This paper proposes a methodology for architecting microstructures with extremal stiffness, yield, and buckling strength using topology optimization. The optimized microstructures reveal an interesting transition from simple lattice like structures for yield-dominated situations to hierarchical lattice structures for buckling-dominated situations. The transition from simple to hierarchical is governed by the relative yield strength of the constituent base material as well as the volume fraction. The overall performances of the optimized microstructures indicate that maximum strength is determined by the buckling strength at low volume fractions and yield strength at higher volume fractions, regardless of the base material's relative yield strength. The non-normalized properties of the optimized microstructures show that higher base material Young's modulus leads to both higher Young's modulus and strength of the architected microstructures. Furthermore, the polynomial order of the maximum strength lines with respect to mass density obtained from the optimized microstructures reduces as base material relative yield strength decreases, reducing from 2.3 for buckling dominated Thermoplastic Polyurethane to 1 for yield dominated steel microstructures.

翻译：本文提出了一种通过拓扑优化来建立具有极限刚度、屈曲强度和屈服强度的微结构的方法。优化后的微结构在屈服受支配的情况下表现为简单的晶格结构，而在屈曲受支配的情况下则呈现出分层的晶格结构。从简单的到分层的转变取决于构成基材的相对屈服强度和体积分数。优化后的微结构整体性能表明，无论基材的相对屈服强度如何，最大强度都由低体积分数时的屈曲强度和高体积分数时的屈服强度决定。优化后的微结构的非标准化特性表明，高基材杨氏模量会导致建构的微结构具有更高的杨氏模量和强度。此外，对于热塑性聚氨酯这种屈曲受支配的微结构来说，质量密度与最大强度直线的多项式阶数随基材相对屈服强度的降低而降至1。