COMPUTING LIMIT LOADS BY MINIMIZING A SUM OF NORMS

This paper treats the problem of computing the collapse state in limit analysis for a solid with a quadratic yield condition, such as, for e xample, the von Mises condition. After discretization with the finite element method, using divergence-free elements for the plastic ow, the kinematic formulation reduces to the problem of minimizing a sum of E uclidean vector norms, subject to a single linear constraint. This is a nonsmooth minimization problem, since many of the norms in the sum m ay vanish at the optimal point. Recently an efficient solution algorit hm has been developed for this particular convex optimization problem in large sparse form. The approach is applied to test problems in limi t analysis in two different plane models: plane strain and plates. In the first case more than 80% of the terms in the objective function ar e zero in the optimal solution, causing extreme ill conditioning. In t he second case all terms are nonzero. In both cases the method works v ery well, and problems are solved which are larger by at least an orde r of magnitude than previously reported. The relative accuracy for the solution of the discrete problems, measured by duality gap and feasib ility, is typically of the order 10(-8).