An upper bound limit analysis formulation for thin plates Available to Purchase

In the late 1960s, in the field of upper bound limit analysis of Kirchhoff plates, Hodge and Belytschko suggested the use of an element with quadratic transverse displacements, where the rotations were permitted to be discontinuous. In recent years, various discretisation schemes have been applied making comparisons with the results of that paper. However, 50 years ago, the optimisers were very weak, and could not even take advantage of the convexity of the problem. The aim of this paper is to revisit this rigorous formulation for second-order cone-related yield functions such as Nielsen's and von Mises'. It is shown that with a suitable formulation as a case of second-order cone programming, in the dual static form, the problem can be solved very fast and this simple element provides results that are competitive to those of various other displacement discretisation schemes combined with the same optimiser. Details on how to handle Nielsen's criterion are also given.