Abstract A design framework is here presented for the development of an architected solid with targeted mechanical properties thanks to an optimized porosity distribution. A 2D lattice of regular hexagons is considered as core element of a sandwich panel and a Bloch-Floquet-based approach is adopted to derive homogenized equivalent properties. The density distribution of the equivalent continuum is taken as objective function to be minimized in the optimization process. To this end, suitable constraints are designed to avoid empty regions and ensure a minimized density where required by the mechanical actions. A de-homogenization process is carried out on the optimized equivalent continuum to derive the configuration of regular hexagons with optimally varying wall thickness. Static and buckling responses of the optimized architected solid are compared with that of a 2D continuum whose material density distribution is determined through a classical topology optimization. It is shown that the architected 2D solid can absorb higher strain energy, with respect to classically optimized structures, which suffer a buckling-driven collapse below the elasticity threshold. The architected solid is also shown to have an improved energy absorption capability, that may increase considerably its performance, depending on the ductility of the adopted material.

中文翻译：

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具有优化分级特性的建筑复合结构的多尺度设计

摘要 这里提出了一个设计框架，用于开发具有目标机械性能的结构实体，这要归功于优化的孔隙率分布。正六边形的二维晶格被认为是夹心板的核心元素，并采用基于 Bloch-Floquet 的方法来推导均质等效属性。等效连续体的密度分布作为优化过程中要最小化的目标函数。为此，设计了合适的约束来避免空区域并确保机械动作所需的密度最小。在优化的等效连续体上执行去均化过程，以导出具有最佳壁厚变化的正六边形的配置。将优化后的结构实体的静态和屈曲响应与 2D 连续体的静态和屈曲响应进行比较，后者的材料密度分布是通过经典拓扑优化确定的。结果表明，相对于经典优化结构，结构化的 2D 实体可以吸收更高的应变能，这些结构在弹性阈值以下会发生屈曲驱动的坍塌。建筑固体还显示出具有改进的能量吸收能力，这可能会显着提高其性能，具体取决于所采用材料的延展性。在弹性阈值以下遭受屈曲驱动的坍塌。建筑固体还显示出具有改进的能量吸收能力，这可能会显着提高其性能，具体取决于所采用材料的延展性。在弹性阈值以下遭受屈曲驱动的坍塌。建筑固体还显示出具有改进的能量吸收能力，这可能会显着提高其性能，具体取决于所采用材料的延展性。