异形弹体高速侵彻/穿甲机理研究进展

doi:10.12382/bgxb.2024.0040

摘要/Abstract

摘要：

为支撑超高声速武器终点毁伤效应评估,满足异形弹体侵彻力学理论发展需求,异形弹体侵彻机理是当前亟需研究的关键基础科学问题。对异形弹体侵彻行为、弹靶作用机制、弹道稳定性与结构响应研究现状进行全面综述,对现有研究工作进行梳理与总结,搭建异形弹体侵彻问题研究的基本框架;以异形弹体侵彻/穿甲过程中出现的新质弹靶作用现象、机理为脉络,突出异形弹体结构对载荷环境表征、弹道及结构稳定性控制等方面带来的新挑战,并提出了异形弹体未来研究的3个建议,供相关研究者参考。

关键词: 异形弹体, 侵彻机理, 弹道稳定性, 结构稳定性

Abstract:

To support the theoretical design of the hypersonic missile’s terminal effect and meet the development demand of penetration mechanics theory of non-circular projectiles, the penetration mechanism of non-circular projectilesis a key scientific problem required to be solved. A comprehensive review is conducted on the penetration behavior, penetration mechanism, ballistic stability, and structural response of non-circular projectiles.It is a review and summary of the existing research work, aiming to establish a basic framework for researching the penetration problem of non-circular projectiles.Moreover, the new phenomena and mechanisms introduced by the structural changes of non-circular projectiles are highlighted. Three suggestions for the future research of the non-circular projectiles are put forward for the reference of relevant researchers.

Key words: non-circular projectile, penetration mechanics, ballistic stability, structuralresponse

中图分类号:

O385

董恒, 黄风雷, 武海军, 邓希旻, 李萌, 刘龙龙. 异形弹体高速侵彻/穿甲机理研究进展[J]. 兵工学报, 2024, 45(9): 2863-3887.

DONG Heng, HUANG Fenglei, WU Haijun, DENG Ximin, LI Meng, LIU Longlong. Penetration and Perforation Mechanism of High-speed Non-circular Projectilesa: A State-of-the-Art Review[J]. Acta Armamentarii, 2024, 45(9): 2863-3887.

图/表 44

图1 猎鹰HTV-2号高超声速飞行器

Fig.1 HTV-2 hypersonic technology vehicle

图2 圆形(左)与异形(右)战斗部空间利用率对比

Fig.2 Comparison of space utilizationofcircular(left) and non-circular(right) projectiles

图3 异形弹体示意图

Fig.3 Schematic diagram of a special shaped projectile

图4 等截面三角形、方形、圆形长杆弹侵深[25]

Fig.4 Penetration depths of equal cross-section triangular, square, and circular long rod projectiles[25]

图5 异形长杆弹坑截面形状(上)与“蘑菇头” 自锐效(下)[27]

Fig.5 Crater cross-sectional shape(up) and “mushroom head” self-sharpening effect(down) of a special shaped rod[27]

图6 双卵型弹体示意图[38]

Fig.6 Diagram of a double-oval projectile[38]

图7 头部非对称刻槽弹体结构图(左为弹体侧视图, 右为俯视图)[39]

Fig.7 Diagram of projectiles with asymmetrically grooved-tapered nose (left: side view, right: top view)[39]

图8 头部对称刻槽弹体结构图(上为弹体侧视图,下为局部刻槽图)[40]

Fig.8 Diagram of projectiles with symmetrically grooved-tapered nose (upper: the side view of the projectile, below: the partial diagram of the grooved structure)[40]

图9 齿形头部异形弹体(左)与多点压入应力分布(右)[42]

Fig.9 Toothed head projectile (left) and theMulti-point indentation stress cloud (right)[42]

图10 头部带肋板异形弹体(左)及其斜侵彻弹道模拟(右)[43]

Fig.10 Ribbed-head projectile (left) and its oblique penetration trajectory simulation (right) [43]

图11 高速深侵彻缩比概念弹结构示意图(左为弹身截面图,右为弹身正视图)[45]

Fig.11 Diagram of a high-speed deep penetration scaled-down concept projectile (left: the cross-section of the projectile, right: the front view of the projectile)[45]

图12 弹身刻槽弹体[48-49]

Fig.12 Projectiles with grooves in its shank[48-49]

图13 圆截面与椭圆截面弹体及对应靶体开坑(左: C1圆形弹,中:E1椭圆弹,右:E2椭圆弹)[52]

Fig.13 Circular and elliptical cross-section projectiles and corresponding target cratering (left:C1 projectile,medial: E1 projectile,and right:E2 projectile)[52]

图14 椭圆弹体侵彻铝靶扩孔模式(上)与花瓣分布特征(下)[53]

Fig.14 Characteristics of enlargement pattern (upper) and petal distribution (below) of aluminum target with the penetration of the elliptical projectile[53]

图15 椭圆弹体侵彻下铝靶表面应变分布特征[54]

Fig.15 Characteristic of strain distribution of aluminum target surfaceunder the elliptical projectile penetrating[54]

图16 椭圆弹体头部形状系数与应力分布特征[55]

Fig.16 Characteristic of nose shape coefficients and stress distribution of the elliptical projectile[55]

图17 椭圆弹体应力修正系数与侵彻深度分析图[50]

Fig.17 Stress modified coefficient and penetration depth of elliptical projectile[50]

图18 椭圆截面弹体无量纲侵深P/d与冲击函数I关系

Fig.18 Relationship between the depth of penetration P/d and the impact function I for elliptical projectiles

