Showing papers on "Smoothed finite element method published in 1990"
TL;DR: The equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established, which enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the Mixed method.
919 citations
TL;DR: Space-time finite element methods are presented to accurately solve elastodynamics problems that include sharp gradients due to propagating waves in this paper, where linear stabilizing mechanisms are included which do not degrade the accuracy of the space time finite element formulation.
Abstract: Space-time finite element methods are presented to accurately solve elastodynamics problems that include sharp gradients due to propagating waves. The new methodology involves finite element discretization of the time domain as well as the usual finite element discretization of the spatial domain. Linear stabilizing mechanisms are included which do not degrade the accuracy of the space-time finite element formulation. Nonlinear discontinuity-capturing operators are used which result in more accurate capturing of steep fronts in transient solutions while maintaining the high-order accuracy of the underlying linear algorithm in smooth regions. The space-time finite element method possesses a firm mathematical foundation in that stability and convergence of the method have been proved. In addition, the formulation has been extended to structural dynamics problems and can be extended to higher-order hyperbolic systems.
310 citations
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01 Jan 1990
TL;DR: This poster presents a probabilistic procedure to estimate the number of elements in a collection of Roman numerals using a computer program called LaSalle’s Grammar.
Abstract: Keywords: Mecanique des roches ; Analyse numerique ; Methode des elements finis Reference Record created on 2004-09-07, modified on 2016-08-08
240 citations
TL;DR: In this article, the p- and the h-p versions of the finite element method are surveyed and an up-to-date list of references related to these methods is provided.
Abstract: We survey the advances in the p- and the h-p versions of the finite element method. An up-to-date list of references related to these methods is provided.
232 citations
TL;DR: In this paper, a mixed Eulerian-Lagrangian finite element method for simulation of forming processes is presented, which permits incremental adaptation of nodal point locations independently from the actual material displacements, thus numerical difficulties due to large element distortions, as may occur when the updated Lagrange method is applied, can be avoided.
Abstract: A review is given of a mixed Eulerian-Lagrangian finite element method for simulation of forming processes. This method permits incremental adaptation of nodal point locations independently from the actual material displacements. Hence numerical difficulties due to large element distortions, as may occur when the updated Lagrange method is applied, can be avoided. Movement of (free) surfaces can be taken into account by adapting nodal surface points in a way that they remain on the surface. Hardening and other deformation path dependent properties are determined by incremental treatment of convective terms. A local and a weighed global smoothing procedure is introduced in order to avoid numerical instabilities and numerical diffusion. Prediction of contact phenomena such as gap openning and/or closing and sliding with friction is accomplished by a special contact element. The method is demonstrated by simulations of an upsetting process and a wire drawing process.
105 citations
89 citations
TL;DR: In this article, a finite element formulation of the linear biphasic model for articular cartilage and other hydrated soft tissues consisting of an incompressible, inviscid fluid phase and a solid phase is presented, and the Galerkin weighted residual method is applied to the momentum equation and mechanical boundary conditions of both the solid phase and the fluid phase.
86 citations
TL;DR: An elementary theory giving bounds on the condition numbers which do not depend on the number of elements if a sparse system with only few variables per element is solved in each iteration is developed.
Abstract: We study a class of substructuring methods well-suited for iterative solution of large systems of linear equations arising from the p-version finite element method. The p-version offers a natural decomposition with every element treated as a substructure. We use the preconditioned conjugate gradient method with preconditioning constructed by a decomposition of the local function space on each element. We develop an elementary theory giving bounds on the condition numbers which do not depend on the number of elements if a sparse system with only few variables per element is solved in each iteration. This bound can be evaluated considering one element at a time and we compute such condition numbers numerically for various elements.
76 citations
62 citations
TL;DR: In this article, a Galerkin finite element solution technique for the Maxwell's equations is discussed, which can be viewed as a generalization of certain staggered-grid finite difference schemes to arbitrary meshes.
56 citations
TL;DR: In this paper, a quantitative method of a posteriori error estimation based on finite element solutions is developed, which can estimate the error of solutions obtained by the finite element method for two-dimensional elastic problems with 4-node elements.
Abstract: A quantitative method of a posteriori error estimation based on finite element solutions is developed. The proposed method can estimate the error of solutions obtained by the finite element method for two-dimensional elastic problems with 4-node elements. Since the error is estimated element by element, the proposed method does not require a large memory or long computing time. Not only rectangular elements but also arbitrarily shaped 4-node elements can be used in this method for estimating the error in the finite element computation with high accuracy. The finite element solutions are improved by adding the estimated errors onto the original solutions. The proposed method can be utilized for any type of linear problem if an isoparametric finite element method is used.
