连续体结构动力拓扑优化中局部模态处理的新方法

采用固体各向同性材料惩罚模型（solid isotropic material with penalization， SIMP） 进行动力拓朴优化通常在优化过程中会出现虚假的局部振动模态，为消除这种虚假模态产生的不利影响，提出了移频与虚假模态识别相结合的通用方法. 研究中考虑以材料体积为约束、结构基频最大化为目标的优化模型，并采用节点设计变量描述设计域内材料分布. 基于虚假模态的特性，首先在特征值分析中应用移频方法排除特征值接近于零的低阶虚假模态，然后再依据虚假模态识别准则判定并剔除其他可能存在的虚假模态，从而可以高效可靠地确定结构真实的固有振动模态. 数值算例表明，提出的方法可以有效地消除动力拓扑优化中虚假模态可能产生的不利影响，并保证优化解的可靠性. 

A NEW METHOD FOR DEALING WITH PSEUDO MODES IN TOPOLOGY OPTIMIZATION OF CONTINUA FOR FREE VIBRATION

Pseudo modes may appear in topology optimization of continua when the SIMP (Solid Isotropic Material with Penalization) material model is used for eigenvalue problems. A new method based on the combined use of the frequency shift technique and pseudo mode identification is proposed to eliminate the detrimental effect of such pseudo modes. The topology optimization of continuum structures for maximum fundamental frequency subjected to volume constraint is considered in the study. The nodal densities are taken as design variables to describe the material distribution in the design domain. Based on an investigation of the characteristics of pseudo vibration modes, the eigenvalue shift technique is suggested for avoiding low-order pseudo modes with small eigenvalues from the eigenmode extraction, and further a pseudo mode identification criterion is constructed to exclude other high-order pseudo modes. A highly efficient and reliable algorithm for the topology optimization is then made possible. Numerical examples are presented illustrating the effectiveness of the proposed method.