Topology Optimization for Design of Hybrid Lattice Structures with Multiple Functional Microstructure Configurations

Introduction: Lattice structures (LSs) have been an emerging solution toward lightweight and mechanically efficient structures [2-3]. However, while the lattice structure presents a vast design space and advantage, it also poses a challenge to existing design methods. Existing LSs design methods rarely consider microstructures with functionalities, like negative Poisson's ratio [8] and extreme thermal expansion [5]; Therefore, this work proposes a method based on topology optimization and homogenization theory to design hybrid lattice structures with multiple functional microstructure configurations to fill the gap in the design approach for multi-functional lattice structures. The flow chart of the proposed method is shown in Fig 1. There are two steps in this method. At first, multiple functional microstructure lattice units are obtained through topology optimization and homogenization theory. Then, the microstructures are treated as homogeneous materials with effectively homogenized properties for macroscopic analysis, and the ordered SIMP (Solid isotropic material with penalization) interpolation method [7] is applied to achieve the interpolation of multiple microstructures. Finally, the obtained hybrid lattice structure theoretically has both the properties of macroscopic optimization and the functionalities of microstructure units. Both the microstructure and macrostructure design variables are updated by the Method of Moving Asymptote (MMA) algorithm [4]. To verify this proposed method, an optimization model that the functional microstructure is set to be zero thermal expansion coefficient, and a standard minimized compliance problem is considered in macroscale is created. Numerical examples and data comparisons are presented.