Limit Design in the Absense of a Given Layout: A Finite Element, Zero-One Programming Approach∗

Abstract

Limit design in three dimensions is discussed and formulated as a constrained minimax problem in kinematic and geometric variables. A finite element discretization is proposed which, combined with piecewise linearization of the yield surfaces, reduces the minimum weight design to a pair of dual problems in linear mixed zero one programming. The relevant duality theory is shown to be useful for the theoretical frame of the mechanical problem. Various ways of reducing the number of variables and constraints are pointed out, in order to make available algorithms economically applicable to practical situations.