We propose an approach to design an optimized heterogeneous interconnected porous structure over a fixed macro-design mesh for performance optimization, which has seldom been addressed despite its extensive potential industrial applications. We achieve this by introducing the concept of the extended triply periodic minimal surface (ETPMS), defined by an implicit function with additional control parameters that can prescribe the element anisotropy and heterogeneity consistently. The control parameters are expressed as continuous explicit functions of spatial coordinates, and ultimately generate a porous structure with perfect geometric connections and fully interconnected pore networks. The modeling advantages of the ETPMS come at the cost of challenges in its efficient simulation and optimization owing to its large number of varied ETPMS elements and their geometric validity requirements. These issues are further resolved using a strategy of offline pre-computation; in particular, parametric homogenization and several carefully designed optimization techniques. The performance of the approach is demonstrated using a suite of three-dimensional benchmark examples.

我们提出了一种在固定的宏设计网格上设计优化的异构互连多孔结构以优化性能的方法，尽管其潜在的工业应用广泛，但很少有人提出。我们通过引入扩展的三重周期周期性最小曲面的概念来实现这一目标（ETPMS），由具有附加控制参数的隐式函数定义，这些参数可以一致地规定元素的各向异性和异质性。控制参数表示为空间坐标的连续显式函数，并最终生成具有完美几何连接和完全互连的孔网络的多孔结构。ETPMS的建模优势在于，由于其数量众多的ETPMS元素及其几何有效性要求，因此其高效的仿真和优化面临挑战的代价。使用脱机预计算策略可进一步解决这些问题；特别是参数同质化和几种精心设计的优化技术。使用一组三维基准示例演示了该方法的性能。