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- 2018
任意负泊松比超材料结构设计的功能基元拓扑优化法
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Abstract:
基于拓扑优化方法，提出了设计具有任意负泊松比超材料及结构的功能基元拓扑优化法。针对功能基元的不同初始拓扑基结构，包括矩形和三角形初始拓扑基结构，以指定的负泊松比值作为约束条件，以功能基元柔顺度最大化为目标函数，建立了任意负泊松比超材料拓扑优化模型并求解。提取拓扑优化得到的功能基元最优构型，经周期性分布从而形成负泊松比结构。建立优化得到的超材料结构有限元模型，验算了功能基元的泊松比，计算分析了该超材料试件的静、动力学特性。结果表明，该负泊松比效应超材料试件具有较好的承载能力，且在中低频段有较好的减振效果。 Based on the topology optimization method, the functional element topology optimization method was proposed to design a metamaterial and a functional element's structure with arbitrary negative Poisson's ratio. For different initial topological substrate structures of the functional element, including the rectangular and triangular initial topological substrate structure, with the specified negative Poisson's ratio as the constraint condition, the compliance of functional element was maximized as the objective function, and the topology optimization model with arbitrary negative Poisson's ratio was established and solved. The functional element was extracted by the topology optimal results, and the functional elements were periodically distributed to form a negative Poisson's structure. Then, the finite element model of the optimized metamaterial structure was established, and the Poisson's ratio of the functional element was calculated by the formula. Finally, the static and dynamic characteristics of the metamaterials were calculated and analyzed. The results demonstrate that this negative Poisson's ratio effect metamaterial specimen has good bearing capacity and has better vibration reduction performance in the middle and low frequency range. 国家自然科学基金（51479115）
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