抗侵彻孔结构装甲的可靠性优化设计

姚晨辉; 杨刚; 张哲; 李安祺

doi:10.11858/gywlxb.20220507

抗侵彻孔结构装甲的可靠性优化设计

doi: 10.11858/gywlxb.20220507

湖南大学机械与运载工程学院特种装备先进设计技术与仿真教育部重点实验室, 湖南长沙　410082

基金项目: 国防基础科研项目（JCKY2019110D008）

详细信息

作者简介:
姚晨辉（1997－），男，硕士研究生，主要从事结构可靠性优化研究.E-mail：S2002W0238@hnu.edu.cn

通讯作者:
杨　刚（1981－），男，博士，教授，主要从事冲击动力学与计算力学研究.E-mail：yanggang@hnu.edu.cn

中图分类号: O385; TJ02
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出版历程
- 收稿日期: 2022-01-28
- 修回日期: 2022-02-26
- 录用日期: 2022-02-26
- 网络出版日期: 2022-07-21
- 刊出日期: 2022-07-28

Reliability Optimization Design of Anti-Penetration Perforated Armor

Key Laboratory of Advanced Design and Simulation Techniques for Special Equipment, Ministry of Education, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, Hunan, China

摘要

摘要: 孔结构装甲在满足抗侵彻性能的同时需实现减重，因而轻量化设计具有工程实际意义。以孔结构装甲的轻量化为设计目标，抗侵彻性能为约束条件，考虑不确定性因素的影响，开展孔结构装甲的可靠性优化设计。样本点采用最优拉丁超立方法设计生成，孔结构装甲抗侵彻仿真的参数化建模及响应计算通过商业软件ANSYS的二次开发实现，引入Kriging代理模型和期望改变量（expected improvement, EI）加点法构建性能函数，最后采用序列优化与可靠性评估方法（sequential optimization and reliabilityassessment, SORA）进行可靠性优化设计。结果表明，可靠性优化后，孔结构装甲在满足抗侵彻性能和相关可靠度指标的前提下，可有效地实现减重11.5%。研究结果可为其他抗侵彻防护结构的可靠性优化设计提供参考。
- 孔结构装甲 /
- 轻量化设计 /
- Kriging模型 /
- 可靠性优化
Abstract: Perforated armor can effectively reduce weight while meeting anti-penetration performance. Structural lightweight design of perforated armor has practical engineering significance. Considering the influence of uncertain factors, a reliability optimization design of a perforated armor was realized in this research. In the process of the reliability optimization design, the light weight of the perforated armor was taken as the goal of the design, and the anti-penetration performance was taken as the constraint condition. The optimal Latin hypercube design method was used to generate sample points. Based on a development of the commercial software ANSYS, the parametric modeling and the response calculation of the anti-penetration simulation of the perforated armor were realized. The Kriging surrogate model and the expected improvement maximization method were introduced to construct the performance functions. The sequential optimization and the reliability assessment method were applied in the reliability optimization design of the perforated armor. Under the premise of meeting the anti-penetration performance requirements and having a related reliability indicator of 0.9, the weight of the perforated armor after the reliability optimization can be effectively reduced by 11.5%. The research can provide references for the reliability optimization design of other anti-penetration structures.
- perforated armor /
- lightweight design /
- Kriging model /
- reliability optimization

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图 1 孔结构装甲可靠性优化设计流程

Figure 1. Flow chart of reliability optimization designfor perforated armor

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图 2 子弹侵彻孔结构装甲的数值模型

Figure 2. Numerical model of bullet penetration into perforated armor

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图 3 子弹侵彻后孔结构装甲毁伤的仿真结果与实验结果^[3]对比

Figure 3. Comparison of the simulation and the experimental^[3] results of the damage in the perforated armor after the bullet penetration

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图 4 实心装甲损伤的数值仿真结果与实验结果^[3]对比

Figure 4. Comparison of the numerical simulation and the experimental^[3] results of the damage in the solid armor

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图 5 孔结构装甲抗侵彻性能函数代理模型构建流程

Figure 5. Flow chart of the construction process of surrogate model for anti-penetration performance function of perforated armor

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图 6 抗侵彻孔结构装甲的原型

Figure 6. Numerical model of the prototype of the anti-penetration perforated structure armor

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图 7 孔结构装甲抗侵彻分析的参数化流程

Figure 7. Flow chart of parameterized process of anti-penetration analysis of perforated armor

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图 8 孔结构装甲可靠性优化流程

Figure 8. Flow chart of reliability optimization process of perforated armor

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图 9 可靠性优化设计前后的孔结构装甲

Figure 9. Perforated armor before and after reliability optimization

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表 1 弹体与装甲材料参数^[3]

Table 1. Material parameters of bullet and armor^[3]

Component	ρ/(kg·m⁻³)	E/GPa	G/GPa	v	A/MPa	B/MPa	n	C	$\dot{\varepsilon}$ ₀/s⁻¹	c_p/(J·kg⁻¹·K⁻¹)	T₀/K	T_m/K	m
Target material	7 850	206	80	0.30	1200	1 580	0.175	0.004	0.000 1	450	300	1 800	1.00
Bullet core	7 850	206	80	0.30	1900	1 100	0.065	0.050	0.001 0	477	300	1 800	1.00
Brass jacket	8 960	124	46	0.34	90	292	0.310	0.025	1.000 0	386	300	1 356	1.09

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表 2 孔结构装甲可靠性优化设计相关变量的约束范围

Table 2. Ranges of the relevant variables in reliability optimization design of perforated structure armor

