrete Beam with Corroded Reinforcement

NASA Astrophysics Data System (ADS)

Kanchana Devi, A.; Ramajaneyulu, K.; Sundarkumar, S.; Ramesh, G.; Bharat Kumar, B. H.; Krishna Moorthy, T. S.

2017-12-01

Corrosion of reinforcement reduces the load carrying capacity, energy dissipation and ductility of Reinforced Concrete (RC) members. In the present study, reinforcements of RC beam are subjected to 10, 25, and 30% corrosion and the respective RC beams are tested to evaluate their ultimate load behaviour. A huge drop in energy dissipation capacity of the RC beam is observed beyond the corrosion level of 10%. Further, nonlinear finite element analysis is employed to assess the load-displacement behaviour and ultimate load of RC beam. The corrosion induced damage to the reinforcement is represented in the finite element model by modifying its mechanical properties based on the results reported in the literature. The resultant load versus displacement curves of reinforced concrete beams are obtained. Good correlation is observed between the finite element analysis results and that obtained from experimental investigation on the control beam. The experimental results are also compared with the finite element analysis results for RC beams with corroded reinforcement. In order to understand the effect of corrosion on the mechanical properties of reinforcement, the corroded reinforcements are modelled in nonlinear finite element analysis by (i) reducing the area of reinforcement alone (ii) by reducing both area and mechanical properties and (iii) reducing the mechanical properties without reducing the area of steel as reported in literature. The results obtained for the beam with corroded reinforcement confirms reduction in yield stress and ultimate stress of the reinforcement steel.

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

PubMed

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

2016-01-01

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

A finite element beam propagation method for simulation of liquid crystal devices.

PubMed

Vanbrabant, Pieter J M; Beeckman, Jeroen; Neyts, Kristiaan; James, Richard; Fernandez, F Anibal

2009-06-22

An efficient full-vectorial finite element beam propagation method is presented that uses higher order vector elements to calculate the wide angle propagation of an optical field through inhomogeneous, anisotropic optical materials such as liquid crystals. The full dielectric permittivity tensor is considered in solving Maxwell's equations. The wide applicability of the method is illustrated with different examples: the propagation of a laser beam in a uniaxial medium, the tunability of a directional coupler based on liquid crystals and the near-field diffraction of a plane wave in a structure containing micrometer scale variations in the transverse refractive index, similar to the pixels of a spatial light modulator.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-07-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space-times. In this paper, we assume the background space-time to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local time-stepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed space-times. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-03-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

Subleading soft graviton theorem for loop amplitudes

NASA Astrophysics Data System (ADS)

Sen, Ashoke

2017-11-01

Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.

An extension of the finite cell method using boolean operations

NASA Astrophysics Data System (ADS)

Abedian, Alireza; Düster, Alexander

2017-05-01

In the finite cell method, the fictitious domain approach is combined with high-order finite elements. The geometry of the problem is taken into account by integrating the finite cell formulation over the physical domain to obtain the corresponding stiffness matrix and load vector. In this contribution, an extension of the FCM is presented wherein both the physical and fictitious domain of an element are simultaneously evaluated during the integration. In the proposed extension of the finite cell method, the contribution of the stiffness matrix over the fictitious domain is subtracted from the cell, resulting in the desired stiffness matrix which reflects the contribution of the physical domain only. This method results in an exponential rate of convergence for porous domain problems with a smooth solution and accurate integration. In addition, it reduces the computational cost, especially when applying adaptive integration schemes based on the quadtree/octree. Based on 2D and 3D problems of linear elastostatics, numerical examples serve to demonstrate the efficiency and accuracy of the proposed method.

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.

Optimal control penalty finite elements - Applications to integrodifferential equations

NASA Astrophysics Data System (ADS)

Chung, T. J.

The application of the optimal-control/penalty finite-element method to the solution of integrodifferential equations in radiative-heat-transfer problems (Chung et al.; Chung and Kim, 1982) is discussed and illustrated. The nonself-adjointness of the convective terms in the governing equations is treated by utilizing optimal-control cost functions and employing penalty functions to constrain auxiliary equations which permit the reduction of second-order derivatives to first order. The OCPFE method is applied to combined-mode heat transfer by conduction, convection, and radiation, both without and with scattering and viscous dissipation; the results are presented graphically and compared to those obtained by other methods. The OCPFE method is shown to give good results in cases where standard Galerkin FE fail, and to facilitate the investigation of scattering and dissipation effects.

Efficient finite element modeling of radiation forces on elastic particles of arbitrary size and geometry.

PubMed

Glynne-Jones, Peter; Mishra, Puja P; Boltryk, Rosemary J; Hill, Martyn

2013-04-01

A finite element based method is presented for calculating the acoustic radiation force on arbitrarily shaped elastic and fluid particles. Importantly for future applications, this development will permit the modeling of acoustic forces on complex structures such as biological cells, and the interactions between them and other bodies. The model is based on a non-viscous approximation, allowing the results from an efficient, numerical, linear scattering model to provide the basis for the second-order forces. Simulation times are of the order of a few seconds for an axi-symmetric structure. The model is verified against a range of existing analytical solutions (typical accuracy better than 0.1%), including those for cylinders, elastic spheres that are of significant size compared to the acoustic wavelength, and spheroidal particles.

Overset meshing coupled with hybridizable discontinuous Galerkin finite elements

DOE PAGES

Kauffman, Justin A.; Sheldon, Jason P.; Miller, Scott T.

2017-03-01

We introduce the use of hybridizable discontinuous Galerkin (HDG) finite element methods on overlapping (overset) meshes. Overset mesh methods are advantageous for solving problems on complex geometrical domains. We also combine geometric flexibility of overset methods with the advantages of HDG methods: arbitrarily high-order accuracy, reduced size of the global discrete problem, and the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. This approach to developing the ‘overset HDG’ method is to couple the global solution from one mesh to the local solution on the overset mesh. We present numerical examples for steady convection–diffusionmore » and static elasticity problems. The examples demonstrate optimal order convergence in all primal fields for an arbitrary amount of overlap of the underlying meshes.« less

A globally well-posed finite element algorithm for aerodynamics applications

NASA Technical Reports Server (NTRS)

Iannelli, G. S.; Baker, A. J.

1991-01-01

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations

NASA Astrophysics Data System (ADS)

Vaziri Astaneh, Ali; Fuentes, Federico; Mora, Jaime; Demkowicz, Leszek

2018-04-01

This work represents the first endeavor in using ultraweak formulations to implement high-order polygonal finite element methods via the discontinuous Petrov-Galerkin (DPG) methodology. Ultraweak variational formulations are nonstandard in that all the weight of the derivatives lies in the test space, while most of the trial space can be chosen as copies of $L^2$-discretizations that have no need to be continuous across adjacent elements. Additionally, the test spaces are broken along the mesh interfaces. This allows one to construct conforming polygonal finite element methods, termed here as PolyDPG methods, by defining most spaces by restriction of a bounding triangle or box to the polygonal element. The only variables that require nontrivial compatibility across elements are the so-called interface or skeleton variables, which can be defined directly on the element boundaries. Unlike other high-order polygonal methods, PolyDPG methods do not require ad hoc stabilization terms thanks to the crafted stability of the DPG methodology. A proof of convergence of the form $h^p$ is provided and corroborated through several illustrative numerical examples. These include polygonal meshes with $n$-sided convex elements and with highly distorted concave elements, as well as the modeling of discontinuous material properties along an arbitrary interface that cuts a uniform grid. Since PolyDPG methods have a natural a posteriori error estimator a polygonal adaptive strategy is developed and compared to standard adaptivity schemes based on constrained hanging nodes. This work is also accompanied by an open-source $\\texttt{PolyDPG}$ software supporting polygonal and conventional elements.

Two variants of minimum discarded fill ordering

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

D'Azevedo, E.F.; Forsyth, P.A.; Tang, Wei-Pai

1991-01-01

It is well known that the ordering of the unknowns can have a significant effect on the convergence of Preconditioned Conjugate Gradient (PCG) methods. There has been considerable experimental work on the effects of ordering for regular finite difference problems. In many cases, good results have been obtained with preconditioners based on diagonal, spiral or natural row orderings. However, for finite element problems having unstructured grids or grids generated by a local refinement approach, it is difficult to define many of the orderings for more regular problems. A recently proposed Minimum Discarded Fill (MDF) ordering technique is effective in findingmore » high quality Incomplete LU (ILU) preconditioners, especially for problems arising from unstructured finite element grids. Testing indicates this algorithm can identify a rather complicated physical structure in an anisotropic problem and orders the unknowns in the preferred'' direction. The MDF technique may be viewed as the numerical analogue of the minimum deficiency algorithm in sparse matrix technology. At any stage of the partial elimination, the MDF technique chooses the next pivot node so as to minimize the amount of discarded fill. In this work, two efficient variants of the MDF technique are explored to produce cost-effective high-order ILU preconditioners. The Threshold MDF orderings combine MDF ideas with drop tolerance techniques to identify the sparsity pattern in the ILU preconditioners. These techniques identify an ordering that encourages fast decay of the entries in the ILU factorization. The Minimum Update Matrix (MUM) ordering technique is a simplification of the MDF ordering and is closely related to the minimum degree algorithm. The MUM ordering is especially for large problems arising from Navier-Stokes problems. Some interesting pictures of the orderings are presented using a visualization tool. 22 refs., 4 figs., 7 tabs.« less

Development of Finite Elements for Two-Dimensional Structural Analysis Using the Integrated Force Method

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Patnaik, Surya N.; Hopkins, Dale A.

1996-01-01

The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.

Prediction of Path Deviation in Robot Based Incremental Sheet Metal Forming by Means of a New Solid-Shell Finite Element Technology and a Finite Elastoplastic Model with Combined Hardening

NASA Astrophysics Data System (ADS)

Kiliclar, Yalin; Laurischkat, Roman; Vladimirov, Ivaylo N.; Reese, Stefanie

2011-08-01

The presented project deals with a robot based incremental sheet metal forming process, which is called roboforming and has been developed at the Chair of Production Systems. It is characterized by flexible shaping using a freely programmable path-synchronous movement of two industrial robots. The final shape is produced by the incremental infeed of the forming tool in depth direction and its movement along the part contour in lateral direction. However, the resulting geometries formed in roboforming deviate several millimeters from the reference geometry. This results from the compliance of the involved machine structures and the springback effects of the workpiece. The project aims to predict these deviations caused by resiliences and to carry out a compensative path planning based on this prediction. Therefore a planning tool is implemented which compensates the robots's compliance and the springback effects of the sheet metal. The forming process is simulated by means of a finite element analysis using a material model developed at the Institute of Applied Mechanics (IFAM). It is based on the multiplicative split of the deformation gradient in the context of hyperelasticity and combines nonlinear kinematic and isotropic hardening. Low-order finite elements used to simulate thin sheet structures, such as used for the experiments, have the major problem of locking, a nonphysical stiffening effect. For an efficient finite element analysis a special solid-shell finite element formulation based on reduced integration with hourglass stabilization has been developed. To circumvent different locking effects, the enhanced assumed strain (EAS) and the assumed natural strain (ANS) concepts are included in this formulation. Having such powerful tools available we obtain more accurate geometries.

Finite elements for the calculation of turbulent flows in three-dimensional complex geometries

NASA Astrophysics Data System (ADS)

Ruprecht, A.

A finite element program for the calculation of incompressible turbulent flows is presented. In order to reduce the required storage an iterative algorithm is used which solves the necessary equations sequentially. The state of turbulence is defined by the k-epsilon model. In addition to the standard k-epsilon model, the modification of Bardina et al., taking into account the rotation of the mean flow, is investigated. With this program, the flow in the draft tube of a Kaplan turbine is examined. Calculations are carried out for swirling and nonswirling entrance flow. The results are compared with measurements.

Domain decomposition for a mixed finite element method in three dimensions

USGS Publications Warehouse

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

2003-01-01

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

In-memory integration of existing software components for parallel adaptive unstructured mesh workflows

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

Smith, Cameron W.; Granzow, Brian; Diamond, Gerrett

Unstructured mesh methods, like finite elements and finite volumes, support the effective analysis of complex physical behaviors modeled by partial differential equations over general threedimensional domains. The most reliable and efficient methods apply adaptive procedures with a-posteriori error estimators that indicate where and how the mesh is to be modified. Although adaptive meshes can have two to three orders of magnitude fewer elements than a more uniform mesh for the same level of accuracy, there are many complex simulations where the meshes required are so large that they can only be solved on massively parallel systems.

In-memory integration of existing software components for parallel adaptive unstructured mesh workflows

DOE PAGES

Smith, Cameron W.; Granzow, Brian; Diamond, Gerrett; ...

2017-01-01

Unstructured mesh methods, like finite elements and finite volumes, support the effective analysis of complex physical behaviors modeled by partial differential equations over general threedimensional domains. The most reliable and efficient methods apply adaptive procedures with a-posteriori error estimators that indicate where and how the mesh is to be modified. Although adaptive meshes can have two to three orders of magnitude fewer elements than a more uniform mesh for the same level of accuracy, there are many complex simulations where the meshes required are so large that they can only be solved on massively parallel systems.

The finite element simulation analysis research of 38CrSi cylindrical power spinning

NASA Astrophysics Data System (ADS)

Liang, Wei; Lv, Qiongying; Zhao, Yujuan; Lv, Yunxia

2018-01-01

In order to grope for the influence of the main cylindrical spinning process parameters on the spinning process, this paper combines with real tube power spinning process and uses ABAQUS finite element analysis software to simulate the tube power spinning process of 38CrSi steel materials, through the analysis of the stress, strain of the part forming process, analyzes the influence of the thickness reduction and the feed rate to the forming process, and analyzes the variation of the spinning force, finally determines the reasonable main spinning process parameters combination.

A Variational Formulation for the Finite Element Analysis of Sound Wave Propagation in a Spherical Shell

NASA Technical Reports Server (NTRS)

Lebiedzik, Catherine

1995-01-01

Development of design tools to furnish optimal acoustic environments for lightweight aircraft demands the ability to simulate the acoustic system on a workstation. In order to form an effective mathematical model of the phenomena at hand, we have begun by studying the propagation of acoustic waves inside closed spherical shells. Using a fully-coupled fluid-structure interaction model based upon variational principles, we have written a finite element analysis program and are in the process of examining several test cases. Future investigations are planned to increase model accuracy by incorporating non-linear and viscous effects.

A combined experimental and finite element analysis method for the estimation of eddy-current loss in NdFeB magnets.

PubMed

Fratila, Radu; Benabou, Abdelkader; Tounzi, Abdelmounaïm; Mipo, Jean-Claude

2014-05-14

NdFeB permanent magnets (PMs) are widely used in high performance electrical machines, but their relatively high conductivity subjects them to eddy current losses that can lead to magnetization loss. The Finite Element (FE) method is generally used to quantify the eddy current loss of PMs, but it remains quite difficult to validate the accuracy of the results with complex devices. In this paper, an experimental test device is used in order to extract the eddy current losses that are then compared with those of a 3D FE model.

Localisation of flow separation and transition over a pitching NACA0012 airfoil at transitional Reynolds number

NASA Astrophysics Data System (ADS)

Rudmin, Daniel

Ionic polymer-metal composites (IPMCs) are some of the most well-known electro-active polymers. This is due to their large deformation provided a relatively low voltage source. IPMCs have been acknowledged as a potential candidate for biomedical applications such as cardiac catheters and surgical probes; however, there is still no existing mass manufacturing of IPMCs. This study intends to provide a theoretical framework which could be used to design practical purpose IPMCs depending on the end users interest. This study begins by investigating methodologies used to develop quantify the physical actuation of an IPMC in 3-dimensional space. This approach is taken in two separate means; however, both approaches utilize the finite element method. The first approach utilizes the finite element method in order to describe the dynamic response of a segmented IPMC actuator. The first approach manually constructs each element with a local coordinate system. Each system undergoes a rigid body motion along the element and deformation of the element is expressed in the local coordinate frame. The physical phenomenon in this system is simplified by utilizing a lumped RC model in order to simplify the electro-mechanical phenomena in the IPMC dynamics. The second study investigates 3D modeling of a rod shaped IPMC actuator by explicitly coupling electrostatics, transport phenomenon, and solid mechanics. This portion of the research will briefly discuss the mathematical background that more accurately quantifies the physical phenomena. Solving for the 3-dimensional actuation is explicitly carried out again by utilizing the finite element method. The numerical result is conducted in a software package known as COMSOL MULTIPHYSICS. This simulation allows for explicit geometric rendering as well as more explicit quantification of the physical quantities such as concentration, electric field, and deflection. The final study will conduct design optimization on the COMSOL simulation in order to provide conceptual motivation for future designs. Utilizing a multi-physics analysis approach on a three dimensional cylinder and tube type IPMC provides physically accurate results for time dependent end effector displacement given a voltage source. Simulations are conducted with the finite element method and are also validated with empirical evidences. Having an in-depth understanding of the physical coupling provides optimal design parameters that cannot be altered from a standard electro-mechanical coupling. These parameters are altered in order to determine optimal designs for end-effector displacement, maximum force, and improved mobility with limited voltage magnitude. Design alterations are conducted on the electrode patterns in order to provide greater mobility, electrode size for efficient bending, and Nafion diameter for improved force. The results of this study will provide optimal design parameters of the IPMC for different applications.

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.

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.

An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations

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

Key, S.W.; Heinstein, M.W.; Stone, C.M.

1997-12-31

Considerable effort has been expended in perfecting the algorithmic properties of 8-node hexahedral finite elements. Today the element is well understood and performs exceptionally well when used in modeling three-dimensional explicit transient dynamic events. However, the automatic generation of all-hexahedral meshes remains an elusive achievement. The alternative of automatic generation for all-tetrahedral finite element is a notoriously poor performer, and the 10-node quadratic tetrahedral finite element while a better performer numerically is computationally expensive. To use the all-tetrahedral mesh generation extant today, the authors have explored the creation of a quality 8-node tetrahedral finite element (a four-node tetrahedral finite elementmore » enriched with four midface nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping and the element`s performance in applications are presented. In particular, they examine the 80node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element only samples constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the 8-node, mean-quadrature hexahedral finite element. Given automatic all-tetrahedral meshing, the 8-node, constant-strain tetrahedral finite element is a suitable replacement for the 8-node hexahedral finite element and handbuilt meshes.« less

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

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Otto, John C.

