强冲击载荷下单向加筋板拉伸撕裂的临界条件

姚熊亮; 周晏霈; 王治; 魏庆媛

doi:10.11883/bzycj-2023-0182

强冲击载荷下单向加筋板拉伸撕裂的临界条件

doi: 10.11883/bzycj-2023-0182

1.
哈尔滨工程大学船舶工程学院，黑龙江哈尔滨 150001
2.
哈尔滨工程大学机电工程学院，黑龙江哈尔滨 150001

基金项目: 国家自然科学基金( 52001091)，中央高校基本科研业务费专项资金（3072022TS2608），黑龙江省自然科学基金联合引导项目（LH2020E075）

详细信息

作者简介:
姚熊亮（1963－　），男，博士，教授，xiongliangyao@hrbeu.edu.cn

通讯作者:
王　治（1985－　），男，博士，副教授，wang_z@hrbeu.edu.cn

中图分类号: O383; O347.3
计量
- 文章访问数: 161
- HTML全文浏览量: 44
- PDF下载量: 68
- 被引次数: 0
出版历程
- 收稿日期: 2023-05-17
- 修回日期: 2023-10-17
- 网络出版日期: 2023-12-21
- 刊出日期: 2024-02-06

Critical condition for tensile tearing failure of unidirectional stiffened plate under strong impact load

1.
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China
2.
College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China

摘要

摘要: 针对固支单向加筋板在冲击载荷下的拉伸撕裂临界条件开展研究，首先将均布冲击载荷下的固支单向加筋板简化为带板梁模型，基于固支梁冲击变形理论解给出了加筋板最大永久变形理论解，之后基于复合运动场模型，修正了固支梁端点拉伸应变与最大永久变形关系式，并以等效应变达到失效应变作为拉伸撕裂条件，建立了加筋板在冲击载荷下的拉伸撕裂临界条件。经过数值模拟验证，该最大永久变形理论解和拉伸撕裂临界条件具有适用性，理论与数值误差小于15%。
- 加筋板 /
- 拉伸撕裂 /
- 塑性大变形 /
- 冲击载荷 /
- 毁伤评估
Abstract: The critical condition of tensile tearing failure of stiffened plate under impact load was studied. Firstly, the unidirectional stiffened plate with fixed support under uniform impact load was simplified into beam structure model attached with band plate. Based on the theoretical solution of the impact deformation of the fixed beam, the theoretical solution of the maximum deformation of the stiffened plate was given. At the same time, the applicable condition for calculating the large deformation of the unidirectional stiffened plate by using the “beam theory” model was given. Then, the motion mode of the fixed beam under strong impact load was divided into four stages. Based on the composite motion model, the relation between the tensile strain at the end of fixed beam and the maximum deformation of beam was corrected. Finally, taking equivalent strain equal to failure strain as the tensile tear condition, the critical condition of tensile tear of stiffened plate under impact load was established. In this paper, three unidirectional stiffened plates of T profile with different stiffness were selected, and the maximum deformation and critical tensile tearing load of the stiffened plates were analyzed by commercial finite element software LS-DYNA. The numerical simulation results show that the theoretical solution of maximum deformation of unidirectional stiffened plate and the critical condition of tensile tear failure based on the “beam theory” are applicable, and The error of theoretical and numerical simulation is less than 15%. Therefore, the theory in this paper can be applied to practical engineering prediction and has certain guiding significance.
- stiffened plate /
- tensile tear /
- large plastic deformation /
- impact load /
- damage evaluation

HTML全文

图 1 带板梁示意图

Figure 1. Schematic diagram of beam structure model attached with band plate

下载: 全尺寸图片幻灯片

图 2 等效载荷示意图

Figure 2. Schematic diagram of equivalent load

下载: 全尺寸图片幻灯片

图 3 板的最终运动场示意图

Figure 3. Schematic diagram of the final motion mode of the plate

下载: 全尺寸图片幻灯片

图 4 简化的单一运动场示意图^[20]

Figure 4. Schematic diagram of simplified single motion mode^[20]

下载: 全尺寸图片幻灯片

图 5 小变形阶段塑性铰长度示意^[22]

Figure 5. Schematic of plastic hinge length in small deformation stage^[22]