图19 静水压/等比例位移边界下椭圆空腔扩孔模式对比[52]

Fig.19 Comparison of elliptical cavity reaming patterns under hydrostatic pressure/equal scale displacement boundary conditions[52]

图20 平面无旋流势函数与流函数关系图

Fig.20 Potential function and stream function for planar spinless flow

图21 空腔周围法向应力分布[73]

Fig.21 Normal stress distribution around the cavity[73]

图22 空腔周围剪应力分布[73]

Fig.22 Shear stress distribution around the cavity[73]

图23 空腔周围法向应力与剪应力分布[73]

Fig.23 Distribution of normal and shear stresses around the cavity[73]

图24 三类椭圆空腔无量纲阻力模型对比[73]

Fig.24 Comparison of three types of elliptical cavity dimensionless resistance models[73]

图25 低速弹体贯穿下945平板靶板变形与破坏模式[75]

Fig.25 Deformation and damage patterns of 945 plate target under perforation of the low velocity projectiles[75]

图26 不同初速下921薄靶靶板横向变形及塑性区半径[77]

Fig.26 Transverse deformation and radius of plastic deformation zone of 921 target plate at different initial velocities[77]

图27 非对称椭圆弹体贯穿过程[57]

Fig.27 Perforation process of asymmetric elliptical projectiles[57]

图28 弹体高速贯穿有限厚靶载荷作用位置[77]

Fig.28 Location of the load action when the projectile penetrates a finite thickness target at high velocity[77]

图29 头部侵入阶段不同时刻靶体速度分布[79]

Fig.29 Distribution of velocitiesin targetat different moments of the head penetration phase[79]

图30 能量法与微分面力法[73]

Fig.30 Energy method and differential surface force method[73]

图31 柱形、锥形与刻槽弹体结构示意图及弹道特性[93]

Fig.31 Schematic structure and ballistic characterization of cylindrical, conical and grooved projectiles[93]

图32 圆形与椭圆截面弹体载荷特征[94]

Fig.32 Load characteristics of circular and elliptical cross-section projectiles[94]

图33 滚转角作用下弹体运动参量(a/b=2.0,θ=30°,ψ=-30°)[94]

Fig.33 Parameters of projectile motion under the action of the roll angle(a/b=2.0,θ=30°,ψ=-30°)[94]

图34 非对称椭圆截面弹体结构示意图[99]

Fig.34 Schematic of an asymmetric elliptical cross-section projectile[99]

图35 非对称椭圆形弹体侵彻混凝土靶弹道[100]

Fig.35 Ballistic trajectory of an asymmetric elliptical cross-sectional projectile penetrating into concrete target[100]

图36 CC/EC/AC弹体穿甲过程及弹体姿态角变化规律[101]

Fig.36 Armor-piercing process of CC/EC/AC projectiles and the variation of those attitude angles[101]

图37 弹体正向撞击下典型破坏模式

Fig.37 Typical damage patterns of projectiles under normal impact

图38 端部冲击载荷作用下弹体变形模式[111]

Fig.38 Deformation pattern of the projectile subjected to impact loading at the free end[111]

图39 椭圆弹体斜侵彻双层薄钢靶实验和数值模拟[113]

Fig.39 Experimental and numerical simulation of oblique penetration of elliptical projectiles perforation a double-layer thin steel target[113]

图40 任意位置受载荷时弹体内力分布(形成塑性铰之前)[113]

Fig.40 Distribution of internal stresses in theprojectilesubjected to impact loading at any cross-section along its span (before the appearance of plastic hinge)[113]

图41 截面形状的结构优化示意图[115]

Fig.41 Structural optimization methods for elliptical cross-sectional projectile[115]

图42 弹体空腔表面应力考察点[52]

Fig.42 Typical points of stresses on the surface of the projectile cavity[52]

图43 典型空腔弹体等效应力时程曲线[52]

Fig.43 Equivalent stress curve of typical cavity projectiles[52]

