A NEW FINITE ELEMENT FORMULATION FOR PLANAR ELASTIC DEFORMATION

Abstract

For the stress analysis of planar deformable bodies, we usually refer to either plane stress or plane strain hypothesis. Three-dimensional analysis is required when neither hypothesis is applicable, e.g. bodies with finite thickness. In this paper, we derive an ‘exact’ solution for the plane stress problem based on a less restrictive hypothesis than σz=0. By requiring the out-plane stress σz to be a harmonic function, the three-dimensional solution is obtained. In addition, we present a two-dimensional finite element for planar analysis of problems where the thickness of the body 2h is comparable to other characteristic dimensions. This element is presented as a substitute for classical plane stress and plane strain finite elements. The typical plane stress and plane strain state are recovered in the case where h→0 and the case h→∞, respectively. As an example for the application of such formulation, the behaviour of a concrete gravity dam is investigated. It is shown that this structure, typically analysed by using plane strain hypothesis, has its out-plane stress underestimated. © 1997 John Wiley & Sons, Ltd.