静动态多目标下的连续体结构拓扑优化

Static and Dynamic Multi-objective Topological Optimization of Continuum Structure

为实现静动态多目标下的拓扑优化结构设计,以静态柔顺度或节点位移最小化和动态特征值最大化加权函数为目标,提出并建立静动态多目标连续体结构拓扑优化模型。单元形函数插值作用下的节点独立变量场具有零阶连续性,在连续体结构拓扑描述一定程度上避免棋盘格现象。变量独立性在单元刚度阵、单元质量阵和单元体积的建模中更具有灵活性。规一化目标函数避免不同性质目标函数的量级差异。基于过滤法进一步改善目标函数的光滑性,克服了连续体拓扑优化中常见数值不稳定性问题。数值算例结果表明,模型和方法在静动态多目标下连续体结构拓扑优化设计中的可行性和有效性。

A multi-objective programming scheme for continuum topology optimization is proposed,in which both compliance,displacement of nodes and eigenfrequency are regarded as static and dynamic optimization objectives,respectively.Node-based independent variables which ensure continuity in design domain are taken as design variables.The method is immune to checkerboard instabilities that are a concern with element-based design variables.Modeling of stiffness matrix,mass matrix and volume of element are more flexibl...