木贼属植物仿生薄壁结构的耐撞性优化

刘飞明; 雷建银; 乔力; 刘志芳

doi:10.11858/gywlxb.20220516

木贼属植物仿生薄壁结构的耐撞性优化

doi: 10.11858/gywlxb.20220516

太原理工大学机械与运载工程学院应用力学研究所, 山西太原　030024

基金项目: 国家自然科学基金（11902215, 11772216）

详细信息

作者简介:
刘飞明（1995-），男，硕士研究生，主要从事薄壁结构的耐撞性研究. E-mail：1637752941@qq.com

通讯作者:
雷建银（1989-），男，博士，副教授，主要从事仿生结构的力学行为研究.E-mail：leijianyin@tyut.edu.cn

中图分类号: O341
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出版历程
- 收稿日期: 2022-02-18
- 修回日期: 2022-05-20
- 刊出日期: 2022-10-11

Crashworthiness Optimization of Horsetail-Bionic Thin-Walled Structures

Institute of Applied Mechanics, College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China

摘要

摘要: 利用ABAQUS有限元软件构建木贼属植物仿生薄壁结构（horsetail-bionic thin-walled structure，HBTS）在侧向冲击下的数值模型，分析了结构的壁厚、内径和肋骨数对其耐撞性能和变形模态的影响。结果表明：肋骨数和整体壁厚的增加会明显提高HBTS的比吸能和最大峰值载荷，HBTS不同部分的壁厚变化显著影响其变形模态和耐撞性能。为了综合考虑HBTS各部分的壁厚、肋骨数、内径5个参数对耐撞性能的影响，集成modeFRONTIER优化软件与ABAQUS软件，通过参数化建模在设计空间上构建有限元模型，建立比吸能和最大峰值载荷的Kriging代理模型。使用基于Kriging代理模型的多目标优化方法获取Pareto前沿，以同时实现比吸能最大化和峰值载荷最小化。最后分析了Pareto前沿面上各HBTS的设计参数分布情况，并验证了优化结果，该方法可为薄壁结构的优化设计提供新思路。
- 仿生薄壁结构 /
- 多目标优化 /
- modeFRONTIER /
- Pareto前沿
Abstract: Numerical model of horsetail-bionic thin-walled structure (HBTS) under the lateral impact was constructed using ABAQUS. The effects of wall thickness, inner diameter and number of ribs on the crashworthiness performance and deformation modes were analyzed. The results indicate that the specific energy absorption and peak load of HBTS can be significantly enhanced with the increase of the number of ribs and the overall wall thickness. The changes in the wall thickness of each part significantly affects its deformation mode and crashworthiness performance. Based on the above results, the optimization software modeFRONTIER and the finite element analysis software ABAQUS were integrated to explore the influence of five design parameters, in terms of wall thickness, number of ribs, inner diameter and so on. Finite element models were uniformly distributed on the design space through parametric modeling method, hence the Kriging surrogate models for the specific energy absorption and peak load were established. Then, Pareto front was obtained using Kriging surrogate model-based multi-objective optimization method for the specific energy absorption maximization and peak load minimization simultaneously in one model. Finally, the distribution of each HBTS’s design parameters on Pareto front was analyzed and the optimization results were verified. The method is expected to provide new thoughts for the optimization design of the thin-walled structure.
- bionic thin-walled structure /
- multi-objective optimization /
- modeFRONTIER /
- Pareto front

HTML全文

图 1 3种木贼属植物：(a)沼泽问荆，(b)野生问荆，(c)斑纹木贼^[11]

Figure 1. Three horsetails: (a) Marsh horsetail, (b) field horsetail and (c) variegated horsetail^[11]

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图 2 模型的载荷条件(a)和横截面(b)

Figure 2. Load condition (a) and cross section (b) of the model

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图 3 网格收敛结果：(a)载荷-位移曲线, (b)吸能量和计算时间

Figure 3. Mesh convergence results: (a) load-displacement curves, (b) energy absorption and computation time

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图 4 实验^[14]与有限元模拟的比较：(a) 变形模态，(b) 载荷-位移曲线

Figure 4. Comparison between experiment^[14] and finite element simulation: (a) deformation mode, (b) load-displacement curves

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图 5 n、d和t对$S_{ \text{EA}}$的影响

Figure 5. Effects of n, d and t on $S_{ \text{EA}}$

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图 7 n、d和t对$C_{\text{FE}}$的影响