1993-01-01

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

On cell entropy inequality for discontinuous Galerkin methods

NASA Technical Reports Server (NTRS)

Jiang, Guangshan; Shu, Chi-Wang

1993-01-01

We prove a cell entropy inequality for a class of high order discontinuous Galerkin finite element methods approximating conservation laws, which implies convergence for the one dimensional scalar convex case.

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 refined shear deformation theory for the analysis of laminated plates

NASA Technical Reports Server (NTRS)

Reddy, J. N.

1986-01-01

A refined, third-order plate theory that accounts for the transverse shear strains is presented, the Navier solutions are derived for certain simply supported cross-ply and antisymmetric angle-ply laminates, and finite-element models are developed for general laminates. The new theory does not require the shear correction factors of the first-order theory (i.e., the Reissner-Mindlin plate theory) because the transverse shear stresses are represented parabolically in the present theory. A mixed finite-element model that uses independent approximations of the generalized displacements and generalized moments, and a displacement model that uses only the generalized displacements as degrees of freedom are developed. The displacement model requires C sup 1-continuity of the transverse deflection across the inter-element boundaries, whereas the mixed model requires a C sup 0-element. Also, the mixed model does not require continuous approximations (between elements) of the bending moments. Numerical results are presented to show the accuracy of the present theory in predicting the transverse stresses. Numerical results are also presented for the nonlinear bending of plates, and the results compare well with the experimental results available in the literature.

Patient-specific finite element modeling of bones.

PubMed

Poelert, Sander; Valstar, Edward; Weinans, Harrie; Zadpoor, Amir A

2013-04-01

Finite element modeling is an engineering tool for structural analysis that has been used for many years to assess the relationship between load transfer and bone morphology and to optimize the design and fixation of orthopedic implants. Due to recent developments in finite element model generation, for example, improved computed tomography imaging quality, improved segmentation algorithms, and faster computers, the accuracy of finite element modeling has increased vastly and finite element models simulating the anatomy and properties of an individual patient can be constructed. Such so-called patient-specific finite element models are potentially valuable tools for orthopedic surgeons in fracture risk assessment or pre- and intraoperative planning of implant placement. The aim of this article is to provide a critical overview of current themes in patient-specific finite element modeling of bones. In addition, the state-of-the-art in patient-specific modeling of bones is compared with the requirements for a clinically applicable patient-specific finite element method, and judgment is passed on the feasibility of application of patient-specific finite element modeling as a part of clinical orthopedic routine. It is concluded that further development in certain aspects of patient-specific finite element modeling are needed before finite element modeling can be used as a routine clinical tool.

KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Abrashkevich, A. G.; Amaya-Tapia, A.; Kaschiev, M. S.; Larsen, S. Y.; Vinitsky, S. I.

2007-10-01

A FORTRAN 77 program is presented which calculates energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on the finite interval with homogeneous boundary conditions of the third type. The resulting system of radial equations which contains the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite-element method. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials. Program summaryProgram title: KANTBP Catalogue identifier: ADZH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4224 No. of bytes in distributed program, including test data, etc.: 31 232 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM: depends on (a) the number of differential equations; (b) the number and order of finite-elements; (c) the number of hyperradial points; and (d) the number of eigensolutions required. Test run requires 30 MB Classification: 2.1, 2.4 External routines: GAULEG and GAUSSJ [W.H. Press, B.F. Flanery, S.A. Teukolsky, W.T. Vetterley, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986] Nature of problem: In the hyperspherical adiabatic approach [J. Macek, J. Phys. B 1 (1968) 831-843; U. Fano, Rep. Progr. Phys. 46 (1983) 97-165; C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142], a multi-dimensional Schrödinger equation for a two-electron system [A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Comm. 90 (1995) 311-339] or a hydrogen atom in magnetic field [M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352] is reduced by separating the radial coordinate ρ from the angular variables to a system of second-order ordinary differential equations which contain potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite-element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions for such systems of coupled differential equations. Solution method: The boundary problems for coupled differential equations are solved by the finite-element method using high-order accuracy approximations [A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Comm. 85 (1995) 40-64]. The generalized algebraic eigenvalue problem AF=EBF with respect to pair unknowns ( E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. The generalized algebraic eigenvalue problem (A-EB)F=λDF with respect to pair unknowns (λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDL factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials described in [Yu. A. Kuperin, P.B. Kurasov, Yu.B. Melnikov, S.P. Merkuriev, Ann. Phys. 205 (1991) 330-361; O. Chuluunbaatar, A.A. Gusev, S.Y. Larsen, S.I. Vinitsky, J. Phys. A 35 (2002) L513-L525; N.P. Mehta, J.R. Shepard, Phys. Rev. A 72 (2005) 032728-1-11; O. Chuluunbaatar, A.A. Gusev, M.S. Kaschiev, V.A. Kaschieva, A. Amaya-Tapia, S.Y. Larsen, S.I. Vinitsky, J. Phys. B 39 (2006) 243-269]. For this benchmark model the needed analytical expressions for the potential matrix elements and first-derivative coupling terms, their asymptotics and asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system. Restrictions: The computer memory requirements depend on: (a) the number of differential equations; (b) the number and order of finite-elements; (c) the total number of hyperradial points; and (d) the number of eigensolutions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Long Write-Up and listing for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMSC (when solving the scattering problem) that evaluate the asymptotics of the radial wave functions at the right boundary point in case of a boundary condition of the third type, respectively. Running time: The running time depends critically upon: (a) the number of differential equations; (b) the number and order of finite-elements; (c) the total number of hyperradial points on interval [0,ρ]; and (d) the number of eigensolutions required. The test run which accompanies this paper took 28.48 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz.

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time: application to non-rigid neuroimage registration.

PubMed

Wittek, Adam; Joldes, Grand; Couton, Mathieu; Warfield, Simon K; Miller, Karol

2010-12-01

Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer. Copyright © 2010 Elsevier Ltd. All rights reserved.

A fictitious domain finite element method for simulations of fluid-structure interactions: The Navier-Stokes equations coupled with a moving solid

NASA Astrophysics Data System (ADS)

Court, Sébastien; Fournié, Michel

2015-05-01

The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an optimal approximation of the normal stress tensor at the interface. The dynamics of the solid is governed by the Newton's laws and the interface between the fluid and the structure is materialized by a level-set which cuts the elements of the mesh. An algorithm is proposed in order to treat the time evolution of the geometry and numerical results are presented on a classical benchmark of the motion of a disk falling in a channel.

A three dimensional immersed smoothed finite element method (3D IS-FEM) for fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong

2013-02-01

A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.

Optimal vibration control of a rotating plate with self-sensing active constrained layer damping

NASA Astrophysics Data System (ADS)

Xie, Zhengchao; Wong, Pak Kin; Lo, Kin Heng

2012-04-01

This paper proposes a finite element model for optimally controlled constrained layer damped (CLD) rotating plate with self-sensing technique and frequency-dependent material property in both the time and frequency domain. Constrained layer damping with viscoelastic material can effectively reduce the vibration in rotating structures. However, most existing research models use complex modulus approach to model viscoelastic material, and an additional iterative approach which is only available in frequency domain has to be used to include the material's frequency dependency. It is meaningful to model the viscoelastic damping layer in rotating part by using the anelastic displacement fields (ADF) in order to include the frequency dependency in both the time and frequency domain. Also, unlike previous ones, this finite element model treats all three layers as having the both shear and extension strains, so all types of damping are taken into account. Thus, in this work, a single layer finite element is adopted to model a three-layer active constrained layer damped rotating plate in which the constraining layer is made of piezoelectric material to work as both the self-sensing sensor and actuator under an linear quadratic regulation (LQR) controller. After being compared with verified data, this newly proposed finite element model is validated and could be used for future research.

Comparisons of Particle Tracking Techniques and Galerkin Finite Element Methods in Flow Simulations on Watershed Scales

NASA Astrophysics Data System (ADS)

Shih, D.; Yeh, G.

2009-12-01

This paper applies two numerical approximations, the particle tracking technique and Galerkin finite element method, to solve the diffusive wave equation in both one-dimensional and two-dimensional flow simulations. The finite element method is one of most commonly approaches in numerical problems. It can obtain accurate solutions, but calculation times may be rather extensive. The particle tracking technique, using either single-velocity or average-velocity tracks to efficiently perform advective transport, could use larger time-step sizes than the finite element method to significantly save computational time. Comparisons of the alternative approximations are examined in this poster. We adapt the model WASH123D to examine the work. WASH123D is an integrated multimedia, multi-processes, physics-based computational model suitable for various spatial-temporal scales, was first developed by Yeh et al., at 1998. The model has evolved in design capability and flexibility, and has been used for model calibrations and validations over the course of many years. In order to deliver a locally hydrological model in Taiwan, the Taiwan Typhoon and Flood Research Institute (TTFRI) is working with Prof. Yeh to develop next version of WASH123D. So, the work of our preliminary cooperationx is also sketched in this poster.

Partition of unity finite element method for quantum mechanical materials calculations

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

Pask, J. E.; Sukumar, N.

The current state of the art for large-scale quantum-mechanical simulations is the planewave (PW) pseudopotential method, as implemented in codes such as VASP, ABINIT, and many others. However, since the PW method uses a global Fourier basis, with strictly uniform resolution at all points in space, it suffers from substantial inefficiencies in calculations involving atoms with localized states, such as first-row and transition-metal atoms, and requires significant nonlocal communications, which limit parallel efficiency. Real-space methods such as finite-differences (FD) and finite-elements (FE) have partially addressed both resolution and parallel-communications issues but have been plagued by one key disadvantage relative tomore » PW: excessive number of degrees of freedom (basis functions) needed to achieve the required accuracies. In this paper, we present a real-space partition of unity finite element (PUFE) method to solve the Kohn–Sham equations of density functional theory. In the PUFE method, we build the known atomic physics into the solution process using partition-of-unity enrichment techniques in finite element analysis. The method developed herein is completely general, applicable to metals and insulators alike, and particularly efficient for deep, localized potentials, as occur in calculations at extreme conditions of pressure and temperature. Full self-consistent Kohn–Sham calculations are presented for LiH, involving light atoms, and CeAl, involving heavy atoms with large numbers of atomic-orbital enrichments. We find that the new PUFE approach attains the required accuracies with substantially fewer degrees of freedom, typically by an order of magnitude or more, than the PW method. As a result, we compute the equation of state of LiH and show that the computed lattice constant and bulk modulus are in excellent agreement with reference PW results, while requiring an order of magnitude fewer degrees of freedom to obtain.« less

Partition of unity finite element method for quantum mechanical materials calculations

DOE PAGES

Pask, J. E.; Sukumar, N.

2016-11-09

The current state of the art for large-scale quantum-mechanical simulations is the planewave (PW) pseudopotential method, as implemented in codes such as VASP, ABINIT, and many others. However, since the PW method uses a global Fourier basis, with strictly uniform resolution at all points in space, it suffers from substantial inefficiencies in calculations involving atoms with localized states, such as first-row and transition-metal atoms, and requires significant nonlocal communications, which limit parallel efficiency. Real-space methods such as finite-differences (FD) and finite-elements (FE) have partially addressed both resolution and parallel-communications issues but have been plagued by one key disadvantage relative tomore » PW: excessive number of degrees of freedom (basis functions) needed to achieve the required accuracies. In this paper, we present a real-space partition of unity finite element (PUFE) method to solve the Kohn–Sham equations of density functional theory. In the PUFE method, we build the known atomic physics into the solution process using partition-of-unity enrichment techniques in finite element analysis. The method developed herein is completely general, applicable to metals and insulators alike, and particularly efficient for deep, localized potentials, as occur in calculations at extreme conditions of pressure and temperature. Full self-consistent Kohn–Sham calculations are presented for LiH, involving light atoms, and CeAl, involving heavy atoms with large numbers of atomic-orbital enrichments. We find that the new PUFE approach attains the required accuracies with substantially fewer degrees of freedom, typically by an order of magnitude or more, than the PW method. As a result, we compute the equation of state of LiH and show that the computed lattice constant and bulk modulus are in excellent agreement with reference PW results, while requiring an order of magnitude fewer degrees of freedom to obtain.« less

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

NASA Technical Reports Server (NTRS)

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

1996-01-01

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

Numerical investigation of the mechanical properties of the additive manufactured bone scaffolds fabricated by FDM: The effect of layer penetration and post-heating.

PubMed

Naghieh, S; Karamooz Ravari, M R; Badrossamay, M; Foroozmehr, E; Kadkhodaei, M

2016-06-01

In recent years, thanks to additive manufacturing technology, researchers have gone towards the optimization of bone scaffolds for the bone reconstruction. Bone scaffolds should have appropriate biological as well as mechanical properties in order to play a decisive role in bone healing. Since the fabrication of scaffolds is time consuming and expensive, numerical methods are often utilized to simulate their mechanical properties in order to find a nearly optimum one. Finite element analysis is one of the most common numerical methods that is used in this regard. In this paper, a parametric finite element model is developed to assess the effects of layers penetration׳s effect on inter-layer adhesion, which is reflected on the mechanical properties of bone scaffolds. To be able to validate this model, some compression test specimens as well as bone scaffolds are fabricated with biocompatible and biodegradable poly lactic acid using fused deposition modeling. All these specimens are tested in compression and their elastic modulus is obtained. Using the material parameters of the compression test specimens, the finite element analysis of the bone scaffold is performed. The obtained elastic modulus is compared with experiment indicating a good agreement. Accordingly, the proposed finite element model is able to predict the mechanical behavior of fabricated bone scaffolds accurately. In addition, the effect of post-heating of bone scaffolds on their elastic modulus is investigated. The results demonstrate that the numerically predicted elastic modulus of scaffold is closer to experimental outcomes in comparison with as-built samples. Copyright © 2016 Elsevier Ltd. All rights reserved.

Finite element modelling for mode-I fracture behaviour of CFRP

NASA Astrophysics Data System (ADS)

Chetan, H. C.; Kattimani, Subhaschandra; Murigendrappa, S. M.

2018-04-01

Debonding is a major failure mechanism in Carbon Fiber Reinforced Polymer (CFRP) due to presence of many adhesion joins, in between many layers. In the current study a finite element simulation is carried out using Virtual Crack Closure Technique (VCCT) and Cohesive Zone Modelling (CZM) using Abaqus as analysis tool. A comparative study is performed in to order analyze convergence of results from CZM and VCCT. It was noted that CZM results matched well with published literature. The results from VCCT were also in good comparison with experimental data of published literature, but were seen to be overestimated. Parametric study is performed to evaluate the variation of input parameters like initial stiffness, element size, peak stress and energy release rate `G'. From the numerical evaluation, it was noted that CZM simulation relies largely on element size and peak stress.

A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

2015-12-01

Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties. Several representative numerical examples are discussed to illustrate the importance of the proposed numerical formulations to accurately describe various aspects of mixing process in chaotic flows and to simulate transport in highly heterogeneous anisotropic media.

Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration

NASA Astrophysics Data System (ADS)

Li, G. Q.; Zhu, Z. H.

2015-12-01

Dynamic modeling of tethered spacecraft with the consideration of elasticity of tether is prone to the numerical instability and error accumulation over long-term numerical integration. This paper addresses the challenges by proposing a globally stable numerical approach with the nodal position finite element method (NPFEM) and the implicit, symplectic, 2-stage and 4th order Gaussian-Legendre Runge-Kutta time integration. The NPFEM eliminates the numerical error accumulation by using the position instead of displacement of tether as the state variable, while the symplectic integration enforces the energy and momentum conservation of the discretized finite element model to ensure the global stability of numerical solution. The effectiveness and robustness of the proposed approach is assessed by an elastic pendulum problem, whose dynamic response resembles that of tethered spacecraft, in comparison with the commonly used time integrators such as the classical 4th order Runge-Kutta schemes and other families of non-symplectic Runge-Kutta schemes. Numerical results show that the proposed approach is accurate and the energy of the corresponding numerical model is conservative over the long-term numerical integration. Finally, the proposed approach is applied to the dynamic modeling of deorbiting process of tethered spacecraft over a long period.

Summary Report of Working Group 2: Computation

NASA Astrophysics Data System (ADS)

Stoltz, P. H.; Tsung, R. S.

2009-01-01

The working group on computation addressed three physics areas: (i) plasma-based accelerators (laser-driven and beam-driven), (ii) high gradient structure-based accelerators, and (iii) electron beam sources and transport [1]. Highlights of the talks in these areas included new models of breakdown on the microscopic scale, new three-dimensional multipacting calculations with both finite difference and finite element codes, and detailed comparisons of new electron gun models with standard models such as PARMELA. The group also addressed two areas of advances in computation: (i) new algorithms, including simulation in a Lorentz-boosted frame that can reduce computation time orders of magnitude, and (ii) new hardware architectures, like graphics processing units and Cell processors that promise dramatic increases in computing power. Highlights of the talks in these areas included results from the first large-scale parallel finite element particle-in-cell code (PIC), many order-of-magnitude speedup of, and details of porting the VPIC code to the Roadrunner supercomputer. The working group featured two plenary talks, one by Brian Albright of Los Alamos National Laboratory on the performance of the VPIC code on the Roadrunner supercomputer, and one by David Bruhwiler of Tech-X Corporation on recent advances in computation for advanced accelerators. Highlights of the talk by Albright included the first one trillion particle simulations, a sustained performance of 0.3 petaflops, and an eight times speedup of science calculations, including back-scatter in laser-plasma interaction. Highlights of the talk by Bruhwiler included simulations of 10 GeV accelerator laser wakefield stages including external injection, new developments in electromagnetic simulations of electron guns using finite difference and finite element approaches.

Summary Report of Working Group 2: Computation

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

Stoltz, P. H.; Tsung, R. S.