17 Apr 1990
TL;DR: In this article, a finite-element modeling of open boundary problems is presented and applied to magnetostatic problems in two and three dimensions, and it is shown that computation of the magnetic field is achieved with very good accuracy and good speed.
Abstract: A finite-element modeling of open boundary problems is presented and applied to magnetostatic problems in two and three dimensions. It is shown that computation of the magnetic field is achieved with a very good accuracy and good speed. It is noted that the general matrix formulation described permits the efficient use of a transformation more complex than that given by J. Imhoff et al. (1989). Implementation in existing finite-element software is very simple. Although the case of magnetostatic problems has been considered for simplicity, it is quite possible to apply the method to other kinds of problems (magnetodynamic ones or those for which a variational formulation is nonexistent). Such a technique of resolution of unbounded problems is really performant in comparison with other methods, and one of its advantages is the rapidity of calculation. >
TL;DR: In this paper, the tangential vector finite element method and the transfinite element method are applied to the analysis of microwave devices in 3D space, and the authors describe the application of two new finite element techniques for modelling three-dimensional microwave devices.
Abstract: There are two major difficulties in applying the finite element method to the analysis of microwave devices in three dimensions. One is to obtain a stable vector finite element which does not generate spurious modes, or non-physical solutions, in the numerical analysis. The other is to model efficiently the coupling of port regions and the discontinuity region. In this paper, we describe the application of two new finite element techniques, the tangential vector finite element method and the transfinite element method, for modelling three-dimensional microwave devices. The tangential vector finite element method, unlike the conventional nodal finite element methods, imposes only the tangential continuity of the vector unknown across elements' boundaries. As a result, there would be no spurious modes, and reliable solutions are obtained. The transfinite element method, which combines the modal basis functions and the finite element basis functions through the variational technique, provides an efficient way to model the open boundary nature of the device. To validate the current analysis, a low VSWR waveguide connector and two microstrip low-pass filters are analysed. Numerical results agree very well with the measurements or those obtained by other methods.
TL;DR: In this paper, the methods and results of using partial differential equation techniques for the solution of RF radiation and scattering problems are extensively covered, and two-dimensional and three-dimensional formulations and computational results are presented.
Abstract: This paper presents the methods and results of using partial differential equation techniques for the solution of RF radiation and scattering problems. Specifically, frequency domain finite elements coupled with absorbing boundary conditions are extensively covered. Two-dimensional and three-dimensional formulations and computational results are presented. The two-dimensional formulation uses standard finite elements with either the Engquist-Majda or Bayliss-Turkel absorbing boundary conditions. The three-dimensional formulation also uses absorbing boundary conditions and finite elements, however, new, non-standard finite element basis functions specifically developed for vector field problems are used. These vector finite element basis functions are known as “edge-elements.” [1]
TL;DR: In this article, applications of p- and h-p extension procedures in solid mechanics are discussed and examples of error estimation and quality control procedures made possible by p-extensions are described.
Abstract: Applications of p- and h-p extension procedures in solid mechanics are discussed. Error estimation and quality control procedures made possible by p-extensions are described and illustrated by examples.
01 Jan 1990
TL;DR: In the finite element calculations of problems in solid mechanics, the method of selected reduced integration (SRI) is frequently used to eliminate locking phenomena as mentioned in this paper, and often SRI is equivalent to the application of a mixed method.
Abstract: In the finite element calculations of problems in solid mechanics the method of selected reduced integration (SRI) is frequently used to eliminate locking phenomena. Often SRI is equivalent to the application of a mixed method. When multigrid methods are applied, the formulation as a mixed method is by far superior. This is shown by an analysis of the Timoshenko beam.
TL;DR: In this article, the behavior errors of an approximate solution, resulting from violation of fundamental physical constraints occurring in a diffusion transport phenomenon, are compared for weighted residual-based and control volume-based finite element methods.
Abstract: Behavioral errors of an approximate solution, resulting from violation of fundamental physical constraints occurring in a diffusion transport phenomenon, are compared for Ike weighted residual-based and control volume-based finite element methods. Because of its physical background, the latter method offers a higher accuracy, better stability and oscillation characteristics, and preservation of the discrete maximum principle in coarse time-space discretization grids. Furthermore, it gives a simple, physically justified way for setting up a computationally convenient lumped mass matrix model in high-order finite element grids.