图44 椭圆弹体自由梁双向弯曲示意图

Fig.44 Free-beam bidirectional bending diagram of elliptical projectile

参考文献 115

[23]	李永池, 孙宇新, 胡秀章, 等. 混凝土靶抗贯穿的一种新工程分析方法[J]. 爆炸与冲击, 2000, 20(1):13-18.
	LI Y C, SUN Y X, HU X Z, et al. A new engineering analysis method for anti-penetration of concrete targets[J]. Explosion and Shock Waves, 2000, 20(1):13-18. (in Chinese)
[24]	BLESS S J. Penetration mechanics of non-circular rods[J]. AIP Conference Proceedings, 1996, 370(1):1119-1122.
[25]	杜忠华, 曾国强, 余春祥, 等. 异型侵彻体垂直侵彻半无限靶板试验研究[J]. 弹道学报, 2008, 20(1):19-21.
	DU Z H, ZENG G Q, YU C X, et al. Experimentalresearch of novel penetrator vertically penetrating semi infinite target[J]. Journal of Ballistics, 2008, 20(1):19-21. (in Chinese)
[26]	杜忠华, 朱建生, 王贤治, 等. 异型侵彻体垂直侵彻半无限靶板的分析模型[J]. 兵工学报, 2009, 30(4):403-407.
	DU Z H, ZHU J S, WANG X Z, et al. Analyticalmodel on non-circular penetrator impacting semi infinite target perpendicularly[J]. Acta Armamentarii, 2009, 30(4):403-407. (in Chinese)
[27]	王晓东, 王江波, 徐立志, 等. 异型截面长杆弹侵彻半无限厚金属靶板实验研究[J]. 爆炸与冲击, 2021, 41(3):37-46.
	WANG X D, WANG J B, XUE L Z, et al. Experimental study on penetration of non-circular cross-section long-rod projectiles into semi-infinite metal target[J]. Explosion and Shock Waves, 2021, 41(3):37-46. (in Chinese)
[28]	高光发, 李永池, 刘卫国, 等. 长杆弹截面形状对垂直侵彻深度的影响[J]. 兵器材料科学与工程, 2011, 34(3):5-8.
	GAO G F, LI Y C, LIU W G, et al. Influence of the cross-section shapes of long rod projectile on the vertical penetration depth[J]. Ordnance Material Science and Engineering, 2011, 34(3):5-8. (in Chinese)
[29]	GUO C, QIAN J P, GU W B, et al. Penetration characteristics of a penetrator with triangular cross-section impacting semi-infinite targets[J]. Mechanics Based Design of Structures and Machines, 2023, 51(3):1335-1348.
[30]	LI J C, CHEN X W, HUANG F L. FEM analysis on the “self-sharpening” behavior of tungsten fiber/metallic glass matrix composite long rod[J]. International Journal of Impact Engineering, 2015, 86(4):67-83.
[31]	ANDERSON C E, LILLEFIELD D L, WALKER J D. Long-rod penetration, target resistance, and hypervelocity impact[J]. International Journal of Impact Engineering, 1993, 14(1-4):1-12.
[32]	HAN J, ZHANG Y J, WANG W H. Effect of grooves on the double-nosed projectile penetrating into plain concrete target[J]. International Journal of Impact Engineering, 2020, 140:103544.
[33]	BORVIK T, LANGSETH M, HOPPERSTAD O S. Perforation of 12mm thick steel plates by 20mm diameter projectiles with flat, hemispherical and conical noses[J]. International Journal of Impact Engineering, 2002, 27(1):19-35.
[34]	孙传杰, 卢永刚, 张方举, 等. 新型头形弹体对混凝土的侵彻效能[J]. 弹道学报, 2009, 21(4):63-67.
	SUN C J, LU Y G, ZHANG F J, et al. Performance of a new-nose-tip Projectile Penetrating Into Concrete Target[J]. Journal of Ballistics, 2009, 21(4):63-67. (in Chinese)
[35]	庞春旭, 何勇, 沈晓军, 等. 刻槽弹体旋转侵彻混凝土效应试验研究[J]. 兵工学报, 2015, 36(1):46-52. doi: 10.3969/j.issn.1000-1093.2015.01.007
	PANG C X, HE Y, SHEN X J, et al. Experimentalinvestigation on penetration of grooved projectiles into concrete targets[J]. Acta Armamentarii, 2015, 36(1):46-52. (in Chinese)
[36]	庞春旭, 何勇, 沈晓军, 等. 刻槽弹体旋转侵彻铝靶试验与数值模拟[J]. 弹道学报, 2015, 27(1):70-75.
	PANG C X, HE Y, SHEN X J, et al. Experimentalinvestigation and numerical simulation on grooved projectilerotationally penetrating into aluminum target[J]. Journal of Ballistics, 2015, 27(1):70-75. (in Chinese)
[37]	柴传国, 武海军, 皮爱国, 等. 异形头部弹体中低速侵彻混凝土的实验研究[J]. 北京理工大学学报, 2015, 35(8):787-791.
	CHAI C G, WU H J, PI A G, et al. Experimentalstudy on nose headed penetrator penetrating to concrete target with middle and low speed[J]. Transactions of Beijing Institute of Technology, 2015, 35(8):787-791. (in Chinese)
[38]	LIU J C, PI A G, HUANG F L. Penetration performance of double-ogive-nose projectiles[J]. International Journal of Impact Engineering, 2015, 84:13-23.
[39]	邓佳杰, 张先锋, 刘闯, 等. 头部非对称刻槽弹体侵彻混凝土目标性能研究[J]. 兵工学报, 2018, 39(7):1249-1258. doi: 10.3969/j.issn.1000-1093.2018.07.001
	DENG J J, ZHANG X F, LIU C, et al. Research on penetration of asymmetrically grooved nose projectile into concrete target[J]. Acta Armamentarii, 2018, 39(7):1249-1258. (in Chinese)
[40]	邓佳杰, 张先锋, 刘闯, 等. 头部对称刻槽弹体侵彻半无限厚铝合金靶实验与理论模型[J]. 爆炸与冲击, 2018, 38(6):1231-1240.
