A decomposition procedure for large‐scale optimum plastic design problems

A decomposition procedure is proposed in this paper for solving a class of large‐scale optimum design problems for perfectly‐plastic structures under several alternative loading conditions. The conventional finite element method is used to cast the problem into a finite dimensional constrained nonlinear programming problem. Structures of practically meaningful size and complexity tend to give rise to a large number of variables and constraints in the corresponding mathematical model. The difficulty is that the state‐of‐the‐art mathematical programming theory does not provide reliable and efficient ways of solving large‐scale constrained nonlinear programming problems. The natural idea to deal with the large‐scale structural problem is somehow to decompose the problem into a collection of small‐size problems each of which represents an analysis of the behaviour of each finite element under a single loading condition. This paper proposes one such way of decomposition based on duality theory and a recently developed iterative algorithm called the proximal point algorithm.