An efficient implementation of limit state calculations based on lower-bound solutions

Abstract

Limit state problems are formulated in a general finite element format with stress-based elements. The analysis method is based on the lower-bound theorem which states that stress fields in equilibrium not violating the yield criteria are possible solutions. The solution method is to find the optimal stress distribution which maximizes the load. Linearization of the yield criteria leads to a linear programming problem. In order to have an efficient implementation we have made two improvements compared to previous studies. The first implies that the number of stress parameters are reduced a priori via the equilibrium equations, and the second concerns the linear programming problem, where the traditional non-negative parameter requirement is avoided. The method is described via the plane frame problem but has also been implemented for plates.