2009-01-22

The working group on computation addressed three physics areas: (i) plasma-based accelerators (laser-driven and beam-driven), (ii) high gradient structure-based accelerators, and (iii) electron beam sources and transport [1]. Highlights of the talks in these areas included new models of breakdown on the microscopic scale, new three-dimensional multipacting calculations with both finite difference and finite element codes, and detailed comparisons of new electron gun models with standard models such as PARMELA. The group also addressed two areas of advances in computation: (i) new algorithms, including simulation in a Lorentz-boosted frame that can reduce computation time orders of magnitude, and (ii) newmore » hardware architectures, like graphics processing units and Cell processors that promise dramatic increases in computing power. Highlights of the talks in these areas included results from the first large-scale parallel finite element particle-in-cell code (PIC), many order-of-magnitude speedup of, and details of porting the VPIC code to the Roadrunner supercomputer. The working group featured two plenary talks, one by Brian Albright of Los Alamos National Laboratory on the performance of the VPIC code on the Roadrunner supercomputer, and one by David Bruhwiler of Tech-X Corporation on recent advances in computation for advanced accelerators. Highlights of the talk by Albright included the first one trillion particle simulations, a sustained performance of 0.3 petaflops, and an eight times speedup of science calculations, including back-scatter in laser-plasma interaction. Highlights of the talk by Bruhwiler included simulations of 10 GeV accelerator laser wakefield stages including external injection, new developments in electromagnetic simulations of electron guns using finite difference and finite element approaches.« less

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

A finite element model of the human head for auditory bone conduction simulation.

PubMed

Taschke, Henning; Hudde, Herbert

2006-01-01

In order to investigate the mechanisms of bone conduction, a finite element model of the human head was developed. The most important steps of the modelling process are described. The model was excited by means of percutaneously applied forces in order to get a deeper insight into the way the parts of the peripheral hearing organ and the surrounding tissue vibrate. The analysis is done based on the division of the bone conduction mechanisms into components. The frequency-dependent patterns of vibration of the components are analyzed. Furthermore, the model allows for the calculation of the contribution of each component to the overall bone-conducted sound. The components interact in a complicated way, which strongly depends on the nature of the excitation and the spatial region to which it is applied.

Modeling of heterogeneous elastic materials by the multiscale hp-adaptive finite element method

NASA Astrophysics Data System (ADS)

Klimczak, Marek; Cecot, Witold

2018-01-01

We present an enhancement of the multiscale finite element method (MsFEM) by combining it with the hp-adaptive FEM. Such a discretization-based homogenization technique is a versatile tool for modeling heterogeneous materials with fast oscillating elasticity coefficients. No assumption on periodicity of the domain is required. In order to avoid direct, so-called overkill mesh computations, a coarse mesh with effective stiffness matrices is used and special shape functions are constructed to account for the local heterogeneities at the micro resolution. The automatic adaptivity (hp-type at the macro resolution and h-type at the micro resolution) increases efficiency of computation. In this paper details of the modified MsFEM are presented and a numerical test performed on a Fichera corner domain is presented in order to validate the proposed approach.

A Note on Substructuring Preconditioning for Nonconforming Finite Element Approximations of Second Order Elliptic Problems

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.

High dimensional model representation method for fuzzy structural dynamics

NASA Astrophysics Data System (ADS)

Adhikari, S.; Chowdhury, R.; Friswell, M. I.

2011-03-01

Uncertainty propagation in multi-parameter complex structures possess significant computational challenges. This paper investigates the possibility of using the High Dimensional Model Representation (HDMR) approach when uncertain system parameters are modeled using fuzzy variables. In particular, the application of HDMR is proposed for fuzzy finite element analysis of linear dynamical systems. The HDMR expansion is an efficient formulation for high-dimensional mapping in complex systems if the higher order variable correlations are weak, thereby permitting the input-output relationship behavior to be captured by the terms of low-order. The computational effort to determine the expansion functions using the α-cut method scales polynomically with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is first illustrated for multi-parameter nonlinear mathematical test functions with fuzzy variables. The method is then integrated with a commercial finite element software (ADINA). Modal analysis of a simplified aircraft wing with fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations. It is shown that using the proposed HDMR approach, the number of finite element function calls can be reduced without significantly compromising the accuracy.

Development of higher-order modal methods for transient thermal and structural analysis

NASA Technical Reports Server (NTRS)

Camarda, Charles J.; Haftka, Raphael T.

1989-01-01

A force-derivative method which produces higher-order modal solutions to transient problems is evaluated. These higher-order solutions converge to an accurate response using fewer degrees-of-freedom (eigenmodes) than lower-order methods such as the mode-displacement or mode-acceleration methods. Results are presented for non-proportionally damped structural problems as well as thermal problems modeled by finite elements.

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

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

Gerritsma, Marc; Bochev, Pavel

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

Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields.

PubMed

Steffen, Michael; Curtis, Sean; Kirby, Robert M; Ryan, Jennifer K

2008-01-01

Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators--integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated--smoothness which is not available at the inter-element level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by inter-element discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-enhancing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through numerical example the computational trade-offs exhibited when one applies such a strategy.

Application of Dynamic Analysis in Semi-Analytical Finite Element Method.

PubMed

Liu, Pengfei; Xing, Qinyan; Wang, Dawei; Oeser, Markus

2017-08-30

Analyses of dynamic responses are significantly important for the design, maintenance and rehabilitation of asphalt pavement. In order to evaluate the dynamic responses of asphalt pavement under moving loads, a specific computational program, SAFEM, was developed based on a semi-analytical finite element method. This method is three-dimensional and only requires a two-dimensional FE discretization by incorporating Fourier series in the third dimension. In this paper, the algorithm to apply the dynamic analysis to SAFEM was introduced in detail. Asphalt pavement models under moving loads were built in the SAFEM and commercial finite element software ABAQUS to verify the accuracy and efficiency of the SAFEM. The verification shows that the computational accuracy of SAFEM is high enough and its computational time is much shorter than ABAQUS. Moreover, experimental verification was carried out and the prediction derived from SAFEM is consistent with the measurement. Therefore, the SAFEM is feasible to reliably predict the dynamic response of asphalt pavement under moving loads, thus proving beneficial to road administration in assessing the pavement's state.

Experimental study and finite element analysis based on equivalent load method for laser ultrasonic measurement of elastic constants.

PubMed

Zhan, Yu; Liu, Changsheng; Zhang, Fengpeng; Qiu, Zhaoguo

2016-07-01

The laser ultrasonic generation of Rayleigh surface wave and longitudinal wave in an elastic plate is studied by experiment and finite element method. In order to eliminate the measurement error and the time delay of the experimental system, the linear fitting method of experimental data is applied. The finite element analysis software ABAQUS is used to simulate the propagation of Rayleigh surface wave and longitudinal wave caused by laser excitation on a sheet metal sample surface. The equivalent load method is proposed and applied. The pulsed laser is equivalent to the surface load in time and space domain to meet the Gaussian profile. The relationship between the physical parameters of the laser and the load is established by the correction factor. The numerical solution is in good agreement with the experimental result. The simple and effective numerical and experimental methods for laser ultrasonic measurement of the elastic constants are demonstrated. Copyright © 2016. Published by Elsevier B.V.

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

DOE PAGES

Gerritsma, Marc; Bochev, Pavel

2016-03-22

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

Numerical investigation of diffraction of acoustic waves by phononic crystals

NASA Astrophysics Data System (ADS)

Moiseyenko, Rayisa P.; Declercq, Nico F.; Laude, Vincent

2012-05-01

Diffraction as well as transmission of acoustic waves by two-dimensional phononic crystals (PCs) composed of steel rods in water are investigated in this paper. The finite element simulations were performed in order to compute pressure fields generated by a line source that are incident on a finite size PC. Such field maps are analyzed based on the complex band structure for the infinite periodic PC. Finite size computations indicate that the exponential decrease of the transmission at deaf frequencies is much stronger than that in Bragg band gaps.

Detailed analysis and test correlation of a stiffened composite wing panel

NASA Technical Reports Server (NTRS)

Davis, D. Dale, Jr.

1991-01-01

Nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings supplied by the Bell Helicopter Textron Corporation, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain (ANS) elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain displacements relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis. Strain predictions from both the linear and nonlinear stress analyses are shown to compare well with experimental data up through the Design Ultimate Load (DUL) of the panel. However, due to the extreme nonlinear response of the panel, the linear analysis was not accurate at loads above the DUL. The nonlinear analysis more accurately predicted the strain at high values of applied load, and even predicted complicated nonlinear response characteristics, such as load reversals, at the observed failure load of the test panel. In order to understand the failure mechanism of the panel, buckling and first ply failure analyses were performed. The buckling load was 17 percent above the observed failure load while first ply failure analyses indicated significant material damage at and below the observed failure load.

A priori error estimates for an hp-version of the discontinuous Galerkin method for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Bey, Kim S.; Oden, J. Tinsley

1993-01-01

A priori error estimates are derived for hp-versions of the finite element method for discontinuous Galerkin approximations of a model class of linear, scalar, first-order hyperbolic conservation laws. These estimates are derived in a mesh dependent norm in which the coefficients depend upon both the local mesh size h(sub K) and a number p(sub k) which can be identified with the spectral order of the local approximations over each element.

Prediction of contact path and load sharing in spiral bevel gears

NASA Technical Reports Server (NTRS)

Bibel, George D.; Tiku, Karuna; Kumar, Ashok

1994-01-01

A procedure is presented to perform a contact analysis of spiral bevel gears in order to predict the contact path and the load sharing as the gears roll through mesh. The approach utilizes recent advances in automated contact methods for nonlinear finite element analysis. A sector of the pinion and gear is modeled consisting of three pinion teeth and four gear teeth in mesh. Calculation of the contact force and stresses through the gear meshing cycle are demonstrated. Summary of the results are presented using three dimensional plots and tables. Issues relating to solution convergence and requirements for running large finite element analysis on a supercomputer are discussed.

Reduced complexity structural modeling for automated airframe synthesis

NASA Technical Reports Server (NTRS)

Hajela, Prabhat

1987-01-01

A procedure is developed for the optimum sizing of wing structures based on representing the built-up finite element assembly of the structure by equivalent beam models. The reduced-order beam models are computationally less demanding in an optimum design environment which dictates repetitive analysis of several trial designs. The design procedure is implemented in a computer program requiring geometry and loading information to create the wing finite element model and its equivalent beam model, and providing a rapid estimate of the optimum weight obtained from a fully stressed design approach applied to the beam. The synthesis procedure is demonstrated for representative conventional-cantilever and joined wing configurations.

Static analysis of rectifier cabinet for nuclear power generating stations based on finite element method

NASA Astrophysics Data System (ADS)

Yin, Qiang; Chen, Tian-jin; Li, Wei-yang; Xiong, Ze-cheng; Ma, Rui

2017-09-01

In order to obtain the deformation map and equivalent stress distribution of rectifier cabinet for nuclear power generating stations, the quality distribution of structure and electrical are described, the tensile bond strengths of the rings are checked, and the finite element model of cabinet is set up by ANSYS. The transport conditions of the hoisting state and fork loading state are analyzed. The deformation map and equivalent stress distribution are obtained. The attentive problems are put forward. It is a reference for analysis method and the obtained results for the transport of rectifier cabinet for nuclear power generating stations.

Wakefield Computations for the CLIC PETS using the Parallel Finite Element Time-Domain Code T3P

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

Candel, A; Kabel, A.; Lee, L.

In recent years, SLAC's Advanced Computations Department (ACD) has developed the high-performance parallel 3D electromagnetic time-domain code, T3P, for simulations of wakefields and transients in complex accelerator structures. T3P is based on advanced higher-order Finite Element methods on unstructured grids with quadratic surface approximation. Optimized for large-scale parallel processing on leadership supercomputing facilities, T3P allows simulations of realistic 3D structures with unprecedented accuracy, aiding the design of the next generation of accelerator facilities. Applications to the Compact Linear Collider (CLIC) Power Extraction and Transfer Structure (PETS) are presented.

Modeling aluminum-lithium alloy welding characteristics

NASA Technical Reports Server (NTRS)

Bernstein, Edward L.

1996-01-01

The purpose of this project was to develop a finite element model of the heat-affected zone in the vicinity of a weld line on a plate in order to determine an accurate plastic strain history. The resulting plastic strain increments calculated by the finite element program were then to be used to calculate the measure of damage D. It was hoped to determine the effects of varying welding parameters, such as beam power, efficiency, and weld speed, and the effect of different material properties on the occurrence of microfissuring. The results were to be compared first to the previous analysis of Inconel 718, and then extended to aluminum 2195.

A general algorithm using finite element method for aerodynamic configurations at low speeds

NASA Technical Reports Server (NTRS)

Balasubramanian, R.

1975-01-01

A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.

Pelvic modelling and the comparison between plate position for double pelvic osteotomy using artificial cancellous bone and finite element analysis.

PubMed

McCartney, William; MacDonald, Bryan; Ober, Ciprian Andrei; Lostado-Lorza, Rubén; Gómez, Fátima Somovilla

2018-03-20

Finite element analysis was used to compare fixation methods for double pelvic osteotomy (DPO). Using 3D scanning a stereolithography (stl) image was produced of a canine pelvis and this was subsequently refined in computer aided design (CAD). Using the CAD files, the images were imported in MSC Marc software to produce a working finite element (FE) model with 3 dimensional tetrahedral elements with linear shaped functions. The dimensions of a precontoured pelvic osteotomy plate with eight screws and a twisted seven screw straight plate were used to build the 2 fixations implants for the FE models. An equivalent load of 300 N was applied progressively on all FE models in order to facilitate its convergence. The load was applied in a distributed manner on the femur-hip joint contact area in order to simulate the actual behavior of the joint. The aim of the present study was to analyze the difference in stiffness and behavior under loading between a lateral vs ventral plate fixation, with unlocked screws and different gap scenarios, for stabilization of a pelvic osteotomy using finite element analysis. From both configurations the maximum displacement of the ventral plate with 7 screws without gap had a value of 1.988 mm, while in the DPO plate had a maximum displacement of 2.191 mm. The load applied for each of the different configurations studied when a gap of 1° was considered and also when a condition of no gap was considered. The ventral plate was stiffer than the lateral plate when a gap was not present. When the gap was closed in the ventral plate, the stiffness increased until a point that remained constant. Ventral plate fixation can be as or more stiff as lateral plate fixation and provides flexible fixation. This behavior should reduce screw loosening. Using ventral plate fixation is recommended to reduce screw loosening or failure.

Three-Dimensional Simulations of Marangoni-Benard Convection in Small Containers by the Least-Squares Finite Element Method

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao; Jiang, Bo-Nan; Wu, Jie; Duh, J. C.

1996-01-01

This paper reports a numerical study of the Marangoni-Benard (MB) convection in a planar fluid layer. The least-squares finite element method (LSFEM) is employed to solve the three-dimensional Stokes equations and the energy equation. First, the governing equations are reduced to be first-order by introducing variables such as vorticity and heat fluxes. The resultant first-order system is then cast into a div-curl-grad formulation, and its ellipticity and permissible boundary conditions are readily proved. This numerical approach provides an equal-order discretization for velocity, pressure, vorticity, temperature, and heat conduction fluxes, and therefore can provide high fidelity solutions for the complex flow physics of the MB convection. Numerical results reported include the critical Marangoni numbers (M(sub ac)) for the onset of the convection in containers with various aspect ratios, and the planforms of supercritical MB flows. The numerical solutions compared favorably with the experimental results reported by Koschmieder et al..

Finite Element Analysis of Folded Airbag in Frontal Impact of Adapted Vehicles for Disabled Drivers

NASA Astrophysics Data System (ADS)

Masiá, J.; Eixerés, B.; Dols, J. F.; Esquerdo, T. V.

2009-11-01

The car control adaptations are used in vehicles in order to facilitate the driving to persons with physical handicaps. This does not have to suppose a decrease of the passive safety that is required to the vehicles. In order to analyze this relation there will be characterized the different control adaptations that are in use together with the different devices of passive safety that can be mounted in the vehicles in diverse cases of impact in order to generate models of simulation. The methodology used to generate this simulation consists of the first phase in which there develops the three-dimensional model of the driving place. For it, there has been used a commercial software of three-dimensional design. Once realized this one divides, the model is imported to the finite elements software in which meshing is generated. Finally, dynamic simulation software is used to assign the most important characteristics like material properties, contact interfaces, gas expansion models, airbag fold types, etc.

Efficient calculation of higher-order optical waveguide dispersion.

PubMed

Mores, J A; Malheiros-Silveira, G N; Fragnito, H L; Hernández-Figueroa, H E

2010-09-13

An efficient numerical strategy to compute the higher-order dispersion parameters of optical waveguides is presented. For the first time to our knowledge, a systematic study of the errors involved in the higher-order dispersions' numerical calculation process is made, showing that the present strategy can accurately model those parameters. Such strategy combines a full-vectorial finite element modal solver and a proper finite difference differentiation algorithm. Its performance has been carefully assessed through the analysis of several key geometries. In addition, the optimization of those higher-order dispersion parameters can also be carried out by coupling to the present scheme a genetic algorithm, as shown here through the design of a photonic crystal fiber suitable for parametric amplification applications.

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2000-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

A comparison between different finite elements for elastic and aero-elastic analyses.

PubMed

Mahran, Mohamed; ELsabbagh, Adel; Negm, Hani

2017-11-01

In the present paper, a comparison between five different shell finite elements, including the Linear Triangular Element, Linear Quadrilateral Element, Linear Quadrilateral Element based on deformation modes, 8-node Quadrilateral Element, and 9-Node Quadrilateral Element was presented. The shape functions and the element equations related to each element were presented through a detailed mathematical formulation. Additionally, the Jacobian matrix for the second order derivatives was simplified and used to derive each element's strain-displacement matrix in bending. The elements were compared using carefully selected elastic and aero-elastic bench mark problems, regarding the number of elements needed to reach convergence, the resulting accuracy, and the needed computation time. The best suitable element for elastic free vibration analysis was found to be the Linear Quadrilateral Element with deformation-based shape functions, whereas the most suitable element for stress analysis was the 8-Node Quadrilateral Element, and the most suitable element for aero-elastic analysis was the 9-Node Quadrilateral Element. Although the linear triangular element was the last choice for modal and stress analyses, it establishes more accurate results in aero-elastic analyses, however, with much longer computation time. Additionally, the nine-node quadrilateral element was found to be the best choice for laminated composite plates analysis.

Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems

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

Cai, Wei

Understanding electromagnetic phenomena is the key in many scientific investigation and engineering designs such as solar cell designs, studying biological ion channels for diseases, and creating clean fusion energies, among other things. The objectives of the project are to develop high order numerical methods to simulate evanescent electromagnetic waves occurring in plasmon solar cells and biological ion-channels, where local field enhancement within random media in the former and long range electrostatic interactions in the latter are of major challenges for accurate and efficient numerical computations. We have accomplished these objectives by developing high order numerical methods for solving Maxwell equationsmore » such as high order finite element basis for discontinuous Galerkin methods, well-conditioned Nedelec edge element method, divergence free finite element basis for MHD, and fast integral equation methods for layered media. These methods can be used to model the complex local field enhancement in plasmon solar cells. On the other hand, to treat long range electrostatic interaction in ion channels, we have developed image charge based method for a hybrid model in combining atomistic electrostatics and continuum Poisson-Boltzmann electrostatics. Such a hybrid model will speed up the molecular dynamics simulation of transport in biological ion-channels.« less

Improving a complex finite-difference ground water flow model through the use of an analytic element screening model

USGS Publications Warehouse

Hunt, R.J.; Anderson, M.P.; Kelson, V.A.

