Shakedown analysis for complex loading using superposition

Bounding techniques for calculating shakedown loads are of great importance as design criteria since these eliminate the need for performing full cyclic loading programs either numerically or experimentally. The classical Melan theorem provides a way to recognize whether or not elastic shakedown occurs under a specified loading. Polizzotto extended Melan's theorem to the case where a combination of steady and cyclic loads are acting on the structure. The purpose of this paper is to present a finite element method, based on Polizzotto's theorem, to estimate elastic shakedown for a structure subjected to loads resulting from a combination of steady and cyclic mechanical loads. This method, called non-linear superposition, is then applied to investigate the shakedown behaviour of a biaxially loaded square plate with a central hole. Results obtained for the plate with a hole problem are compared with those available in the literature and are verified by means of cyclic elastoplastic finite element analysis