Topology optimization of structures under multiple load cases using a fiber-reinforced composite material model

Abstract

This paper presents a method to optimize the topology of structures under multiple load cases with stress constraints. Fiber-reinforced orthotropic composite is employed as the material model to simulate the constitutive relation of truss-like continua. The fiber densities and orientations at the nodes are taken as design variables. First, for each load case, the fiber orientations are aligned with the orientations of principal stress and the fiber densities are adjusted according to the strains along the fiber orientations. Then, to optimize the structure, the fiber densities and orientations under multiple load cases are determined by constraining its elastic matrix to approach the elastic matrix of the optimum structures defined for each single load case. Finally the member distribution in the optimal structure is suggested by the continuous lines formed according to the fiber densities and orientations. Several examples are presented to demonstrate the effectiveness of the proposed approach.