Impact resistance of thickness-graded arrow-shaped honeycomb pedestals with negative Poisson’s ratio
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摘要: 设计了一种箭形负泊松比的蜂窝基座结构，推导了其胞元结构的力学性能解析公式，并利用有限元方法研究了具有厚度梯度箭形负泊松比蜂窝材料的抗冲击性能。基于功能梯度材料，其基体呈连续梯度变化的概念，以胞元壁厚为自变量，设计了顺厚度梯度、逆厚度梯度型和均匀厚度的蜂窝层，并建立基座模型。在基座质量不变的前提下具体讨论了蜂窝胞元凹角及厚度梯度的不同设置情况对基座抗冲击性能的影响。结果表明，相同梯度设置情况下，胞角的变化会引起蜂窝结构等效弹性模量的变化，进而改变基座的抗冲击性能，而将胞壁厚度较小的蜂窝层放置于迎冲端时，基座整体的应力水平明显降低；将壁厚较大的蜂窝层放置于迎冲端时，基座面板的输出冲击环境能够有效地得到控制。Abstract: An arrow-shaped honeycomb pedestal with negative Poisson’s ratio was designed. An analytical formula was derived for the mechanical properties of the cell structures, and the impact resistance of the thickness-graded arrow-shaped honeycomb materials with negative Poisson's ratio was numerically studied by the explicit dynamic finite element method. Based on the concept of functionally-graded materials, honeycomb layers with pathwise thickness gradient, inverse thickness gradient and uniform thickness were designed, by taking the thickness of the cell wall as the independent variable, the relevant model was established. The influence of thickness gradients on the impact resistance of the pedestal was discussed concretely under the premise of constant pedestal mass. The results show that, under the same gradient setting, the change of cell angle will cause the change of equivalent elastic modulus of the honeycomb structure, thus changing the impact resistance of the pedestal. When the honeycomb layer with a thinner cell wall is placed at the impact end, the stress level of the pedestal is significantly reduced. By placing a honeycomb layer with a thicker cell wall on the impact end, the output impact environment of the pedestal panel can be effectively controlled.
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图 3 有限元与解析公式计算结果的对比
Figure 3. Comparison between the results by finite element simulation and analytical formula calculation
图 4 厚度梯度型负泊松比蜂窝基座结构
Figure 4. The thickness-graded honeycomb pedestal with negative Poisson’s ratio
图 7 有限元模型及实验基座结构
Figure 7. The finite element model and the corresponding pedestal structure used in test
图 9
$ {\theta }_{1} $ 为65°的均匀厚度蜂窝结构von Mises应力云图Figure 9. Von-Mises stress distribution in the layered honeycomb structure with uniform thickness for θ1 = 65°
图 10 胞角
$ {\theta }_{1} $ 为65°的蜂窝结构各分层内出现的最大von Mises应力Figure 10. The maximum von-Mises stress in the every layer of the honeycomb structure with θ1 = 65°
图 11 胞角
$ {\theta }_{1} $ 为60°的蜂窝结构各分层内出现的最大von Mises应力Figure 11. The maximum von-Mises stress in the every layer of the honeycomb structure with θ1 = 60°
图 12 胞角
$ {\theta }_{1} $ 为55°的蜂窝结构各分层内出现的最大von Mises应力Figure 12. The maximum von-Mises stress in the every layer of the honeycomb structure with θ1 = 55°
图 13 各工况下基座的最大von Mises应力
Figure 13. The maximum von Mises stresses in the pedestals under various working conditions
图 15 不同工况下基座面板测点处的加速度时历曲线
Figure 15. Acceleration-time curves at the measuring points of the base panel under different working condition
图 16 不同工况下蜂窝基座面板测点处的冲击谱
Figure 16. Impact spectra at the measuring points of the honeycomb pedestal panels under different working conditions
表 1 厚度梯度基座工况设置
Table 1. Condition settings for thickness gradient pedestals
胞角$ {\theta }_{1} $/(°) 工况 层1厚度/mm 层2厚度/mm 层3厚度/mm 55 均匀厚度 3 3 3 顺厚度梯度 2 3 4 逆厚度梯度 4 3 2 60 均匀厚度 3 3 3 顺厚度梯度 2 3 4 逆厚度梯度 4 3 2 65 均匀厚度 3 3 3 顺厚度梯度 2 3 4 逆厚度梯度 4 3 2 
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