	DENG J J, ZHANG X F, LIU C, et al. Experimental and theoretical study of symmetrical grooved-nose projectile penetrating into semi-infinite aluminum target[J]. Explosion and Shock Waves, 2018, 38(6):1231-1240. (in Chinese)
[41]	CHEREPANOV G P. An analysis of two models of super-deep penetration[J]. Engineering Fracture Mechanics, 1996, 53(3):399-423.
[42]	臧晓京, 朱爱平. MBDA公司为AASM研制新型战斗部[J]. 飞航导弹, 2009(7):2-3.
	ZANG X J, ZHU A P. MBDA develops a new warhead for AASM[J]. Aerospace Technology, 2009(7):2-3. (in Chinese)
[43]	张健东, 武海军, 李伟, 等. 头部带肋板的异形结构弹体斜贯穿混凝土薄靶实验和数值模拟[J]. 高压物理学报, 2021, 35(6):186-194.
	ZHANG J D, WU H J, LI W, et al. Experiment andnumerical simulation on oblique penetrating concrete targets by a special-shaped projectile with rbbed head[J]. Chinese Journal of High Pressure Physics, 2021, 35(6):186-194. (in Chinese)
[44]	ERENGIL M E, CARGILE D J. Advanced projectile concept for high speed penetration of concrete targets[C]//Proceedings of the 20th International Symposium on Ballistics.Orlando,FL, US:IBC, 2002.
[45]	梁斌, 陈小伟, 姬永强, 等. 先进钻地弹概念弹的次口径高速深侵彻实验研究[J]. 爆炸与冲击, 2008, 28(1):1-9.
	LIANG B, CHEN X W, JI Y Q, et al. Experimental study on deep penetration of reduced-scale advanced earth penetrating weapon[J]. Explosion and Shock Waves, 2008, 28(1):1-9. (in Chinese)
[46]	WU H J, WANG Y N, HUANG F L. Penetration concrete targets experiments with non-ideal & high velocity between 800 and 1100m/s[J]. International Journal of Modern Physics B, 2008, 22(9-11):1087-1093.
[47]	ZHANG S, WU H J, ZHANG X X, et al. High-velocity penetration of concrete targets with three types of projectiles: experiments and analysis[J]. Latin American Journal of Solids and Structures, 2017, 14(9):1614-1628.
[48]	张欣欣, 武海军, 黄风雷, 等. 刻槽弹侵彻混凝土的机理研究[C]//第11届全国冲击动力学学术会议论文集. 咸阳: 中国力学学会, 2013.
	ZHANG X X, WU H J, HUANG F L, et al. The mechanism of the grooved-tapered projectile penetrating the concrete targets[C]//Proceedings of the 11st National Symposium on the Impact Dynamics. Xianyang: the Chinese Society of Theoretical and Applied Mechanics, 2013. (in Chinese)
[49]	范少博, 陈智刚, 侯秀成, 等. 旋进侵彻弹丸数值模拟与试验研究[J]. 弹箭与制导学报, 2013, 33(1):80-83.
	FAN S B, CHEN Z G, HOU X C, et al. Numerical simulations and experimental study on novel rotating penetrating projectile[J]. Journal of Projectiles,Rockets,Missiles and Guidance, 2013, 33(1):80-83. (in Chinese)
[50]	LIU J W, ZHANG X F, WEI H Y, et al. Study on the penetration of elliptical cross-section projectiles into concrete targets: theory and experiment[J]. Latin American Journal of Solids and Structures, 2022, 19(3):e439.
[51]	郭磊, 何勇, 潘绪超, 等. 非圆截面弹体侵彻混凝土靶试验与仿真研究[J]. 兵器材料科学与工程, 2019, 42(3):62-68.
	GUO L, HE Y, PAN X C, et al. Experimental and numerical investigation on the penetration mechanics of non-circular projectile into concrete[J]. Ordnance Material Science and Engineering, 2019, 42(3):62-68. (in Chinese)
[52]	董恒. 椭圆截面弹体侵彻混凝土靶作用过程与结构响应研究[D]. 北京: 北京理工大学, 2021.
	DONG H. Penetration mechanism and structural response of elliptical cross-sectional projectile penetrating into concrete target[D]. Beijing: Beijing Institute of Technology, 2021. (in Chinese)
[53]	刘均伟, 张先锋, 赵瑶瑶, 等. 在椭圆横截面弹体正侵彻下有限厚铝靶的破坏模式及响应特性[J]. 爆炸与冲击, 2022, 42(12):81-94.
	LIU J W, ZHANG X F, ZHAO Y Y, et al. Failure modes and response characteristics of finite-thickness aluminum targets under normal penetration of elliptical cross-section projectiles[J]. Explosion and Shock Waves, 2022, 42(12):81-94. (in Chinese)
[54]	LIU J W, LIU C, ZHANG X F, et al. Research on the penetration characteristics of elliptical cross-section projectile into semi-infinite metal targets[J]. International Journal of Impact Engineering, 2023, 173:104438.
[55]	DAI X H, WANG K H, LI M R, et al. Rigid elliptical cross-section ogive-nose projectiles penetration into concrete targets[J]. Defence Technology, 2020, 17(3):800-811.
[56]	FORRESTAL M J, LUK V K. Penetration into soil targets[J]. International Journal of Impact Engineering, 1992, 12(3):427-444.
[57]	马晓荷. 非对称椭球形弹体侵彻金属靶弹道特性研究[D]. 北京: 北京理工大学, 2022.
	MA X H. Ballistic characteristics of asymmetric ellipsoidal projectiles penetrating into metal plates[D]. Beijing: Beijing Institute of Technology, 2022. (in Chinese)
[58]	LI Q M, CHEN X W. Dimensionless formulae for penetration depth of concrete target impacted by a non-deformable projectile[J]. International Journal of Impact Engineering, 2003, 28(1):93-116.
