Theoretical and practical aspects of finite elements in the context of some problems of solid mechanics
type: Item
instance of: scholarly article
title: Theoretical and practical aspects of finite elements in the context of some problems of solid mechanics
zbMATH Open document ID: 0701.73058
author: John Whiteman
author: A. E. Beagles
author: M. K. Warby
published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
publication date: 1990-01-01T00:00:00Z
review text: This paper is concerned with the use of computational modelling to produce approximations to the solutions of certain linear and nonlinear problems of solid mechanics. The aims are as follows: to describe the forms of the mathematical models of the problems, indicating the major differences between the various contexts and explaining what assumptions have been made in these concerning the physics; to desribe the application of the finite element method using Galerkin techniques for each problem and to give some theoretical finite element error estimates where this is possible. In the context of error estimates the phenomenon of superconvergence is introduced. We have shown the applicability and state of knowledge in the use of finite element methods in the context of linear elasticity, elastoplasticity and viscoelasticity. The major differences between these result from the different constitutive relations required. In the simplest case of linear elasticity no time or history effects are involved and the theory is well developed. However with the more complicated materials the models may involve time and history effects. In the elastoplastic model the resulting equations are nonlinear. This model involves a ``time'' parameter as a result of the incremental loading procedure, as well as indirectly in the integration of the hardening rule. The history affects the value of the hardening parameters. In the viscoelastic model time and history effects are explicitly involved through the constitutive equations. In both these cases the theory concerning error estimates is much less developed than for the case of linear elasticity.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74Hxx
zbMATH DE Number: 4149685
zbMATH Keywords: computational modelling
zbMATH Keywords: nonlinear problems
zbMATH Keywords: Galerkin techniques
zbMATH Keywords: finite element error estimates
zbMATH Keywords: superconvergence
zbMATH Keywords: linear elasticity
zbMATH Keywords: elastoplasticity
zbMATH Keywords: viscoelasticity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4149685