Study on the Topology Optimization Method of High-strength Light-weight Component Based on Homogenization Theory
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摘要: 对复合材料微观结构的拓扑优化进行研究。采用有限元理论,以微观单元的密度为设计变量、材料体积分数为优化约束条件、渐进均匀化理论求得的材料宏观力学性能为优化目标建立模型。并采用变密度法描述问题,优化准则法进行求解,通过Matlab语言编程实现微观结构的拓扑优化,得到具有最优等效力学性能的微结构构型。讨论了过滤半径、网格密度以及惩罚因子对优化过程及结果的影响,选取适当的参数建立优化模型,并将上述优化模型用于冲孔板的优化,实现了构件轻质高强设计。Abstract: The topology optimization of microstructure for composite material is studied. Based on the finite element method, the mode is established by using the density of micro-unit as the design variable, the volume fraction as the optimization constraints, the mechanical properties as the optimization objective. The solid isotropic material with penalization is adopted to describe the model, with the optimization criterion method as the solution algorithm. And the topology optimization of mierostructure is realized by using Maflab language. Therefore, the optimal effec-tive properties are obtained. Different filter radius, mesh sizes and penalization factors are discussed to obtain the optimal parameters. The optimization model is used on the design of porous plate, and the implementation of the components with light weight and high strength is done.
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Key words:
- composite material /
- microstructure /
- topology optimization /
- homogenization theory /
- filtering
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