Functional element topology optimization method based on multiple evaluation points for metamaterial design with zero Poisson’s ratio

Abstract

The functional element topology optimization method based on multiple evaluation points was proposed to design metamaterial with zero Poisson’s ratio. The zero Poisson’s ratio effect of a cell was achieved through multiple evaluation points that defined positive and negative Poisson’s ratio constraints in one topological ground structure. Topology optimization models were established by minimal mass and maximal compliance objective functions, and corresponding functional element configurations with zero Poisson’s ratio were optimized and designed, which were similar to semi re-entrant hexagonal honeycomb. The optimal functional element configurations were extracted and periodic arranged as metamaterial structure with zero Poisson’s ratio. The finite element method (FEM) was used to verify the Poisson’s ratio of these functional elements. The static and dynamic characteristics of metamaterial structures were also analyzed through finite element models. The results show that the metamaterial structure based on maximal compliance objective has better in-plane specific stiffness and vibration isolation performance, and its Poisson’s ratio is closer to zero compared with minimal mass objective model. The structures of double-layered cylindrical shells with conventional solid ring-rib and zero Poisson’s ratio metamaterial ring-rib were designed, and the analysis under static pressure from outer shell and underwater radiation noise caused by internal equipment were conducted. By converting the compression deformation of the outer shell into the rotation of the inner shell, the zero Poisson’s ratio metamaterial ring-rib achieves shape conservation of the inner shell. The metamaterial ring-rib can also reduce the underwater radiation noise from cylindrical shell.