Showing papers on "Extended finite element method published in 1985"
TL;DR: Making use of a perturbed Lagrangian formulation, a finite element procedure for contact problems is developed for the general case in which node-to-node contact no longer holds, which leads naturally to a discretization of the contact interface into contact segments.
435 citations
Book•
01 Jan 1985
TL;DR: The Finite Element Method (FE) is the most widely used method for numerical approximation for partial differential equations defining engineering and scientific problems as mentioned in this paper, and it has been widely used in the field of structural engineering.
Abstract: THE FINITE ELEMENT METHOD : Basic Concepts and ApplicationsDarrell Pepper, Advanced Projects Research, Inc. California, and Dr . JuanHeinrich, University of Arizona, TucsonTh i s introductory textbook is designed for use in undergraduate, graduate, andshort courses in structural engineering and courses devoted specifically to thefinite element method. This method is rapidly becoming the most widely usedstandard for numerical approximation for partial differential equations definingengineering and scientific problems.The authors present a simplified approach to introducing the method and a coherentand easily digestible explanation of detailed mathematical derivations andtheory Example problems are included and can be worked out manually Anaccompanying floppy disk compiling computer codes is included and required forsome of the multi-dimensional homework problems.
391 citations
366 citations
353 citations
TL;DR: In this article, a new plane-stress triangular element is derived using the free formulation of Bergan and Nygard, which possesses nine degrees of freedom: six corner translations and three corner normal rotations.
307 citations
TL;DR: It is shown that the conductivity distribution in the field can be estimated from the impedance data obtained for the body surface leads and the finite element model must be chosen properly to provide the unique solution.
Abstract: A simulation study of electrical impedance computed tomography is presented. This is an inverse problem. A field is discretized by the finite element method and an iterative approach derived from the sensitivity theorem is examined for leads taken on the field surface. It is shown that the conductivity distribution in the field can be estimated from the impedance data obtained for the body surface leads. Simulation suggests the availability and the limitation for impedance plethysmography application. The finite element model must be chosen properly to provide the unique solution.
283 citations
Book•
01 Dec 1985
Abstract: Finite Element Structural Analysis The finite element method (FEM) is a powerful technique originally developed for numerical solution of complex problems in structural mechanics, and it remains the method of choice for complex systems.In the FEM, the structural system is modeled by a set of appropriate finite elements interconnected at discrete points called nodes. Elements may have physical properties such as thickness ...
274 citations
TL;DR: In this article, a joint/interface element for three-and two-dimensional finite element analysis is presented, which can model joints/interfaces between solid finite elements and shell finite elements.
Abstract: A generally applicable and simple joint/interface element for three- and two-dimensional finite element analysis is presented. The proposed element can model joints/interfaces between solid finite elements and shell finite elements. The derivation of the joint element stiffness is presented and algorithms for the treatment of nonlinear joint behaviour discussed. The performance of the element is tested on typical problems involving shell-to-shell and shell-to-solid interfaces.
272 citations
TL;DR: In this paper, a displacement methodology for Mindlin elements, recently employed in the development of an efficient, four-node quadrilateral (MIN4), is the basis for a three-node, explicitly integrated triangular element (MIN3).
263 citations
TL;DR: In this article, a finite element method for calculating the energy release rate is proposed based on a continuum mechanics formulation of the virtual crack extension principle and can be used with linear elastic materials as well as materials following the deformation theory of plasticity.
202 citations
TL;DR: In this paper, some finite elements which are used in the approximation of the Stokes problem were studied, so as to obtain error estimates of optimal order, and they were used for approximating the optimal order of Stokes problems.
Abstract: We study some finite elements which are used in the approximation of the Stokes problem, so as to obtain error estimates of optimal order. Resume. Nous etudions deux elements finis utilises pour l'approximation du probleme de Stokes et obtenons des estimations d'erreur d'ordre optimal.