下载: 全尺寸图片幻灯片

图 6 第1阶段变形

Figure 6. Deformation diagram of the first stage

下载: 全尺寸图片幻灯片

图 7 第2阶段变形

Figure 7. Deformation diagram of the second stage

下载: 全尺寸图片幻灯片

图 8 第3阶段变形

Figure 8. Deformation diagram of the third stage

下载: 全尺寸图片幻灯片

图 9 第4阶段变形

Figure 9. Deformation diagram of the fourth stage

下载: 全尺寸图片幻灯片

图 10 单向加筋板结构示意

Figure 10. Schematic of unidirectional stiffened plates

下载: 全尺寸图片幻灯片

图 11 单向加筋板结构模型

Figure 11. Unidirectional stiffened plate structure model

下载: 全尺寸图片幻灯片

图 12 实验舱室与数值模拟模型舱室

Figure 12. Experimental cabin and numerical simulation model cabin

下载: 全尺寸图片幻灯片

图 13 S1舱壁实验与模拟毁伤效果

Figure 13. Experimental and simulation damage of S1 bulkhead

下载: 全尺寸图片幻灯片

图 14 单向加筋板在8 MPa矩形冲击载荷下的位移云图

Figure 14. Displacement contour of unidirectional stiffened plate under 8 MPa rectangular impact load

下载: 全尺寸图片幻灯片

图 15 不同加筋板的变形量计算误差

Figure 15. Calculation error of deformation of different stiffened plates

下载: 全尺寸图片幻灯片

表 1 T型钢结构参数

Table 1. Structural parameters of stiffeners

加强筋	尺寸/mm
1	$ \bot \dfrac{{5 \times 80}}{{8 \times 80}}$
2	$ \bot \dfrac{{5 \times 80}}{{8 \times 100}}$
3	$ \bot \dfrac{{5 \times 100}}{{8 \times 100}}$

下载: 导出CSV

表 2 Q345钢参数

Table 2. Parameters of Q345 steel

$\rho $/(kg·m⁻³)	$E$/GPa	$\nu$	${\sigma _{\text{0}}}$/MPa	${E_{\text{t}}}$/MPa	$C$	$q$	$ {\varepsilon _{\text{f}}} $
7870	212	0.31	345	1291	40	5	0.348
注：ρ为密度，ν为泊松比。

下载: 导出CSV

表 3 实验舱壁结构参数

Table 3. Experimental bulkhead structural parameters

舱壁编号	板厚/mm	加强筋尺寸/mm	加强筋间距/mm	加强筋方向
S1	8	$ \bot \dfrac{{8 \times 60}}{{8 \times 18}}$	600	背爆
S2			600	迎爆
S3			300	背爆
S4			300	迎爆

下载: 导出CSV

表 4 实验与模拟结果对比

Table 4. Comparison of experimental and numerical simulation results

舱壁	最大永久变形量/mm		误差/%
舱壁	实验	模拟	误差/%
S1	39.0	41.7	6.92
S2	37.0	39.2	5.95
S3	31.5	33.4	6.03
S4	27.5	27.2	1.09

下载: 导出CSV

表 5 单向加筋板变形量对比

Table 5. Comparison of deformation of unidirectional stiffened plates

加强筋	矩形载荷/ MPa	最大永久变形/mm		误差/ %	加强筋	矩形载荷/ MPa	最大永久变形/mm		误差/ %	加强筋	矩形载荷/ MPa	最大永久变形/mm		误差/ %
加强筋	矩形载荷/ MPa	理论	数值模拟	误差/ %	加强筋	矩形载荷/ MPa	理论	数值模拟	误差/ %	加强筋	矩形载荷/ MPa	理论	数值模拟	误差/ %
1	8	366	326	12.27	2	8	327	320	2.19	3	8	306	307	0.33
	9	413	372	11.02		9	370	364	1.65		9	346	350	1.14
	10	459	416	10.34		10	412	405	1.73		10	387	390	0.77
	11	505	459	10.02		11	453	445	1.80		11	426	432	1.39
	12	550	502	9.56		12	494	485	1.86		12	466	471	1.06

下载: 导出CSV

表 6 临界撕裂载荷验证

Table 6. Verification of critical tearing failure load

型材类型	临界载荷/MPa			与模拟结果的误差/%
型材类型	文献[20]	本文修正	模拟结果	文献[20]	本文修正
型材1	26.9	16.8	17.1	57.31	1.75
型材2	30.0	18.5	17.5	71.42	5.71
型材3	31.2	20.0	17.8	75.28	12.36

下载: 导出CSV

参考文献(26)

