多孔结构导电性能拓扑优化设计与实验验证

针对结构电导率受构型影响、导电性能难以准确评估等问题，提出一种多孔结构导电性能拓扑优化设计与实验验证方法。首先，研究了基于静电场理论的三维数值均匀化方法，实现了对三维多孔结构等效导电属性的评价。其次，基于变密度拓扑优化方法，以体积分数为约束条件，结合均匀化理论建立了微观尺度下多孔结构电导率最大化拓扑优化模型。然后，采用伴随变量法对目标函数进行了灵敏度分析，通过优化准则算法进行了求解，实现了不同初始结构设计和体积分数下多孔结构拓扑优化设计。最后，通过有限元分析和实验进一步验证了多孔结构的等效导电属性。结果表明：本文方法可有效优化多孔结构导电性能。

Topological optimization design and experimental verification of electrical conductivity for cellular structures

Aiming at the problems that the electrical conductivity of the structure is affected by the configuration and the electrical conductivity is difficult to evaluate accurately. A topology optimization design and experimental verification method for the electrical conductivity of cellular structures is proposed. Firstly, a three-dimensional numerical homogenization method based on electrostatic field theory is studied. The evaluation of the equivalent conductive properties of three-dimensional cellular structures is realized. Secondly, a topology optimization model for maximizing the electrical conductivity of cellular structures at the microscopic scale is established. It is based on the variable density topology optimization method subject to volume fraction constraint. Thirdly, the sensitivity of the objective function is analyzed using the adjoint variable method. The Optimality Criteria is used to solve the model. The topology optimization design of cellular structure under different initial structure designs and volume fractions is realized. Finally, the equivalent conductive properties of the cellular structures are further verified by finite element analysis and experiment. The study shows that this method can effectively optimize the electrical conductivity of cellular structures.