﻿ 冲击波作用下变形圆板表面载荷研究
 舰船科学技术  2024, Vol. 46 Issue (5): 21-26    DOI: 10.3404/j.issn.1672-7649.2024.05.004 PDF

1. 武汉理工大学 船海与能源动力工程学院，湖北 武汉 430063;
2. 中国船舶及海洋工程设计研究院，上海 200011;
3. 中国船舶工业系统工程研究院，北京 100036

Research on surface load of deformation circular plate under blast wave
GUO Jia-kai1, ZHU Chun-xiao2, SHI Rui3, CHEN Wei1, LI Xiao-bin1
1. School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China;
2. Marine Design and Research Institute of China, Shanghai 200011, China;
3. Systems Engineering Research Institute, Beijing 100036, China
Abstract: To quickly determine the load on the deformed surface under the action of blast wave, firstly, the interaction process between the blast wave and the clamped circular plate is investigated through numerical simulation, and the distribution law of explosion load on the deformed surface of the circular plate is obtained. Then, dimensional analysis is introduced to explore the influence of such factors as the radius and thickness of the circular plate, the distance between the explosion center and the circular plate, the distance between the target point and the circular center, and TNT equivalent on the deformed surface blast load. Finally, combined with numerical simulation and dimensional analysis, the calculation formula of explosion load ( maximum impulse ) at any point on the deformed surface of circular plate is derived. The results show that the distribution of blast load is non-uniform on the deformed surface of the circular plate, and the peak pressure and impulse in the middle of the circular plate are higher than those at the edge; The derived formula can be used to calculate the deformation surface load of the circular plate quickly. The research results can provide quick and simple parameter input for the design and safety assessment of relevant protective structures.
Key words: blast wave     deformed plate     load distribution     dimensional analysis
0 引　言

1 数值仿真 1.1 有限元模型

 图 1 2D有限元计算模型 Fig. 1 2D Finite element calculation model

 $P = \left( {\gamma - 1} \right)\rho {e_0}。$ (1)

 $P = A\left( {1 - \frac{\omega }{{{R_1}V}}} \right){e^{ - {R_1}V}} + B\left( {1 - \frac{\omega }{{{R_2}V}}} \right){e^{ - {R_2}V}} + \frac{{\omega e}}{V} 。$ (2)

 $\sigma {\text{ = }}\left( {A + B{\varepsilon ^n}} \right)\left( {1 + C\ln {{\dot \varepsilon }^*}} \right)\left( {1 - {T^{*m}}} \right)。$ (3)

1.2 仿真模型的验证

 $\begin{split} \left\{\begin{array}{l} \Delta {P}_{m}=\frac{1.4072}{\overline{R}} + \frac{0.554}{{\overline{R}}^{2}}-\frac{0.0357}{{\overline{R}}^{3}}\text{ + }\frac{0.000625}{{\overline{R}}^{4}}，\text{0}\text{.05}\leqslant \overline{R}\leqslant 0.3 ，\\ \Delta {P}_{m}=\frac{0.6194}{\overline{R}} + \frac{0.0326}{{\overline{R}}^{2}} + \frac{0.2132}{{\overline{R}}^{3}}，\,\qquad\quad \text{0}\text{.3}＜\overline{R}\leqslant 1 ，\\ \Delta {P}_{m}=\frac{0.066}{\overline{R}} + \frac{0.405}{{\overline{R}}^{2}} + \frac{0.3288}{{\overline{R}}^{3}}，\qquad\quad\;\;\;\;\text{1}＜\overline{R}\leqslant \text{10}。\end{array}\right.\\[-1pt] \end{split}$ (4)

 图 2 各监测点的超压峰值曲线 Fig. 2 Overpressure peak curves of each monitoring point
1.3 结果分析

 图 3 爆炸波传播与板相互作用过程 Fig. 3 Blast wave propagation and its interaction with the plate

 图 4 圆板不同位置处位移曲线 Fig. 4 Displacement curves of circular plate at different positions

 图 5 圆板迎爆面各监测点的压力及冲量时程曲线 Fig. 5 Pressure and impulse time history curves of each monitoring point

 图 6 刚性圆板表面与变形圆板表面中心处载荷对比 Fig. 6 Comparison of loads at the center of rigid round plate surface and deformed surface
2 变形圆板表面爆炸载荷计算公式 2.1 表面载荷量纲分析

 图 7 模型示意图 Fig. 7 Schematic diagram of model

 $I = f(R,t,Z,r,\rho ,\sigma ,c,m,e,{R_T},{\rho _0},{c_0}) 。$ (5)

 $\frac{{Ic}}{{\sigma t}} = f \left(\frac{R}{t},\frac{Z}{t},\frac{r}{t},\frac{{\rho {c^2}}}{\sigma },\frac{{m{c^2}}}{{\sigma {t^3}}},\frac{e}{{{c^2}}},\frac{{{R_T}}}{t},\frac{{{\rho _0}{c^2}}}{\sigma },\frac{{{c_0}}}{c}\right)。$ (6)

 $\alpha = \frac{r}{R}，$ (7)
 $\sec \theta = \frac{{\sqrt {{Z^2} + {{\left( {\alpha R} \right)}^2}} }}{Z} = \sqrt {1 + {{\left( {\frac{{\alpha R}}{Z}} \right)}^2}}。$ (8)

