Object-Oriented Nonlinear Finite Element Programming: A Primer

Abstract

This article describes an introductory object-oriented finite element program for static and dynamic nonlinear applications. This work can be considered as an extension of the original FEM_Object environment dealing with linear elasticity [1] and nonlinearity [2]. Mainly the static aspects are discussed in this paper. Interested readers will find a detailed discussion of the object-oriented approach applied to finite element programming in [15-18] and also in [7-8] and references therein. Our ambition, in this paper, is limited to a presentation of an introductory object-oriented finite element package for nonlinear analysis. Our goal is to make a starting package available to newcomers to the object-oriented approach and to provide an answer to the large number of demands for such a program received in recent time. In the first part of the paper, a brief recall of the basics of finite element modeling applied to continuum mechanics is given. Von Mises plasticity including isotropic and kinematic hardening, which is used as model problem, is described. This first part also presents an overview of the main features of the object-oriented approach. In the second part of this paper, classes and associated tasks forming the kernel of the code are described in detail. A hierarchy of classes is proposed and discussed; it provides an immediate overview of the program's capabilities. Finally interactions between classes are explained and numerical examples illustrate the approach.