【摘要】 研究由宏观上均匀多孔材料制成的结构的优化设计问题,待设计的结构受到给定的外力与温度载荷作用,优化设计旨在给定结构允许使用的材料体积约束下,设计宏观结构的拓扑及多孔材料的微结构,使得结构柔度最小。本文提出了一种宏观结构与微观单胞构型并发优化设计的方法,在此方法中,引入宏观密度和微观密度两类设计变量,在微观层次上采用带惩罚的实心各向同性材料法SIMP(Solid Isotropic Material with Penalty),在宏观层次上采用带惩罚的多孔各向异性材料法PAMP(Porous Anisotropic Material with Penalty),借助均匀化方法建立两个层次间的联系,通过优化方法自动确定实体材料在结构与材料两个层次上的分配,得到优化设计;提供的数值算例检验了本文所提方法及计算模型,并讨论了温度变化、材料体积及计算参数对优化结果的影响。研究结果表明同时考虑热和机械载荷时,采用多孔材料可以降低结构柔顺性。更多还原

【Abstract】 This paper presents an optimization technique for structures composed of uniform cellular materials in macro scale.The optimization aims at to obtain optimal configurations of macro scale structures and microstructures of material under certain mechanical and thermal loads with specific base material volume. A concurrent topology optimization method is proposed for structures and materials to minimize compliance of thermoelastic structures.In this method macro and micro densities are introduced as the design variables for structure and material microstructure independently.Penalization approaches are adopted at both scales to ensure clear topologies,i.e.SIMP(Solid Isotropic Material Penalization) in micro-scale and PAMP(Porous Anisotropic Material Penalization) in macro-scale.Optimizations in two scales are integrated into one system with homogenization theory and the distribution of base material between two scales can be decided automatically by the optimization model.Microstructure of materials is assumed to be uniform at macro scale to reduce manufacturing cost.The proposed method and computational model are validated by some numerical experiments.The effects of temperature differential,volume of base material,numerical parameters on the optimal results are also discussed.At last,for cases in which both mechanical and thermal loads are applied,the configuration of cellular material can help to reduce the system compliance.更多还原