不同泊松比蜂窝结构抗冲击性能数值分析

宫晓博; 刘宇鸿; 于昌利; 桂洪斌

doi:10.19693/j.issn.1673-3185.02744

不同泊松比蜂窝结构抗冲击性能数值分析

doi: 10.19693/j.issn.1673-3185.02744

哈尔滨工业大学（威海）海洋工程学院，山东威海 264209

基金项目: 国家自然科学基金资助项目（11902100，11902099）；山东省自然科学基金资助项目（ZR2019PA001）；山东省重点研发计划资助项目（2019GHZ011，2021CXGC010702）

详细信息

作者简介:
宫晓博，男，1989年生，博士，讲师。研究方向：智能结构设计及其在船海方面的应用。E-mail：xiaobogong@hit.edu.cn

刘宇鸿，男，1997年生，硕士生。研究方向：蜂窝结构抗冲击性能研究

于昌利，男，1981年生，博士，副教授。研究方向：水下智能装备。E-mail：yuchangli@hitwh.edu.cn

桂洪斌，男，1967年生，博士，教授。研究方向：船舶结构力学。E-mail：guihongbin@sina.com

通信作者:
桂洪斌

中图分类号: U661.4；U668.5
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出版历程
- 收稿日期: 2021-12-31
- 修回日期: 2022-03-23
- 网络出版日期: 2022-09-07
- 刊出日期: 2023-04-28

Numerical analysis of impact resistance of honeycomb structures with different Poisson's ratios

School of Ocean Engineering, Harbin Institute of Technology (Weihai), Weihai 264209, China

不同泊松比蜂窝结构抗冲击性能数值分析由宫晓博，等创作，采用知识共享署名4.0国际许可协议进行许可。

摘要

摘要: 目的对不同泊松比蜂窝结构的抗冲击性能进行分析。方法基于显式动力有限元方法，分析不同泊松比蜂窝结构在面内冲击载荷作用下的动态力学性能，探究蜂窝结构泊松比对其抗冲击性能的影响规律。选取3类具有负/零/正泊松比的典型蜂窝拓扑结构（内凹六边形、六边形和半内凹六边形），通过改变几何参数使其具有相同的相对密度和不同的泊松比（−2.76 ～3.63），分析结构在低/中/高速动态位移载荷作用下的动态力学性能。结果结果显示：零泊松比半内凹六边形蜂窝在压缩变形时不产生横向变形，具有最好的结构稳定性；在不发生结构失稳的前提下，平台应力与泊松比的关联不大；致密应变会随泊松比绝对值的增大而增大；单位体积能量吸收EA随泊松比绝对值的增大而增大。在进行蜂窝结构设计时，如果需要平台应力较大（抵抗变形能力强）的结构，可以选择壁厚/壁长（t/l）较大、胞元倾斜角θ较小的负泊松比内凹六边形蜂窝结构；如果需要较强的EA，可以选择t/l和θ均较小的正泊松比六边形蜂窝结构；如果需要结构有很好的稳定性，可以采用零泊松比半内凹六边形蜂窝结构。结论所做研究可为舷侧抗冲击蜂窝结构的选型和几何参数设计提供参考。
- 蜂窝结构 /
- 数值模拟 /
- 能量吸收 /
- 冲击载荷 /
- 泊松比
Abstract: Objectives This papers aims to analyze the impact resistance of honeycomb structure with different Poisson's ratio. Methods Based on the explicit dynamic finite element method, this paper analyzes the dynamic mechanical properties of honeycomb structures with different Poisson's ratios under in-plane impact load, and explores the influence laws of Poisson's ratios on their impact resistance. Three typical honeycomb structures with negative/zero/positive Poisson's ratios (reentrant hexagon, hexagon and semi-reentrant hexagon) are selected, their geometric parameters are changed to give them the same relative density and different Poisson's ratios (−2.76 – +3.63), and their dynamic mechanical properties under low/medium/high-speed dynamic displacement loads are analyzed. Results The results show that the zero Poisson's ratio semi-reentrant honeycomb structure has the best structural stability without transverse deformation under compression deformation; without structural instability, the platform stress has little correlation with the Poisson's ratio; and the compact strain and total energy absorbtion increases with the absolute value of the Poisson's ratio. Negative Poisson's ratio honeycomb structures with large t/l and small θ are suitable for applications with high platform stress (strong deformation resistance), and negative Poisson's ratio honeycomb structures with small t/l and small θ are suitable for high total energy absorbtion applications, while zero Poisson's ratio semi-reentrant honeycomb structures are suitable for applications with high platform stress (strong deformation resistance). Conclusions This study can provide references for the type selection and geometric parameter design of side impact honeycomb structures .
- honeycomb structure /
- numerical simulation /
- energy absorbtion /
- impact load /
- Poisson's ratio