[1]	NURICK G N, OLSON M D, FAGNAN J R, et al. Deformation and tearing of blast-loaded stiffened square plates [J]. International Journal of Impact Engineering, 1995, 16(2): 273–291. DOI: 10.1016/0734-743X(94)00046-Y.
[2]	CHUNG KIM YUEN S, NURICK G N. Experimental and numerical studies on the response of quadrangular stiffened plates. Part Ⅰ: subjected to uniform blast load [J]. International Journal of Impact Engineering, 2005, 31(1): 55–83. DOI: 10.1016/j.ijimpeng.2003.09.048.
[3]	RUDRAPATNA N S, VAZIRI R, OLSON M D. Deformation and failure of blast-loaded stiffened plates [J]. International Journal of Impact Engineering, 2000, 24(5): 457–474. DOI: 10.1016/S0734-743X(99)00172-4.
[4]	LANGDON G S, CHUNG KIM YUEN S, NURICK G N. Experimental and numerical studies on the response of quadrangular stiffened plates. Part Ⅱ: localised blast loading [J]. International Journal of Impact Engineering, 2005, 31(1): 85–111. DOI: 10.1016/j.ijimpeng.2003.09.050.
[5]	牟金磊, 朱锡, 张振华, 等. 水下爆炸载荷作用下加筋板的毁伤模式 [J]. 爆炸与冲击, 2009, 29(5): 457–462. DOI: 10.3321/j.issn:1001-1455.2009.05.002. MOU J L, ZHU X, ZHANG Z H, et al. Failure modes of stiffened plates subjected to underwater explosion [J]. Explosion and Shock Waves, 2009, 29(5): 457–462. DOI: 10.3321/j.issn:1001-1455.2009.05.002.
[6]	郑成, 孔祥韶, 徐维铮, 等. 舱内爆炸载荷作用下加筋板动态响应试验研究 [J]. 中国造船, 2018, 59(2): 129–139. DOI: 10.3969/j.issn.1000-4882.2018.02.014. ZHENG C, KONG X S, XU W Z, et al. Experimental study on dynamic response of stiffened plates subjected to internal blast loads [J]. Shipbuilding of China, 2018, 59(2): 129–139. DOI: 10.3969/j.issn.1000-4882.2018.02.014.
[7]	焦立启, 侯海量, 陈鹏宇, 等. 爆炸冲击载荷下固支单向加筋板的动响应及破损特性研究 [J]. 兵工学报, 2019, 40(3): 592–600. DOI: 10.3969/j.issn.1000-1093.2019.03.019. JIAO L Q, HOU H L, CHEN P Y, et al. Research on dynamic response and damage characteristics of fixed supported one-way stiffened plates under blast loading [J]. Acta Armamentarii, 2019, 40(3): 592–600. DOI: 10.3969/j.issn.1000-1093.2019.03.019.
[8]	LI Y, REN X B, ZHAO T, et al. Dynamic response of stiffened plate under internal blast: experimental and numerical investigation [J]. Marine Structures, 2021, 77: 102957. DOI: 10.1016/j.marstruc.2021.102957.
[9]	SCHUBAK R B, OLSON M D, ANDERSON D L. Rigid-plastic modelling of blast-loaded stiffened plates-Part I: one-way stiffened plates [J]. International Journal of Mechanical Sciences, 1993, 35(3/4): 289–306. DOI: 10.1016/0020-7403(93)90083-7.
[10]	SCHUBAK R B, OLSON M D, ANDERSON D L. Rigid-plastic modelling of blast-loaded stiffened plates-Part II: partial end fixity, rate effects and two-way stiffened plates [J]. International Journal of Mechanical Sciences, 1993, 35(3/4): 307–324. DOI: 10.1016/0020-7403(93)90084-8.
[11]	刘土光, 胡要武, 郑际嘉. 固支加筋方板在爆炸载荷作用下的刚塑性动力响应分析 [J]. 爆炸与冲击, 1994, 14(1): 55–65. LIU T G, HU Y W, ZHENG J J. Dynamic response analysis of rigid perfectly plastic clamped square plates with stiffener subjected to blast loading [J]. Explosion and Shock Waves, 1994, 14(1): 55–65.
