【摘要】 本文旨在通过拓扑优化方法设计一种具有优异吸能性能的负泊松比超材料，通过试验对其性能进行验证。基于SIMP(solid isotropic material penalty)法，本文以最小化柔顺度为目标函数、以体积分数为约束条件建立了拓扑优化模型，优化出三种具有指定负泊松比的单胞结构。通过对TPU(thermoplastic polyurethane)材料标准试验件进行拉伸与松弛试验，验证了超弹性Ogden模型和黏弹性Prony级数在模拟TPU材料力学性能方面的适用性。结合静力学仿真与试验，系统分析了不同周期排列、结构厚度及负泊松比值对应结构下的吸能特性。通过进一步的频响分析和振动测试，评估了结构的动态响应和减振能力。研究表明，负泊松比超材料在压缩变形过程中能够有效吸收外部能量，排列方式与结构厚度对吸能性能有显著影响，不同负泊松比值对应的结构在减振性能上表现出明显差异。本文通过数值模拟与试验验证，为负泊松比超材料的结构优化设计提供了数值参考与试验支持。更多还原

【Abstract】 This study aims to design a negative Poisson’s ratio metamaterial with excellent energy absorption performance using topology optimization,and to experimentally validate its performance. Based on the SIMP method,a topology optimization model was established with the objective of minimizing compliance and the volume fraction as the constraint, through which three unit cell structures with specified negative Poisson’s ratios were obtained. Tensile and relaxation tests were performed on standard TPU specimens to verify the applicability of the hyperelastic Ogden model and viscoelastic Prony series in simulating the mechanical behavior of TPU materials. Combining static simulation with experimental analysis,the energy absorption characteristics of the structures with different periodic arrangements,structural thicknesses, and corresponding negative Poisson’s ratios were systematically examined. Further frequency response analysis and vibration testing were performed to evaluate the dynamical response and vibration reduction capabilities of the structures. The results show that the negative Poisson’s ratio metamaterials effectively absorb external energy during compression deformation,with the arrangement and thickness of the structure significantly influencing their energy absorption performance. Structures with different negative Poisson’s ratios exhibit distinct in vibration reduction performance. Numerical simulations and experimental validation confirm the excellent vibration reduction effect,which provid numerical references and experimental support for the structural optimization design of negative Poisson’s ratio metamaterials.更多还原