Showing papers on "Smoothed finite element method published in 2001"
Book•
01 Jan 2001
TL;DR: This paper proposes a method for guaranteed a-posteriori error estimation, and Guaranteed a-PosterIORi estimation of the pollution error in the finite element method.
Abstract: Preface 1. Introduction 2. Mathematical formulation of the model problem 3. The finite element method 4. Local behaviour in the finite element method 5. A-posteriori estimation of the error 6. Guaranteed a-posteriori error estimation, and a-posteriori estimation of the pollution error Appendix Index
770 citations
TL;DR: Advanced finite element techniques for the simulation of materials behavior under mechanical loading are reviewed andvantages, limitations and perspectives of different approaches are analyzed.
Abstract: Advanced finite element techniques for the simulation of materials behavior under mechanical loading are reviewed. Advantages, limitations and perspectives of different approaches are analyzed for the simulation of deformation, damage and fracture of mate
101 citations
TL;DR: In this article, the combined finite and discrete element technique has been considered for the compaction of an assembly of particles, where each particle is mapped with finite elements and the interaction between particles is solved using a discrete element approach.
64 citations
TL;DR: Numerical results obtained with the meshfree contact algorithm show that this new contact algorithm can accurately predict the contact as well as separation of projectile and target.
64 citations
TL;DR: In this paper, two different finite element method (FEM) codes: static-explicit ITAS3D and dynamicexplicit ABAQUS/Explicit were used in numerical simulations to simulate the wrinkling of conical cups.
61 citations
14 Oct 2001
TL;DR: A new approach to cutting in Finite Element models is described, not to introduce new nodes/elements but to displace the existing ones to account for the topological changes introduced by a cut.
Abstract: Virtual reality based surgical simulators offer a very elegant approach to enhancing traditional training in endoscopic surgery. In this context a realistic soft tissue model is of central importance. The most accurate procedures for modeling elastic deformations of tissue use the Finite Element Method to solve the governing mechanical equations. Therapeutic interventions (e.g. cutting) require topological changes of the Finite Element mesh, thus making a non-trivial remeshing step necessary. This paper describes a new approach to cutting in Finite Element models. The central idea is not to introduce new nodes/elements but to displace the existing ones to account for the topological changes introduced by a cut. After the displacement of the nodes/elements the mesh is homogenized to avoid tiny elements which destabilize the explicit time integration necessary for solving the equations of motion.
53 citations
TL;DR: Some subjects such as the solution technique of the non-linear equilibrium equations and the constitutive model for concrete and reinforcement steel are emphasised and commented and a robust method for the evaluation of the intersecting points of the embedded reinforcement bars into the three-dimensional finite element mesh is presented.
48 citations
TL;DR: An assumed hybrid-stress finite element model together with a new super singular wedge-tip element with numerical eigensolutions is developed to study the bimaterial wedge/notch problems as discussed by the authors.
44 citations
TL;DR: In this article, a finite element code is developed for the two-dimensional cure simulation of thick composite structures, which can easily model composite structures with arbitrary shapes including the mandrel used for the cure set-up.
Abstract: A finite element code is developed for the two-dimensional cure simulation of thick composite structures. In contrast to one or two-dimensional codes based on the finite difference method, the present finite element method can easily model composite structures with arbitrary shapes including the mandrel used for the cure set-up. For the two-dimensional cure simulation, a degeneration method to build the thermal conductivity matrix is proposed. The present finite element method is verified by two numerical examples. The numerical results show good agreement with the measured data appeared in the literatures. However, a full three-dimensional cure simulation is needed for more accurate cure simulation.
42 citations
TL;DR: In this paper, the problem of non-linear planetary dynamos with a prescribed two-or three-dimensional, time-dependent α is investigated using a finite element method, where magnetic fields are generated in a turbulent electrically conducting fluid spherical shell of constant electric conductivity surrounded by an electrically insulating uniform mantle.
TL;DR: In this paper, the first-order least-squares method is employed instead of the Galerkin's method for numerical integration in mesh-free mesh-based methods, which is expected to remove some of the integration-related problems.
Abstract: A new efficient meshfree method is presented in which the first-order least-squares method is employed instead of the Galerkin's method. In the meshfree methods based on the Galerkin formulation, the source of many difficulties is in the numerical integration. The current method, in this respect, has different characteristics and is expected to remove some of the integration-related problems. It is demonstrated through numerical examples that the present formulation is highly robust to integration errors. Therefore, numerical integration can be performed with great ease and effectiveness using very simple algorithms. Copyright © 2001 John Wiley & Sons, Ltd.
08 Jul 2001
TL;DR: In this paper, a general approach based on discrete system analysis is developed for investigating the stability behavior of time-domain finite element methods (TDFEM), which is applied to a variety of recently developed TDFEM schemes.
