Limit analysis for plates: the exact solution for a clamped square plate of isotropic homogeneous material obeying the square yield criteron and loaded by uniform pressure

Abstract

Known exact solutions in limit analysis for rigid-perfectly plastic plates are relatively scarce because of their probable complexity even for simple loading and edge conditions. This complexity is exemplified in the present exact solution for the problem of a uniformly distributed load on a clamped square plate of isotropic homogeneous material obeying the square yield criterion in bending. The solution is extended to cover the case of a uniformly distributed load on a clamped plate of any regular polygonal shape. A comparison of the present exact results and those of Fox (1972) with earlier upper bound solutions is evidence that close upper bounds for the collapse load will normally be obtainable by the use of assumed mechanisms much simpler than the exact mechanism.