Concurrent material and structural optimization of hollow plate with truss-like material

Abstract

In this paper, optimum stress distribution for hollow plates composed of linear cellular materials (LCMs), a kind of truss-like material, is investigated. To reduce the computational cost, we model the material as micropolar continua representation. Two classes of design variables, relative density, and cell-size distribution of truss-like materials are to be determined by optimization under given total material volume constraint. And the concurrent designs of material and structure are obtained for three different optimization formulations. For the first formulation, we aim at the minimization of the maximum stress that appears at the initial uniform design; for the second formulation, we minimize the highest stress within the specified point set. As the yield strength of truss-like material is dependent on the relative material density, we minimize the ratio of stress over the corresponding yield strength along the hole boundary in our third formulation, which maximizes the strength reserve and seems more rational. The numerical results for the three objectives validate the concurrent optimization method proposed in this paper. And the influence of ply angle (angle between the principle direction of material and the axes of the system’s coordinates) on the optimum result is discussed. The dependence of optimum design on finite element meshes is also investigated. An approximate discrete model is established to verify the method proposed in this paper, and the stress concentration near a hole is reduced significantly.