超高速撞击下瓦楞型Whipple防护结构参数优化

郭家傲; 杨秋足; 刘小川; 尹云飞; 李志强

doi:10.11858/gywlxb.20251276

超高速撞击下瓦楞型Whipple防护结构参数优化

doi: 10.11858/gywlxb.20251276

郭家傲^1,,
杨秋足^1,*, ,,
刘小川²,
尹云飞¹,
李志强^{1, 3, 4, 5}

1.
太原理工大学航空航天学院, 山西太原　030024
2.
中国飞机强度研究所, 陕西西安　710065
3.
太原理工大学材料强度与结构冲击山西省重点实验室, 山西太原　030024
4.
太原理工大学山西省力学基础学科研究中心, 山西太原　030024
5.
太原理工大学国家力学实验教学示范中心, 山西太原　030024

基金项目: 国家自然科学基金（1227021021）；山西省自然科学青年基金（202203021212292）

详细信息

作者简介:
郭家傲（2002－），女，硕士研究生，主要从事冲击动力学研究. E-mail：jiaaoguo2023@163.com

通讯作者:
杨秋足（1991－），男，博士，讲师，主要从事计算力学与冲击动力学研究. E-mail：yangqz@tyut.edu.cn

中图分类号: O347; O521.9; V423.4
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出版历程
- 收稿日期: 2025-12-09
- 修回日期: 2026-01-30
- 网络出版日期: 2026-02-12

Parameter Optimization of the Corrugated Whipple Protective Structure under Hypervelocity Impact

GUO Jia’ao^1
,,
YANG Qiuzu^{1,*
, ,},
LIU Xiaochuan²,
YIN Yunfei¹,
LI Zhiqiang^{1, 3, 4, 5}

1.
College of Aeronautics and Astronautics, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
2.
Aircraft Strength Research Institute of China, Xi’an 710065, Shaanxi, China
3.
Shanxi Provincial Key Laboratory of Material Strength & Structural Impact, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
4.
Shanxi Basic Disciplines Research Center for Mechanics, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
5.
National Experimental Teaching Demonstration Center for Mechanics, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China

摘要

摘要: 瓦楞型Whipple防护结构的几何构型是影响其防护性能的重要因素。为优化瓦楞型Whipple防护结构在超高速撞击下的防护性能，提出了一种结合有限元-光滑粒子流体动力学（finite element method-smoothed particle hydrodynamics，FEM-SPH）耦合算法与正交试验设计的综合优化方法。通过构建可靠的数值仿真模型，引入z轴动量密度作为防护性能评价指标，系统研究了瓦楞厚度、跨度与角度3个因素对防护效果的影响。正交试验结果表明，按照因素的影响程度，由高到低依次为厚度、角度、跨度。进一步开展了双因素密集试验，并建立了二次多项式模型，获取了最优几何参数组合，其防护性能较平板提升了33.72%。研究证实，优化后的瓦楞构型Whipple防护结构能够有效促进弹丸破碎与碎片云扩散，实现动量三维重分布，从而显著提升结构的防护性能，为航天器防护设计提供理论依据与参数优化路径。
- Whipple防护结构 /
- 超高速碰撞 /
- FEM-SPH耦合算法 /
- 正交试验
Abstract: The geometric configuration of the corrugated Whipple protective structure significantly influences their protective capability against hypervelocity impact. To optimize the performance of the corrugated Whipple protective structures under hypervelocity impact, an integrated optimization method combining the finite element method-smoothed particle hydrodynamics (FEM-SPH) coupled algorithm with orthogonal experimental design was proposed. A reliable numerical simulation model was constructed, and the z-axis momentum density was introduced as an evaluation factor for protective performance. The three geometric parameters of the corrugation, namely thickness, span, and angle, were systematically investigated for their protective effects on the shielding. Orthogonal test results indicated that the order of influence of these factors, in descending order of magnitude, is thickness, angle, and span. Further double-factor refined tests were conducted, and a quadratic polynomial model was developed to identify the optimal geometric parameters. The optimal configuration improved the protective performance by 33.72% compared to a flat plate. The study confirms that the optimized corrugated structure effectively promotes projectile fragmentation and debris cloud dispersion, facilitating three-dimensional redistribution of the momentum, thereby significantly enhancing protective performance of the shield. This research provides a theoretical basis and a parameter optimization pathway to the design of spacecraft protective structures.
- Whipple protective structure /
- hypervelocity impact /
- finite element method-smoothed particle hydrodynamics (FEM-SPH) coupling algorithm /
- orthogonal tests

