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中文摘要：
以结构最小柔顺性为目标，提出了考虑均一微结构的结构／材料两级协同优化方法。出于制造考虑,假设了材料微结构在宏观上具有相同的构形。为实现拓扑优化．本方法在两个尺度上独立定义了单元密度作为设计变量，分别引入了SIMP（Solid Isotropie Material with Penalization）和PAMP（Porous Anisotropic Material with Penalization）方法对密度进行惩罚，并且采用了周长约束控制微结构拓扑的复杂度。借助均匀化方法建立了结构和材料之间的联系，从而将两个尺度上的设计纳入到一个优化模型中，实现了协同求解。数值算例验证了本方法的有效性和正确性，讨论了各参数的影响，优化结果体现了类桁架材料的优越性。
英文摘要：
This paper presents a concurrent topology optimization method to simultaneously achieve the optimum structure and material microstructure for minimum system compliance. Microstructure is assumed to be uniform in macro-scale to meet manufacturing requirements. Design variables for structure and material microstructure are independently defined and then integrated into one system with the help of homogenization theory. Penalization approaches are adopted in both scales to ensure clear topologies, i.e. SIMP （Solid Isotropic Material with Penalization） in micro-scale and PAMP （Porous Anisotropic Material with Penalization） in macro-scale. Numerical experiments for two examples validate the proposed method and also demonstrate the superiority of truss-like material.
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