基于动态设计域的结构基频拓扑优化方法

Topology Optimization for Structural Fundamental Frequency Based on Dynamic Design Domain

在基于变密度法的传统结构基频拓扑优化中,会遇到局部模态的现象。根据实体材料阈值提取实体材料区域,有限元分析被限制在实体材料中进行,避免了局部模态的出现。利用图形学的膨胀算子扩展出实体材料的虚拟边界,并利用滤波器将实体材料的敏度延拓至虚拟边界,根据敏度实现被移除材料的重现。动态设计域由实体材料和虚拟边界构成,并在迭代过程中根据背景网格信息动态重构设计域和有限元模型。此外,对于优化过程中可能出现的孤岛和非流形点等不稳定结构,通过火烧法识别并将其从实体材料中删除,进而稳定优化过程。所提方法被集成到COMSOL软件中,并通过几个数值算例,证明了所提方法的有效性。结果表明,所提方法能够有效的避免局部模态问题,获得稳定的收敛解。

The phenomenon of localized modes often occurs in the traditional topology optimization for structural fundamental frequency based on the density method.In this paper,the solid material region is extracted according to the solid material threshold,and finite element analysis is limited to the solid material to avoid the appearance of localized modes.The virtual boundary of the solid material is extended by the expansion operator of graphics;the sensitivity of the solid material is extended to the virtual boundary by the filter;and the reproduction of the removed material is realized according to the sensitivity.The dynamic design domain is composed of solid material and virtual boundary,and the design domain and finite element model are reconstructed dynamically according to the background grid information in the iterative process.In addition,unstable structures such as islands and non-manifold points that may appear in the optimization process are identified and removed from the solid material by fire-burning method to stabilize the optimization process.The proposed method is integrated into the COMSOL software,and several numerical examples demonstrate the effectiveness of the proposed method.The results show that the proposed method can effectively avoid the localized modes and obtain a stable convergence solution.