A formulation for multiple loading cases in plastic topology design of continua

Abstract

In the real life, most industrial structures are subject to multiple load cases. The present paper proposes a topology optimization formulation for multiple loading cases. It is based on the recently developed Direct Method of Limit Analysis for plastic topology Design (LADM). In this formulation, a single mathematical problem is considered to optimize structures under multiple loading cases; each case acts independently at a different time. For the continuous design problem, as in LADM, a unique iteration is considered. For the discrete, i.e. black and white, topology optimization problem, the same approach used in LADM is conserved with the use of a sequence of conic programming problems of the same form as the continuous design problem. The proposed method is illustrated with continuous and discrete example design problems. Examples with multiple loading cases confirm the conservation of the LADM features.