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针对质量最小化、位移为约束条件的结构材料优化问题,提出了一种变位移约束的结构材料拓扑优化方法。采用分式有理式识别结构材料单元特性参数,以细观单元拓扑变量倒数为设计变量,结合均匀化方法求出宏观结构单元的等效刚度矩阵以及其对细观单元设计变量的导数,进而得到位移的一阶近似展开式。结合变约束限的思想,得到了以结构质量作为目标函数、位移作为约束条件的连续体细观结构拓扑优化近似模型;并采用对偶方法进行求解。对几种典型结构,进行了考虑单个和多个位移约束的结构材料优化设计,所得结果验证了本文方法的有效性和可行性。
Aimed at optimization of structural materials with minimized mass and displacement as constraints, a topology optimization method of structural materials with varying displacement constraints is proposed. In this paper, the rational parameters are used to identify the structural parameters of structural materials. The inverse stiffness of the topological variables is used as the design variable. The equivalent stiffness matrix of the macroscopic structural elements and the derivative of the design variables of the mesoscopic elements are obtained by the homogenization method. Displacement of the first order approximate expansion. Combining with the idea of variable constraint, a topology approximation model of continuous mesostructure with structure quality as objective function and displacement as constraint condition is obtained. The duality method is used to solve the problem. For several typical structures, the optimal design of structural materials considering single and multiple displacement constraints is validated. The obtained results verify the effectiveness and feasibility of the proposed method.