Decomposition in optimal plastic design of structures

Abstract

A structural synthesis procedure based on the Dantzig-Wolfe decomposition principle is developed for the optimal plastic design of structures subject to multiple load conditions. The decomposed structural synthesis problems consist of a restricted master and a number of subproblems. Each subproblem is further divided into second-level subproblems for which closed form solutions are obtained. The decomposition procedure generates not only an optimal solution for the plastic design problem but also the collapse mechanism associated with the optimal design. An optimal solution generated by the decomposition procedure is shown to be a saddle point for the associated Lagrangian function, which is sufficient for global optimally and zero duality gap. The dual problem for the optimal plastic structural design is interpreted as the maximization of the total power of loads, subject to limitations on the total specific power of dissipation in each structural member. Numerical results for a collection of two- and three-dimensional structures are generated by the decomposition procedure. The computational efficiency and numerical accuracy are confirmed by comparison with previously reported results for trusses and approximate solutions for plane stress structures.