Two-scale concurrent topology optimization method of hierarchical structures with self-connected multiple lattice-material domains

Abstract

This paper proposes a two-scale concurrent topology optimization method for the structures composed of multiple lattice materials, in which the microstructures of lattice materials, the structural topology and the distribution of multiple lattice materials are concurrently optimized with the connection between different lattice materials assured. In the two-scale framework, a multi-domain self-connected material interpolation model is defined to describe the topology (the distribution of holes), the distribution of different lattice materials and their interfaces on the macroscale. It is emphasized that the interface region between different lattice materials can be accurately identified in the macro-interpolation. Thus, only microstructures of the interface region need to preset a frame-undesignable domain as a simple but reliable geometric connection measure. At the same time, the Solid Isotropic Material with Penalization (SIMP) interpolation is applied to model the microstructural topology on the microscale. Besides, the homogenization method is taken as a bridge between two scales, which evaluates the effective material properties of microstructures. The standard optimized formula which considers structural compliance as the objective function is used to design the structure. Several 2D and 3D examples verify the effectiveness of the proposed method and the superior mechanical properties of the designable structure.