1998-01-01

This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.

Nonlinear thermo-mechanical analysis of stiffened composite laminates by a new finite element

NASA Astrophysics Data System (ADS)

Barut, Atila

A new stiffened shell element combining shallow beam and shallow shell elements is developed for geometrically nonlinear analysis of stiffened composite laminates under thermal and/or mechanical loading. The formulation of this element is based on the principal of virtual displacements in conjunction with the co-rotational form of the total Lagrangian description of motion. In the finite element formulation, both the shell and the beam (stiffener) elements account for transverse shear deformations and material anisotropy. The cross-section of the stiffener (beam) can be arbitrary in geometry and lamination. In order to combine the stiffener with the shell element, constraint conditions are applied to the displacement and rotation fields of the stiffener. These constraint conditions ensure that the cross-section of the stiffener remains co-planar with the shell section after deformation. The resulting expressions for the displacement and rotation fields of the stiffener involve only the nodal unknowns of the shell element, thus reducing the total number of degrees of freedom. Also, the discretization of the entire stiffened shell structure becomes more flexible.

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

DOE PAGES

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.; ...

2016-09-22

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

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

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

Verification of a non-hydrostatic dynamical core using the horizontal spectral element method and vertical finite difference method: 2-D aspects

NASA Astrophysics Data System (ADS)

Choi, S.-J.; Giraldo, F. X.; Kim, J.; Shin, S.

2014-11-01

The non-hydrostatic (NH) compressible Euler equations for dry atmosphere were solved in a simplified two-dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. By using horizontal SEM, which decomposes the physical domain into smaller pieces with a small communication stencil, a high level of scalability can be achieved. By using vertical FDM, an easy method for coupling the dynamics and existing physics packages can be provided. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind-biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative and integral terms. For temporal integration, a time-split, third-order Runge-Kutta (RK3) integration technique was applied. The Euler equations that were used here are in flux form based on the hydrostatic pressure vertical coordinate. The equations are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate was implemented in this model. We validated the model by conducting the widely used standard tests: linear hydrostatic mountain wave, tracer advection, and gravity wave over the Schär-type mountain, as well as density current, inertia-gravity wave, and rising thermal bubble. The results from these tests demonstrated that the model using the horizontal SEM and the vertical FDM is accurate and robust provided sufficient diffusion is applied. The results with various horizontal resolutions also showed convergence of second-order accuracy due to the accuracy of the time integration scheme and that of the vertical direction, although high-order basis functions were used in the horizontal. By using the 2-D slice model, we effectively showed that the combined spatial discretization method of the spectral element and finite difference methods in the horizontal and vertical directions, respectively, offers a viable method for development of an NH dynamical core.

Delamination Defect Detection Using Ultrasonic Guided Waves in Advanced Hybrid Structural Elements

NASA Astrophysics Data System (ADS)

Yan, Fei; Qi, Kevin ``Xue''; Rose, Joseph L.; Weiland, Hasso

2010-02-01

Nondestructive testing for multilayered structures is challenging because of increased numbers of layers and plate thicknesses. In this paper, ultrasonic guided waves are applied to detect delamination defects inside a 23-layer Alcoa Advanced Hybrid Structural plate. A semi-analytical finite element (SAFE) method generates dispersion curves and wave structures in order to select appropriate wave structures to detect certain defects. One guided wave mode and frequency is chosen to achieve large in-plane displacements at regions of interest. The interactions of the selected mode with defects are simulated using finite element models. Experiments are conducted and compared with bulk wave measurements. It is shown that guided waves can detect deeply embedded damages inside thick multilayer fiber-metal laminates with suitable mode and frequency selection.

Finite and spectral cell method for wave propagation in heterogeneous materials

NASA Astrophysics Data System (ADS)

Joulaian, Meysam; Duczek, Sascha; Gabbert, Ulrich; Düster, Alexander

2014-09-01

In the current paper we present a fast, reliable technique for simulating wave propagation in complex structures made of heterogeneous materials. The proposed approach, the spectral cell method, is a combination of the finite cell method and the spectral element method that significantly lowers preprocessing and computational expenditure. The spectral cell method takes advantage of explicit time-integration schemes coupled with a diagonal mass matrix to reduce the time spent on solving the equation system. By employing a fictitious domain approach, this method also helps to eliminate some of the difficulties associated with mesh generation. Besides introducing a proper, specific mass lumping technique, we also study the performance of the low-order and high-order versions of this approach based on several numerical examples. Our results show that the high-order version of the spectral cell method together requires less memory storage and less CPU time than other possible versions, when combined simultaneously with explicit time-integration algorithms. Moreover, as the implementation of the proposed method in available finite element programs is straightforward, these properties turn the method into a viable tool for practical applications such as structural health monitoring [1-3], quantitative ultrasound applications [4], or the active control of vibrations and noise [5, 6].

FINITE ELEMENT MODEL FOR TIDAL AND RESIDUAL CIRCULATION.

USGS Publications Warehouse

Walters, Roy A.

1986-01-01

Harmonic decomposition is applied to the shallow water equations, thereby creating a system of equations for the amplitude of the various tidal constituents and for the residual motions. The resulting equations are elliptic in nature, are well posed and in practice are shown to be numerically well-behaved. There are a number of strategies for choosing elements: the two extremes are to use a few high-order elements with continuous derivatives, or to use a large number of simpler linear elements. In this paper simple linear elements are used and prove effective.

WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS

PubMed Central

MU, LIN; WANG, JUNPING; WEI, GUOWEI; YE, XIU; ZHAO, SHAN

2013-01-01

Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both L2 and L∞ norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order O(h) to O(h1.5) for the solution itself in L∞ norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order O(h1.75) to O(h2) in the L∞ norm for C1 or Lipschitz continuous interfaces associated with a C1 or H2 continuous solution. PMID:24072935

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.

Equivalent model construction for a non-linear dynamic system based on an element-wise stiffness evaluation procedure and reduced analysis of the equivalent system

NASA Astrophysics Data System (ADS)

Kim, Euiyoung; Cho, Maenghyo

2017-11-01

In most non-linear analyses, the construction of a system matrix uses a large amount of computation time, comparable to the computation time required by the solving process. If the process for computing non-linear internal force matrices is substituted with an effective equivalent model that enables the bypass of numerical integrations and assembly processes used in matrix construction, efficiency can be greatly enhanced. A stiffness evaluation procedure (STEP) establishes non-linear internal force models using polynomial formulations of displacements. To efficiently identify an equivalent model, the method has evolved such that it is based on a reduced-order system. The reduction process, however, makes the equivalent model difficult to parameterize, which significantly affects the efficiency of the optimization process. In this paper, therefore, a new STEP, E-STEP, is proposed. Based on the element-wise nature of the finite element model, the stiffness evaluation is carried out element-by-element in the full domain. Since the unit of computation for the stiffness evaluation is restricted by element size, and since the computation is independent, the equivalent model can be constructed efficiently in parallel, even in the full domain. Due to the element-wise nature of the construction procedure, the equivalent E-STEP model is easily characterized by design parameters. Various reduced-order modeling techniques can be applied to the equivalent system in a manner similar to how they are applied in the original system. The reduced-order model based on E-STEP is successfully demonstrated for the dynamic analyses of non-linear structural finite element systems under varying design parameters.

Establishing the 3-D finite element solid model of femurs in partial by volume rendering.

PubMed

Zhang, Yinwang; Zhong, Wuxue; Zhu, Haibo; Chen, Yun; Xu, Lingjun; Zhu, Jianmin

2013-01-01

It remains rare to report three-dimensional (3-D) finite element solid model of femurs in partial by volume rendering method, though several methods of femoral 3-D finite element modeling are already available. We aim to analyze the advantages of the modeling method by establishing the 3-D finite element solid model of femurs in partial by volume rendering. A 3-D finite element model of the normal human femurs, made up of three anatomic structures: cortical bone, cancellous bone and pulp cavity, was constructed followed by pretreatment of the CT original image. Moreover, the finite-element analysis was carried on different material properties, three types of materials given for cortical bone, six assigned for cancellous bone, and single for pulp cavity. The established 3-D finite element of femurs contains three anatomical structures: cortical bone, cancellous bone, and pulp cavity. The compressive stress primarily concentrated in the medial surfaces of femur, especially in the calcar femorale. Compared with whole modeling by volume rendering method, the 3-D finite element solid model created in partial is more real and fit for finite element analysis. Copyright © 2013 Surgical Associates Ltd. Published by Elsevier Ltd. All rights reserved.

A Dynamic Finite Element Method for Simulating the Physics of Faults Systems

NASA Astrophysics Data System (ADS)

Saez, E.; Mora, P.; Gross, L.; Weatherley, D.

2004-12-01

We introduce a dynamic Finite Element method using a novel high level scripting language to describe the physical equations, boundary conditions and time integration scheme. The library we use is the parallel Finley library: a finite element kernel library, designed for solving large-scale problems. It is incorporated as a differential equation solver into a more general library called escript, based on the scripting language Python. This library has been developed to facilitate the rapid development of 3D parallel codes, and is optimised for the Australian Computational Earth Systems Simulator Major National Research Facility (ACcESS MNRF) supercomputer, a 208 processor SGI Altix with a peak performance of 1.1 TFlops. Using the scripting approach we obtain a parallel FE code able to take advantage of the computational efficiency of the Altix 3700. We consider faults as material discontinuities (the displacement, velocity, and acceleration fields are discontinuous at the fault), with elastic behavior. The stress continuity at the fault is achieved naturally through the expression of the fault interactions in the weak formulation. The elasticity problem is solved explicitly in time, using the Saint Verlat scheme. Finally, we specify a suitable frictional constitutive relation and numerical scheme to simulate fault behaviour. Our model is based on previous work on modelling fault friction and multi-fault systems using lattice solid-like models. We adapt the 2D model for simulating the dynamics of parallel fault systems described to the Finite-Element method. The approach uses a frictional relation along faults that is slip and slip-rate dependent, and the numerical integration approach introduced by Mora and Place in the lattice solid model. In order to illustrate the new Finite Element model, single and multi-fault simulation examples are presented.

Micro-finite-element method to assess elastic properties of trabecular bone at micro- and macroscopic level.

PubMed

Rieger, R; Auregan, J C; Hoc, T

2018-03-01

The objective of the present study is to assess the mechanical behavior of trabecular bone based on microCT imaging and micro-finite-element analysis. In this way two methods are detailed: (i) direct determination of macroscopic elastic property of trabecular bone; (ii) inverse approach to assess mechanical properties of trabecular bone tissue. Thirty-five females and seven males (forty-two subjects) mean aged (±SD) 80±11.7 years from hospitals of Assistance publique-Hôpitaux de Paris (AP-HP) diagnosed with osteoporosis following a femoral neck fracture due to a fall from standing were included in this study. Fractured heads were collected during hip replacement surgery. Standardized bone cores were removed from the femoral head's equator by a trephine in a water bath. MicroCT images acquisition and analysis were performed with CTan ® software and bone volume fraction was then determined. Micro-finite-element simulations were per-formed using Abaqus 6.9-2 ® software in order to determine the macroscopic mechanical behaviour of the trabecular bone. After microCT acquisition, a longitudinal compression test was performed and the experimental macroscopic Young's Modulus was extracted. An inverse approach based on the whole trabecular bone's mechanical response and micro-finite-element analysis was performed to determine microscopic mechanical properties of trabecular bone. In the present study, elasticity of the tissue was shown to be similar to that of healthy tissue but with a lower yield stress. Classical histomorphometric analysis form microCT imaging associated with an inverse micro-finite-element method allowed to assess microscopic mechanical trabecular bone parameters. Copyright © 2017 Elsevier Masson SAS. All rights reserved.

Modeling Progressive Failure of Bonded Joints Using a Single Joint Finite Element

NASA Technical Reports Server (NTRS)

Stapleton, Scott E.; Waas, Anthony M.; Bednarcyk, Brett A.

2010-01-01

Enhanced finite elements are elements with an embedded analytical solution which can capture detailed local fields, enabling more efficient, mesh-independent finite element analysis. In the present study, an enhanced finite element is applied to generate a general framework capable of modeling an array of joint types. The joint field equations are derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields are used to generate shape functions and a stiffness matrix for a single joint finite element. This single finite element thus captures the detailed stress and strain fields within the bonded joint, but it can function within a broader structural finite element model. The costs associated with a fine mesh of the joint can thus be avoided while still obtaining a detailed solution for the joint. Additionally, the capability to model non-linear adhesive constitutive behavior has been included within the method, and progressive failure of the adhesive can be modeled by using a strain-based failure criteria and re-sizing the joint as the adhesive fails. Results of the model compare favorably with experimental and finite element results.

The Blended Finite Element Method for Multi-fluid Plasma Modeling

DTIC Science & Technology

2016-07-01

Briefing Charts 3. DATES COVERED (From - To) 07 June 2016 - 01 July 2016 4. TITLE AND SUBTITLE The Blended Finite Element Method for Multi-fluid Plasma...BLENDED FINITE ELEMENT METHOD FOR MULTI-FLUID PLASMA MODELING Éder M. Sousa1, Uri Shumlak2 1ERC INC., IN-SPACE PROPULSION BRANCH (RQRS) AIR FORCE RESEARCH...MULTI-FLUID PLASMA MODEL 2 BLENDED FINITE ELEMENT METHOD Blended Finite Element Method Nodal Continuous Galerkin Modal Discontinuous Galerkin Model

Spatial Convergence of Three Dimensional Turbulent Flows

NASA Technical Reports Server (NTRS)

Park, Michael A.; Anderson, W. Kyle

2016-01-01

Finite-volume and finite-element schemes, both implemented within the FUN3D flow solver, are evaluated for several test cases described on the Turbulence-Modeling Resource (TMR) web site. The cases include subsonic flow over a hemisphere cylinder, subsonic flow over a swept bump configuration, and supersonic flow in a square duct. The finite- volume and finite-element schemes are both used to obtain solutions for the first two cases, whereas only the finite-volume scheme is used for the supersonic duct. For the hemisphere cylinder, finite-element solutions obtained on tetrahedral meshes are compared with finite- volume solutions on mixed-element meshes. For the swept bump, finite-volume solutions have been obtained for both hexahedral and tetrahedral meshes and are compared with finite-element solutions obtained on tetrahedral meshes. For the hemisphere cylinder and the swept bump, solutions are obtained on a series of meshes with varying grid density and comparisons are made between drag coefficients, pressure distributions, velocity profiles, and profiles of the turbulence working variable. The square duct shows small variation due to element type or the spatial accuracy of turbulence model convection. It is demonstrated that the finite-element scheme on tetrahedral meshes yields similar accuracy as the finite- volume scheme on mixed-element and hexahedral grids, and demonstrates less sensitivity to the mesh topology (biased tetrahedral grids) than the finite-volume scheme.

Center for Efficient Exascale Discretizations Software Suite

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

Kolev, Tzanio; Dobrev, Veselin; Tomov, Vladimir

The CEED Software suite is a collection of generally applicable software tools focusing on the following computational motives: PDE discretizations on unstructured meshes, high-order finite element and spectral element methods and unstructured adaptive mesh refinement. All of this software is being developed as part of CEED, a co-design Center for Efficient Exascale Discretizations, within DOE's Exascale Computing Project (ECP) program.

Dental application of novel finite element analysis software for three-dimensional finite element modeling of a dentulous mandible from its computed tomography images.

PubMed

Nakamura, Keiko; Tajima, Kiyoshi; Chen, Ker-Kong; Nagamatsu, Yuki; Kakigawa, Hiroshi; Masumi, Shin-ich

2013-12-01

This study focused on the application of novel finite-element analysis software for constructing a finite-element model from the computed tomography data of a human dentulous mandible. The finite-element model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography-based finite-element analysis software was solely applied to the finite-element analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed finite-element model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell elements. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional finite-element model of a dentulous mandible from the computed tomography data without the need for any other software.

A parametric finite element method for solid-state dewetting problems with anisotropic surface energies

NASA Astrophysics Data System (ADS)

Bao, Weizhu; Jiang, Wei; Wang, Yan; Zhao, Quan

2017-02-01

We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the sharp-interface models belong to a new type of high-order (4th- or 6th-order) geometric evolution partial differential equations about open curve/surface interface tracking problems which include anisotropic surface diffusion flow and contact line migration. Compared to the traditional methods (e.g., marker-particle methods), the proposed PFEM not only has very good accuracy, but also poses very mild restrictions on the numerical stability, and thus it has significant advantages for solving this type of open curve evolution problems with applications in the simulation of solid-state dewetting. Extensive numerical results are reported to demonstrate the accuracy and high efficiency of the proposed PFEM.

Full Wave Analysis of RF Signal Attenuation in a Lossy Rough Surface Cave using a High Order Time Domain Vector Finite Element Method

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

Pingenot, J; Rieben, R; White, 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 ordermore » 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.« less

2-D to 3-D global/local finite element analysis of cross-ply composite laminates

NASA Technical Reports Server (NTRS)

Thompson, D. Muheim; Griffin, O. Hayden, Jr.

1990-01-01

An example of two-dimensional to three-dimensional global/local finite element analysis of a laminated composite plate with a hole is presented. The 'zoom' technique of global/local analysis is used, where displacements of the global/local interface from the two-dimensional global model are applied to the edges of the three-dimensional local model. Three different hole diameters, one, three, and six inches, are considered in order to compare the effect of hole size on the three-dimensional stress state around the hole. In addition, three different stacking sequences are analyzed for the six inch hole case in order to study the effect of stacking sequence. The existence of a 'critical' hole size, where the interlaminar stresses are maximum, is indicated. Dispersion of plies at the same angle, as opposed to clustering, is found to reduce the magnitude of some interlaminar stress components and increase others.