[59]	CHEN X W, LI Q M. Deep penetration of a non-deformable projectile with different geometrical characteristics[J]. International Journal of Impact Engineering, 2002, 27(6):619-637.
[60]	WEI H Y, ZHANG X F, LIU C, et al. Oblique penetration of ogive-nosed projectile into aluminum alloy targets[J]. International Journal of Impact Engineering, 2021, 148:103745.
[61]	DONG H, LIU Z H, WU H J, et al. Study on penetration characteristics of high-speed elliptical cross-sectional projectiles into concrete[J]. International Journal of Impact Engineering, 2019, 132: 103311.
[62]	王文杰, 张先锋, 邓佳杰, 等. 椭圆截面弹体侵彻砂浆靶规律分析[J]. 爆炸与冲击, 2018, 38(1):164-173.
	WANG W J, ZHANG X F, DENG J J, et al. Analysis of projectile penetrating into mortar target with elliptical cross-section[J]. Explosion and Shock Waves, 2018, 38(1):164-173. (in Chinese)
[63]	刘均伟, 张先锋, 刘闯, 等. 椭圆截面弹体侵彻性能的影响因素分析[J]. 爆炸与冲击, 2023, 43(9):155-168.
	LIU J W, ZHANG X F, LIU C, et al. Influencing factors of penetration performance of an elliptical cross-section projectile[J]. Explosion and Shock Waves, 2023, 43(9):155-168. (in Chinese)
[64]	李萌, 武海军, 董恒, 等. 基于机器学习的混凝土侵彻深度预测模型[J]. 兵工学报, 2023, 44(12):3771-3782. doi: 10.12382/bgxb.2023.0291
	LI M, WU H J, DONG H, et al. Machinelearning-based models for predicting the depth of concrete penetration[J]. Acta Armamentarii, 2023, 44(12):3771-3782. (in Chinese)
[65]	魏悦广. 用摄动法计算椭圆形巷道的弹塑性问题[J]. 工程力学, 1990, 7(2):93-102.
	WEI Y G. Calculatingelasto-plastic problem of elliptical tunnel with perturbation methods[J]. Engineering Mechanics, 1990, 7(2):93-102. (in Chinese)
[66]	周航, 孔纲强, 曹兆虎, 等. 椭圆形孔扩张弹性分析[J]. 固体力学学报, 2015, 36(1):85-91.
	ZHOU H, KONG G Q, CAO Z H, et al. Elastic analysis of elliptical cavity expansion. Chinese[J]. Journal of Solid Mechanics, 2015, 36(1):85-91. (in Chinese)
[67]	ZHOU H, LIU H L, KONG G Q. Elastic analysis of a pile rectangular cross section under lateral load[J]. Soil Mechanics and Foundation Engineering, 2014, 51(3):126-131.
[68]	周航, 孔纲强, 刘汉龙. 正方形孔扩张的弹性分析[J]. 工程力学, 2013, 30(12):183-188.
	ZHOU H, KONG G Q, LIU H L. Elasticanalysis of square cavity expansion[J]. Engineering Mechanics, 2013, 30(12):183-188. (in Chinese)
[69]	WOO H J. Cavity expansion analysis of non-circular cross-sectional penetration problems[D]. Austin, DX, US: The University of Texas at Austin, 1997.
[70]	ZHOU H, SHEIL B, LIU H L. Noncircular cavity expansion in undrained soil:semi-analytical solution[J]. Journal of Engineering and Orcid, 2022, 148(7): 04022032.
[71]	ZHOU H, YUAN J R, LIU H L. A general analytical solution for lateral soil response of non-circular cross-sectional pile segment[J]. Applied Mathematical Modelling, 2019, 71:601-631.
[72]	ZHOU H, LIU H L, YUAN J R. A novel analytical approach for predicting the noncylindrical pile penetration-induced soil displacement in undrained soil by combining use of cavity expansion and strain path methods[J]. International Journal for Numerical and Analytical Methods In Geomechanics, 2018, 42(11):1270-1305.
[73]	董恒. 椭圆截面弹体侵彻机理相关问题研究[R]. 北京: 北京理工大学, 2023.
	DONG H. Relatedproblems in penetration mechanism of elliptical cross-sectional projectile[R]. Beijing: Beijing Institute of Technology Post-Doc Report, 2023. (in Chinese)
[74]	WOOD D M. Soil behaviour and critical state soil mechanics[M]. Cambridge, UK: Cambridge University Press,1990.
[75]	王浩, 潘鑫, 武海军, 等. 椭圆截面截卵形刚性弹体正贯穿加筋板能量耗散分析[J]. 爆炸与冲击, 2019, 39(10):71-82.
	WANG H, PAN X, WU H J, et al. Energy dissipation analysis of elliptical truncated oval rigid projectile penetrating stiffened plate[J]. Explosion and Shock Waves, 2019, 39(10):71-82. (in Chinese)
[76]	王浩. 椭圆变截面弹体贯穿加筋板破坏模式与偏转机理研究[D]. 北京: 北京理工大学, 2020.
	WANG H. The failure mode and deflection mechanism of projectiles with tapered-elliptic cross-section perforation into stiffened plates[D]. Beijing: Beijing Institute of Technology, 2020. (in Chinese)
[77]	魏海洋. 椭圆截面弹体斜侵彻金属靶弹道特性研究[D]. 南京: 南京理工大学, 2022.
	WEI H Y. Research on thecharacteristics of penetration trajectory of elliptical cross-section projectile into metal targets[D]. Nanjing: Nanjing University of Science and Technology, 2022. (in Chinese)
[78]	田泽, 王浩, 武海军, 等. 椭圆变截面弹体斜贯穿薄靶姿态偏转机理研究[J]. 兵工学报, 2022, 43(7):1537-1552. doi: 10.12382/bgxb.2021.0367
