波纹芯层夹芯管的轴向压缩吸能特性与多目标优化

马梦娇; 刘志芳; 李世强

doi:10.11858/gywlxb.20220554

波纹芯层夹芯管的轴向压缩吸能特性与多目标优化

doi: 10.11858/gywlxb.20220554

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（12072219）

详细信息

作者简介:
马梦娇（1997－），女，硕士研究生，主要从事轻质材料的冲击动力学行为研究. E-mail：sunnymamj@163.com

通讯作者:
李世强（1986－），男，博士，副教授，主要从事冲击动力学研究. E-mail：lishiqiang@tyut.edu.cn

中图分类号: O347.1; O521.9
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出版历程
- 收稿日期: 2022-04-01
- 修回日期: 2022-04-16
- 网络出版日期: 2022-10-11
- 刊出日期: 2022-12-05

Energy Absorption and Multi-Objective Optimization for Sandwich Tubes with a Corrugated Core under Axial Compression

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

摘要

摘要: 将正弦波纹薄壁管作为芯层引入多边形薄壁管，获得了四边形、五边形、六边形3种波纹芯层夹芯管。首先，采用实验与数值模拟相结合的方法研究了3种波纹芯层夹芯管在轴向准静态压缩载荷下的力学响应，包括能量吸收性能，分析了结构壁厚和芯层波幅对夹芯管压缩性能的影响，数值模拟与实验结果吻合较好。其次，基于超折叠单元理论，给出了准静态压缩载荷下波纹芯层夹芯管的平均轴向压缩力的解析解。其中，波纹芯层六边形夹芯管在准静态轴向压缩过程中表现出渐进折叠屈曲的变形模式，理论预测的平均压缩力与实验结果吻合较好，相对误差为6.1%，与数值模拟结果相比，相对误差均在9.8%以内。波纹芯层夹芯管的比吸能随着结构壁厚和芯层波幅的增大而增大；而当波幅和壁厚相同时，六边形夹芯管的吸能能力优于四边形夹芯管和五边形夹芯管。最后，以最大比吸能和最小初始峰值力为目标，对3种结构的芯层波幅和结构壁厚进行了多目标优化，给出了最大比吸能与最小峰值载荷之间的平衡策略，得到了相应的Pareto前沿。
- 夹芯管 /
- 能量吸收 /
- 平均压缩力 /
- 多目标优化
Abstract: Sinusoidal corrugated thin-walled tubes are introduced as a core layer into polygonal thin-walled tubes, and quadrilateral, pentagonal and hexagonal sandwich tubes with corrugated cores are then obtained. First of all, their mechanical responses including energy absorption performance under quasi-static axial compression are studied by a combination of experiment, numerical simulation and theoretical analysis. Effects of the structural wall thickness and the wave amplitude of the core layer on the compression performance of the sandwich tube are analyzed, and the numerical simulation results agree well with the experimental ones. Then, the analytical solution for the mean compression force of the sandwich tube with corrugated cores under quasi-static compression is derived based on the simplified super folding element theory. The hexagonal sandwich tube subjected to quasi-static axial compression exhibits a deformation mode of progressive folding collapse. The theoretical mean compression force of the hexagonal sandwich tube agrees approximately with the experimental results with a relative error of 6.1%, while at a relative error within 9.8% compared to the simulation results. The specific energy absorption of the sandwich tubes with corrugated cores increases with increasing structure wall thickness and core-layer wave amplitude. For the same wave amplitude and wall thickness, the energy absorption capacity of the hexagonal sandwich tube is better than those of the quadrilateral and pentagonal sandwich tubes. Finally, with the objectives of maximum specific energy absorption and minimum initial peak force, multi-objective optimization is carried out on the core wave amplitude and structure wall thickness of the three types of sandwich tubes. The compromise and balance scheme for the maximum specific energy absorption and minimum peak crushing force is given, and the corresponding Pareto front is obtained.
- sandwich tube /
- energy absorption /
- mean compression force /
- multi-objective optimization

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图 1 波纹芯层

Figure 1. Corrugated core

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图 2 QSTCC、PSTCC和HSTCC的结构设计

Figure 2. Structural design of QSTCC, PSTCC and HSTCC

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图 3 有限元模型

Figure 3. Finite element model

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图 4 Al6061-T5的真实应力-应变曲线^[13]