Transition from two-dimensional photonic crystals to dielectric metasurfaces in the optical diffraction with a fine structure

PubMed Central

Rybin, Mikhail V.; Samusev, Kirill B.; Lukashenko, Stanislav Yu.; Kivshar, Yuri S.; Limonov, Mikhail F.

2016-01-01

We study experimentally a fine structure of the optical Laue diffraction from two-dimensional periodic photonic lattices. The periodic photonic lattices with the C4v square symmetry, orthogonal C2v symmetry, and hexagonal C6v symmetry are composed of submicron dielectric elements fabricated by the direct laser writing technique. We observe surprisingly strong optical diffraction from a finite number of elements that provides an excellent tool to determine not only the symmetry but also exact number of particles in the finite-length structure and the sample shape. Using different samples with orthogonal C2v symmetry and varying the lattice spacing, we observe experimentally a transition between the regime of multi-order diffraction, being typical for photonic crystals to the regime where only the zero-order diffraction can be observed, being is a clear fingerprint of dielectric metasurfaces characterized by effective parameters. PMID:27491952

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Higher-Order Adaptive Finite-Element Methods for Kohn-Sham Density Functional Theory

DTIC Science & Technology

2012-07-03

systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemi- cal accuracy...calculations. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of materials systems contain- ing a...benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy

Finite element implementation of Robinson's unified viscoplastic model and its application to some uniaxial and multiaxial problems

NASA Technical Reports Server (NTRS)

Arya, V. K.; Kaufman, A.

1989-01-01

A description of the finite element implementation of Robinson's unified viscoplastic model into the General Purpose Finite Element Program (MARC) is presented. To demonstrate its application, the implementation is applied to some uniaxial and multiaxial problems. A comparison of the results for the multiaxial problem of a thick internally pressurized cylinder, obtained using the finite element implementation and an analytical solution, is also presented. The excellent agreement obtained confirms the correct finite element implementation of Robinson's model.

Finite element implementation of Robinson's unified viscoplastic model and its application to some uniaxial and multiaxial problems

NASA Technical Reports Server (NTRS)

Arya, V. K.; Kaufman, A.

1987-01-01

A description of the finite element implementation of Robinson's unified viscoplastic model into the General Purpose Finite Element Program (MARC) is presented. To demonstrate its application, the implementation is applied to some uniaxial and multiaxial problems. A comparison of the results for the multiaxial problem of a thick internally pressurized cylinder, obtained using the finite element implementation and an analytical solution, is also presented. The excellent agreement obtained confirms the correct finite element implementation of Robinson's model.

Demonstration Of Ultra HI-FI (UHF) Methods

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2004-01-01

Computational aero-acoustics (CAA) requires efficient, high-resolution simulation tools. Most current techniques utilize finite-difference approaches because high order accuracy is considered too difficult or expensive to achieve with finite volume or finite element methods. However, a novel finite volume approach (Ultra HI-FI or UHF) which utilizes Hermite fluxes is presented which can achieve both arbitrary accuracy and fidelity in space and time. The technique can be applied to unstructured grids with some loss of fidelity or with multi-block structured grids for maximum efficiency and resolution. In either paradigm, it is possible to resolve ultra-short waves (less than 2 PPW). This is demonstrated here by solving the 4th CAA workshop Category 1 Problem 1.

Spectrally formulated user-defined element in conventional finite element environment for wave motion analysis in 2-D composite structures

NASA Astrophysics Data System (ADS)

Khalili, Ashkan; Jha, Ratneshwar; Samaratunga, Dulip

2016-11-01

Wave propagation analysis in 2-D composite structures is performed efficiently and accurately through the formulation of a User-Defined Element (UEL) based on the wavelet spectral finite element (WSFE) method. The WSFE method is based on the first-order shear deformation theory which yields accurate results for wave motion at high frequencies. The 2-D WSFE model is highly efficient computationally and provides a direct relationship between system input and output in the frequency domain. The UEL is formulated and implemented in Abaqus (commercial finite element software) for wave propagation analysis in 2-D composite structures with complexities. Frequency domain formulation of WSFE leads to complex valued parameters, which are decoupled into real and imaginary parts and presented to Abaqus as real values. The final solution is obtained by forming a complex value using the real number solutions given by Abaqus. Five numerical examples are presented in this article, namely undamaged plate, impacted plate, plate with ply drop, folded plate and plate with stiffener. Wave motions predicted by the developed UEL correlate very well with Abaqus simulations. The results also show that the UEL largely retains computational efficiency of the WSFE method and extends its ability to model complex features.

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

NASA Astrophysics Data System (ADS)

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

1986-12-01

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

A High-Order Finite Spectral Volume Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2001-01-01

A time accurate, high-order, conservative, yet efficient method named Finite Spectral Volume (FSV) is developed for conservation laws on unstructured grids. The concept of a 'spectral volume' is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multi-domain spectral methods. In addition, each spectral volume is further sub-divided into control volumes (CVs), and cell-averaged data from these control volumes is used to reconstruct a high-order approximation in the spectral volume. Riemann solvers are used to compute the fluxes at spectral volume boundaries. Then cell-averaged state variables in the control volumes are updated independently. Furthermore, TVD (Total Variation Diminishing) and TVB (Total Variation Bounded) limiters are introduced in the FSV method to remove/reduce spurious oscillations near discontinuities. A very desirable feature of the FSV method is that the reconstruction is carried out only once, and analytically, and is the same for all cells of the same type, and that the reconstruction stencil is always non-singular, in contrast to the memory and CPU-intensive reconstruction in a high-order finite volume (FV) method. Discussions are made concerning why the FSV method is significantly more efficient than high-order finite volume and the Discontinuous Galerkin (DG) methods. Fundamental properties of the FSV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.

A method for reducing the order of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Masri, S. F.; Miller, R. K.; Sassi, H.; Caughey, T. K.

1984-06-01

An approximate method that uses conventional condensation techniques for linear systems together with the nonparametric identification of the reduced-order model generalized nonlinear restoring forces is presented for reducing the order of discrete multidegree-of-freedom dynamic systems that possess arbitrary nonlinear characteristics. The utility of the proposed method is demonstrated by considering a redundant three-dimensional finite-element model half of whose elements incorporate hysteretic properties. A nonlinear reduced-order model, of one-third the order of the original model, is developed on the basis of wideband stationary random excitation and the validity of the reduced-order model is subsequently demonstrated by its ability to predict with adequate accuracy the transient response of the original nonlinear model under a different nonstationary random excitation.

Stress-intensity factors for small surface and corner cracks in plates

NASA Technical Reports Server (NTRS)

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

1988-01-01

Three-dimensional finite-element and finite-alternating methods were used to obtain the stress-intensity factors for small surface and corner cracked plates subjected to remote tension and bending loads. The crack-depth-to-crack-length ratios (a/c) ranged from 0.2 to 1 and the crack-depth-to-plate-thickness ratios (a/t) ranged from 0.05 to 0.2. The performance of the finite-element alternating method was studied on these crack configurations. A study of the computational effort involved in the finite-element alternating method showed that several crack configurations could be analyzed with a single rectangular mesh idealization, whereas the conventional finite-element method requires a different mesh for each configuration. The stress-intensity factors obtained with the finite-element-alternating method agreed well (within 5 percent) with those calculated from the finite-element method with singularity elements.

Sound transmission analysis of partially treated MR fluid-based sandwich panels using finite element method

NASA Astrophysics Data System (ADS)

Hemmatian, M.; Sedaghati, R.

2017-04-01

This study aims at developing a finite element model to predict the sound transmission loss (STL) of a multilayer panel partially treated with a Magnetorheological (MR) fluid core layer. MR fluids are smart materials with promising controllable rheological characteristics in which the application of an external magnetic field instantly changes their rheological properties. Partial treatment of sandwich panels with MR fluid core layer provides an opportunity to change stiffness and damping of the structure without significantly increasing the mass. The STL of a finite sandwich panel partially treated with MR fluid is modeled using the finite element (FE) method. Circular sandwich panels with clamped boundary condition and elastic face sheets in which the core layer is segmented circumferentially is considered. The MR fluid core layer is considered as a viscoelastic material with complex shear modulus with the magnetic field and frequency dependent storage and loss moduli. Neglecting the effect of the panel's vibration on the pressure forcing function, the work done by the acoustic pressure is expressed as a function of the blocked pressure in order to calculate the force vector in the equation of the motion of the panel. The governing finite element equation of motion of the MR sandwich panel is then developed to predict the transverse vibration of the panel which can then be utilized to obtain the radiated sound using Green's function. The developed model is used to conduct a systematic parametric study on the effect of different locations of MR fluid treatment on the natural frequencies and the STL.

An interactive graphics system to facilitate finite element structural analysis

NASA Technical Reports Server (NTRS)

Burk, R. C.; Held, F. H.

1973-01-01

The characteristics of an interactive graphics systems to facilitate the finite element method of structural analysis are described. The finite element model analysis consists of three phases: (1) preprocessing (model generation), (2) problem solution, and (3) postprocessing (interpretation of results). The advantages of interactive graphics to finite element structural analysis are defined.

Hybrid High-Order methods for finite deformations of hyperelastic materials

NASA Astrophysics Data System (ADS)

Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas

2018-01-01

We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order k≥1 on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of a broken nonlinear elastic energy where a local reconstruction of the displacement gradient is used. Two HHO methods are considered: a stabilized method where the gradient is reconstructed as a tensor-valued polynomial of order k and a stabilization is added to the discrete energy functional, and an unstabilized method which reconstructs a stable higher-order gradient and circumvents the need for stabilization. Both methods satisfy the principle of virtual work locally with equilibrated tractions. We present a numerical study of the two HHO methods on test cases with known solution and on more challenging three-dimensional test cases including finite deformations with strong shear layers and cavitating voids. We assess the computational efficiency of both methods, and we compare our results to those obtained with an industrial software using conforming finite elements and to results from the literature. The two HHO methods exhibit robust behavior in the quasi-incompressible regime.

Integrated transient thermal-structural finite element analysis

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Dechaumphai, P.; Wieting, A. R.; Tamma, K. K.

1981-01-01

An integrated thermal structural finite element approach for efficient coupling of transient thermal and structural analysis is presented. Integrated thermal structural rod and one dimensional axisymmetric elements considering conduction and convection are developed and used in transient thermal structural applications. The improved accuracy of the integrated approach is illustrated by comparisons with exact transient heat conduction elasticity solutions and conventional finite element thermal finite element structural analyses.

Final Report - Subcontract B623760

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

Bank, R.

2017-11-17

During my visit to LLNL during July 17{27, 2017, I worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear systems arising from hp adaptive finite element calculations, and is implemented in the PLTMG software package, version 12. This preconditioner typically requires 3-20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive de nite elliptic equations, convection dominated convection-diffusion equations, and highly indefinite Helmholtz equations, among others). The convergence rate is not independent ofmore » the polynomial degree p as p ! 1, but but remains strong for p 9, which is the highest polynomial degree allowed in PLTMG, due to limitations of the numerical quadrature rules implemented in the software package. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in. Like traditional geometric multilevel methods, this scheme relies on knowledge of the underlying finite element space in order to construct the smoother and the coarse grid correction.« less

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Simulating correction of adjustable optics for an x-ray telescope

NASA Astrophysics Data System (ADS)

Aldcroft, Thomas L.; Schwartz, Daniel A.; Reid, Paul B.; Cotroneo, Vincenzo; Davis, William N.

2012-10-01

The next generation of large X-ray telescopes with sub-arcsecond resolution will require very thin, highly nested grazing incidence optics. To correct the low order figure errors resulting from initial manufacture, the mounting process, and the effects of going from 1 g during ground alignment to zero g on-orbit, we plan to adjust the shapes via piezoelectric "cells" deposited on the backs of the reflecting surfaces. This presentation investigates how well the corrections might be made. We take a benchmark conical glass element, 410×205 mm, with a 20×20 array of piezoelectric cells 19×9 mm in size. We use finite element analysis to calculate the influence function of each cell. We then simulate the correction via pseudo matrix inversion to calculate the stress to be applied by each cell, considering distortion due to gravity as calculated by finite element analysis, and by putative low order manufacturing distortions described by Legendre polynomials. We describe our algorithm and its performance, and the implications for the sensitivity of the resulting slope errors to the optimization strategy.

Modeling a surface-mounted Lamb wave emission-reception system: applications to structural health monitoring.

PubMed

Moulin, Emmanuel; Grondel, Sébastien; Assaad, Jamal; Duquenne, Laurent

2008-12-01

The work described in this paper is intended to present a simple and efficient way of modeling a full Lamb wave emission and reception system. The emitter behavior and the Lamb wave generation are predicted using a two-dimensional (2D) hybrid finite element-normal mode expansion model. Then the receiver electrical response is obtained from a finite element computation with prescribed displacements. A numerical correction is applied to the 2D results in order to account for the in-plane radiation divergence caused by the finite length of the emitter. The advantage of this modular approach is that realistic configurations can be simulated without performing cumbersome modeling and time-consuming computations. It also provides insight into the physical interpretation of the results. A good agreement is obtained between predicted and measured signals. The range of application of the method is discussed.

SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics

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

Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.

1999-03-01

This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples ofmore » the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.« less

Temperature Control and Numerical Analysis for Mass Concrete Pile Cap of Hai-huang Bridge

NASA Astrophysics Data System (ADS)

Shi, Han; Hao, Yang; Yong-liang, Wang

2018-05-01

In order to study the heat of hydration in massive concrete, this paper takes Hai-huang bridge for engineering background and uses the finite element analysis software of FEA to analyze the heat of hydration effect of the cushion cap. Comparing the measured data with the theory data, the results showed that the concrete crack was controlled effectively and ensure the construction quality by adopted reasonable temperature control measures. The results of the research prove that the measured data was consistent with calculation data, and it proves the accuracy of the finite element analysis. Finally, the study provides certain reference and guiding significance for similar project.

Modeling and Control of the Redundant Parallel Adjustment Mechanism on a Deployable Antenna Panel

PubMed Central

Tian, Lili; Bao, Hong; Wang, Meng; Duan, Xuechao

2016-01-01

With the aim of developing multiple input and multiple output (MIMO) coupling systems with a redundant parallel adjustment mechanism on the deployable antenna panel, a structural control integrated design methodology is proposed in this paper. Firstly, the modal information from the finite element model of the structure of the antenna panel is extracted, and then the mathematical model is established with the Hamilton principle; Secondly, the discrete Linear Quadratic Regulator (LQR) controller is added to the model in order to control the actuators and adjust the shape of the panel. Finally, the engineering practicality of the modeling and control method based on finite element analysis simulation is verified. PMID:27706076

A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form

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

Mu, Lin; Wang, Junping; Ye, Xiu

We developed a new finite element method for the Reissner–Mindlin equations in its primary form by using the weak Galerkin approach. Like other weak Galerkin finite element methods, this one is highly flexible and robust by allowing the use of discontinuous approximating functions on arbitrary shape of polygons and, at the same time, is parameter independent on its stability and convergence. Furthermore, error estimates of optimal order in mesh size h are established for the corresponding weak Galerkin approximations. Numerical experiments are conducted for verifying the convergence theory, as well as suggesting some superconvergence and a uniform convergence of themore » method with respect to the plate thickness.« less

A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-10-04

We developed a new finite element method for the Reissner–Mindlin equations in its primary form by using the weak Galerkin approach. Like other weak Galerkin finite element methods, this one is highly flexible and robust by allowing the use of discontinuous approximating functions on arbitrary shape of polygons and, at the same time, is parameter independent on its stability and convergence. Furthermore, error estimates of optimal order in mesh size h are established for the corresponding weak Galerkin approximations. Numerical experiments are conducted for verifying the convergence theory, as well as suggesting some superconvergence and a uniform convergence of themore » method with respect to the plate thickness.« less

Seismic waves in heterogeneous material: subcell resolution of the discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Castro, Cristóbal E.; Käser, Martin; Brietzke, Gilbert B.

2010-07-01

We present an important extension of the arbitrary high-order discontinuous Galerkin (DG) finite-element method to model 2-D elastic wave propagation in highly heterogeneous material. In this new approach we include space-variable coefficients to describe smooth or discontinuous material variations inside each element using the same numerical approximation strategy as for the velocity-stress variables in the formulation of the elastic wave equation. The combination of the DG method with a time integration scheme based on the solution of arbitrary accuracy derivatives Riemann problems still provides an explicit, one-step scheme which achieves arbitrary high-order accuracy in space and time. Compared to previous formulations the new scheme contains two additional terms in the form of volume integrals. We show that the increasing computational cost per element can be overcompensated due to the improved material representation inside each element as coarser meshes can be used which reduces the total number of elements and therefore computational time to reach a desired error level. We confirm the accuracy of the proposed scheme performing convergence tests and several numerical experiments considering smooth and highly heterogeneous material. As the approximation of the velocity and stress variables in the wave equation and of the material properties in the model can be chosen independently, we investigate the influence of the polynomial material representation on the accuracy of the synthetic seismograms with respect to computational cost. Moreover, we study the behaviour of the new method on strong material discontinuities, in the case where the mesh is not aligned with such a material interface. In this case second-order linear material approximation seems to be the best choice, with higher-order intra-cell approximation leading to potential instable behaviour. For all test cases we validate our solution against the well-established standard fourth-order finite difference and spectral element method.

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

NASA Astrophysics Data System (ADS)

Paul, Prakash

2009-12-01

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

Performance analysis of smart laminated composite plate integrated with distributed AFC material undergoing geometrically nonlinear transient vibrations

NASA Astrophysics Data System (ADS)

Shivakumar, J.; Ashok, M. H.; Khadakbhavi, Vishwanath; Pujari, Sanjay; Nandurkar, Santosh

2018-02-01

The present work focuses on geometrically nonlinear transient analysis of laminated smart composite plates integrated with the patches of Active fiber composites (AFC) using Active constrained layer damping (ACLD) as the distributed actuators. The analysis has been carried out using generalised energy based finite element model. The coupled electromechanical finite element model is derived using Von Karman type nonlinear strain displacement relations and a first-order shear deformation theory (FSDT). Eight-node iso-parametric serendipity elements are used for discretization of the overall plate integrated with AFC patch material. The viscoelastic constrained layer is modelled using GHM method. The numerical results shows the improvement in the active damping characteristics of the laminated composite plates over the passive damping for suppressing the geometrically nonlinear transient vibrations of laminated composite plates with AFC as patch material.

Finite element analysis of structural engineering problems using a viscoplastic model incorporating two back stresses

NASA Technical Reports Server (NTRS)

Arya, Vinod K.; Halford, Gary R.

