Strain-energy bounds in finite-element analysis by slab analogy

Abstract

It is well known that in approximate analysis of elasticity problems lower and upper bounds to the true strain-energy content can be obtained by the alternative assumptions of compatible displacement fields or of equilibrating stress fields. While formulations based on the first are relatively easy to achieve those based on the second present many difficulties. In this paper it is shown how by virtue of the analogy between plane-elasticity and slab-deflection problems compatible-displacement formulations in either one can be used to generate equilibrating formulations in the other. This should result in a direct application of existing programmes to a wider range of problems.