MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION OF PHONONIC CRYSTALS CONSIDERING MANUFACTURING CONSTRAINT

Topology optimization of phononic crystals can achieve the structures with the targeted band-gap characteristics, which provides potential applications in the vibration reduction and sound insulation. However, the topology optimization results of phononic crystals often have isolated material elements, which are rather difficult to be manufactured. In this paper, a manufacturing-constrained topology optimization model considering both the band-gap performance and the manufacturability for the multi-objective topology optimization of two-dimensional (2D) multi-phase phononic crystals is proposed. The objective functions for maximizing the band-gap width in a specified frequency range and minimizing the structural weight are established. The manufacturing constraint is additionally introduced based on the connectivity analysis of the micro-structures of the constituent materials. The optimization problem is solved by the finite element method (FEM) and the non-dominated sorting genetic algorithm II (NSGA-II). The rationality and effectiveness of the proposed model and strategy are demonstrated by representative numerical examples. The results show that the isolated material elements can be avoided effectively by introducing an additional manufacturing constraint. Moreover, the optimized results can ensure both the band-gap performance and the manufacturability requirement. Compared with the results of the single-objective optimization (SOOP), the multi-objective optimization (MOOP) shows great advantages, since it can obtain non-dominated solution sets and achieve a balance between different optimization objectives.