基于BESO方法的多孔微观结构材料优化设计

Optimal Design of Microstructural Materials Based on the BESO Method

轻质多孔微结构材料以其优异的性能,在工程中应用广泛。多孔材料的性能可通过设计其微结构几何构型来实现。首先通过均匀化方法,建立周期多孔材料的宏观性能与其微结构几何构型之间的关系;然后,针对双向渐进结构优化方法(Bidirectional Evolutionary Structural Optimization,BESO)中结构边界不够光滑的问题,采用形函数插值技术对边界单元进行细化处理,改进BESO方法;最后,基于改进的BESO方法,以材料体积模量和剪切模量最大化为目标,对多孔材料周期微结构进行拓扑优化设计,得到体积模量及剪切模量最大化的多孔材料微结构构型。

Lightweight porous microstructural materials are widely used in engineering applications because of their excellent material properties.The specified properties of the porous materials can be tailored by designing their microstructural topologies.In this paper,relationship between the macroscopic properties of the periodic porous materials and their microstructural configurations is established by the homogenization method.Then,to tackle the zigzag boundary problem which is inevitable in the Bidirectional Evolutionary Structural Optimization(BESO)method,the shape function is adopted to interpolate and refine the boundary elements so as to improve the BESO method.Finally,the improved BESO method is used to optimize the periodic microstructural topologies of the porous material for maximizing its material bulk and shear moduli,respectively,and the microstructural configurations of the porous materials with maximum bulk and shear moduli are obtained.