TL;DR: In this paper, the stabilization vector γ can be obtained naturally by taking the partial derivatives with respect to the natural coordinates, and the components of the stresses and stresses can be expressed in terms of a set of orthogonal coordinates.
TL;DR: In this paper, a finite element-based solution procedure for high-speed inviscid compressible flow problems is described, which is computationally more efficient than the one-step Taylor-Galerkin approach and better suited for implementation on the modern generation of vector computers.
TL;DR: The use of a complete and nonsingular set of Trefftz functions in the solution of quasi-harmonic equations is demonstrated and shown to be often superior to the more conventional singularity distribution in boundary-type approximation as mentioned in this paper.
Abstract: The use of a complete and nonsingular set of Trefftz functions in the solution of quasi-harmonic equations is demonstrated and shown to be often superior to the more conventional singularity distribution in boundary-type approximation. Procedures for coupling separate domains of such solution and indeed of deriving equivalent finite elements are demonstrated.
TL;DR: In this article, a mixed finite element method was developed to approximate the solution of a quasilinear second-order elliptic partial differential equation, and the existence and uniqueness of the approximation were demonstrated and optimal rate error estimates were derived.
Abstract: A mixed finite element method is developed to approximate the solution of a quasilinear second-order elliptic partial differential equation. The existence and uniqueness of the approximation are demonstrated and optimal rate error estimates are derived.
TL;DR: In this article, the bridge response is formulated in modal co-ordinates to reduce the number of equations to be solved within each time step, which reduces the complexity of solving the moving load problem.
TL;DR: A nonlinear numerical algorithm for the analysis of stresses and displacements in partly wrinkled flat membranes, and its implementation on the SAP VII finite-element code are described in this article, with excellent agreement, with good convergence of the required iterative procedure.
TL;DR: A new Petrov-Galerkin method for convection-dominated flow problems which is conservative and satisfies the discrete maximum principle is presented, which possesses no spurious crosswind diffusion and gives very accurate solutions.
TL;DR: In this article, the problem of estimating the electric potential distribution in proximity of the heart from potential data given on the body is reformulated as a control problem in terms of a transfer operator and stabilized by means of a suitable regularization operator.
Abstract: This paper investigates the problem of estimating the electric potential distribution in proximity of the heart from potential data given on the body and is here reformulated as a control problem in terms of a «transfer» operator and stabilized by means of a suitable regularization operator. The numerical approximation by means of the finite element method of the regularized problem is investigated; convergence results and error estimates are established.
TL;DR: In this paper, a finite element formulation for the analysis of nonuniform and localized deformations in rate-dependent single crystals is presented, but the main focus is on issues relating to the formulation and implementation of finite element methods for crystalline solids.
TL;DR: It is concluded that the Delaunay triangulation provides the best method of mesh refinement, while complementary variational principles provide accurate error bounds on the solution.
Abstract: Adaptive mesh refinement has the potential of making the finite element computation of magnetic field problems completely automatic. In adaptive procedures, the field problem is solved iteratively, beginning with a coarse mesh and refining it in locations of greatest error. Methods of mesh refinement for triangular finite element grids are surveyed and the use of local error estimates in the adaptive process is described. It is concluded that the Delaunay triangulation provides the best method of mesh refinement, while complementary variational principles provide accurate error bounds on the solution.
TL;DR: In this article, the authors proposed a finite element method to solve the stationary form of the Fokker-Planck-Kolmogorov equation for the random response of a certain class of non-linear systems.
TL;DR: In this article, a streamline upwind approximation for treating advectiondominatcd transport is presented, which is quite simple to implement with existing finite element methods and is used in a two-dimensional finite element computer program.
TL;DR: In this paper, the authors considered the finite element method of second order elliptic problems on convex domains and homogeneous Dirichlet condition on the boundary and proved that in two dimensions the convergence is of orderh inL 2 and in three dimensions of order h 1/2.
