考虑微观尺度和宏观尺度的关联,将微结构胞元设计和多尺度均匀化设计结合,建立了由相同尺寸和内部构型的微结构胞元组成的复合材料结构的材料/结构一体化动力学优化设计方法,给出了相应的算例。方法中引入了微观和宏观两个尺度上的独立密度变量,采用材料属性的合理近似模型对密度进行惩罚,利用有限元超单元技术建立材料与结构的联系。基于算例获得了超单元尺寸与微观、宏观材料用量对结构拓扑构型的影响规律。将算例结果与已有方法的结果比较,表明本文方法具有合理有效性,可作为对轻质结构进行动力学设计的一种新方法。
A concurrent topology optimization method for dynamic designs associating materials and structures with periodical microstructures of different sizes was presented and related numerical experiments were carried out.In the method,the optimization object was to maximize the structure fundamental frequency,rational approximation of material properties（RAMP） was adopted to ensure clear topologies in both macro and micro scales,and design variables for macro structure and microstructures were defined separately and integrated into one system by using the super-element technique.Based on the numerical experiments,the effects of representative volume element（RVE） sizes and materials ratios of both the macro-scale and the micro-scale on structural topology were investigated,and the results indicate that the proposed method is effective and can be used as an innovative dynamic design one for lightweight structures.
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