Assessing the comprehensive strength of structures under multiple loading conditions is crucial for designing microstructures. This paper proposes the use of the least failure energy density (LFED) to measure the comprehensive strength of heterogeneous periodic structures, which corresponds to the minimum energy density required to destroy a structure. To enhance the comprehensive strength of a periodic structure, the LFED can be maximized. We constructed a two-layer optimization algorithm and found that the high time consumption renders topology optimization unfeasible. We subsequently developed an approach for solving inner-layer optimization analytically and quickly so that the problem becomes a single-layer optimization. We compared the LFED of several classical structures, including plate structures, lattice structures, and TPMSs. The calculations reveal that plate structures exhibit the best performance in terms of LFED, followed by TPMSs whereas truss structures have the poorest performance. Among the three types of classical structures, the octet plate, Schwartz-D minimal surface, and octet truss structures are the best-performing types, respectively. Additionally, the LFED is combined with the BESO topology optimization method to obtain the best 2D periodical structure, a 2D curved-edge kagome structure. For optimal 3D periodical structures, rarely discussed space kagome structures (plate or lattice) are obtained with an LFED superior to that of other counterpart classical structures.

中文翻译：

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最小失效能量密度：用于评估和优化非均质周期性结构的综合强度指标


评估结构在多种载荷条件下的综合强度对于设计微观结构至关重要。本文提出使用最小失效能量密度 （LFED） 来测量异质周期性结构的综合强度，它对应于破坏结构所需的最小能量密度。为了增强周期性结构的综合强度，LFED 可以最大化。我们构建了一个两层优化算法，发现高耗时导致拓扑优化不可行。随后，我们开发了一种分析快速解决内层优化的方法，使问题成为单层优化。我们比较了几种经典结构的 LFED，包括板结构、晶格结构和 TPMS。计算表明，板式结构在 LFED 方面表现出最佳性能，其次是 TPMS，而桁架结构的性能最差。在三种类型的经典结构中，八位组板、Schwartz-D 最小表面和八位组桁架结构分别是性能最好的类型。此外，LFED 与 BESO 拓扑优化方法相结合，以获得最佳的 2D 周期性结构，即 2D 曲面边缘笼目结构。对于最佳的 3D 周期性结构，很少讨论的太空笼目结构（板或晶格）是用优于其他对应经典结构的 LFED 获得的。