Abstract: Considerable attention has been devoted to time-domain numerical methods for simulating electromagnetic transient phenomena. A general approach based on discrete system analysis is developed for investigating the stability behavior of time-domain finite element methods (TDFEM). This approach is applied to a variety of recently developed TDFEM schemes. These include: (1) time-domain finite element modeling of dispersive media; (2) time-domain finite element-boundary integral (FE-BI) method; (3) higher-order time-domain finite element schemes; and (4) orthogonal time-domain finite element method. Numerical results demonstrate the validity of the proposed approach for stability analysis.
TL;DR: A finite element model for studying fluid-filled pipes is developed by combining an axisymmetric shell element and a one-dimensional fluid element and taking the interaction between shell and fluid into account as mentioned in this paper.
Patent•
17 Apr 2001
TL;DR: In this article, the authors propose a method for performing finite element simulation, which includes switching between an implicit method and an explicit method during the simulation, so that an accurate solution can be obtained quickly and reliably.
Abstract: A method for performing a finite element simulation. The method includes switching between an implicit method and an explicit method during the finite element simulation. By switching between the implicit and explicit methods during a simulation, an accurate solution can be obtained quickly and reliably.
TL;DR: In this paper, edge-based data structures are used to improve computational efficiency of inexact Newton methods for solving finite element non-linear solid mechanics problems on unstructured meshes.
Abstract: Edge-based data structures are used to improve computational efficiency of inexact Newton methods for solving finite element non-linear solid mechanics problems on unstructured meshes. Edge-based data structures are employed to store the stiffness matrix coefficients and to compute sparse matrix–vector products needed in the inner iterative driver of the inexact Newton method. Numerical experiments on three-dimensional plasticity problems have shown that memory and computer time are reduced, respectively, by factors of 4 and 6, compared with solutions using element-by-element storage and matrix–vector products. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: A very simple and efficient finite element method is introduced for two and three dimensional viscous incompressible flows using the vorticity formulation, which is particularly suited for moderate to high Reynolds number flows.
Abstract: A very simple and efficient finite element method is introduced for two and three dimensional viscous incompressible flows using the vorticity formulation. This method relies on recasting the traditional finite element method in the spirit of the high order accurate finite difference methods introduced by the authors in another work. Optimal accuracy of arbitrary order can be achieved using standard finite element or spectral elements. The method is convectively stable and is particularly suited for moderate to high Reynolds number flows.
TL;DR: In this paper, an object-oriented finite element program for static and dynamic nonlinear applications is presented, which can be considered as an extension of the original FEM_Object environment dealing with linear elasticity [Elmepress Int (1993)] and nonlinearity [Comput Struct 49 (1993) 767].
TL;DR: In this paper, certain critical issues and associated methodologies to develop a three dimensional Finite Element based code for bulk forming simulations are addressed and described, and several forming and heat treatment applications are presented.
01 Jan 2001-Compel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering
TL;DR: The harmonic balanced finite element method (HBFEM) as mentioned in this paper is a state-of-the-art finite element simulator for the quasi-static simulation of electromagnetic devices operating at steady-state.
Abstract: The harmonic balanced finite element method offers a valuable alternative to the transient finite element method for the quasi‐static simulation of electromagnetic devices operating at steady‐state. The specially designed iterative solver, the adaptive relaxation of the non‐linear loop and the embedding of the harmonic balanced finite element method within a state‐of‐the‐art finite element package, leads to a solver in the frequency domain that is competitive to time stepping. The benefits of this approach are illustrated by its application to an inductor with a ferromagnetic core.
TL;DR: In this article, a basic geometric model of the planetary rolling mill that considers roll profiles and offset angle of the rolls was constructed, and a three-dimensional elastic-plastic finite element simulation was used to analyze both the deformation characteristics of this process and the distributions of stress and strain in the workpieces.
01 Jan 2001
TL;DR: The proposed Mesh-Based Geometry (MBG) serves as an alternative to the CAD-based syst em currently in use in Sandia National Laboratory's, CUBIT mesh generat ion toolkit and enables the mesh-based geometry to work seamlessly with existing geometry and meshing tools already de veloped within the CUBit environment.