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图 1 几何参数不同时的蜂窝结构泊松比

Figure 1. Poisson's ratios of honeycomb structure with different geometric parameters

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图 2 3类蜂窝结构有限元模型

Figure 2. Finite element model of three types of honeycomb structure

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图 3 蜂窝结构压缩实验结果与数值模拟结果的对比

Figure 3. Comparisons between compression experiment results and simulation results of honeycomb structure

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图 4 实验与模拟结果的应力−应变曲线对比

Figure 4. Stress-strain curves comparison between experimental and simulation results

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图 5 不同泊松比蜂窝结构的3种变形模式

Figure 5. Three types of deformation modes of honeycomb structure with different Poisson's ratios

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图 6 负泊松比蜂窝结构的失稳过程和2种失稳形式

Figure 6. Instability process and two instability modes of negative Poisson's ratio honeycomb structure

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图 7 不同冲击载荷下3类蜂窝结构的应力−应变曲线

Figure 7. Stress-strain curves of three types of honeycomb structure under different impact loads

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图 8 不同泊松比蜂窝结构的平台应力曲线

Figure 8. Plateau stress curves of honeycomb structure with different Poisson's ratios

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图 9 不同泊松比蜂窝结构的致密应变曲线

Figure 9. Densified strain curves of honeycomb structure with different Poisson's ratios

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图 10 不同冲击载荷下蜂窝结构的EA

Figure 10. EA of honeycomb structure under different impact loads

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图 11 10 m/s冲击速度下3类蜂窝结构的EA

Figure 11. EA of three types of honeycomb structure at 10 m/s of impact velocity

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图 12 50 m/s冲击速度下3类蜂窝结构的EA

Figure 12. EA of three types of honeycomb structure at 50 m/s of impact velocity

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图 13 100 m/s冲击速度下3类蜂窝结构的EA

Figure 13. EA of three types of honeycomb structure at 100 m/s of impact velocity

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表 1 3类不同泊松比蜂窝结构的型式及相应的泊松比表达式

Table 1. Three types of different Poisson's ratio honeycomb structure and corresponding Poisson's ratio expression

蜂窝类型		泊松比公式
六边形蜂窝		$\nu = \dfrac{{{{\cos }^2}\theta }}{{(h/l + \sin \theta )\sin \theta }}$
内凹六边形蜂窝		$\nu = - \dfrac{{{{\cos }^2}\theta }}{{(h{\text{/}}l - \sin \theta )\sin \theta }}$
半内凹六边形蜂窝		ν = 0

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表 2 不同几何蜂窝结构在3种冲击载荷作用下的变形模式

Table 2. Deformation modes of different geometrical honeycomb structures under three impact loads

t/l	θ/(°)	六边形蜂窝			内凹六边形蜂窝			半内凹六边形蜂窝
t/l	θ/(°)	V = 10 m/s	V = 50 m/s	V = 100 m/s	V = 10 m/s	V = 50 m/s	V = 100 m/s	V = 10 m/s	V = 50 m/s	V = 100 m/s
0.04	15	1	2	3	X	X	X	1	3	3
	20	1	2	3	X	2	2	1	3	3
	25	1	2	3	X	2	3	3	3	3
	30	2	3	3	X	3	3	3	3	3
0.05	15	1	2	3	X	2	X	1	3	3
	20	1	2	3	1	2	3	3	3	3
	25	2	3	3	1	3	3	3	3	3
	30	2	3	3	2	3	3	3	3	3
0.06	15	1	2	3	X	X	2	1	3	3
	20	2	3	3	1	3	3	3	3	3
	25	2	3	3	2	3	3	3	3	3
	30	3	X	3	3	3	3	3	3	3
0.07	15	2	X	3	X	X	3	3	3	3
	20	2	3	3	1	3	3	3	3	3
	25	2	3	3	X	3	3	3	3	3
	30	3	3	3	3	3	3	3	3	3

