宏观结构性能约束下的材料微结构拓扑优化

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。

Topology optimization for microstructures of materials with macrostructure property constraint

To design periodic optimized microstructures of cellular steel or steel/aluminum composites,a topologi-cal optimization model was developed by independent continuous mapping method where minimized total mass of structure was taken as obj ective,and nodal displacement was referred to as constraint condition.It is assumed that macrostructure is made of cellular materials or composites whose effective properties are calculated through the hom-ogenization theory.Topological variables in micromaterials were defined.Nodal displacement constraint was approx-imately formulated in terms of the first-order Taylor expansion.Various demands for designing materials were trea-ted as constraint conditions in optimization model.The sensitivities expression of nodal displacement and total mass were derived.Filtering method by solving partial differential equation was adopted to eliminate numerical instabili-ties.A variety of optimal material microstructures which meet design requirements have been obtained in some 2D numerical examples.The results validate the feasibility and effectiveness of the proposed method for the topology optimization design for microstructures of materials.