Abstract: A new system for defining geometry based on feature s of a finite element mesh is described. A systemat ic approach to building a complete geometric and topologic representation of a model given only the finite element description i s proposed. Geometry and topology entities including volumes, surfaces, curv es and vertices, can be implied based on user defin ed boundary conditions or surface features. Curve and surface geometry is de scribed by either linear triangular facets or G 1 continuous 4th order Bezier patches. The proposed Mesh-Based Geometry (MBG) sy stem serves as an alternative to the CAD-based syst em currently in use in Sandia National Laboratory's, CUBIT mesh generat ion toolkit. CGM enables the mesh-based geometry t o work seamlessly with existing geometry and meshing tools already de veloped within the CUBIT environment. * Sandia is a multiprogram laboratory operated by San dia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000. 1.INTRODUCTION CAD programs and libraries provide an ideal geometr ic foundation for finite element mesh generation. Mos t automaticmeshingalgorithmsrequireageometry framework upon which the mesh may be developed. I n some cases, the analyst or designer may be unable t o take advantage of CAD geometry, consequently precluding the useofautomaticmeshingormeshimprovement algorithms. The basis for precluding the use of CA D geometry may include one or more of the following: 1. The finite element model may be legacy data. In some cases, old archived mesh files may be the only representation of the model available to the analys t. Design modifications or more advanced computational methods may require changing or modifying the mesh. Where associated CAD data is not available, or geometryformatshavebecomeobsolete,mesh modificationsmaybeimpracticalorextremely tedious. 2. Remeshing of deformed finite element data is requir ed. For dynamic remeshing problems, although an initial CAD-based geometric model may have been used to define the model, computed deformations may change curve and surface definitions, such that the origin al geometry is no longer valid. 3. Interoperabilitybetweenpreprocessingprograms. Designers and analysts will frequently use several software tools to develop a finite element mesh for analysis. For example, an analyst may generate the mesh in one system and smooth it in a second or generate a structured grid in one and an unstructur ed grid in another. Although these tools may support CAD geometry, even small modifications to the geometry may preclude its use in other software. T he …
TL;DR: In this article, the authors present an adequate set of tests which every new finite element should pass, and a thorough account of the patch test is also included in view of its significance in the validation of new elements.
Abstract: The finite element method entails several approximations. Hence it is essential to subject all new finite elements to an adequate set of pathological tests in order to assess their performance. Many such tests have been proposed by researchers from time to time. We present an adequate set of tests, which every new finite element should pass. A thorough account of the patch test is also included in view of its significance in the validation of new elements.
01 Jan 2001
01 Jan 2001
TL;DR: The objective of this course is to present briefly each of the above aspects of the finite element analysis and thus to provide a basis for the understanding of the complete solution process.
Abstract: Preface Today the finite element method (FEM) is considered as one of the well established and convenient technique for the computer solution of complex problems in different fields can be examined as a powerful tool for the approximate solution of differential equations describing different physical processes. The success of FEM is based largely on the basic finite element procedures used: the formulation of the problem in variational form, the finite element dicretization of this formulation and the effective solution of the resulting finite element equations. These basic steps are the same whichever problem is considered and together with the use of the digital computer present a quite natural approach to engineering analysis. The objective of this course is to present briefly each of the above aspects of the finite element analysis and thus to provide a basis for the understanding of the complete solution process. According to three basic areas in which knowledge is required, the course is divided into three parts. The first part of the course comprises the formulation of FEM and the numerical procedures used to evaluate the element matrices and the matrices of the complete element assemblage. In the second part, methods for the efficient solution of the finite element equilibrium equations in static and dynamic analyses will be discussed. In the third part of the course, some modelling aspects and general features of some Finite Element Programs (ANSYS, NISA, LS-DYNA) will be briefly examined. To acquaint more closely with the finite element method, some excellent books, like [1-4], can be used.
TL;DR: In this paper, the infsup condition is considered from an engineering perspective, so as to be able to incorporate it into the package of tools used in the development of finite element formulations.
Abstract: Engineers have developed robust and efficient incompressible finite element formulations using tools such as the Patch Test and the counting of constraints/variables, the first one aimed at the development of consistent elements and the second one aimed at the development of non‐locking and stable elements. The mentioned tools are rooted in the physics of the continuum mechanics problem. Mathematicians, on the other side, developed complex and powerful tools to examine the convergence of finite element formulations, such as the inf‐sup condition, these methods are based on the properties of the elliptical PDEs that constitute the mathematical model of the continuum mechanics problem. In this paper we intend to understand the inf‐sup condition from an engineering perspective, so as to be able to incorporate it into the package of tools used in the development of finite element formulations.
TL;DR: In this paper, an operator that extends functions in finite element spaces to the exact domain is constructed and some estimates in the boundary skin are presented, which is successfully used to prove uniform solvability in approximate domains for problems subject to slip boundary conditions and so on.
Abstract: Uniform solvability of finite element solutions in approximate domains is studied. An operator that extends functions in finite element spaces to the exact domain is constructed and some estimates in the boundary skin are presented. The extension operator is successfully used to prove uniform solvability in approximate domains for problems subject to slip boundary conditions and so on.
TL;DR: In this article, a numerical scheme for the computation of conservative fluid velocity, pressure and temperature fields in a porous medium is presented, which is based on the primal-dual mixed finite element method of Trujillo and Thomas.
TL;DR: In this article, an adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed, based on a combination of finite element and finite difference techniques.
Abstract: Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the space-time meshes. Basic error estimates in L∞ (L2) norm, that is maximum-norm in time, L2-norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.