Implementation of Local Effects into Conventional and Non Conventional Finite Element Formulations

Abstract

The first part of this contribution is concerned with the problem of including load dependent stress singularities (such as e.g. those due to concentrated loads) into conventional assumed displacement elements. It is shown that such singularities may be conveniently handled in the form of appropriate initial strain and stresses, each of which may be accounted for following standard finite element technology. A numerical example illustrates the efficiency of the method which does not require any mesh refinement in the vicinity of the singularities. The second part of this contribution presents the concept of the so-called large finite elements (LFEs). This concept, which may be viewed as a finite element form of the Trefftz's method (ref.l), is based on using parametric displacement fields satisfying, a priori, the governing differential problem equations. Any local solution representing a stress singularity or stress concentration may be used as the LFE expansion basis. Boundary conditions and interelernent continuity are implicitly imposed by making use of a simple stationary principle and an auxiliary compatible interelernent displacement field. The excellent efficiency of the approach is demonstrated by several examples.