二维多孔结构具有轻质、比强度高、隔音、吸能特性优异等特性，是工程中应用最广泛的结构之一。本文根据应用环境的不同，在满足相对密度一致的前提下，提出了三种不同的优化设计方案，从理论分析和数值模拟结果出发，探究了这几种优化结构在抗拉、缓冲吸能等方面性能与传统结构的差异。主体研究内容可以分为：

单轴静态拉伸的加载条件下，首次提出了生成voronoi多边形的梯度栅格随机撒布法，实现了胞元尺寸在整个模型区域内的非均匀设计。并对生成的多孔结构施加静态单轴拉伸载荷，结果显示，在相对密度相等时，梯度多孔结构的单轴拉伸性能优于均匀结构，梯度系数增大，增强效果更明显，且上下边缘胞元尺寸小的结构抗拉能力最优，梯度结构的抗拉性能最大可比均匀结构提高70.5%。

在动态冲击的加载条件下，本文设计了胞元尺寸正负梯度分布的模型。对比吸能效率可以发现，冲击速度与吸能效率呈正相关，模型之间的吸能效率存在负梯度模型＞正梯度模型＞均匀模型的关系。同时，本文以传统的一维冲击波模型为基础，提出了适用于梯度结构的冲击波模型，并从波阵面后相对密度的差异解释了各个模型之间吸能效率差异的本质原因，并通过比较冲击端平台应力的理论解和有限元结果，验证了本文提出模型的正确性。

以纤维复合材料为背景，并引入增强体材料和基体材料，本文设计出了纤维定向排布模型，通过与增强体集中排布模式、短纤维随机均布模式的Voronoi结构做对比，从承载能力上看，长纤维定向分布模型其承载能力较增强体集中排布模型和短纤维随机均布模型分别提高了45.12%和36.9%。在3m/s的冲击载荷作用下，长纤维定向分布模型的多孔结构在能量吸收上分别比增强体集中排布模型和短纤维随机均布模型提升32.6%和29.3%。通过横向对比不同纤维长度的模型发现，模型中单根纤维长度占总长度的比例在70%-80%的区间范围，可以保证多孔结构自身的受压稳定性。

Two-dimensional cellular structure is one of the most widely used structures in engineering because of its light weight, high specific strength, excellent sound insulation and energy absorption characteristics. According to the different application environments and the same relative density, three different optimum design schemes are proposed. Based on the theoretical analysis and numerical simulation results, the differences between the performance of these optimum structures and traditional structures in tension resistance, cushioning and energy absorption are explored. Subject research can be divided into:

Under uniaxial static tension, the gradient grid random distribution method for Voronoi polygon generation is proposed for the first time, which realizes the non-uniform design of cell size in the whole model area. The static uniaxial tension load is applied to the cellular structure. The results show that the uniaxial tension performance of gradient cellular structure is better than that of uniform structure when the relative density is equal. With the increase of gradient coefficient, the reinforcement effect is more obvious. The structure with small cell size at upper and lower edges has the best tensile capacity, and the tensile performance of gradient structure can be improved by 70.5% as compared with that of uniform structure.

Under the loading condition of dynamic impact, the model of positive and negative gradient distribution of cell size is designed in this paper. By comparing the energy absorption efficiency, it can be found that the impact velocity is positively correlated with the energy absorption efficiency. There is a negative gradient model, a positive gradient model and a uniform model for the energy absorption efficiency between the models. At the same time, based on the traditional one-dimensional shock wave model, a shock wave model suitable for gradient structure is proposed, and the essential reason for the difference of energy absorption efficiency between the models is explained from the difference of relative density behind the wave front. The correctness of the proposed model is verified by comparing the theoretical solutions and finite element results of the platform stress at the impact end.

Based on the background of fiber composites and introducing reinforcing materials and matrix materials, this paper designs a fiber orientation layout model. By comparing with Voronoi structure of reinforcing body centralized layout model and short fiber random uniform distribution model, the long fiber orientation distribution model has higher load-carrying capacity than the reinforced body centralized layout model and the short fiber random uniform distribution model, respectively. It was 45.12% and 36.9% higher. Under the impact load of 3m/s, the energy absorption of the cellular structure of the long fiber oriented distribution model is 32.6% and 29.3% higher than that of the reinforced body concentrated arrangement model and the short fiber random uniform distribution model, respectively. By comparing the models of different fiber lengths, it is found that the ratio of single fiber length to total fiber length in the model is in the range of 70% to 80%, which can ensure the compressive stability of the cellular structure itself.