In this study, we propose a multiscale thickness optimization method for designing micro-shell structure assuming that the macrostructure consists of multiple micro-shell structures. The micro-shell structures are connected to the macrostructure using the NIAH (Novel numerical implementation of asymptotic homogenization) method. The distributed thickness of the micro-shell structures is used as design variable. A squared error norm between actual and target displacements is minimized for controlling the displacements at arbitrary points of the macrostructure to the target values under the total volume constraint including the volume of the micro-shell structures. This design is formulated as a distributed optimization problem, and the thickness gradient function is theoretically derived. The derived sensitivity function is applied to the scalar-type H1 gradient method to efficiently obtain the optimal thickness distribution of the micro-shell structures. Numerical examples demonstrate the effectiveness of the proposed method to optimize the thickness distribution of complex micro-shell structures.

中文翻译：

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嵌入 3D 宏观结构中的微壳结构的最佳厚度设计方法


在本研究中，我们提出了一种多尺度厚度优化方法，用于设计微壳结构，假设宏观结构由多个微壳结构组成。使用 NIAH（渐近均质化的新型数值实现）方法将微壳结构连接到宏观结构。微壳结构的分布厚度用作设计变量。在总体积约束（包括微壳结构的体积）下，为了控制宏观结构任意点的位移到目标值，实际位移和目标位移之间的平方误差模最小化。该设计被表述为分布式优化问题，并从理论上推导了厚度梯度函数。将推导的灵敏度函数应用于标量型 H1 梯度法，以有效地获得微壳结构的最佳厚度分布。数值算例证明了所提出的方法在优化复杂微壳结构的厚度分布方面的有效性。