08 Jan 1990
TL;DR: The solution of Helmhohz's equation in regions of arbitrary cross-section is obtained by the finite element method.
Abstract: In this paper the solution of Helmhohz's equation in regions of arbitrary cross-section is obtained by the finite element method.
TL;DR: In this article, a quadrilateral membrane finite element with rotational degrees of freedom (drilling degrees) is presented for analysis of shells, and the finite element interpolation field is enriched by a set of incompatible modes.
TL;DR: In this paper, an arbitrary Lagrangian-Eulerian kinematic description is implemented for enhanced accuracy and performance of the analysis of elastic-viscoplastic materials.
Abstract: This paper aims at simulating a few typical extrusion processes, using the finite element method for large deformation analysis of elastic-viscoplastic materials. An arbitrary Lagrangian-Eulerian kinematic description is implemented for enhanced accuracy and performance of the analysis. Various schemes for moving the three-dimensional computational grid are experimented with, for analysis up to large degrees of deformation.
01 Jan 1990
TL;DR: This paper presents some general results on the construction of piecewise polynomial interpolation of class C k on a triangulated domain in ℝ n and investigates the evaluation of smoothing surfaces with a finite element minimization.
Abstract: This paper is devoted to the presentation of algorithms for interpolating with Simplicial Polynomial Finite Elements. We present first some general results on the construction of piecewise polynomial interpolation of class C k on a triangulated domain in ℝ n . Then, we focus on the computation of surfaces interpolating scattered data of Lagrange or Hermite type. Finally, we investigate the evaluation of smoothing surfaces with a finite element minimization.
TL;DR: In this paper, the generalized multipole technique (GMT) with the finite element (FE) method can enhance the advantages of both techniques and help to overcome their specific weaknesses, and a few examples which show the benefits of the joint technique are presented.
Abstract: It is shown how the coupling of the generalized multipole technique (GMT) with the finite-element (FE) method can enhance the advantages of both technique sand help to overcome their specific weaknesses. The FE technique allows the simulation of nonlinear and anisotropic materials and the GMT allows the simulation of all the linear paths of the problem even for regions of infinite extent with fewer unknowns than the usual methods. A few examples which show the benefits of the joint technique are presented. Particular attention is given to the calculation of a nonlinear coil. >
TL;DR: In this paper, a method for analyzing 3D open-boundary magnetic field problems using infinite elements has been developed, which has the advantage that the bandwidth of the coefficient matrix and the number of unknown variables are reduced.
Abstract: A method for analyzing 3-D open-boundary magnetic field problems using infinite elements has been developed. The infinite problem has the advantage that the bandwidth of the coefficient matrix and the number of unknown variables are reduced. Moreover, no experience is necessary in determining decay parameters. The effectiveness of the infinite-element method is illustrated by the accuracy and the CPU time obtained when various boundary conditions are applied. >
TL;DR: In this article, the applicability of the finite difference method to problems in solid mechanics was investigated by formulating the coefficients of the Taylor series expansion to approximate derivative quantities in terms of physically interpretable strain gradients.
Abstract: Procedures are developed that improve the applicability of the finite difference method to problems in solid mechanics. This is accomplished by formulating the coefficients of the Taylor series expansion used to approximate derivative quantities in terms of physically interpretable strain gradients. Improvements realized include modeling of boundary conditions that has intuitive appeal and the use of irregular grids in a natural manner. These developments are demonstrated for the analysis of plane stress problems with traction boundary conditions. The results compare well with finite element solutions. The approach suggests further generalization of the finite difference method.
TL;DR: In this paper, a finite element formulation is proposed for solution of the time-dependent coupled wave equation over an infinite fluid domain, which is based on a finite computational fluid domain surrounding the structure and incorporates a sequence of boundary operators on the fluid truncation boundary.
Abstract: In this paper a finite element formulation is proposed for solution of the time-dependent coupled wave equation over an infinite fluid domain. The formulation is based on a finite computational fluid domain surrounding the structure and incorporates a sequence of boundary operators on the fluid truncation boundary. These operators are designed to minimize reflection of outgoing waves and are based on an asymptotic expansion of the exact solution for the time-dependent problem. The variational statement of the governing equations is developed from a Hamiltonian approach that is modified for nonconservative systems. The dispersive properties of finite element semidiscretizations of the three dimensional wave equation are examined. This analysis throws light on the performance of the finite element approximation over the entire range of wavenumbers and the effects of the order of interpolation, mass lumping, and direction of wave propagation are considered.