基于广义模态截断扩增方法的结构频响拓扑变量灵敏度分析

基于结构拓扑优化设计中的变密度法，采用伴随法推导结构在简谐激励下的频响振幅对单元设计变量的解析灵敏度列式。针对灵敏度数值求解中传统模态位移法引发的低精度问题，通过引入计算成本较低的广义模态截断扩增方法提升灵敏度的计算精度。数值算例将该文方法与全局有限差分法和其他灵敏度计算方法进行了比较。结果证明了该文方法在不同的激励频率及有限元网格密度下高效求解高精度灵敏度的有效性。

SENSITIVITY ANALYSIS OF STRUCTURAL TOPOLOGY DESIGN VARIABLES UNDER HARMONIC EXCITATIONS BASED ON GENERALIZED MODAL TRUNCATION AUGMENTATION METHOD

Based on the variable density method for structural topology optimization, the analytical sensitivity formulation of the frequency response displacement amplitude of structures under harmonic excitations is proposed using the adjoint method. The generalized modal truncation augmentation method is introduced to obtain high accuracy without high computational cost in contrast to the poor accuracy of the traditional modal displacement method in sensitivity computation. Numerical examples are presented to compare the proposed method with the global finite difference method and other computation methods. The computational results demonstrate the effectiveness of the proposed method in computing accurate sensitivities with high efficiency under different excitation frequencies and different densities of finite element meshes.