Figure 7. Effects of n, d and t on $C_{\text{FE}}$

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图 6 n、d和t对$F_{\text{max}}$的影响

Figure 6. Effects of n, d and t on $F_{\text{max}}$

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图 8 不同壁厚下HBTS的变形模态

Figure 8. Deformation modes of HBTS with different wall thicknesses

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图 9 多目标优化流程图

Figure 9. Multi-objective optimization flow chart

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图 10 S_EA和F_max的Pareto前沿

Figure 10. Pareto front of S_EA and F_max

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图 11 Pareto前沿面上各HBTS的参数分布：(a) 壁厚分布，(b) 内径和肋骨数分布

Figure 11. Parameter distribution of each structure on the Pareto front：(a) distribution of wall thickness, (b) distributions of inner diameter and number of ribs

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图 12 不同${{F}}_{\text{max}}$限制下最优HBTS的载荷-位移曲线

Figure 12. Load-displacement curves of optimal HBTSs with different ${{F}}_{\text{max}}$ limits

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表 1 铝合金AA6061的材料参数

Table 1. Parameters of aluminum alloy AA6061

Density/(g∙cm⁻³)	Poisson’s ratio	Elastic modulus/GPa	Yield stress/MPa	Ultimate strength/MPa
2.70	0.3	70.0	137.03	223.53

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表 2 HBTS的耐撞性比较

Table 2. Comparison of crashworthiness of HBTS

Structure	${ {t} }{_{\text{R} }}$/mm	${ {t} }{_{\text{I} }}$/mm	${ {t} }{_{\text{r} }}$/mm	M/g	${ {E} }{_{\text{A} }}$/J	${ {S} }{_{ \text{EA} } }$/(J∙g⁻¹)	${ {F} }{_{\text{max} }}$/kN	${ {C} }{_{\text{FE} }}$/%
a	0.800	0.100	0.100	110.2	70.16	0.637	1.841	82.8
b	0.158	0.800	0.158	110.2	28.02	0.254	1.125	54.1
c	0.271	0.271	0.800	110.2	49.11	0.446	1.401	76.2
d	1.500	0.800	0.800	308.1	361.61	1.174	9.095	86.4
e	0.858	1.500	0.858	308.1	390.85	1.268	9.691	87.7
f	0.971	0.971	1.500	308.1	315.82	1.025	8.110	84.7

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表 3 壁厚与内径水平

Table 3. Wall thickness and inner diameter level

Level	${ {t} }{_{\mathrm{R} }}$/mm	${ {t} }{_{\text{I} }}$/mm	${ {t} }{_{\text{r} }}$/mm	d/mm
1	0.10	0.10	0.10	10.0
2	0.45	0.45	0.45	17.5
3	0.80	0.80	0.80	25.0
4	1.15	1.15	1.15	32.5
5	1.50	1.50	1.50	40.0

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表 4 Kriging代理模型精度

Table 4. Accuracy assessment of the Kriging surrogate models

${ {S} }{_{ \text{EA} } }$			${ {F} }{_{\text{max} } }$
${ {R} }{^{\text{2} }}$	δ_ARE/%	δ_RAAE/%	${ {R} }{^{\text{2} }}$	δ_ARE/%	δ_RAAE/%
0.989	1.52	1.33	0.996	1.68	0.67

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表 5 不同$F_{\text{max}}$限制下的最优HBTS

Table 5. Optimal HBTSs with different $F_{\text{max}}$ limits

Type	Design parameters					${ {S} }{_{ \text{EA} } }$/(J∙g⁻¹)		$\delta_{S_{\rm EA}} $/%	${ {F} }{_{\text{max} }}$/(J∙g⁻¹)		$\delta_{F_{\max}}$/%
Type	${ {t} }{_{\text{R} }}$/mm	${ {t} }{_{\text{I} } }$/mm	${ {t} }{_{\text{r} } }$/mm	n	d/mm	Kriging	FE	$\delta_{S_{\rm EA}} $/%	Kriging	FE	$\delta_{F_{\max}}$/%
${ {F} }{_{\text{max} }}$<5 kN	0.759	0.413	0.775	16	13.9	1.054	1.026	2.73	4.994	4.953	0.83
${ {F} }{_{\text{max} } }$<10 kN	0.954	1.221	1.064	16	31.9	1.347	1.348	−0.07	9.952	10.111	−1.57

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