HTML全文

图 1 实验^[34]（左）与FEM-SPH自适应耦合方法（右）得到的6.5 μs时的碎片云结构比较

Figure 1. Comparison of the debris cloud structure at 6.5 μs obtained by experiment^[34] (left) and FEM-SPH adaptive coupling method (right)

下载: 全尺寸图片幻灯片

图 2 瓦楞构型结构的几何形状和几何参数

Figure 2. Geometric shape and geometrical parameters of corrugated structures

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图 3 弹丸撞击瓦楞构型防护结构模型

Figure 3. Model of projectile impacting into corrugated protective structure

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图 4 10 μs时弹丸撞击平板和瓦楞型防护结构形成的碎片云形貌（左：正视图；右：俯视图）

Figure 4. Morphologies of the debris cloud following the projectile impacting the flat plate and the corrugated protective structure at 10 μs (Left: front view; right: top view.)

下载: 全尺寸图片幻灯片

图 5 沿速度矢量投射到虚拟背面的危险碎片示意图

Figure 5. Schematic diagram for hazardous debris projected onto the virtual backside along the velocity vector

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图 6 10 μs时弹丸撞击平板和瓦楞板防护结构时碎片云z轴动量密度分布对比

Figure 6. Comparison of the z-axis momentum distribution of the debris cloud for the flat plate and corrugated plate protection structures impacted by a projectile at 10 μs

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图 7 瓦楞型Whipple防护结构的z轴动量密度响应面

Figure 7. z-axis momentum density response surface of the corrugated Whipple protective structure

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图 8 弹丸超高速碰撞具有最优构型的瓦楞型Whipple防护结构过程

Figure 8. Process of the corrugated Whipple protection structure with the optimal configuration impacted by hypervelocity projectile

下载: 全尺寸图片幻灯片

图 9 弹丸超高速碰撞具有最优构型的瓦楞型Whipple防护结构时弹丸内部的应力云图演变

Figure 9. Evolution of the stress contour within the projectile during hypervelocity impact on a corrugated Whipple shield with an optimal configuration

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表 1 正交试验设计因素和水平

Table 1. Orthogonal test design factors and levels

Level	Factor
Level	H/mm	λ/mm	θ/(°)
1	0.9	0.2	30
2	1.4	0.6	45
3	1.9	1.0	60

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表 2 正交试验方案及试验结果

Table 2. Orthogonal test program and results

No.	H/mm	λ/mm	θ/(°)	ρ_pz/(kg·m⁻¹·s⁻¹)	No.	H/mm	λ/mm	θ/(°)	ρ_pz/(kg·m⁻¹·s⁻¹)
1	0.9	0.2	60	5719.63	6	1.4	1.0	45	5931.89
2	0.9	0.6	45	2780.70	7	1.9	0.2	45	394.47
3	0.9	1.0	30	2244.38	8	1.9	0.6	30	2250.10
4	1.4	0.2	30	1672.53	9	1.9	1.0	60	1066.58
5	1.4	0.6	60	2091.21

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表 3 极差分析结果

Table 3. Results of the variance analysis

Factor	K₁	K₂	K₃	k₁	k₂	k₃	R
H	10744.71	9695.63	3711.15	3581.57	3231.88	1237.05	2344.52
λ	7786.63	7122.00	9242.85	2595.54	2374.00	3080.95	706.95
θ	8877.42	9107.05	6167.01	2959.14	3035.68	2055.67	980.01

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表 4 双因素三水平密集试验方案及结果

Table 4. Test program and results for double-factor, three-level encryption

No.	H/mm	θ/(°)	ρ_pz/(kg·m⁻¹·s⁻¹)	No.	H/mm	θ/(°)	ρ_pz/(kg·m⁻¹·s^-¹)
D1	1.8	35	2340.74	D6	1.9	55	542.27
D2	1.8	45	1566.87	D7	2.0	35	1113.50
D3	1.8	55	1195.35	D8	2.0	45	673.06
D4	1.9	35	1461.78	D9	2.0	55	1347.03
D5	1.9	45	394.47

下载: 导出CSV

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