点阵材料微极连续介质模型的应力优化设计

在将二维周期性点阵类材料等效为具有非局部化本构的微极连续介质的基础上，运用优化技术，探讨了基于材料相对密度和微单胞特征尺度两类变量的优化结构应力的方法，给出了针对最小化结构关键部位应力、结构最大应力最小化、最大化结构关键部位安全储备三类特定目标的结构与材料一体化协同优化结果．利用圆板小孔应力集中的数值算例验证了方法的有效性．

Stress optimization for truss-like materials based on micropolar continuum representation

In this paper,the optimum stress distribution around a hole is investigated for LCMs materials with micropolar continuum representation to reduce the computational cost. Two classes of design variables, relative density and cell size distribution of the truss-like materials, are to be determined by optimization under the given total material volume constraint. The concurrent designs of materials and structures are obtained for three different optimization formulations. In the first formulation, one minimizes the stress around the hole; in the second formulation, one minimizes the highest stress within the whole structure. Since the yield strength of truss-like materials depends on the relative material density, we minimize the ratio of stress over the corresponding effective yield strength along the hole boundary in our third formulation, which maximizes the strength reserve, which seems more rational. Numerical results for the three objectives validate the method proposed in this paper.The influence of the ply angle (angle between the principle direction of material and the axes of system's coordinate) on the optimum result is discussed. The dependence of the optimum design on finite element meshes is also investigated.