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表 3 不同几何蜂窝结构在3种冲击载荷作用下的平台应力

Table 3. Plateau stress of different geometrical honeycomb structures under three impact loads

t/l	θ（°）	平台应力/MPa
		六边形蜂窝			内凹六边形蜂窝			半内凹六边形蜂窝
		V = 10 m/s	V = 50 m/s	V = 100 m/s	V = 10 m/s	V = 50 m/s	V = 100 m/s	V = 10 m/s	V = 50 m/s	V = 100 m/s
0.04	15	1.60	4.62	6.12	1.63	4.49	5.99	1.47	4.49	5.99
	20	1.32	4.30	5.82	1.38	4.22	5.76	1.13	4.11	5.63
	25	1.24	4.25	5.68	1.24	4.17	5.62	1.10	4.06	5.49
	30	1.10	4.08	5.53	1.14	4.06	5.52	1.05	4.01	5.46
0.05	15	1.66	4.63	6.10	1.76	4.73	6.20	1.61	4.64	6.11
	20	1.45	4.41	5.95	1.53	4.38	5.89	1.35	4.31	5.85
	25	1.30	4.30	5.72	1.25	4.25	5.67	1.31	4.31	5.73
	30	1.13	4.12	5.61	1.15	4.11	5.64	1.11	4.02	5.53
0.06	15	1.78	4.78	6.30	1.81	4.71	6.22	1.67	4.58	6.14
	20	1.55	4.54	6.10	1.55	4.56	6.12	1.44	4.43	5.91
	25	1.33	4.33	5.81	1.28	4.28	5.77	1.32	4.26	5.76
	30	1.17	4.13	5.62	1.18	4.27	5.77	1.25	4.32	5.82
0.07	15	1.81	4.80	6.32	1.86	4.80	6.30	1.83	4.82	6.32
	20	1.56	4.56	6.06	1.58	4.57	6.07	1.60	4.78	6.26
	25	1.38	4.35	5.84	1.45	4.42	5.91	1.42	4.57	5.92
	30	1.22	4.22	5.65	1.26	4.33	5.67	1.39	4.46	5.85

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表 4 不同几何蜂窝结构在3种冲击载荷作用下的致密应变

Table 4. Densified strain ofdifferent geometrical honeycomb structures under three impact loads

t/l	θ/(°)	致密应变/%
		六边形蜂窝			内凹六边形蜂窝			半内凹六边形蜂窝
		V = 10 m/s	V = 50 m/s	V = 100 m/s	V = 10 m/s	V = 50 m/s	V = 100 m/s	V = 10 m/s	V = 50 m/s	V = 100 m/s
0.04	15	88.3	93.2	95.6	80.2	84.6	88.1	85.2	87.1	92.2
	20	86.2	92.1	95.3	79.8	89.8	94.1	83.4	85.7	90.9
	25	84.8	91.4	94.7	79.2	90.4	94.4	83.0	84.8	90.0
	30	84.2	90.3	93.4	78.9	86.0	90.0	80.3	82.5	87.5
0.05	15	86.6	92.5	95.6	79.5	90.1	88.5	84.3	86.3	91.3
	20	85.7	91.8	95.0	79.2	89.4	93.4	82.7	85.0	89.7
	25	85.1	90.5	93.1	86.7	88.7	92.8	82.4	84.4	89.4
	30	84.1	90.1	93.4	84.6	86.6	90.9	81.4	83.1	88.2
0.06	15	86.5	92.6	95.6	78.3	84.1	93.4	83.9	85.9	90.9
	20	86.4	92.7	95.0	86.2	88.2	92.2	82.1	84.0	89.1
	25	84.9	90.1	93.1	84.0	86.0	90.0	81.2	83.1	88.1
	30	81.0	87.2	93.4	81.2	83.2	87.8	80.5	82.5	87.5
0.07	15	85.3	88.3	95.0	78.0	80.5	92.5	82.4	84.5	89.4
	20	84.3	91.7	94.7	82.9	84.9	88.8	82.1	83.9	89.1
	25	83.1	91.2	93.1	77.6	83.7	87.8	79.9	81.6	86.9
	30	82.7	89.7	92.8	79.9	81.9	86.3	78.7	80.1	85.9

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