To capitalize on the advantages of concurrent topology optimization while alleviating computational burdens, this paper introduces a novel design methodology termed (TVCTO) with differentiable microstructures. The filled differentiable microstructures represent a collection of parametrically controlled microstructures that are differentiable with respect to geometric and physical properties. This paper employs the minimum compliance model constrained by volume to optimize the density of the macrostructure, considering three types of design variables: the element density of the macrostructure, the initial microstructure value, and its deformation parameters. Concurrently, microstructures are generated starting from an initial microstructure using the thermal diffusion process and then are optimized through backward derivation. The proposed TVCTO offers flexible adaptability to various working conditions while significantly mitigating dependence on initial input microstructures. Numerical experiments validate the feasibility and effectiveness of the proposed algorithm, demonstrating the capability to inherently resolve connectivity challenges.

中文翻译：

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具有微分微观结构的多尺度复合材料的并行拓扑优化


为了利用并发拓扑优化的优势，同时减轻计算负担，本文引入了一种具有可微结构的新型设计方法（TVCTO）。填充的可微结构代表了参数控制微结构的集合，这些结构在几何和物理属性方面是可微的。本文采用体积约束的最小柔度模型来优化宏观结构的密度，考虑了三类设计变量：宏观结构的单元密度、初始微观结构值及其变形参数。同时，使用热扩散过程从初始微观结构开始生成微观结构，然后通过向后推导进行优化。所提出的 TVCTO 能够灵活适应各种工作条件，同时显着减轻对初始输入微观结构的依赖。数值实验验证了所提出算法的可行性和有效性，展示了从本质上解决连接挑战的能力。