Finite element planar stress analysis

For the stress analysis of planar deformable bodies, we usually refer to either a plane stress or plane strain hypothesis. Three-dimensional analysis is required when neither hypothesis is applicable, e.g. bodies with fmite thicknesses. In this paper, we derive an ‘exact’ solution for the plane stress problem based on a less restrictive hypothesis than o, = 0. By requiring the out-ofplane stress 0, 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 -+ co, respectively. As an example for the application of such formulation, the behavior of a concrete gravity dam is investigated. Copyright 0 1996 Elsevier Science Ltd.