Topology Optimization of Truss-Like Structure with Stress Constraints Under Multiple-Load Cases

Abstract

A new method for topology optimization of truss-like structures with stress constraints under multiple-load cases (MLCs) is presented. A spatial truss-like material model with three families of orthotropic members is adopted, in which the three families of members along three orthotropic directions are embedded continuously in a weak matrix. The densities and directions of the three families of members at the nodes are taken as the design variables. An optimality criterion is suggested based on the concept of directional stiffness. First, under each single-load case (SLC), the truss-like structure is optimized as per the fully stressed criterion. Accordingly, the directional stiffness of the optimal structure under an SLC at every node is obtained. Next, the directional stiffness of the truss-like structure under MLCs is determined by ensuring that the directional stiffness is as similar as possible to the maximum directional stiffness of the optimal structure under every SLC along all directions. Finally, the directions and densities of the members in the optimal truss-like structures under MLCs are obtained by solving the eigenvalue problems of the coefficient matrix of the directional stiffness at every node. Two examples are presented to demonstrate the effectiveness and efficiency of the method.