基于变频率区间约束的结构材料优化设计

针对频率约束的结构材料优化问题,基于结构拓扑优化思想,提出变频率区间约束的结构材料优化方法。借鉴均匀化及ICM(独立、连续、映射)方法,以微观单元拓扑变量倒数为设计变量,导出宏观单元等效质量矩阵及导数,进而获得频率一阶近似展开式。结合变频率区间约束思想,获得以结构质量为目标函数、频率为约束条件的连续体微结构拓扑优化近似模型;采用对偶方法求解。通过算例验证该方法的有效性及可行性,表明考虑质量矩阵变化影响所得优化结果更合理。

Topology optimization of micro structures with varying frequency interval constraints

Based on the structural topology optimization idea, a structural material optimization method with varying frequency interval constraints was proposed to solve the problem of structural material optimization with frequency constraints. By use of homogenization and ICM (Independent Continuous and Mapping) method, the effective mass matrix and its derivatives were established through taking the reciprocal topological variables of micro structural elements as design variables, and the one order approximate explicit functions of frequency interval constraints were constructed. Integrated with the idea of varying frequency interval constraints, a topological optimization model of micro structures was formed by taking the structural mass as objective function and the frequency as constraint functions. Then, a dual solving method was adopted. Two example results show that the proposed method is feasible and effective, and the optimal result obtained by the proposed method in which the change quantities of the mass matrix is considered, are more reasonable.