Figure 4. True stress-strain curve of Al6061-T5^[13]

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图 5 网格敏感性验证

Figure 5. Validation of meshing sensitivity

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图 6 准静态轴向压缩实验装置和试件

Figure 6. Setup and specimen for the quasi-static axial compression experiment

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图 7 HSTCC的力-位移曲线

Figure 7. Force-displacement curves of HSTCC

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图 8 HSTCC的变形模式

Figure 8. Deformation modes of HSTCC

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图 9 基本折叠单元的理想折叠过程

Figure 9. Ideal folding process of a basic folding element

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图 10 基本结构单元简化

Figure 10. Simplification of basic constitutive elements

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图 11 QSTCC、PSTCC和HSTCC的横截面

Figure 11. Cross-sections of the QSTCC, PSTCC and HSTCC

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图 12 不同波幅（A）和壁厚（t）的QSTCC、PSTCC、HSTCC的吸能特性

Figure 12. Energy absorption characteristics of QSTCC, PSTCC and HSTCC with different amplitudes (A) and wall thicknesses (t)

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图 13 MCF的理论预测与数值模拟结果对比

Figure 13. Comparison of the theoretical prediction and simulation results on the MCF

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图 14 优化流程

Figure 14. Optimization process

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图 15 QSTCC、PSTCC和HSTCC的SEA-PCF关系的Pareto 前沿

Figure 15. Pareto front of the SEA-PCF relationship for QSTCC, PSTCC and HSTCC

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表 1 模拟和实验得到的吸能评价指标对比

Table 1. Comparison of the energy absorption evaluation indices between simulation and experiment

PCF			SEA
Sim./kN	Exp./kN	Error/%	Sim./(J·g⁻¹)	Exp./(J·g⁻¹)	Error/%
34.71	38.90	−10.7	31.77	29.83	6.3

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表 2 准静态载荷下MCF的理论预测值与模拟结果的对比（部分）

Table 2. Comparison of the theoretical prediction and finite element simulation results on the MCF under quasi-static loading (partial)

Type	A/mm	t/mm	MCF/kN		Error/%
Type	A/mm	t/mm	Sim.	Theor.	Error/%
QSTCC	2	0.5	13.76	14.42	4.8
	2	1.0	37.48	40.78	8.8
	4	0.5	15.29	15.03	−1.7
	4	1.0	44.57	45.52	−4.6
	5	0.5	15.88	15.56	−2.0
	5	1.0	50.21	46.15	−8.1
PSTCC	2	0.5	15.76	16.23	3.0
	2	1.0	43.00	45.89	6.7
	4	0.5	18.40	17.38	−5.6
	4	1.0	54.52	49.18	−9.8
	6	0.5	19.57	19.38	−1.0
	6	1.0	56.96	54.88	−3.7
HSTCC	2	0.5	18.24	18.05	−1.0
	2	1.0	52.20	50.85	−2.6
	4	0.5	21.14	19.78	−6.4
	4	1.0	64.59	58.68	−9.1
	6	0.5	22.71	22.63	−0.4
	6	1.0	67.93	64.00	−5.8

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表 3 响应面模型精度评估

Table 3. Accuracy evaluation of the response surface model

Type	PCF		SEA
Type	R²	RMSE	R²	RMSE
QSTCC	0.968	0.049	0.988	0.027
PSTCC	0.999	0.010	0.961	0.054
HSTCC	0.998	0.013	0.982	0.038

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表 4 优化与模拟结果对比

Table 4. Comparison between the optimized and simulation results

Type	A/ mm	t/ mm	PCF			SEA
Type	A/ mm	t/ mm	Opt./kN	Sim./kN	Error/%	Opt./(J·g⁻¹)	Sim./(J·g⁻¹)	Error/%
QSTCC	4.6	0.5	27.39	28.60	−4.23	26.31	26.40	−0.34
QSTCC	5.0	1.0	64.47	64.45	0.03	42.94	42.95	−0.02
PSTCC	4.0	0.5	30.87	30.98	−0.36	28.98	27.91	3.83
PSTCC	5.0	1.0	75.80	76.73	−1.21	42.54	41.25	3.05
HSTCC	6.0	0.5	34.49	34.71	−0.63	31.36	31.77	−1.29
HSTCC	5.7	1.0	87.11	88.34	−1.39	47.79	49.11	−2.69

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