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为了设计周期性多孔钢或钢/铝复合材料优化微结构,基于独立连续映射法,建立了以结构总质量最小化为目标,节点位移为约束的拓扑优化模型。假设宏观结构由多孔材料或复合材料组成,其等效特性采用均匀化理论计算得到。定义了微观材料拓扑变量,节点位移约束采用一阶泰勒展开近似。各种材料设计要求作为约束条件纳入到优化模型中。推导了节点位移和总质量的敏度表达式。采用基于求解偏微分的过滤方法消除了数值不稳定性。在二维数值算例中获得了各种满足设计要求的优化材料微结构。结果表明:提出的方法在材料微结构拓扑优化设计中具有可行性和有效性。
In order to design periodic microstructures of porous steel or steel / aluminum composites, a topology optimization model was established based on the independent continuous mapping method, which minimized the total mass of the structure and the node displacement was constrained. It is assumed that the macrostructure consists of a porous material or a composite material, and its equivalent property is calculated using the homogenization theory. The topological variables of the microscopic material are defined, and the first-order Taylor expansion approximation of the node displacement constraints is given. Various material design requirements are incorporated into the optimization model as constraints. The sensitivity expression of node displacement and total mass is deduced. The numerical instability is eliminated by the filtering method based on solving partial differential. In the two-dimensional numerical example, various optimized microstructures that meet the design requirements were obtained. The results show that the proposed method is feasible and effective in topology optimization of material microstructure.