考虑稳定性约束的五零能模式材料结构设计方法研究

五零能模式材料是一种声学超材料，虽然它一般采用固体材料设计，并且单胞常应用微桁架构型，但理论上这种材料设计的结构是不稳定的。本文从分析设计结构整体出发，探讨一种通过施加预载荷，确保五零能模式材料结构稳定性的方法，并给出了保证结构稳定性的充分条件，且应用典型的五零能模式材料单胞构型加以验证。同时，为方便提出的稳定性条件在设计过程中的实施，将五零能模式材料结构的设计过程描述为五零能模式材料的变换过程，采用结构尺寸优化模型来描述。当材料单胞为微桁架构型时，这一结构尺寸优化模型简单，结构稳定性约束和五零能模式材料性质约束均为线性约束。

Research on the structure design method of Pentamode Materials by considering global stability of structures

Pentamode Materials are novel artificial acoustic metamaterials. And they are usually designed by using solid materials, which microstructures are micro truss structures. However, the structures constructed by Pentamode Materials are theoretically unstable. From the perspective of global analysis of the entire structure, this paper proposes a method by employing preloads to insure the stability of the designed structures with Pentamode Materials, and a sufficient condition for the stability of structures with Pentamode Materials is presented. Meanwhile, two numerical examples of typical microstructures of Pentamode Materials are offered to verify the condition. Furthermore, in order to apply and implement the stability condition of structures in the structural design procedure, an optimization model of structures is established to describe the design problem, which views the structure design with Pentamode Materials as the transformation procedure of Pentamode Materials. As a result, if the unit cells of Pentamode Materials are constructed by micro trusses the optimization model is simple, both of the structure stability constraints and the characteristic constraints of Pentamode Materials are linear.