	TIAN Z, WANG H, WU H J, et al. Attitudedeflection mechanism of projectiles with variable elliptical cross-sections obliquely perforating thin targets[J]. Acta Armamentarii, 2022, 43(7):1537-1552. (in Chinese)
[79]	邓希旻, 田泽, 武海军, 等. 上下非对称结构弹体侵彻金属薄板的特性及薄板破坏形式[J]. 兵工学报, 2023, 44(12):3836-3850. doi: 10.12382/bgxb.2022.0724
	DENG X M, TIAN Z, WU H J, et al. Penetrationcharacteristics and plate failure modes of asymmetric shaped projectiles penetrating thin metal targets[J]. Acta Armamentarii, 2023, 44(12):3836-3850. (in Chinese)
[80]	魏海洋, 张先锋, 熊玮, 等. 椭圆截面弹体斜侵彻金属靶体弹道研究[J]. 爆炸与冲击, 2022, 42(2):92-104.
	WEI H Y, ZHANG X F, XIONG W, et al. Oblique penetration of elliptical cross-section projectile into metal target[J]. Explosion and Shock Waves, 2022, 42(2):92-104. (in Chinese)
[81]	CHEN X W, FAN S C, LI Q M. Oblique and normal perforation of concrete targets by a rigid projectile[J]. International Journal of Impact Engineering, 2004, 30(6):617-637.
[82]	马兆芳, 段卓平, 欧卓成, 等. 弹体斜侵彻贯穿薄混凝土靶姿态变化实验和理论研究[J]. 兵工学报, 2015, 36(增刊1):248-254.
	MA Z F, DUAN Z P, OU Z C, et al. Theexperimental and theoretical research on attitude of projectile obliquely penetrating into thin concrete target[J]. Acta Armamentarii, 2015, 36(S1):248-254. (in Chinese)
[83]	WU H, CHEN X W, FANG Q, et al. Stability analyses of the mass abrasive projectile high-speed penetrating into concrete target. Part II: Structural stability analyses[J]. Acta Mechanica Sinica, 2014, 30(6):943-955.
[84]	LI Q M, FLORES-JOHNSON E A. Hard projectile penetration and trajectory stability[J]. International Journal of Impact Engineering, 2011, 38(10): 815-823.
[85]	GAO X D, LI Q M. Trajectory instability and convergence of the curvilinear motion of a hard projectile in deep penetration[J]. International Journal of Mechanical Sciences, 2017, 121:123-142.
[86]	ROISMAN I V, YARIN A L, RUBIN M B. Oblique penetration of a rigid projectile into an elastic-plastic target[J]. International Journal of Impact Engineering, 1997, 19(9/10):769-795.
[87]	高世桥, 刘明杰, 谭惠民. 侵彻弹倾斜侵彻半无限混凝土目标时的动力分析[J]. 兵工学报, 1995, 16(4):46-50.
	GAO S Q, LIU M J, TAN H M. Dynamical analysis of oblique perforation of a projectile against half-infinite concrete targect[J]. Acta Armamentarii, 1995, 16(4):46-50. (in Chinese)
[88]	王松川. 弹体斜侵彻弹道快速预测方法研究[D]. 长沙: 国防科学技术大学, 2011.
	WANG S C. Quickprediction method of oblique penetration trajectory[D]. Changsha: National University of Defense Technology, 2011. (in Chinese)
[89]	黄民荣. 刚性弹体对混凝土靶的侵彻与贯穿机理研究[D]. 南京: 南京理工大学, 2011.
	HUANG M R. Penetration and perforation mechanism of rigid projectile into the concrete target.[D]. Nanjing: Nanjing University of Science and Technology, 2011. (in Chinese)
[90]	康海峰. 动能弹非正侵彻弹道性能研究[D]. 南京: 南京理工大学, 2012.
	KANG H F. Study on trajectory performance of non-positivepenetration of kinetic energy projectile[D]. Nanjing: Nanjing University of Science and Technology, 2012. (in Chinese)
[91]	闪雨. 弹体非正侵彻混凝土质量侵蚀与运动轨迹研究[D]. 北京: 北京理工大学, 2015.
	SHAN Y. Investigation on themass abrasion and motion of the projectile non-normal penetrating into concrete[D]. Beijing: Beijing Institute of Technology, 2015. (in Chinese)
[92]	张欣欣. 刻槽弹体高速侵彻混凝土机理研究[D]. 北京: 北京理工大学, 2017.
	ZHANG X X. The mechanism of the grooved projectile penetrating the concrete target[D]. Beijing: Beijing Institute of Technology, 2017. (in Chinese)
[93]	DONG H, ZHANG X X, WU H J, et al. Trajectory prediction of the tapered projectile and grooved projectile in deep penetration[J]. International Journal of Impact Engineering, 2022, 170:104337.
[94]	WU H J, DENG X M, DONG H, et al. hree-dimensional trajectory prediction and analysis of elliptical projectile[J]. International Journal of Impact Engineering, 2023, 174:104497.
[95]	WEI H Y, ZHANG X F, LIU C, et al. Three-dimensional penetration trajectory model for ogive-nosed projectile into metal targets[J]. International Journal of Impact Engineering, 2021, 157:103998.
[96]	CHEN X G, LU F Y, ZHANG D. Penetration trajectory of concrete targets by ogived steel projectiles-experiments and simulations[J]. International Journal of Impact Engineering, 2018, 120:202-213.
[97]	王皓, 高旭东. 类椭圆截面战斗部侵彻混凝土弹道特性研究[J]. 兵工自动化, 2020, 39(5):68-72.
	WANG H, GAO X D. Study onballistic characteristics of concrete penetrating into elliptical section warhead[J]. Ordnance Industry Automation, 2020, 39(5):68-72. (in Chinese)