 $\rho ,\sigma ,c,e,{\rho _0},{c_0} = {\text{const}}。$ (9)

 $\frac{{Ic}}{{\sigma t}} = f \left(\frac{Z}{t},\sec \theta ,\frac{{m{c^2}}}{{\sigma {t^3}}}\right)。$ (10)
2.2 变形圆板表面载荷影响因素分析

 图 8 圆板半径不同对变形圆板表面载荷影响 Fig. 8 Effect of different circular plate radii on deformed surface load

 图 9 圆板厚度不同对变形圆板表面载荷影响 Fig. 9 Effect of different circular plate thickness on deformed surface load

 图 10 爆心距圆板距离不同对变形圆板表面载荷影响 Fig. 10 Effect of different distance between explosion center and circular plate on deformed surface load

 图 11 TNT当量不同对变形圆板表面载荷影响 Fig. 11 Effect of different TNT equivalents on deformed palte surface load
2.3 变形圆板表面载荷计算公式

 $\frac{{Ic}}{{\sigma t}} = 0.0786{\left( {\frac{Z}{t}} \right)^{ - 1.7673}}{\left( {\cos \theta } \right)^{2.9548}}{\left( {\frac{{m{c^2}}}{{\sigma {t^3}}}} \right)^{0.8934}} ，$ (11)

 $I = 514.7\frac{{{m^{0.8934}}{t^{0.0871}}{{\left( {\cos \theta } \right)}^{2.9548}}}}{{{Z^{1.7673}}}} 。$ (12)

3 结　语

1）对比相同条件下变形圆板表面与刚性圆板表面载荷的差异，发现了圆板因表面变形缓冲了部分能量，体现为相对于刚性表面，变形圆板表面上压力在下降阶段小型波峰数量少，下降更为平滑，最大冲量低。

2）分析了圆板半径、圆板厚度、爆心距圆板的距离、目标点距圆心的距离以及TNT当量等因素对固支变形圆板表面爆炸载荷的影响，结合仿真结果得到圆板表面任意一点最大冲量的计算公式。推导的公式能够较好快速计算出变形圆板表面载荷，该公式可为相关防护结构设计和安全评估提供快速简单的参数输入。

 [1] HENRYCH J. The dynamics of explosion and its use [M]. Amsterdam: Elsevier, 1979: 265-266. [2] TM5-1300. Structures to resist the effects of accidental explosions [M]. US Department of the Army, Navy and Air Force Technical Manual, 1990. [3] UFC-3-340-02. Unified facilities criteria UFC DOD structures to resist the effects of accidental explosions [M]. US Department of Defense, 2008. [4] GERETTO C, CHUNG KIM YUEN S, NURICK G N. An experimental study of the effects of degrees of confinement on the response of square mild steel plates subjected to blast loading[J]. International Journal of Impact Engineering, 2015, 79: 32-44. DOI:10.1016/j.ijimpeng.2014.08.002 [5] HELD M, HEEGER P, KIERMEIR J. Displacement device to measure the acceleration of the bulge of RHA plates under anti-tank mine blast [C]// Proceedings of 22nd International Symposium on Ballistics. Vancouver: International Ballistics Committee, 2005: 995 1000. [6] ANDERSON C E, BEHNER T, WEISS C E. Mine blast loading experiments[J]. International Journal of Impact Engineering, 2011, 38(8): 697-706. [7] 侯俊亮, 蒋建伟, 门建兵, 等. 不同形状装药爆炸冲击波场及对靶板作用效应的数值模拟[J]. 北京理工大学学报, 2013, 33(6): 556-561. DOI:10.3969/j.issn.1001-0645.2013.06.002 [8] SHI Y, HAO H, LI Z X. Numerical simulation of blast wave interaction with structure columns[J]. Shock Waves, 2007, 17(1): 113-133. [9] 李臻, 刘彦, 黄风雷, 等. 接触爆炸和近距离爆炸比冲量数值仿真研究[J]. 北京理工大学学报, 2020, 40(2): 143-149. [10] 汪维, 张舵, 卢芳云, 等. 近爆作用下结构表面上爆炸载荷确定方法研究[J]. 兵工学报, 2013, 34: 234-242. [11] 汪维, 刘光昆, 赵强, 等. 近爆作用下方形板表面爆炸载荷分布函数研究[J]. 中国科学:物理学 力学 天文学, 2020, 50(2): 144-152. [12] 陈鹏宇, 侯海量, 金键, 等. 舰船舱内爆炸载荷简化载荷计算模型[J]. 舰船科学技术, 2020, 42(9): 22-29. CHEN P Y, HOU H L, JIN J, et al. Simplified calculation model for explosion loading in ship cabin[J]. Ship Science and Technology, 2020, 42(9): 22-29. DOI:10.3404/j.issn.1672-7649.2020.09.005 [13] 姚熊亮, 屈子悦, 姜子飞, 等. 舰船舱内爆炸载荷特征与板架毁伤规律分析[J]. 中国舰船研究, 2018, 13(3): 140-148. [14] 焦晓龙. 多舱室结构内爆载荷下毁伤效果评估方法研究[D]. 太原: 中北大学, 2020 [15] 郭子涛, 高斌, 郭钊, 等. 基于J-C模型的Q235钢的动态本构关系[J]. 爆炸与冲击, 2018, 38(4): 804-810.