1993-01-01

The feasibility of a viscoplastic model incorporating two back stresses and a drag strength is investigated for performing nonlinear finite element analyses of structural engineering problems. To demonstrate suitability for nonlinear structural analyses, the model is implemented into a finite element program and analyses for several uniaxial and multiaxial problems are performed. Good agreement is shown between the results obtained using the finite element implementation and those obtained experimentally. The advantages of using advanced viscoplastic models for performing nonlinear finite element analyses of structural components are indicated.

3D digital image correlation methods for full-field vibration measurement

NASA Astrophysics Data System (ADS)

Helfrick, Mark N.; Niezrecki, Christopher; Avitabile, Peter; Schmidt, Timothy

2011-04-01

In the area of modal test/analysis/correlation, significant effort has been expended over the past twenty years in order to make reduced models and to expand test data for correlation and eventual updating of the finite element models. This has been restricted by vibration measurements which are traditionally limited to the location of relatively few applied sensors. Advances in computers and digital imaging technology have allowed 3D digital image correlation (DIC) methods to measure the shape and deformation of a vibrating structure. This technique allows for full-field measurement of structural response, thus providing a wealth of simultaneous test data. This paper presents some preliminary results for the test/analysis/correlation of data measured using the DIC approach along with traditional accelerometers and a scanning laser vibrometer for comparison to a finite element model. The results indicate that all three approaches correlated well with the finite element model and provide validation for the DIC approach for full-field vibration measurement. Some of the advantages and limitations of the technique are presented and discussed.

Damping Enhancement of Composite Panels by Inclusion of Shunted Piezoelectric Patches: A Wave-Based Modelling Approach.

PubMed

Chronopoulos, Dimitrios; Collet, Manuel; Ichchou, Mohamed

2015-02-17

The waves propagating within complex smart structures are hereby computed by employing a wave and finite element method. The structures can be of arbitrary layering and of complex geometric characteristics as long as they exhibit two-dimensional periodicity. The piezoelectric coupling phenomena are considered within the finite element formulation. The mass, stiffness and piezoelectric stiffness matrices of the modelled segment can be extracted using a conventional finite element code. The post-processing of these matrices involves the formulation of an eigenproblem whose solutions provide the phase velocities for each wave propagating within the structure and for any chosen direction of propagation. The model is then modified in order to account for a shunted piezoelectric patch connected to the composite structure. The impact of the energy dissipation induced by the shunted circuit on the total damping loss factor of the composite panel is then computed. The influence of the additional mass and stiffness provided by the attached piezoelectric devices on the wave propagation characteristics of the structure is also investigated.

Finite-element time-domain modeling of electromagnetic data in general dispersive medium using adaptive Padé series

NASA Astrophysics Data System (ADS)

Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin; Zhdanov, Michael S.

2017-12-01

The induced polarization (IP) method has been widely used in geophysical exploration to identify the chargeable targets such as mineral deposits. The inversion of the IP data requires modeling the IP response of 3D dispersive conductive structures. We have developed an edge-based finite-element time-domain (FETD) modeling method to simulate the electromagnetic (EM) fields in 3D dispersive medium. We solve the vector Helmholtz equation for total electric field using the edge-based finite-element method with an unstructured tetrahedral mesh. We adopt the backward propagation Euler method, which is unconditionally stable, with semi-adaptive time stepping for the time domain discretization. We use the direct solver based on a sparse LU decomposition to solve the system of equations. We consider the Cole-Cole model in order to take into account the frequency-dependent conductivity dispersion. The Cole-Cole conductivity model in frequency domain is expanded using a truncated Padé series with adaptive selection of the center frequency of the series for early and late time. This approach can significantly increase the accuracy of FETD modeling.

A downloadable meshed human canine tooth model with PDL and bone for finite element simulations.

PubMed

Boryor, Andrew; Hohmann, Ansgar; Geiger, Martin; Wolfram, Uwe; Sander, Christian; Sander, Franz Günter

2009-09-01

The aim of this study is to relieve scientists from the complex and time-consuming task of model generation by providing a model of a canine tooth and its periradicular tissues for Finite Element Method (FEM) simulations. This was achieved with diverse commercial software, based on a micro-computed tomography of the specimen. The Finite Element (FE) Model consists of enamel, dentin, nerve (innervation), periodontal ligament (PDL), and the surrounding cortical bone with trabecular structure. The area and volume meshes are of a very high quality in order to represent the model in a detailed form. Material properties are to be set individually by every user. The tooth model is provided for Abaqus, Ansys, HyperMesh, Nastran and as STL files, in an ASCII format for free download. This can help reduce the cost and effort of generating a tooth model for some research institutions, and may encourage other research groups to provide their high quality models for other researchers. By providing FE models, research results, especially FEM simulations, could be easily verified by others.

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

NASA Astrophysics Data System (ADS)

Hansen, Kirk; Arzani, Amirhossein; Shadden, Shawn

2016-11-01

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

The Applicability of the Generalized Method of Cells for Analyzing Discontinuously Reinforced Composites

NASA Technical Reports Server (NTRS)

Pahr, D. H.; Arnold, S. M.

2001-01-01

The paper begins with a short overview of the recent work done in the field of discontinuous reinforced composites, focusing on the different parameters which influence the material behavior of discontinuous reinforced composites, as well as the various analysis approaches undertaken. Based on this overview it became evident, that in order to investigate the enumerated effects in an efficient and comprehensive manner, an alternative approach to the computationally intensive finite-element based micromechanics approach is required. Therefore, an investigation is conducted to demonstrate the utility of utilizing the generalized method of cells (GMC), a semi-analytical micromechanics-based approach, to simulate the elastic and elastoplastic material behavior of aligned short fiber composites. The results are compared with (1) simulations using other micromechanical based mean field models and finite element (FE) unit cell models found in the literature given elastic material behavior, as well as (2) finite element unit cell and a new semianalytical elastoplastic shear lag model in the inelastic range. GMC is shown to definitely have a window of applicability when simulating discontinuously reinforced composite material behavior.

The Applicability of the Generalized Method of Cells for Analyzing Discontinuously Reinforced Composites

NASA Technical Reports Server (NTRS)

Pahr, D. H.; Arnold, S. M.

2001-01-01

The paper begins with a short overview of the recent work done in the field of discontinuous reinforced composites, focusing on the different parameters which influence the material behavior of discontinuous reinforced composites, as well as the various analysis approaches undertaken. Based on this overview it became evident that in order to investigate the enumerated effects in an efficient and comprehensive manner, an alternative approach to the computationally intensive finite-element based micromechanics approach is required. Therefore, an investigation is conducted to demonstrate the utility of utilizing the generalized method of cells (GMC), a semi-analytical micromechanics-based approach, to simulate the elastic and elastoplastic material behavior of aligned short fiber composites. The results are compared with simulations using other micromechanical based mean field models and finite element (FE) unit cell models found in the literature given elastic material behavior, as well as finite element unit cell and a new semianalytical elastoplastic shear lag model in the inelastic range. GMC is shown to definitely have a window of applicability when simulating discontinuously reinforced composite material behavior.

A nonlinear dynamic finite element approach for simulating muscular hydrostats.

PubMed

Vavourakis, V; Kazakidi, A; Tsakiris, D P; Ekaterinaris, J A

2014-01-01

An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching.

Application of Dynamic Analysis in Semi-Analytical Finite Element Method

PubMed Central

Oeser, Markus

2017-01-01

Analyses of dynamic responses are significantly important for the design, maintenance and rehabilitation of asphalt pavement. In order to evaluate the dynamic responses of asphalt pavement under moving loads, a specific computational program, SAFEM, was developed based on a semi-analytical finite element method. This method is three-dimensional and only requires a two-dimensional FE discretization by incorporating Fourier series in the third dimension. In this paper, the algorithm to apply the dynamic analysis to SAFEM was introduced in detail. Asphalt pavement models under moving loads were built in the SAFEM and commercial finite element software ABAQUS to verify the accuracy and efficiency of the SAFEM. The verification shows that the computational accuracy of SAFEM is high enough and its computational time is much shorter than ABAQUS. Moreover, experimental verification was carried out and the prediction derived from SAFEM is consistent with the measurement. Therefore, the SAFEM is feasible to reliably predict the dynamic response of asphalt pavement under moving loads, thus proving beneficial to road administration in assessing the pavement’s state. PMID:28867813

Adaptive Finite Element Methods for Continuum Damage Modeling

NASA Technical Reports Server (NTRS)

Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.

1995-01-01

The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.

The effect of trench width on the behavior of buried rigid pipes

NASA Astrophysics Data System (ADS)

Balkaya, Müge; Saǧlamer, Ahmet

2014-12-01

In this study, in order to determine the effect of trench width (Bd) on the behavior of buried rigid pipes, a concrete pipe having an outside diameter of 150 cm and wall thickness (t) of 15 cm was analyzed using 2D PLAXIS finite element program. In the analyses, three different trench widths (Bd = 2.20 m, 3.40 m, and 4.40 m) were modeled. The results of the analyses indicated that, as the width of the trench increases, the axial force, shear force, bending moment, effective normal stress, and the earth load acting on the pipe increased. The variations of the loads acting on the pipe due to the increasing trench widths were also evaluated using the Marston load theory. When the loads calculated by the Marston Load Theory and the finite element analysis were compared with each other, it was seen that the Marston Load Theory resulted in slightly higher load values than the finite element analysis. On the other hand, for the two methods, the loads acting on the pipe increased with increasing trench width.

Damping Enhancement of Composite Panels by Inclusion of Shunted Piezoelectric Patches: A Wave-Based Modelling Approach

PubMed Central

Chronopoulos, Dimitrios; Collet, Manuel; Ichchou, Mohamed; Shah, Tahir

2015-01-01

The waves propagating within complex smart structures are hereby computed by employing a wave and finite element method. The structures can be of arbitrary layering and of complex geometric characteristics as long as they exhibit two-dimensional periodicity. The piezoelectric coupling phenomena are considered within the finite element formulation. The mass, stiffness and piezoelectric stiffness matrices of the modelled segment can be extracted using a conventional finite element code. The post-processing of these matrices involves the formulation of an eigenproblem whose solutions provide the phase velocities for each wave propagating within the structure and for any chosen direction of propagation. The model is then modified in order to account for a shunted piezoelectric patch connected to the composite structure. The impact of the energy dissipation induced by the shunted circuit on the total damping loss factor of the composite panel is then computed. The influence of the additional mass and stiffness provided by the attached piezoelectric devices on the wave propagation characteristics of the structure is also investigated. PMID:28787972

High order Nyström method for elastodynamic scattering

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

Axisymmetric solid elements by a rational hybrid stress method

NASA Technical Reports Server (NTRS)

Tian, Z.; Pian, T. H. H.

1985-01-01

Four-node axisymmetric solid elements are derived by a new version of hybrid method for which the assumed stresses are expressed in complete polynomials in natural coordinates. The stress equilibrium conditions are introduced through the use of additional displacements as Lagrange multipliers. A rational procedure is to choose the displacement terms such that the resulting strains are also of complete polynomials of the same order. Example problems all indicate that elements obtained by this procedure lead to better results in displacements and stresses than that by other finite elements.

Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.; Ovall, J.; Holst, M.

2014-12-01

We present a parallel goal-oriented adaptive finite element method for accurate and efficient electromagnetic (EM) modeling of complex 3D structures. An unstructured tetrahedral mesh allows this approach to accommodate arbitrarily complex 3D conductivity variations and a priori known boundaries. The total electric field is approximated by the lowest order linear curl-conforming shape functions and the discretized finite element equations are solved by a sparse LU factorization. Accuracy of the finite element solution is achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by a goal-oriented error estimator that uses a dual-weighted residual method to optimize the mesh for accurate EM responses at the locations of the EM receivers. As a result, the mesh refinement is highly efficient since it only targets the elements where the inaccuracy of the solution corrupts the response at the possibly distant locations of the EM receivers. We compare the accuracy and efficiency of two approaches for estimating the primary residual error required at the core of this method: one uses local element and inter-element residuals and the other relies on solving a global residual system using a hierarchical basis. For computational efficiency our method follows the Bank-Holst algorithm for parallelization, where solutions are computed in subdomains of the original model. To resolve the load-balancing problem, this approach applies a spectral bisection method to divide the entire model into subdomains that have approximately equal error and the same number of receivers. The finite element solutions are then computed in parallel with each subdomain carrying out goal-oriented adaptive mesh refinement independently. We validate the newly developed algorithm by comparison with controlled-source EM solutions for 1D layered models and with 2D results from our earlier 2D goal oriented adaptive refinement code named MARE2DEM. We demonstrate the performance and parallel scaling of this algorithm on a medium-scale computing cluster with a marine controlled-source EM example that includes a 3D array of receivers located over a 3D model that includes significant seafloor bathymetry variations and a heterogeneous subsurface.

Mass-corrections for the conservative coupling of flow and transport on collocated meshes

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

Waluga, Christian, E-mail: waluga@ma.tum.de; Wohlmuth, Barbara; Rüde, Ulrich

2016-01-15

Buoyancy-driven flow models demand a careful treatment of the mass-balance equation to avoid spurious source and sink terms in the non-linear coupling between flow and transport. In the context of finite-elements, it is therefore commonly proposed to employ sufficiently rich pressure spaces, containing piecewise constant shape functions to obtain local or even strong mass-conservation. In three-dimensional computations, this usually requires nonconforming approaches, special meshes or higher order velocities, which make these schemes prohibitively expensive for some applications and complicate the implementation into legacy code. In this paper, we therefore propose a lean and conservatively coupled scheme based on standard stabilizedmore » linear equal-order finite elements for the Stokes part and vertex-centered finite volumes for the energy equation. We show that in a weak mass-balance it is possible to recover exact conservation properties by a local flux-correction which can be computed efficiently on the control volume boundaries of the transport mesh. We discuss implementation aspects and demonstrate the effectiveness of the flux-correction by different two- and three-dimensional examples which are motivated by geophysical applications.« less

Design synthesis and optimization of permanent magnet synchronous machines based on computationally-efficient finite element analysis

NASA Astrophysics Data System (ADS)

Sizov, Gennadi Y.

In this dissertation, a model-based multi-objective optimal design of permanent magnet ac machines, supplied by sine-wave current regulated drives, is developed and implemented. The design procedure uses an efficient electromagnetic finite element-based solver to accurately model nonlinear material properties and complex geometric shapes associated with magnetic circuit design. Application of an electromagnetic finite element-based solver allows for accurate computation of intricate performance parameters and characteristics. The first contribution of this dissertation is the development of a rapid computational method that allows accurate and efficient exploration of large multi-dimensional design spaces in search of optimum design(s). The computationally efficient finite element-based approach developed in this work provides a framework of tools that allow rapid analysis of synchronous electric machines operating under steady-state conditions. In the developed modeling approach, major steady-state performance parameters such as, winding flux linkages and voltages, average, cogging and ripple torques, stator core flux densities, core losses, efficiencies and saturated machine winding inductances, are calculated with minimum computational effort. In addition, the method includes means for rapid estimation of distributed stator forces and three-dimensional effects of stator and/or rotor skew on the performance of the machine. The second contribution of this dissertation is the development of the design synthesis and optimization method based on a differential evolution algorithm. The approach relies on the developed finite element-based modeling method for electromagnetic analysis and is able to tackle large-scale multi-objective design problems using modest computational resources. Overall, computational time savings of up to two orders of magnitude are achievable, when compared to current and prevalent state-of-the-art methods. These computational savings allow one to expand the optimization problem to achieve more complex and comprehensive design objectives. The method is used in the design process of several interior permanent magnet industrial motors. The presented case studies demonstrate that the developed finite element-based approach practically eliminates the need for using less accurate analytical and lumped parameter equivalent circuit models for electric machine design optimization. The design process and experimental validation of the case-study machines are detailed in the dissertation.

Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom

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

Iaroshenko, Oleksandr; Gyrya, Vitaliy; Manzini, Gianmarco

2016-09-01

In this work we consider a modification to an arbitrary order mixed mimetic finite difference method (MFD) for a diffusion equation on general polygonal meshes [1]. The modification is based on moving some degrees of freedom (DoF) for a flux variable from edges to vertices. We showed that for a non-degenerate element this transformation is locally equivalent, i.e. there is a one-to-one map between the new and the old DoF. Globally, on the other hand, this transformation leads to a reduction of the total number of degrees of freedom (by up to 40%) and additional continuity of the discrete flux.

Finite element analysis and genetic algorithm optimization design for the actuator placement on a large adaptive structure

NASA Astrophysics Data System (ADS)

Sheng, Lizeng

The dissertation focuses on one of the major research needs in the area of adaptive/intelligent/smart structures, the development and application of finite element analysis and genetic algorithms for optimal design of large-scale adaptive structures. We first review some basic concepts in finite element method and genetic algorithms, along with the research on smart structures. Then we propose a solution methodology for solving a critical problem in the design of a next generation of large-scale adaptive structures---optimal placements of a large number of actuators to control thermal deformations. After briefly reviewing the three most frequently used general approaches to derive a finite element formulation, the dissertation presents techniques associated with general shell finite element analysis using flat triangular laminated composite elements. The element used here has three nodes and eighteen degrees of freedom and is obtained by combining a triangular membrane element and a triangular plate bending element. The element includes the coupling effect between membrane deformation and bending deformation. The membrane element is derived from the linear strain triangular element using Cook's transformation. The discrete Kirchhoff triangular (DKT) element is used as the plate bending element. For completeness, a complete derivation of the DKT is presented. Geometrically nonlinear finite element formulation is derived for the analysis of adaptive structures under the combined thermal and electrical loads. Next, we solve the optimization problems of placing a large number of piezoelectric actuators to control thermal distortions in a large mirror in the presence of four different thermal loads. We then extend this to a multi-objective optimization problem of determining only one set of piezoelectric actuator locations that can be used to control the deformation in the same mirror under the action of any one of the four thermal loads. A series of genetic algorithms, GA Version 1, 2 and 3, were developed to find the optimal locations of piezoelectric actuators from the order of 1021 ˜ 1056 candidate placements. Introducing a variable population approach, we improve the flexibility of selection operation in genetic algorithms. Incorporating mutation and hill climbing into micro-genetic algorithms, we are able to develop a more efficient genetic algorithm. Through extensive numerical experiments, we find that the design search space for the optimal placements of a large number of actuators is highly multi-modal and that the most distinct nature of genetic algorithms is their robustness. They give results that are random but with only a slight variability. The genetic algorithms can be used to get adequate solution using a limited number of evaluations. To get the highest quality solution, multiple runs including different random seed generators are necessary. The investigation time can be significantly reduced using a very coarse grain parallel computing. Overall, the methodology of using finite element analysis and genetic algorithm optimization provides a robust solution approach for the challenging problem of optimal placements of a large number of actuators in the design of next generation of adaptive structures.

Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations.

PubMed

Nick, H M; Paluszny, A; Blunt, M J; Matthai, S K

2011-11-01

A second order in space accurate implicit scheme for time-dependent advection-dispersion equations and a discrete fracture propagation model are employed to model solute transport in porous media. We study the impact of the fractures on mass transport and dispersion. To model flow and transport, pressure and transport equations are integrated using a finite-element, node-centered finite-volume approach. Fracture geometries are incrementally developed from a random distributions of material flaws using an adoptive geomechanical finite-element model that also produces fracture aperture distributions. This quasistatic propagation assumes a linear elastic rock matrix, and crack propagation is governed by a subcritical crack growth failure criterion. Fracture propagation, intersection, and closure are handled geometrically. The flow and transport simulations are separately conducted for a range of fracture densities that are generated by the geomechanical finite-element model. These computations show that the most influential parameters for solute transport in fractured porous media are as follows: fracture density and fracture-matrix flux ratio that is influenced by matrix permeability. Using an equivalent fracture aperture size, computed on the basis of equivalent permeability of the system, we also obtain an acceptable prediction of the macrodispersion of poorly interconnected fracture networks. The results hold for fractures at relatively low density.

COMPARISONS OF THE FINITE-ELEMENT-WITH-DISCONTIGUOUS-SUPPORT METHOD TO CONTINUOUS-ENERGY MONTE CARLO FOR PIN-CELL PROBLEMS

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

A. T. Till; M. Hanuš; J. Lou

The standard multigroup (MG) method for energy discretization of the transport equation can be sensitive to approximations in the weighting spectrum chosen for cross-section averaging. As a result, MG often inaccurately treats important phenomena such as self-shielding variations across a material. From a finite-element viewpoint, MG uses a single fixed basis function (the pre-selected spectrum) within each group, with no mechanism to adapt to local solution behavior. In this work, we introduce the Finite-Element-with-Discontiguous-Support (FEDS) method, whose only approximation with respect to energy is that the angular flux is a linear combination of unknowns multiplied by basis functions. A basismore » function is non-zero only in the discontiguous set of energy intervals associated with its energy element. Discontiguous energy elements are generalizations of bands and are determined by minimizing a norm of the difference between snapshot spectra and their averages over the energy elements. We begin by presenting the theory of the FEDS method. We then compare to continuous-energy Monte Carlo for one-dimensional slab and two-dimensional pin-cell problem. We find FEDS to be accurate and efficient at producing quantities of interest such as reaction rates and eigenvalues. Results show that FEDS converges at a rate that is approximately first-order in the number of energy elements and that FEDS is less sensitive to weighting spectrum than standard MG.« less

Fatigue Life Variability in Large Aluminum Forgings with Residual Stress

DTIC Science & Technology

2011-07-01

been conducted. A detailed finite element analysis of the forge/ quench /coldwork/machine process was performed in order to predict the bulk residual...forge/ quench /coldwork/machine process was performed in order to predict the bulk residual stresses in a fictitious aluminum bulkhead. The residual...continues to develop the capability for computational simulation of the forge, quench , cold work and machining processes. In order to handle the

Computational aspects of sensitivity calculations in linear transient structural analysis. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Greene, William H.

1990-01-01

A study was performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal of the study was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semi-analytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. In several cases this fixed mode approach resulted in very poor approximations of the stress sensitivities. Almost all of the original modes were required for an accurate sensitivity and for small numbers of modes, the accuracy was extremely poor. To overcome this poor accuracy, two semi-analytical techniques were developed. The first technique accounts for the change in eigenvectors through approximate eigenvector derivatives. The second technique applies the mode acceleration method of transient analysis to the sensitivity calculations. Both result in accurate values of the stress sensitivities with a small number of modes and much lower computational costs than if the vibration modes were recalculated and then used in an overall finite difference method.

Traction free finite elements with the assumed stress hybrid model. M.S. Thesis, 1981

NASA Technical Reports Server (NTRS)

Kafie, Kurosh

1991-01-01

An effective approach in the finite element analysis of the stress field at the traction free boundary of a solid continuum was studied. Conventional displacement and assumed stress finite elements were used in the determination of stress concentrations around circular and elliptical holes. Specialized hybrid elements were then developed to improve the satisfaction of prescribed traction boundary conditions. Results of the stress analysis indicated that finite elements which exactly satisfy the free stress boundary conditions are the most accurate and efficient in such problems. A general approach for hybrid finite elements which incorporate traction free boundaries of arbitrary geometry was formulated.

Phase-space finite elements in a least-squares solution of the transport equation

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

Drumm, C.; Fan, W.; Pautz, S.

2013-07-01

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less

Quality-assurance study of the special - purpose finite-element program - SPECTROM: I. Thermal, thermoelastic, and viscoelastic problems. [Comparison with MARC-CDC

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

Wagner, R.A.

1980-12-01

This comparison study involves a preliminary verification of finite element calculations. The methodology of the comparison study consists of solving four example problems with both the SPECTROM finite element program and the MARC-CDC general purpose finite element program. The results show close agreement for all example problems.

Finite Element Analysis of Particle Ionization within Carbon Nanotube Ion Micro Thruster

DTIC Science & Technology

2017-12-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS Approved for public release. Distribution is unlimited. FINITE ELEMENT ...AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE FINITE ELEMENT ANALYSIS OF PARTICLE IONIZATION WITHIN CARBON NANOTUBE ION MICRO THRUSTER 5...simulation, carbon nanotube simulation, microsatellite, finite element analysis, electric field, particle tracing 15. NUMBER OF PAGES 55 16. PRICE

Modeling and control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.

1988-01-01

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

A finite element code for modelling tracer transport in a non-isothermal two-phase flow system for CO2 geological storage characterization

NASA Astrophysics Data System (ADS)

Tong, F.; Niemi, A. P.; Yang, Z.; Fagerlund, F.; Licha, T.; Sauter, M.

2011-12-01

This paper presents a new finite element method (FEM) code for modeling tracer transport in a non-isothermal two-phase flow system. The main intended application is simulation of the movement of so-called novel tracers for the purpose of characterization of geologically stored CO2 and its phase partitioning and migration in deep saline formations. The governing equations are based on the conservation of mass and energy. Among the phenomena accounted for are liquid-phase flow, gas flow, heat transport and the movement of the novel tracers. The movement of tracers includes diffusion and the advection associated with the gas and liquid flow. The temperature, gas pressure, suction, concentration of tracer in liquid phase and concentration of tracer in gas phase are chosen as the five primary variables. Parameters such as the density, viscosity, thermal expansion coefficient are expressed in terms of the primary variables. The governing equations are discretized in space using the Galerkin finite element formulation, and are discretized in time by one-dimensional finite difference scheme. This leads to an ill-conditioned FEM equation that has many small entries along the diagonal of the non-symmetric coefficient matrix. In order to deal with the problem of non-symmetric ill-conditioned matrix equation, special techniques are introduced . Firstly, only nonzero elements of the matrix need to be stored. Secondly, it is avoided to directly solve the whole large matrix. Thirdly, a strategy has been used to keep the diversity of solution methods in the calculation process. Additionally, an efficient adaptive mesh technique is included in the code in order to track the wetting front. The code has been validated against several classical analytical solutions, and will be applied for simulating the CO2 injection experiment to be carried out at the Heletz site, Israel, as part of the EU FP7 project MUSTANG.

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

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Use of edge-based finite elements for solving three dimensional scattering problems

NASA Technical Reports Server (NTRS)

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

1991-01-01

Edge based finite elements are free from drawbacks associated with node based vectorial finite elements and are, therefore, ideal for solving 3-D scattering problems. The finite element discretization using edge elements is checked by solving for the resonant frequencies of a closed inhomogeneously filled metallic cavity. Great improvements in accuracy are observed when compared to the classical node based approach with no penalty in terms of computational time and with the expected absence of spurious modes. A performance comparison between the edge based tetrahedra and rectangular brick elements is carried out and tetrahedral elements are found to be more accurate than rectangular bricks for a given storage intensity. A detailed formulation for the scattering problem with various approaches for terminating the finite element mesh is also presented.

Specialty functions singularity mechanics problems

NASA Technical Reports Server (NTRS)

Sarigul, Nesrin

1989-01-01

The focus is in the development of more accurate and efficient advanced methods for solution of singular problems encountered in mechanics. At present, finite element methods in conjunction with special functions, boolean sum and blending interpolations are being considered. In dealing with systems which contain a singularity, special finite elements are being formulated to be used in singular regions. Further, special transition elements are being formulated to couple the special element to the mesh that models the rest of the system, and to be used in conjunction with 1-D, 2-D and 3-D elements within the same mesh. Computational simulation with a least squares fit is being utilized to construct special elements, if there is an unknown singularity in the system. A novel approach is taken in formulation of the elements in that: (1) the material properties are modified to include time, temperature, coordinate and stress dependant behavior within the element; (2) material properties vary at nodal points of the elements; (3) a hidden-symbolic computation scheme is developed and utilized in formulating the elements; and (4) special functions and boolean sum are utilized in order to interpolate the field variables and their derivatives along the boundary of the elements. It may be noted that the proposed methods are also applicable to fluids and coupled problems.

A Finite Element Analysis of a Class of Problems in Elasto-Plasticity with Hidden Variables.

DTIC Science & Technology

1985-09-01

RD-R761 642 A FINITE ELEMENT ANALYSIS OF A CLASS OF PROBLEMS IN 1/2 ELASTO-PLASTICITY MIlT (U) TEXAS INST FOR COMPUTATIONAL MECHANICS AUSTIN J T ODEN...end Subtitle) S. TYPE OF REPORT & PERIOD COVERED A FINITE ELEMENT ANALYSIS OF A CLASS OF PROBLEMS Final Report IN ELASTO-PLASTICITY WITH HIDDEN...aieeoc ede It neceeeary nd Identify by block number) ;"Elastoplasticity, finite deformations; non-convex analysis ; finite element methods, metal forming

Stabilized Finite Elements in FUN3D

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Newman, James C.; Karman, Steve L.

2017-01-01

A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

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.

SUPG Finite Element Simulations of Compressible Flows

NASA Technical Reports Server (NTRS)

Kirk, Brnjamin, S.

2006-01-01

The Streamline-Upwind Petrov-Galerkin (SUPG) finite element simulations of compressible flows is presented. The topics include: 1) Introduction; 2) SUPG Galerkin Finite Element Methods; 3) Applications; and 4) Bibliography.

Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations

USGS Publications Warehouse

Walters, R.A.; Carey, G.F.

1983-01-01

The origin and nature of spurious oscillation modes that appear in mixed finite element methods are examined. In particular, the shallow water equations are considered and a modal analysis for the one-dimensional problem is developed. From the resulting dispersion relations we find that the spurious modes in elevation are associated with zero frequency and large wave number (wavelengths of the order of the nodal spacing) and consequently are zero-velocity modes. The spurious modal behavior is the result of the finite spatial discretization. By means of an artificial compressibility and limiting argument we are able to resolve the similar problem for the Navier-Stokes equations. The relationship of this simpler analysis to alternative consistency arguments is explained. This modal approach provides an explanation of the phenomenon in question and permits us to deduce the cause of the very complex behavior of spurious modes observed in numerical experiments with the shallow water equations and Navier-Stokes equations. Furthermore, this analysis is not limited to finite element formulations, but is also applicable to finite difference formulations. ?? 1983.

An Unstructured Finite Volume Approach for Structural Dynamics in Response to Fluid Motions.

PubMed

Xia, Guohua; Lin, Ching-Long

2008-04-01

A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.

Calculating the Malliavin derivative of some stochastic mechanics problems

PubMed Central

Hauseux, Paul; Hale, Jack S.

2017-01-01

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. PMID:29261776

Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES

NASA Astrophysics Data System (ADS)

Marras, Simone; Nazarov, Murtazo; Giraldo, Francis X.

2015-11-01

The high order spectral element approximation of the Euler equations is stabilized via a dynamic sub-grid scale model (Dyn-SGS). This model was originally designed for linear finite elements to solve compressible flows at large Mach numbers. We extend its application to high-order spectral elements to solve the Euler equations of low Mach number stratified flows. The major justification of this work is twofold: stabilization and large eddy simulation are achieved via one scheme only. Because the diffusion coefficients of the regularization stresses obtained via Dyn-SGS are residual-based, the effect of the artificial diffusion is minimal in the regions where the solution is smooth. The direct consequence is that the nominal convergence rate of the high-order solution of smooth problems is not degraded. To our knowledge, this is the first application in atmospheric modeling of a spectral element model stabilized by an eddy viscosity scheme that, by construction, may fulfill stabilization requirements, can model turbulence via LES, and is completely free of a user-tunable parameter. From its derivation, it will be immediately clear that Dyn-SGS is independent of the numerical method; it could be implemented in a discontinuous Galerkin, finite volume, or other environments alike. Preliminary discontinuous Galerkin results are reported as well. The straightforward extension to non-linear scalar problems is also described. A suite of 1D, 2D, and 3D test cases is used to assess the method, with some comparison against the results obtained with the most known Lilly-Smagorinsky SGS model.

A parametric model order reduction technique for poroelastic finite element models.

PubMed

Lappano, Ettore; Polanz, Markus; Desmet, Wim; Mundo, Domenico

2017-10-01

This research presents a parametric model order reduction approach for vibro-acoustic problems in the frequency domain of systems containing poroelastic materials (PEM). The method is applied to the Finite Element (FE) discretization of the weak u-p integral formulation based on the Biot-Allard theory and makes use of reduced basis (RB) methods typically employed for parametric problems. The parametric reduction is obtained rewriting the Biot-Allard FE equations for poroelastic materials using an affine representation of the frequency (therefore allowing for RB methods) and projecting the frequency-dependent PEM system on a global reduced order basis generated with the proper orthogonal decomposition instead of standard modal approaches. This has proven to be better suited to describe the nonlinear frequency dependence and the strong coupling introduced by damping. The methodology presented is tested on two three-dimensional systems: in the first experiment, the surface impedance of a PEM layer sample is calculated and compared with results of the literature; in the second, the reduced order model of a multilayer system coupled to an air cavity is assessed and the results are compared to those of the reference FE model.

Finite Element Modeling of Scattering from Underwater Proud and Buried Military Munitions

DTIC Science & Technology

2017-02-28

FINAL REPORT Finite Element Modeling of Scattering from Underwater Proud and Buried Military Munitions SERDP Project MR-2408 JULY 2017...solution and the red dash-dot line repre- sents the coupled finite -boundary element solution. . . . . . . . . . . . . . . . . . 11 3 The scattering...dot line represents the coupled finite -boundary element solution. . . . . . . . 11 i 4 The scattering amplitude as a function of the receiver angle for

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Cognitive-graphic method for constructing of hierarchical forms of basic functions of biquadratic finite element

NASA Astrophysics Data System (ADS)

Astionenko, I. O.; Litvinenko, O. I.; Osipova, N. V.; Tuluchenko, G. Ya.; Khomchenko, A. N.

2016-10-01

Recently the interpolation bases of the hierarchical type have been used for the problem solving of the approximation of multiple arguments functions (such as in the finite-element method). In this work the cognitive graphical method of constructing of the hierarchical form bases on the serendipity finite elements is suggested, which allowed to get the alternative bases on a biquadratic finite element from the serendipity family without internal knots' inclusion. The cognitive-graphic method allowed to improve the known interpolation procedure of Taylor and to get the modified elements with irregular arrangement of knots. The proposed procedures are universal and are spread in the area of finite-elements.

Engine dynamic analysis with general nonlinear finite element codes. Part 2: Bearing element implementation overall numerical characteristics and benchmaking

NASA Technical Reports Server (NTRS)

Padovan, J.; Adams, M.; Fertis, J.; Zeid, I.; Lam, P.

1982-01-01

Finite element codes are used in modelling rotor-bearing-stator structure common to the turbine industry. Engine dynamic simulation is used by developing strategies which enable the use of available finite element codes. benchmarking the elements developed are benchmarked by incorporation into a general purpose code (ADINA); the numerical characteristics of finite element type rotor-bearing-stator simulations are evaluated through the use of various types of explicit/implicit numerical integration operators. Improving the overall numerical efficiency of the procedure is improved.

Extension to linear dynamics for hybrid stress finite element formulation based on additional displacements

NASA Astrophysics Data System (ADS)

Sumihara, K.

Based upon legitimate variational principles, one microscopic-macroscopic finite element formulation for linear dynamics is presented by Hybrid Stress Finite Element Method. The microscopic application of Geometric Perturbation introduced by Pian and the introduction of infinitesimal limit core element (Baby Element) have been consistently combined according to the flexible and inherent interpretation of the legitimate variational principles initially originated by Pian and Tong. The conceptual development based upon Hybrid Finite Element Method is extended to linear dynamics with the introduction of physically meaningful higher modes.

Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2005-01-01

A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.

Pre- and postprocessing techniques for determining goodness of computational meshes

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Westermann, T.; Bass, J. M.

1993-01-01

Research in error estimation, mesh conditioning, and solution enhancement for finite element, finite difference, and finite volume methods has been incorporated into AUDITOR, a modern, user-friendly code, which operates on 2D and 3D unstructured neutral files to improve the accuracy and reliability of computational results. Residual error estimation capabilities provide local and global estimates of solution error in the energy norm. Higher order results for derived quantities may be extracted from initial solutions. Within the X-MOTIF graphical user interface, extensive visualization capabilities support critical evaluation of results in linear elasticity, steady state heat transfer, and both compressible and incompressible fluid dynamics.

On the performance of piezoelectric harvesters loaded by finite width impulses

NASA Astrophysics Data System (ADS)

Doria, A.; Medè, C.; Desideri, D.; Maschio, A.; Codecasa, L.; Moro, F.

