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
Þnite thickness. In this paper, we derive an ÔexactÕ solution for the plane stress problem based on a less
restrictive hypothesis than pz"0. By requiring the out-plane stress pz to be a harmonic function, the
three-dimensional solution is obtained. In addition, we present a two-dimensional Þnite 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 Þnite elements. The typical
plane stress and plane strain state are recovered in the case where hP0 and the case hPR, 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
