Computational Design of 2D Lattice Structures based on Crystallographic Symmetries

Abstract The design representations of lattice structures are fundamental to the development of computational design approaches. Current applications of lattice structures are characterized by ever-growing demand on the computational resources to solve difficult optimization problems or generate large datasets, opting for the development of efficient design representations which offer a high range of possible design variants, while at the same time generating design spaces with attributes suitable for computational methods to explore. In response, the focus of this work is to propose a parametric design representation based on crystallographic symmetries and investigate its implications for the computational design of lattice structures. The work defines design rules to support the design of functionally graded structures using crystallographic symmetries such that the connectivity between individual members in a structure with varying geometry is guaranteed, and investigates how to use the parametrization in the context of optimization. The results show that the proposed parametrization achieves a compact design representation to benefit the computational design process by employing a small number of design variables to control a broad range of complex geometries. The results also show that the design spaces based on the proposed parametrization can be successfully explored using a direct search-based method.