R/mm	d/mm	v/(m∙s⁻¹)	$\theta$ /(°)
4.5−6.2	7.8−12.4	834−874	85−95

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表 3 最优拉丁超立方法抽取的采样点和响应

Table 3. Sampling points and responses obtained by the optimal Latin hypercube method

R/mm	d/mm	v/(m·s⁻¹)	$\theta$ /(°)	v′/(m·s⁻¹)	m′/g
6.052	10.200	870.522	94.130	811.129	4.662
5.978	8.600	867.043	86.304	808.016	4.889
5.387	8.400	844.435	93.261	760.791	4.854
4.796	12.200	842.696	86.739	675.821	4.112
4.722	8.800	837.478	85.435	603.861	3.958
4.943	11.800	874.000	87.174	710.546	4.245
5.017	11.600	856.609	90.652	667.470	4.005
5.239	10.800	872.261	92.826	780.641	4.506
5.683	11.200	853.130	88.478	754.275	4.529
5.461	9.200	849.652	85.870	747.881	4.622
4.870	9.800	846.174	91.957	691.675	4.366
5.830	11.000	847.913	93.696	762.888	4.720
5.535	12.000	868.783	89.783	761.734	4.493
4.500	12.400	851.391	91.522	568.453	3.551
6.126	10.400	839.217	89.348	782.666	4.794
5.609	7.800	840.957	88.043	788.874	4.941
5.313	10.600	835.739	92.391	719.739	4.375
5.757	9.000	834.000	91.087	759.182	4.708
6.200	8.200	858.348	95.000	814.127	5.034
4.648	11.400	860.087	85.000	701.905	4.282
5.091	9.400	865.304	88.914	725.571	4.170
5.904	10.000	863.565	90.217	800.931	4.745
5.165	8.000	861.826	94.565	767.436	4.786
4.574	9.600	854.870	87.609	648.105	4.038

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表 4 剩余速度响应代理模型构建的新增样本和响应

Table 4. Added samples and responses built by residual velocity response surrogate model

R/mm	d/mm	v/(m·s⁻¹)	$\theta$ /(°)	v′/(m·s⁻¹)
4.668	12.400	835.174	91.508	562.223
6.200	12.400	837.169	92.044	779.260
4.500	9.031	843.095	86.100	604.955
4.501	12.399	857.090	88.573	529.787
4.503	9.796	853.839	86.088	619.838
6.200	12.400	837.029	85.000	757.080

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表 5 剩余质量响应代理模型构建的新增样本和响应

Table 5. Added samples and responses built by residual mass response surrogate model

R/mm	d/mm	v/(m·s⁻¹)	$\theta$ /(°)	m′/g
6.200	12.395	835.626	85.000	4.713
4.500	7.800	873.789	85.000	3.846
4.500	7.800	856.411	88.096	4.159
4.500	12.400	834.180	92.023	3.463
6.200	7.800	834.000	85.000	5.209
4.500	12.400	834.000	94.902	3.448

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表 6 校核样本点和结果

Table 6. Check samples and results

R/mm	d/mm	v/(m·s⁻¹)	$\theta$ /(°)	v′/(m·s⁻¹)		Residual velocity accuracy checking		m′/g		Residual mass accuracy checking
R/mm	d/mm	v/(m·s⁻¹)	$\theta$ /(°)	Sur.	Sim.	AAE/%	MAE/(m·s⁻¹)	Sur.	Sim.	AAE/%	MAE/g
5.860	11.480	874	91	805.051	805.150	0.58	8.394	4.700	4.650	1.58	0.105
4.500	12.400	850	90	555.406	552.960			3.636	3.531
6.200	8.720	842	87	820.845	814.010			5.116	5.048
4.840	9.640	866	85	698.654	690.260			4.159	4.229
5.180	10.560	834	93	697.718	701.010			4.288	4.329
5.520	7.800	858	95	788.991	793.070			4.933	4.929
Note: Sur. means surrogate model.

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表 7 随机变量参数的概率分布信息

Table 7. Probability distribution information of random variables and parameters

Symbol	Distribution pattern	Mean	Variance	Variable upper limit	Variable lower limit
$R$	Normal distribution	${\,\mu _R}$	0.02 ${\,\mu _R}$	4.5 mm	6.2 mm
$d$	Normal distribution	${\,\mu _d}$	0.02 ${\,\mu _d}$	7.8 mm	12.4 mm
$v$	Normal distribution	854 m/s	17.08 m/s
$\theta$	Normal distribution	90°	1.8°

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表 8 孔结构装甲优化参数结果

Table 8. Parameter results of the optimization of perforated structure armor

Variable	R/mm	d/mm	n₁	n₂
Initial design	6.00	10.00	10	11
Reliability optimization	5.06	7.83	13	15
Note: ${n_1}$ is the maximum hole quantity in each row; ${n_2}$ is the maximum hole quantity in each column.

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表 9 输出响应和孔结构装甲质量属性

Table 9. Output responses and the quality attributes of perforated structure armor

Responses	$v'/({\text{m}\cdot\text{s}^{ {-1} } } )$	$m'/{\text{g} }$	$M/{\text{g} }$	$\sigma /({\text{g}\cdot\text{cm}^{{-2} } } )$	$L_{ \rm{wd} }$ /%
Initial design	794.460	4.739	331.168	3.31	0
Reliability optimization	739.480	4.557	292.940	2.93	11.50
Note: $M$ is the mass of the perforated armor; $\sigma$ is the surface density of the perforated armor; $L_{\rm{wd}}$ is the lightweight degree of the perforated armor.

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