Abstract: In this paper we consider the approximation by the finite element method of second order elliptic problems on convex domains and homogeneous Dirichlet condition on the boundary. In these problems the data are Borel measures. Using a quasiuniform mesh of finite elements and polynomials of degree ?1, we prove that in two dimensions the convergence is of orderh inL 2 and in three dimensions of orderh 1/2.
TL;DR: In this article, a finite element formulation is developed with emphasis primarily focused on providing stress predictions for thin to moderately thick plate (shell) type structures, and a selective reduced integration technique is utilized in computing element stiffness matrices.
Abstract: A finite element formulation is developed with emphasis primarily focused on providing stress predictions for thin to moderately thick plate (shell) type structures. Plate element behaviour is specified by prescribing independently the neutral surface displacements and rotations, thus relaxing the Kirchhoff hypothesis. Numerical efficiency is achieved due to the simplicity of the element formulation, i.e. the approach yields a displacement dependent multi-layer model. In-plane layer stresses are determined via the constitutive equations, while the transverse shear and short-transverse normal stresses are determined via the equilibrium equations. Accurate transverse stress variations are obtained by appropriately selecting the displacement field for the element. A selective reduced integration technique is utilized in computing element stiffness matrices. Static and spectral (eigenvalue) tests are performed to demonstrate the element modelling capability.
TL;DR: In this paper, a finite element method is proposed for the analysis of density flow which is induced by a difference of density, employing the idea that density variation can be pursued by using markers distributed in the flow field.
Abstract: A finite element method is proposed for the analysis of density flow which is induced by a difference of density. The method employs the idea that density variation can be pursued by using markers distributed in the flow field. For the numerical integration scheme, the velocity correction method is successfully used, introducing a potential for the correction of velocity. This method is useful because one can use linear interpolation functions for velocity, pressure and potential based on the triangular finite element. The final equations can be formulated using the quasi-explicit finite element method. A flume in a tank with sloping bottom has been analysed by the present method. The computed results show extremely good agreement with the experimental observations.
TL;DR: In this article, a new method of three-dimensional finite element mesh generation is presented, based on an extension of the Delaunay triangulation algorithm to three dimensions, using the mesh generator, problems are defined by means of simple threedimensional solid modeling commands.
Abstract: A new method of three-dimensional finite element mesh generation is presented in this paper. The method is based on an extension of the Delaunay triangulation algorithm to three dimensions, Using the mesh generator, problems are defined by means of simple three-dimensional solid modeling commands. Mesh generation is performed automatically from the objects entered. Various two and three-dimensional Delaunay mesh generation algorithms are also compared and insights to robust mesh generation provided.
01 Aug 1985
TL;DR: In this paper, a technique denoted the finite difference (FD) algorithm, previously described in the literature and applicable to one derivative at a time, is extended to the calculation of several simultaneously.
Abstract: This paper deals with methods for obtaining near-optimum step sizes for finite difference approximations to first derivatives with particular application to sensitivity analysis. A technique denoted the finite difference (FD) algorithm, previously described in the literature and applicable to one derivative at a time, is extended to the calculation of several simultaneously. Both the original and extended FD algorithms are applied to sensitivity analysis for a data-fitting problem in which derivatives of the coefficients of an interpolation polynomial are calculated with respect to uncertainties in the data. The methods are also applied to sensitivity analysis of the structural response of a finite-element-modeled swept wing. In a previous study, this sensitivity analysis of the swept wing required a time-consuming trial-and-error effort to obtain a suitable step size, but it proved to be a routine application for the extended FD algorithm herein.
TL;DR: In this article, a harmonic force matrix of a rectangular element under uniform harmonic excitation was developed for nonlinear forced vibration analysis, where inplane deformation and inertia were both considered in the formulation.
Abstract: The finite element method has been extended to determine the response of large amplitude forced vibrations of thin plates. A harmonic force matrix of a rectangular element under uniform harmonic excitation is developed for nonlinear forced vibration analysis. Inplane deformation and inertia are both considered in the formulation. Results obtained are compared with simple elliptic response, perturbation and other approximation solutions.