[98]	朱超. 椭圆截面弹体斜侵彻典型靶标的动态响应与结构设计方法[D]. 北京: 北京理工大学, 2023.
	ZHU C. Dynamic response and structural design method of elliptical cross-sectional projectile obliquely penetrating into typical targets[D]. Beijing: Beijing Institute of Technology, 2023. (in Chinese)
[99]	岳胜哲, 陈利, 张晓伟, 等. 非对称类椭圆截面弹体斜贯穿铝靶数值模拟研究[J]. 兵器装备工程学报, 2022, 43(4):127-133.
	YUE S Z, CHEN L, ZHANG X W, et al. Numerical simulation of oblique penetration of shaped elliptical cross section projectile through aluminum target[J]. Journal of Ordnance Equipment Engineering, 2022, 43(4):127-133. (in Chinese)
[100]	王皓. 类椭圆截面侵彻体侵彻混凝土规律研究[D]. 南京: 南京理工大学, 2020.
	WANG H. Study on the law of penetration of concrete by quasi-elliptical cross-section penetrator[D]. Nanjing: Nanjing University of Science and Technology, 2020. (in Chinese)
[101]	朱超, 张晓伟, 张庆明, 等. 弹体斜侵彻双层钢板的结构响应和失效研究[J]. 爆炸与冲击, 2023, 43(9):140-154.
	ZHU C, ZHANG X W, ZHANG Q M, et al. Structural response and failure of projectiles obliquely penetrating into double-layered steel plate targets[J]. Explosion and Shock Waves, 2023, 43(9):140-154. (in Chinese)
[102]	XIAO X K, ZHANG W, WEI G, et al. Effect of projectile hardness on deformation and fracture behavior in the Taylor impact test[J]. Materials and Design, 2010, 31(10):4913-4920.
[103]	RAKVAG K G, BORVIK T, HOPPERSTAD O S. A numerical study on the deformation and fracture modes of steel projectiles during Taylor bar impact tests[J]. International Journal of Solids and Structures, 2014, 51(3/4): 808-821.
[104]	皮爱国, 黄风雷. 大长细比结构弹体侵彻2024-O铝靶的弹塑性动力响应[J]. 爆炸与冲击, 2008, 28(3):252-260.
	PI A G, HUANG F L. Elastic-plastic dynamic response of slender projectiles penetrating into 2024-O aluminum targets[J]. Explosion and Shock Waves, 2008, 28(3):252-260. (in Chinese)
[105]	GOLDSMITH W. Non-ideal projectile impact on targets[J]. International Journal of Impact Engineering, 1999, 22(2/3):95-395.
[1]	胡冬冬, 张灿. 美军高超声速武器防御体系建设发展态势及研判[J]. 飞航导弹, 2019(3):34-40.
	HU D D, ZHANG C. The development situation and research of US military hypersonic weapon defense system construction[J]. Aerospace Technology, 2019(3):34-40. (in Chinese)
[2]	陈扶鼎. 2022年国外高超声速武器发展回顾[J]. 中国航天, 2023(2):31-37.
	CHEN F D. Review of the development of foreign hypersonic weapons in 2022[J]. Erospace China, 2023(2):31-37. (in Chinese)
[3]	杨振华, 戎宜生. 非圆截面导弹气动特性数值分析方法研究[J]. 科学技术创新, 2014(17):116,156.
	YANG Z H, RONG Y S. Study on numerical analysis method of aerodynamic characteristics of non-circular cross-section missile[J]. Scientific and Technological Innovation, 2014(17):116,156. (in Chinese)
[4]	董月娟. APTGD巡航导弹的隐身技术分析[J]. 飞航导弹, 1996(5):14-19.
	DONG Y J. Analysis of stealth technology of APTGD cruise missile[J]. Aerospace Technology, 1996(5):14-19. (in Chinese)
[5]	BEN-DOR G, DUBINSKY A, ELPERIN T. High-speed penetration dynamics[M]. Singapore: World Scientific Publishing Co. Pte. Ltd., 2013.
[6]	陈小伟. 穿甲/侵彻力学的理论建模与分析基础科学[M]. 北京: 科学出版社, 2017.
	CHEN X W. Theoreticalmodeling and analysis of armor penetration mechanics[M]. Beijing: Science Press, 2017. (in Chinese)
[7]	ANDERSON C E. Analytical models for penetration mechanics:areview[J]. International Journal of Impact Engineering, 2017, 108(4):3-26.
[8]	钱伟长. 穿甲力学[M]. 北京: 国防工业出版社, 1984.
[106]	陈小伟. 动能深侵彻弹的力学设计(I):侵彻/穿甲理论和弹体壁厚分析[J]. 爆炸与冲击, 2005, 25(6):499-505.
	CHEN X W. Mechanics of structural design of EPW(Ⅰ):the penetration/Perforation theory and the analysis on the cartridge of projectile[J]. Explosion and Shock Waves, 2005, 25(6): 499-505. (in Chinese)
[107]	LEE E H, SYMONDS P S. Large plastic deformations of beams under transverse impact[J]. Journal of Applied Mechanics-Transactions of the ASME, 1952, 19(3):308-314.
[108]	JONES N, WIERZBICKI T. Dynamic plastic failure of a free-free beam[J]. International Journal of Impact Engineering, 1987, 6(3):225-240.
[109]	YANG J L, YU T X, REID S R. Dynamic behaviour of a rigid, perfectly plastic free-free beam subjected to step-loading at any cross-section along its span[J]. International Journal of Impact Engineering, 1998, 21(3):165-175.
[110]	YANG J L, XI F. Experimental and theoretical study of free-free beam subjected to impact at any cross-section along its span[J]. International Journal of Impact Engineering, 2003, 28(7):761-781.
[111]	皮爱国. 大长细比动能弹体结构动态响应研究[D]. 北京: 北京理工大学, 2007.
