Jean-Pierre Pelle

An automatic procedure with a control of accuracy for finite element analysis in 2D elasticity

Abstract This paper gives a procedure for an automation of the entire finite element analysis for 2D or axisymmetric elastic structures with a control of accuracy. The user describes the problem and the level of desired accuracy. The procedure then provides an approximate solution for a minimal computation cost. This procedure uses an error measure based on the constitutive relation [1–5] and an efficient adaptive technique [6] which automatically take account of the regions of stress concentration. Examples are presented for discretizations using 3- or 6-node triangular elements.

A posteriori error estimation for unilateral contact with matching and non-matching meshes

In this paper, we consider the unilateral contact problem between elastic bodies. We propose an error estimator based on the concept of error in the constitutive relation in order to evaluate the finite element approximation involving matching and non-matching meshes on the contact zone. The determination of the a posteriori error estimate is linked to the building of kinematically-admissible stress fields and statically-admissible stress fields. We then propose a finite element method for approximating the unilateral contact problem taking into account matching and non-matching meshes on the contact zone; then, we describe the construction of admissible fields. Lastly, we present optimized computations by using both the error estimates and a convenient mesh adaptivity procedure. ” 2000 Elsevier Science S.A. All rights reserved.

Error estimation and time-space parameters optimization for FEM non-linear computation

In this paper, two adaptive methods which permit the control of the parameters of a finite element computation for time-dependent material models are proposed. These methods use a global error measure in the constitutive relation based on Druckers inequality. This error includes the accuracy of both the finite element model and the algorithm being used, over the studied time interval. In order to master the rnesh element size and the time increments length, an error estimator, which permits the estimation of the errors due to the time discretization, is proposed. Various examples show the reliability of these procedures.

Analyses éléments finis adaptatives pour les structures tridimensionnelles en élasticité

ABSTRACT The design of three-dimensional structures requires finite element computations, whose cost in human and computational time becomes prohibitive when a reasonable criterion of quality is imposed. Methods of control of the discretization errors and optimization of the parameters of the analysis enable the application of finite element analysis; yet, the main difficulty in 3D is the adaptivity of the meshes. The purpose of this paper is to present and compare several methods in order to address this difficulty.

Sur l'adaptativité des maillages à base de quadrilatères

ABSTRACT This paper gives a procedure of mesh adaptivity with quadrilateral elements. This procedure uses an error measure based on the constitutive relation, an efficient adaptive technique which automatically takes account of the singularities and the regions of stress concentration and a mesh generator of quadrilateral elements. We propose as application for 2D elastic structures the extension of automation of the finite element analysis which has been developed for triangular elements to the quadrilateral elements. The user describes the problem and the level of desired accuracy. The procedure then provides an approximate solution for a minimal computation cost with the respect of the desired accuracy. Examples are presented for discretizations using 4- or 8-node quadrilateral elements.

Contrôle et adaptation des calculs éléments finis pour les problèmes de contact unilatéral

ABSTRACT In this paper, we present an error estimator for the contact problem of an elastic body on a rigid foundation in elasticity or Signorinis problem. The estimator is based on the concept of error in the constitutive relation and on techniques of admissible fields building. It is carrying into effect with a particular technique in order to take into account the contact. The convergence rate of this estimator is studied. By using procedures of mesh adaptivity previously developed, we show an example of optimized computations for discretizations with 3-nodes triangles.

Methods and Softwares for the Automation of Finite Element Analyses in 3D

During the design phase of a structure, it is often necessary to conduct several studies of the mechanical behavior whose cost in both human and computer time is often very significant. In the context of finite element computations, in order to decrease costs while respecting the user’s required level of accuracy, it is essential to control discretization errors and to master calculation parameters. However, in 3D, the development of a correctly-adapted mesh presents a real difficulty. The objective of this paper therefore is to present a method based on several software programs in order to overcome this difficulty.

Adaptative Control of the error in the von Mises Stress in 2D Elasticity

In current industrial situations, it is necessary to have reliable evaluations of local quantities such as Von Mises stress. These quantities are evaluated using F.E. code. Even if the mechanical model chosen is adequate, the mesh used in F.E. analysis introduces errors on the quantities being computed. For the engineer, it is essential to study and, if possible, to improve the quality of the computations carried out. In this work, we focus on the quality of a 2D elastic finite element analysis. Our objective is to control the discretization parameters in order to achieve a prescribed local quality level over a dimensioning zone. The method is illustrated through 2D test examples.