零泊松比超材料设计的多评价点功能基元拓扑优化方法

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

提出基于多评价点约束的零泊松比超材料功能基元拓扑优化设计方法。在同一功能基元拓扑基结构中,通过建立对于多个评价点的正、负泊松比约束,实现胞元零泊松比效应。分别采用最小质量和最大柔度目标函数拓扑优化模型优化设计出与半内六角蜂窝相似的零泊松比功能基元最优拓扑构型。提取功能基元最优构型并周期性序构了零泊松比超材料试件,通过有限元方法验证了该功能基元的零泊松比效应,并分析超材料试件的静、动力学特性。计算结果表明,最大柔度目标函数设计的功能基元构型的泊松比更接近于零,且具有更好的承载与隔振性能。设计了零泊松比超材料环肋双层圆柱壳结构,进行外壳静压和内部设备激振下壳体水下辐射噪声分析。研究表明,零泊松比超材料环肋可将外壳压缩变形转换为内外壳间环肋旋转,实现耐压壳内壳的保形,且具有较好的降噪性能。

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 radi-ation 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.