复合材料/结构两尺度动力学拓扑优化设计

Double-scale Dynamic Topology Optimization Design of Composite Materials and Macro-structures

基于均匀化理论,建立以结构第一阶固有频率最大为目标的宏/微观结构构型与材料分布的两尺度动力学拓扑优化模型,推导目标函数和约束函数对宏/微观设计变量的灵敏度,研究两尺度动力学拓扑优化方法。另外,采用一个修正固体各向同性材料惩罚(SIMP)模型避免局部模态现象。相关数值算例说明,该方法可以有效实现结构基频最大化的材料/结构两尺度动力学拓扑优化设计。此外,通过算例研究复合材料的弹性模量对优化结果的影响规律。

Based on the homogenization theory,a double-scale dynamic topology optimization model for the macroscopic structure configuration and the microscopic material distribution is established with maximizing the first natural frequency of the structure as the goal.Then the sensitivity of the objective function and constraint functions to macro/micro design variables is derived.And the double-scale dynamic topology optimization method is studied.In addition,the model of a modified solid isotropic material with a penalization(SIMP)is used to effectively avoid the localized mode phenomenon.Numerical examples show that this method can effectively realize the double-scale dynamic topology optimization design of material/structure with the fundamental frequency of the structure maximized.Finally,the influence of the elastic modulus of the composite material on the optimization results is studied by numerical examples.