[12]	刘土光, 唐文勇. 加筋弧结构在冲击载荷作用下的塑性动力响应 [J]. 华中理工大学学报, 1996, 24(1): 106–109. LIU T G, TANG W Y. The dynamic plastic response of a structure with stiffened plates under impulsive loading [J]. Journal of Huazhong University of Science & Technology, 1996, 24(1): 106–109.
[13]	刘敬喜, 刘尧, 汤皓泉, 等. 爆炸载荷作用下单向加筋方板的大挠度塑性动力响应分析 [J]. 振动与冲击, 2011, 30(4): 182–187. DOI: 10.3969/j.issn.1000-3835.2011.04.038. LIU J X, LIU Y, TANG H Q, et al. Plastic and large deflection dynamic response analysis of a one way stiffened square plate subjected to blast loads [J]. Journal of Vibration and Shock, 2011, 30(4): 182–187. DOI: 10.3969/j.issn.1000-3835.2011.04.038.
[14]	PENG Y, YANG P, HU K. Nonlinear dynamic response of blast-loaded stiffened plates considering the strain rate sensitivity [J]. Marine Structures, 2020, 70: 102699. DOI: 10.1016/j.marstruc.2019.102699.
[15]	YANG B, WANG D Y. Dynamic buckling of stiffened plates with elastically restrained edges under in-plane impact loading [J]. Thin-Walled Structures, 2016, 107: 427–442. DOI: 10.1016/j.tws.2016.06.019.
[16]	张振华, 朱锡, 刘润泉. 潜艇典型结构在爆炸冲击载荷作用下开裂判据的试验研究 [J]. 爆炸与冲击, 2004, 24(6): 541–545. ZHANG Z H, ZHU X, LIU R Q. Experiment research of crack criterion of representative submarine structure subjected to explosive loading [J]. Explosion and Shock Waves, 2004, 24(6): 541–545.
[17]	吴林杰, 朱锡, 侯海量, 等. 空中近距爆炸下加筋板架的毁伤模式仿真研究 [J]. 振动与冲击, 2013, 32(14): 77–81, 126. DOI: 10.3969/j.issn.1000-3835.2013.14.013. WU L J, ZHU X, HOU H L, et al. Simulations for damage modes of a stiffened plate subjected to close-range air-blast loading [J]. Journal of Vibration and Shock, 2013, 32(14): 77–81, 126. DOI: 10.3969/j.issn.1000-3835.2013.14.013.
[18]	支旭东, 张荣, 林莉, 等. Q235B钢动态本构及在LS-DYNA中的应用 [J]. 爆炸与冲击, 2018, 38(3): 596–602. DOI: 10.11883/bzycj-2016-0286. ZHI X D, ZHANG R, LIN L, et al. Dynamic constitutive model of Q235B steel and its application in LS-DYNA [J]. Explosion and Shock Waves, 2018, 38(3): 596–602. DOI: 10.11883/bzycj-2016-0286.
[19]	孙丽萍, 闫发锁. 船舶与海洋工程结构物强度 [M]. 哈尔滨: 哈尔滨工程大学出版社, 2017.
[20]	JONES N. Structural impact [M]. New York: Cambridge University Press, 2012.
[21]	颜丰, 刘敬喜. 爆炸载荷下固支矩形板的大挠度塑性动力响应 [J]. 中国舰船研究, 2013, 8(1): 47–53. DOI: 10.3969/j.issn.1673-3185.2013.01.008. YAN F, LIU J X. The large deflection dynamic plastic response of rectangular plates subjected to blast load [J]. Chinese Journal of Ship Research, 2013, 8(1): 47–53. DOI: 10.3969/j.issn.1673-3185.2013.01.008.
[22]	NONAKA T. Some interaction effects in a problem of plastic beam dynamics—Part 2: analysis of a structure as a system of one degree of freedom [J]. Journal of Applied Mechanics, 1967, 34(3): 631–637. DOI: 10.1115/1.3607754.
[23]	SYMONDS P S, MENTEL T J. Impulsive loading of plastic beams with axial constraints [J]. Journal of the Mechanics and Physics of Solids, 1958, 6(3): 186–202. DOI: 10.1016/0022-5096(58)90025-5.
[24]	米海珍, 胡燕妮. 塑性力学 [M]. 北京: 清华大学出版社, 2014.
[25]	余同希, 邱信明. 冲击动力学 [M]. 北京: 清华大学出版社, 2011.
[26]	QIN Y Z, WANG Y, WANG Z, et al. Investigation on similarity laws of cabin structure under internal blast loading [J]. Ocean Engineering, 2022, 260: 111998. DOI: 10.1016/J.OCEANENG.2022.111998.