﻿ 边界尺寸对爆炸冲击载荷作用下薄板响应影响仿真研究
 舰船科学技术  2018, Vol. 40 Issue (3): 26-29 PDF

Simulation study on the effect of boundary size of the thin plate under explosive impact load
ZHANG Yu-xiang, CHEN Fang
College of Mechanical and Electrical Engineering, Beijing Institute of Technology, Beijing 100081, China
Abstract: The Ship cabin would be subject to high-intensity shock wave load when it was attacked by anti-ship weapons, causing its side board damaged. The time course of the deflection of the thin plate in different boundary size under the impact load was researched by theoretical analysis and numerical simulation. According to the theory of elastic-plastic deformation of the thin plate, the dynamic response equation of the thin plate under the explosion impact load was established with method of energy, and the experimental value was compared with the result from numerical simulation as well as theoretical calculation. It proved that the theoretical calculation method has better reliability and accuracy in different boundary size.
Key words: shock wave load     thin plate     boundary size     elastic-plastic deformation
0 引　言

Richard Villavicencio等[8]研究了边界滑移对横向固支的梁受冲击载荷作用时的响应有十分明显的影响，并用数值模拟方法研究了两边固支的矩形板在冲击载荷作用下的塑性变形情况[9]

1 理论分析

 $\left. {\begin{array}{*{20}{c}}{u = {u_0}\sin \displaystyle\frac{{\pi x}}{X}\cos \frac{{\pi y}}{{2Y}}}\\[8pt]{v = {v_0}\cos \displaystyle\frac{{\pi x}}{{2X}}\sin \frac{{\pi y}}{Y}}\\[8pt]{w = {w_0}\cos \displaystyle\frac{{\pi x}}{{2X}}\cos \frac{{\pi y}}{{2Y}}}\end{array}} \right\}$

 $\begin{split}{U_b} =& \frac{{E{\delta ^3}}}{{24\left( {1 - {\upsilon ^2}} \right)}}\int_0^X {\int_0^Y {\left[ {{{\left( {\frac{{{\partial ^2}w}}{{\partial {x^2}}}} \right)}^2} + {{\left( {\frac{{{\partial ^2}w}}{{\partial {y^2}}}} \right)}^2} + } \right.} } \\& \left. {2\upsilon \frac{{{\partial ^2}w}}{{\partial {x^2}}}\frac{{{\partial ^2}w}}{{\partial {y^2}}} + 2\left( {1 - \upsilon } \right){{\left( {\frac{{{\partial ^2}w}}{{\partial x\partial y}}} \right)}^2}} \right]{ d}x{ d}y\text{。}\end{split}$

 ${U_{me}} \!=\! \frac{{E\delta }}{{2\left( {1 - {\upsilon ^2}} \right)}}\int_0^X {\int_0^Y {\left[ {\varepsilon _x^2 + \varepsilon _y^2 + 2\upsilon {\varepsilon _x}{\varepsilon _y} + \frac{1}{2}\left( {1 - \upsilon } \right)\gamma _{xy}^2} \right]} } { d}x{ d}y\text{。}$

 \begin{align}{U_{mp}} =& \int_0^X {\int_0^Y {\int_0^\delta {\left[ {_0{\varepsilon _x} + {\sigma _0}{\varepsilon _y} + } \right.} } } \\& \left. {\sigma {\tau _p}{\gamma _{xy}} - \frac{1}{2}\left( {{\sigma _0}{\varepsilon _p} + {\sigma _0}{\varepsilon _p} + {\tau _p}{\gamma _p}} \right)} \right]{ d}x{ d}y{ d}z\text{。}\end{align}

 ${U_1} = \int_0^Y {{M_p}} {\theta _1}{ d}y + \int_0^X {{M_p}} {\theta _2}{ d}x\text{。}$

 ${M_p} = 2\int_0^{\frac{\delta }{2}} {{\sigma _0}z{ d}z = } \frac{1}{4}{\sigma _0}{\delta ^2}\text{，}$

 \begin{align}{\left. {{\theta _1} = \frac{{\partial \omega }}{{\partial x}}} \right|_{x = X}} = {\omega _0}\frac{\pi }{{2X}}\cos \frac{{\pi y}}{{2Y}},\\{\left. {{\theta _2} = \frac{{\partial \omega }}{{\partial Y}}} \right|_{y = Y}} = {\omega _0}\frac{\pi }{{2Y}}\cos \frac{{\pi x}}{{2X}}\text{。}\end{align}