	PI A G. Dynamic response of slender kinetic energy projectiles against typical hard targets penetration[D]. Beijing: Beijing Institute of Technology, 2007. (in Chinese)
[112]	刘坚成. 反向撞击下弹体非正侵彻结构响应研究[D]. 北京: 北京理工大学, 2019.
	LIU J C. Structural response of non-normal penetrating projectile under reverse impact[D]. Beijing: Beijing Institute of Technology, 2019. (in Chinese)
[113]	王景琛. 非圆截面弹体斜侵彻薄靶的结构动力响应研究[D]. 北京: 北京理工大学, 2022.
	WANG J C. Study on the dynamic response of non-circular cross-section projectile obliquely penetrating thin targe[D]. Beijing: Beijing Institute of Technology, 2022. (in Chinese)
[114]	王景琛, 张晓伟, 张庆明, 等. 非圆截面弹体斜侵彻薄靶的动态载荷特性研究[J]. 兵器装备工程学报, 2023, 44(1):127-135.
[8]	QIAN W C. Armour piercing mechanics[M]. Beijing: National Defense Industry Press, 1984. (in Chinese)
[9]	王文杰. 椭圆截面弹体侵彻混凝土靶过程研究[D]. 南京: 南京理工大学, 2019.
	WANG W J. Research on the process of elliptical cross-section projectile penetrating concrete target[D]. Nanjing: Nanjing University of Science and Technology, 2019. (in Chinese)
[10]	骆奎. 非旋转对称的椭圆截面弹体对混凝土侵彻问题的研究[D]. 湘潭: 湘潭大学, 2020.
	LUO K. Research on penetration of concrete with non-rotationally symmetrical elliptical cross section[D]. Xiangtan: Xiangtan University, 2020. (in Chinese)
[11]	刘子豪, 武海军, 高旭东, 等. 椭圆截面弹体侵彻混凝土阻力特性研究[J]. 北京理工大学学报, 2019, 39(2):135-141,146.
	LIU Z H, WU H J, GAO X D, et al. Study on theresistance characteristics of elliptical cross-section projectile penetrating concrete[J]. Transactions of Beijing Institute of Technology, 2019, 39(2):135-141,146. (in Chinese)
[12]	YAKUNINA G Y, OSTAPENKO N A. The shape of slender three-dimensional bodies with maximum depth of penetration into dense media[J]. Pmm Journal of Applied Mathematics and Mechanics, 1999, 63(6):953-967.
[13]	BEN-DOR G, DUBINSKY A, ELPERIN T. Optimal 3D impactors penetrating into layered targets[J]. Theoretical & Applied Fracture Mechanics, 1997, 27(3):161-166.
[14]	YAKUNINA G Y. The construction of optimum three-dimensional shapes within the framework of a model of local interaction[J]. Journal of Applied Mathematics & Mechanics, 2000, 64(2):289-298.
[15]	IVANOVA S Y. Shape optimization of rigid 3-D high-speed impactors penetrating into concrete shields[J]. Mechanics Based Design of Structures & Machines, 2008, 36(3):249-259.
[16]	DONG H, WU H J, LIU Z H, et al. Penetration characteristics of pyramidal projectile into concrete target[J]. International Journal of Impact Engineering, 2020, 143:103583.
[17]	BEN-DOR G, DUBINSKY A, ELPERIN T. Analytical engineering models for predicting high speed penetration of hard projectiles into concrete shields:a review[J]. International Journal of Damage Mechanics, 2015, 24(1):76-94.
[18]	KONG X Z, WU H, FANG Q, et al. Rigid and eroding projectile penetration into concrete targets based on an extended dynamic cavity expansion model[J]. International Journal of Impact Engineering, 2017, 100:13-22.
[19]	FENG J, LI W B, WANG X M, et al. Dynamic spherical cavity expansion analysis of rate-dependent concrete material with scale effect[J]. International Journal of Impact Engineering, 2015, 84:24-37.
[20]	JOHNSEN J, HOLMEN J K, WARREN T L, et al. Cylindrical cavity expansion approximations using different constitutive models for the target material[J]. International Journal of Protective Structures, 2018, 9(2):199-225.
[21]	FELDGUN V R, YANKELEVSKY D Z. Quasi-static spherical/cylindrical cavity expansion in a medium with an arbitrary equation of state and a shear strength plasticity envelope[J]. International Journal of Solids Structures, 2019, 191:146-156.
[22]	FDLEGUN V R, YANKELEVSKY D Z, KARINSKI Y S. A new simplified analytical model for soil penetration analysis of rigid projectiles using the riemann problem solution[J]. International Journal of Impact Engineering, 2017, 101:49-65.
[114]	WANG J C, ZHANG X W, ZHANG Q M, et al. Study on dynamic load characteristics of a non-circular cross-section projectile obliquely penetrating into thin targets[J]. Journal of Ordnance Equipment Engineering, 2023, 44(1):127-135. (in Chinese)
[115]	谭远深, 黄风雷, 皮爱国. 椭圆截面侵彻弹体结构优化设计与结构响应[J]. 爆炸与冲击, 2022, 42(6):71-84.
	TAN Y S, HUANG F L, PI A G. Structural optimization design and structural response of elliptical-section penetration projectiles[J]. Explosion and Shock Waves, 2022, 42(6):71-84. (in Chinese)