This work presents a generalized substructuring‐based topology optimization method for the design hierarchical lattice structures to maximize the first eigenvalue. In this method, the macrostructure is assumed to be composed of substructures with a common artificial lattice geometry pattern. And two different yet connected scales are considered through a lattice geometry feature parameter. The feature parameter, which can control the material distribution of the substructure, determines the relative density of corresponding substructure. Each substructure is condensed into a super‐element to obtain the associated density‐related matrices. A surrogate model using cubic spline interpolation has been particularly built to map the density to stiffness and mass matrices of condensed super‐elements. The derivatives of super‐element matrices to the associated densities can be evaluated efficiently and accurately. Here, an augmented penalized density for this surrogate model is introduced. And the conventional optimality criteria method is selected as updating method of the density design variables. Numerical examples under two lattice patterns of substructures are shown to validate the correctness and superiority of this substructure‐based topology optimization method.

中文翻译：

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基于子结构的拓扑优化，以最大化分层晶格结构的第一特征值

这项工作为设计分层格结构提供了一种基于子结构的广义拓扑优化方法，以最大化第一个特征值。在这种方法中，假定宏观结构由具有共同的人造晶格几何图案的子结构组成。并且通过晶格几何特征参数考虑了两个不同但尚未连接的比例尺。可以控制子结构的材料分布的特征参数确定相应子结构的相对密度。每个子结构都被压缩成一个超级元素，以获得相关的密度相关矩阵。特别建立了使用三次样条插值的替代模型，以将密度映射为压缩超元素的刚度和质量矩阵。超元素矩阵对相关密度的导数可以得到有效而准确的评估。在此，引入了针对该替代模型的增加的惩罚密度。并选择了传统的最优准则方法作为密度设计变量的更新方法。显示了两个子结构的格子模式下的数值示例，以验证这种基于子结构的拓扑优化方法的正确性和优越性。