 $W = \int_0^X {\int_0^Y {{ d}\left( {\frac{1}{2}m{V_0}^2} \right)} } \text{。}$

 $W = \frac{{8XYA_i^2}}{{\rho \delta {H^2}}} \cdot {m_{ef}}^{4/3}\text{。}$

 $W = {U_b} + {U_m} + {U_1}\text{，}$

 \begin{align}& \frac{{{\pi ^4}\left( {1 - 2\upsilon } \right)E{\delta ^3}}}{{384\left( {1 - {\upsilon ^2}} \right)}} \cdot \frac{{w_0^2}}{{{a^2}}} + \frac{{{\pi ^4}E\delta }}{{4096\left( {1 - {\upsilon ^2}} \right)}} \cdot \frac{{w_0^4}}{{{a^2}}} + \\& \frac{{\left( {4\sqrt 3 + 3{\pi ^2}} \right)\delta {\sigma _0}}}{{48}} \cdot w_0^2 - \frac{{\left( {4 + \upsilon } \right)\delta \sigma _0^2}}{{3E}} \cdot {a^2} + \\& {\frac{{4{\sigma _0}{\delta ^2}}}{{\sqrt 3 }}{w_0} - \frac{{8A_i^2m_e^{4/3}}}{{\rho \delta {H^2}}} \cdot {a^2} = 0}\text{。}\end{align}

2 数值模拟

 图 1 数值模拟计算模型 Fig. 1 Simulation calculation model

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

 ${T^ * } = \left( {T - T{}_r} \right)/\left( {{T_m} - T} \right){\text{。}}$

 图 2 薄板Mises等效应力变化情况 Fig. 2 Process of Mises equivalent stress of the thin plate

3 边界尺寸影响及分析

 图 3 数值模拟与理论计算值对比 Fig. 3 Comparison of simulation values and theoretical values

4 结　语

 [1] 袁华, 严必虎. 外军反舰导弹装备使用现状及发展趋势研究[J]. 国防科技, 2014 (6): 46–50. [2] WIERZBICKI T, FLORENCE A L. A theoretical and experimental investigation of impulsively loading clamped circular viscoplastic plates[J]. Solid and Structures, 1970, 6: 553–568． [3] RAJENDRAN R, LEE J M. Blast loaded plates[J]. Marine Structures, 2009, 22(2): 99–127. [4] GANGYI H, FEI X, JUN L. The transient responses of two-layered cylindrical shells attacked by underwater explosive shock waves[J]. Composite Structures, 2010, 92(7): 1551–1560. [5] 孔祥韶, 吴卫国, 李晓彬, 等. 舰船舱室内部爆炸的数值模拟研究[J]. 中国舰船研究, 2009, (04): 7–11. [6] 郑成, 孔祥韶, 吴卫国. 爆炸载荷下矩形板弹塑性动态响应研究[J]. 中国造船, 2015, (03): 19–30. [7] 王芳, 冯顺山, 俞为民. 爆炸冲击波作用下靶板的塑性大变形响应研究[J]. 中国安全科学学报, 2003, (03): 61–64+84. http://d.wanfangdata.com.cn/Periodical_zgaqkxxb200303016.aspx [8] VILLAVICENCIO R, LIU B, SOARES C G. Response of stiffeners with attached plate subjected to lateral impact[J]. Electrical Measuring Instruments and Measurements, 2012: 393. https://www.researchgate.net/profile/Carlos_Guedes_Soares/publication/259177314_Response_of_stiffeners_with_attached_plate_subjected_to_lateral_impact/links/0deec52c18508ddf49000000.pdf [9] VILLAVICENCIO R, SOARES C G. Impact response of rectangular and square stiffened plates supported on two opposite edges[J]. Thin-Walled Structures, 2013, 68: 164–182. [10] 张颖军, 朱锡, 梅志远. 冲击波载荷作用下固支正交各向异性薄板挠度特性分析[J]. 海军工程大学学报, 2010, (03): 102–106. [11] 谢岩梦, 蔺晓红. 爆炸载荷下复合材料层合板的抗冲击性能[J]. 舰船科学技术, 2014 (8): 11–18. http://d.wanfangdata.com.cn/Periodical_jckxjs201408004.aspx