Multi-scale structure, which is one of next-generation lightweight structures, has great development potential and application value. In this paper, we propose a concurrent topology optimization framework of multi-scale structures base on the phase-field method. In the framework, an energy-based homogenization approach is adopted to evaluate the macro effectiveness of the micro structure, and the Lagrange multiplier method is used to introduce volume constraints. The macro and micro structures are described with the macro and micro phase field functions, respectively. In addition, the Allen-Cahn equations are solved to update the macro and micro phase field functions. The optimal structure, which has the minimum compliance, is achieved by changing boundaries. The effectiveness and accuracy of the proposed method are verified with several numerical examples, and the effect of the initial structure on the iteration speed is investigated.

中文翻译：

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一种基于相场的多尺度结构并发拓扑优化方法


多尺度结构是新一代轻量化结构之一，具有巨大的发展潜力和应用价值。在本文中，我们提出了一种基于相场法的多尺度结构并发拓扑优化框架。在该框架中，采用基于能量的均质化方法来评估微观结构的宏观有效性，并使用拉格朗日乘子法引入体积约束。宏观和微观结构分别用宏观和微观相场函数来描述。此外，还求解了 Allen-Cahn 方程以更新宏观和微相场函数。通过更改边界来实现具有最低柔度的最佳结构。通过几个数值算例验证了所提方法的有效性和准确性，并研究了初始结构对迭代速度的影响。