2018-02-01

The response of cantilevered piezoelectric harvesters loaded by finite width impulses of base acceleration is studied analytically in the frequency domain in order to identify the parameters that influence the generated voltage. Experimental tests are then performed on harvesters loaded by hammer impacts. The latter are used to confirm analytical results and to validate a linear finite element (FE) model of a unimorph harvester. The FE model is, in turn, used to extend analytical results to more general harvesters (tapered, inverse tapered, triangular) and to more general impulses (heel strike in human gait). From analytical and numerical results design criteria for improving harvester performance are obtained.

Computational fluid mechanics utilizing the variational principle of modeling damping seals

NASA Technical Reports Server (NTRS)

Abernathy, J. M.

1986-01-01

A computational fluid dynamics code for application to traditional incompressible flow problems has been developed. The method is actually a slight compressibility approach which takes advantage of the bulk modulus and finite sound speed of all real fluids. The finite element numerical analog uses a dynamic differencing scheme based, in part, on a variational principle for computational fluid dynamics. The code was developed in order to study the feasibility of damping seals for high speed turbomachinery. Preliminary seal analyses have been performed.

A High-Order, Adaptive, Discontinuous Galerkin Finite Element Method for the Reynolds-Averaged Navier-Stokes Equations

DTIC Science & Technology

2008-09-01

Element Method. Wellesley- Cambridge Press, Wellesly, MA, 1988. [97] E. F. Toro . Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical...introducing additional state variables, are generally asymptotically dual consistent. Numerical results are presented to confirm the results of the analysis...dependence on the state gradient is handled by introducing additional state variables, are generally asymptotically dual consistent. Numerical results are

Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem

NASA Technical Reports Server (NTRS)

Wu, R. W.; Witmer, E. A.

1972-01-01

Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.

Wave Scattering in Heterogeneous Media using the Finite Element Method

DTIC Science & Technology

2016-10-21

AFRL-AFOSR-JP-TR-2016-0086 Wave Scattering in Heterogeneous Media using the Finite Element Method Chiruvai Vendhan INDIAN INSTITUTE OF TECHNOLOGY...Scattering in Heterogeneous Media using the Finite Element Method 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA2386-12-1-4026 5c.  PROGRAM ELEMENT NUMBER 61102F 6...14.  ABSTRACT The primary aim of this study is to develop a finite element model for elastic scattering by axisymmetric bodies submerged in a

Quasi-Static Viscoelastic Finite Element Model of an Aircraft Tire

NASA Technical Reports Server (NTRS)

Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.

1999-01-01

An elastic large displacement thick-shell mixed finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at the 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 is included in the mixed variational functional. The nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the nonlinear elastic 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 computationally simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.

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.

Refinement of Out of Circularity and Thickness Measurements of a Cylinder for Finite Element Analysis

DTIC Science & Technology

2016-09-01

UNCLASSIFIED UNCLASSIFIED Refinement of Out of Circularity and Thickness Measurements of a Cylinder for Finite Element Analysis...significant effect on the collapse strength and must be accurately represented in finite element analysis to obtain accurate results. Often it is necessary...to interpolate measurements from a relatively coarse grid to a refined finite element model and methods that have wide general acceptance are

Artificial Boundary Conditions for Finite Element Model Update and Damage Detection

DTIC Science & Technology

2017-03-01

BOUNDARY CONDITIONS FOR FINITE ELEMENT MODEL UPDATE AND DAMAGE DETECTION by Emmanouil Damanakis March 2017 Thesis Advisor: Joshua H. Gordis...REPORT TYPE AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE ARTIFICIAL BOUNDARY CONDITIONS FOR FINITE ELEMENT MODEL UPDATE AND DAMAGE DETECTION...release. Distribution is unlimited. 12b. DISTRIBUTION CODE 13. ABSTRACT (maximum 200 words) In structural engineering, a finite element model is often

Angular Random Walk Estimation of a Time-Domain Switching Micromachined Gyroscope

DTIC Science & Technology

2016-10-19

1 2. PARAMETRIC SYSTEM IDENTIFICATION BASED ON TIME-DOMAIN SWITCHING ........ 2 3. FINITE ELEMENT MODELING OF RESONATOR...8 3. FINITE ELEMENT MODELING OF RESONATOR This section details basic finite element modeling of the resonator used with the TDSMG. While it...Based on finite element simulations of the employed resonator, it is found that the effects of thermomechanical noise is on par with 10 ps of timing

Verification of finite element analysis of fixed partial denture with in vitro electronic strain measurement.

PubMed

Wang, Gaoqi; Zhang, Song; Bian, Cuirong; Kong, Hui

2016-01-01

The purpose of the study was to verify the finite element analysis model of three-unite fixed partial denture with in vitro electronic strain analysis and analyze clinical situation with the verified model. First, strain gauges were attached to the critical areas of a three-unit fixed partial denture. Strain values were measured under 300 N load perpendicular to the occlusal plane. Secondly, a three-dimensional finite element model in accordance with the electronic strain analysis experiment was constructed from the scanning data. And the strain values obtained by finite element analysis and in vitro measurements were compared. Finally, the clinical destruction of the fixed partial denture was evaluated with the verified finite element analysis model. There was a mutual agreement and consistency between the finite element analysis results and experimental data. The finite element analysis revealed that failure will occur in the veneer layer on buccal surface of the connector under occlusal force of 570 N. The results indicate that the electronic strain analysis is an appropriate and cost saving method to verify the finite element model. The veneer layer on buccal surface of the connector is the weakest area in the fixed partial denture. Copyright © 2015 Japan Prosthodontic Society. Published by Elsevier Ltd. All rights reserved.

The modelling of the flow-induced vibrations of periodic flat and axial-symmetric structures with a wave-based method

NASA Astrophysics Data System (ADS)

Errico, F.; Ichchou, M.; De Rosa, S.; Bareille, O.; Franco, F.

2018-06-01

The stochastic response of periodic flat and axial-symmetric structures, subjected to random and spatially-correlated loads, is here analysed through an approach based on the combination of a wave finite element and a transfer matrix method. Although giving a lower computational cost, the present approach keeps the same accuracy of classic finite element methods. When dealing with homogeneous structures, the accuracy is also extended to higher frequencies, without increasing the time of calculation. Depending on the complexity of the structure and the frequency range, the computational cost can be reduced more than two orders of magnitude. The presented methodology is validated both for simple and complex structural shapes, under deterministic and random loads.

Energy absorption in aluminum extrusions for a spaceframe chassis

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

Logan, R.W.; Perfect, S.A.; Parkinson, R.D.

1994-09-19

This work describes the design, finite-element analysis, and verifications performed by LLNL and Kaiser Aluminum for the prototype design of the CALSTART Running Chassis purpose-built electric vehicle. Component level studies, along with our previous experimental and finite-element works, provided the confidence to study the crashworthiness of a complete aluminum spaceframe. Effects of rail geometry, size, and thickness were studied in order to achieve a controlled crush of the front end structure. These included the performance of the spaceframe itself, and the additive effects of the powertrain cradle and powertrain (motor/controller in this case) as well as suspension. Various design iterationsmore » for frontal impact at moderate and high speed are explored.« less

Modeling of a reinforced concrete beam using shape memory alloy as reinforcement bars

NASA Astrophysics Data System (ADS)

Bajoria, Kamal M.; Kaduskar, Shreya S.

2017-04-01

In this paper the structural behavior of reinforced concrete (RC) beams with smart rebars under three point loading system has been numerically studied, using Finite Element Method. The material used in this study is Superelastic Shape Memory Alloy (SE SMA) which contains nickel and titanium. Shape memory alloys (SMAs) are a unique class of materials which have ability to undergo large deformation and also regain their un-deformed shape by removal of stress or by heating. In this study, a uniaxial SMA model is able to reproduce the pseudo-elastic behavior for the reinforcing SMA wires. Finite element simulation is developed in order to study the load-deflection behavior of smart concrete beams subjected to three-point bending tests.

A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems

NASA Astrophysics Data System (ADS)

Gambolati, Giuseppe; Teatini, Pietro

1996-01-01

A new quasi three-dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss-Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.

Simulation of bone-conducted sound transmission in a three-dimensional finite-element model of a human skull

NASA Astrophysics Data System (ADS)

Chang, You; Kim, Namkeun; Stenfelt, Stefan

2015-12-01

Bone conduction (BC) is the transmission of sound to the inner ear through the bones of the skull. This type of transmission is used in humans fitted with BC hearing aids as well as to classify between conductive and sensorineural hearing losses. The objective of the present study is to develop a finite-element (FE) model of the human skull based on cryosectional images of a female cadaver head in order to gain better understanding of the sound transmission. Further, the BC behavior was validated in terms of sound transmission against experimental data published in the literature. Results showed the responses of the simulated skull FE model were consistent with the experimentally reported data.

State-constrained booster trajectory solutions via finite elements and shooting

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations

NASA Astrophysics Data System (ADS)

Schröder, Jörg; Viebahn, Nils; Wriggers, Peter; Auricchio, Ferdinando; Steeger, Karl

2017-09-01

In this work we investigate different mixed finite element formulations for the detection of critical loads for the possible occurrence of bifurcation and limit points. In detail, three- and two-field formulations for incompressible and quasi-incompressible materials are analyzed. In order to apply various penalty functions for the volume dilatation in displacement/pressure mixed elements we propose a new consistent scheme capturing the non linearities of the penalty constraints. It is shown that for all mixed formulations, which can be reduced to a generalized displacement scheme, a straight forward stability analysis is possible. However, problems based on the classical saddle-point structure require a different analyses based on the change of the signature of the underlying matrix system. The basis of these investigations is the work from Auricchio et al. (Comput Methods Appl Mech Eng 194:1075-1092, 2005, Comput Mech 52:1153-1167, 2013).

A refined finite element method for bending analysis of laminated plates integrated with piezoelectric fiber-reinforced composite actuators

NASA Astrophysics Data System (ADS)

Rouzegar, J.; Abbasi, A.

2018-03-01

This research presents a finite element formulation based on four-variable refined plate theory for bending analysis of cross-ply and angle-ply laminated composite plates integrated with a piezoelectric fiber-reinforced composite actuator under electromechanical loading. The four-variable refined plate theory is a simple and efficient higher-order shear deformation theory, which predicts parabolic variation of transverse shear stresses across the plate thickness and satisfies zero traction conditions on the plate free surfaces. The weak form of governing equations is derived using the principle of minimum potential energy, and a 4-node non-conforming rectangular plate element with 8 degrees of freedom per node is introduced for discretizing the domain. Several benchmark problems are solved by the developed MATLAB code and the obtained results are compared with those from exact and other numerical solutions, showing good agreement.

A review of some problems in global-local stress analysis

NASA Technical Reports Server (NTRS)

Nelson, Richard B.

1989-01-01

The various types of local-global finite-element problems point out the need to develop a new generation of software. First, this new software needs to have a complete analysis capability, encompassing linear and nonlinear analysis of 1-, 2-, and 3-dimensional finite-element models, as well as mixed dimensional models. The software must be capable of treating static and dynamic (vibration and transient response) problems, including the stability effects of initial stress, and the software should be able to treat both elastic and elasto-plastic materials. The software should carry a set of optional diagnostics to assist the program user during model generation in order to help avoid obvious structural modeling errors. In addition, the program software should be well documented so the user has a complete technical reference for each type of element contained in the program library, including information on such topics as the type of numerical integration, use of underintegration, and inclusion of incompatible modes, etc. Some packaged information should also be available to assist the user in building mixed-dimensional models. An important advancement in finite-element software should be in the development of program modularity, so that the user can select from a menu various basic operations in matrix structural analysis.

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

1982-01-01

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

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.

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)

High Performance Computing Technologies for Modeling the Dynamics and Dispersion of Ice Chunks in the Arctic Ocean

DTIC Science & Technology

2016-08-23

SECURITY CLASSIFICATION OF: Hybrid finite element / finite volume based CaMEL shallow water flow solvers have been successfully extended to study wave...effects on ice floes in a simplified 10 sq-km ocean domain. Our solver combines the merits of both the finite element and finite volume methods and...ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 sea ice dynamics, shallow water, finite element , finite volume

KANTBP 2.0: New version of a program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Vinitsky, S. I.; Abrashkevich, A. G.

2008-11-01

A FORTRAN 77 program for calculating energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach is presented. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on a finite interval with homogeneous boundary conditions: (i) the Dirichlet, Neumann and third type at the left and right boundary points for continuous spectrum problem, (ii) the Dirichlet and Neumann type conditions at left boundary point and Dirichlet, Neumann and third type at the right boundary point for the discrete spectrum problem. The resulting system of radial equations containing the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite element method. As a test desk, the program is applied to the calculation of the reaction matrix and radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field. This version extends the previous version 1.0 of the KANTBP program [O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675]. Program summaryProgram title: KANTBP Catalogue identifier: ADZH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 20 403 No. of bytes in distributed program, including test data, etc.: 147 563 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM: This depends on the number of differential equations; the number and order of finite elements; the number of hyperradial points; and the number of eigensolutions required. The test run requires 2 MB Classification: 2.1, 2.4 External routines: GAULEG and GAUSSJ [2] Nature of problem: In the hyperspherical adiabatic approach [3-5], a multidimensional Schrödinger equation for a two-electron system [6] or a hydrogen atom in magnetic field [7-9] is reduced by separating radial coordinate ρ from the angular variables to a system of the second-order ordinary differential equations containing the potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions of the continuum spectrum for such systems of coupled differential equations on finite intervals of the radial variable ρ∈[ρ,ρ]. This approach can be used in the calculations of effects of electron screening on low-energy fusion cross sections [10-12]. Solution method: The boundary problems for the coupled second-order differential equations are solved by the finite element method using high-order accuracy approximations [13]. The generalized algebraic eigenvalue problem AF=EBF with respect to pair unknowns ( E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [14]. The generalized algebraic eigenvalue problem (A-EB)F=λDF with respect to pair unknowns ( λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDL factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [14]. As a test desk, the program is applied to the calculation of the reaction matrix and corresponding radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field described in [9] on finite intervals of the radial variable ρ∈[ρ,ρ]. For this benchmark model the required analytical expressions for asymptotics of the potential matrix elements and first-derivative coupling terms, and also asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system. Restrictions: The computer memory requirements depend on: the number of differential equations; the number and order of finite elements; the total number of hyperradial points; and the number of eigensolutions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Section 3 and [1] for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should also supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMS0 and ASYMSC (when solving the scattering problem) which evaluate asymptotics of the radial wave functions at left and right boundary points in case of a boundary condition of the third type for the above problems. Running time: The running time depends critically upon: the number of differential equations; the number and order of finite elements; the total number of hyperradial points on interval [ ρ,ρ]; and the number of eigensolutions required. The test run which accompanies this paper took 2 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz. References: [1] O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675; http://cpc.cs.qub.ac.uk/summaries/ADZHv10.html. [2] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986. [3] J. Macek, J. Phys. B 1 (1968) 831-843. [4] U. Fano, Rep. Progr. Phys. 46 (1983) 97-165. [5] C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142. [6] A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Commun. 90 (1995) 311-339. [7] M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352. [8] O. Chuluunbaatar, A.A. Gusev, V.L. Derbov, M.S. Kaschiev, L.A. Melnikov, V.V. Serov, S.I. Vinitsky, J. Phys. A 40 (2007) 11485-11524. [9] O. Chuluunbaatar, A.A. Gusev, V.P. Gerdt, V.A. Rostovtsev, S.I. Vinitsky, A.G. Abrashkevich, M.S. Kaschiev, V.V. Serov, Comput. Phys. Commun. 178 (2007) 301 330; http://cpc.cs.qub.ac.uk/summaries/AEAAv10.html. [10] H.J. Assenbaum, K. Langanke, C. Rolfs, Z. Phys. A 327 (1987) 461-468. [11] V. Melezhik, Nucl. Phys. A 550 (1992) 223-234. [12] L. Bracci, G. Fiorentini, V.S. Melezhik, G. Mezzorani, P. Pasini, Phys. Lett. A 153 (1991) 456-460. [13] A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Commun. 85 (1995) 40-64. [14] K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982.

A combined registration and finite element analysis method for fast estimation of intraoperative brain shift; phantom and animal model study.

PubMed

Mohammadi, Amrollah; Ahmadian, Alireza; Rabbani, Shahram; Fattahi, Ehsan; Shirani, Shapour

2017-12-01

Finite element models for estimation of intraoperative brain shift suffer from huge computational cost. In these models, image registration and finite element analysis are two time-consuming processes. The proposed method is an improved version of our previously developed Finite Element Drift (FED) registration algorithm. In this work the registration process is combined with the finite element analysis. In the Combined FED (CFED), the deformation of whole brain mesh is iteratively calculated by geometrical extension of a local load vector which is computed by FED. While the processing time of the FED-based method including registration and finite element analysis was about 70 s, the computation time of the CFED was about 3.2 s. The computational cost of CFED is almost 50% less than similar state of the art brain shift estimators based on finite element models. The proposed combination of registration and structural analysis can make the calculation of brain deformation much faster. Copyright © 2016 John Wiley & Sons, Ltd.

Arbitrary-Lagrangian-Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael

2017-10-01

We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total Lagrangian formulations that are based on a fixed computational grid and which instead evolve the mapping of the reference configuration to the current one. Our new Lagrangian-type DG scheme adopts the novel a posteriori sub-cell finite volume limiter method recently developed in [62] for fixed unstructured grids. In this approach, the validity of the candidate solution produced in each cell by an unlimited ADER-DG scheme is verified against a set of physical and numerical detection criteria, such as the positivity of pressure and density, the absence of floating point errors (NaN) and the satisfaction of a relaxed discrete maximum principle (DMP) in the sense of polynomials. Those cells which do not satisfy all of the above criteria are flagged as troubled cells and are recomputed at the aid of a more robust second order TVD finite volume scheme. To preserve the subcell resolution capability of the original DG scheme, the FV limiter is run on a sub-grid that is 2 N + 1 times finer compared to the mesh of the original unlimited DG scheme. The new subcell averages are then gathered back into a high order DG polynomial by a usual conservative finite volume reconstruction operator. The numerical convergence rates of the new ALE ADER-DG schemes are studied up to fourth order in space and time and several test problems are simulated in order to check the accuracy and the robustness of the proposed numerical method in the context of the Euler and Navier-Stokes equations for compressible gas dynamics, considering both inviscid and viscous fluids. Finally, an application inspired by Inertial Confinement Fusion (ICF) type flows is considered by solving the Euler equations and the PDE of viscous and resistive magnetohydrodynamics (VRMHD).