Dynamic buckling analysis of functionally graded beam under thermal shock in Hamilton system

Zhang Jinghua; Zhao Xingxing; Li Shirong

doi:10.11883/1001-1455(2017)03-0431-08

Volume 37 Issue 3

Apr. 2017

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Explosion And Shock Waves > 2017 > 37(3): 431-438

Xiang Mei, Huang Yi-min, Rao Guo-ning, Peng Jin-hua. Cook-off test and numerical simulation for composite charge at different heating rates[J]. Explosion And Shock Waves, 2013, 33(4): 394-400. doi: 10.11883/1001-1455(2013)04-0394-07

Citation:

Zhang Jinghua, Zhao Xingxing, Li Shirong. Dynamic buckling analysis of functionally graded beam under thermal shock in Hamilton system[J]. Explosion And Shock Waves, 2017, 37(3): 431-438. doi: 10.11883/1001-1455(2017)03-0431-08

Citation:

PDF( 1063 KB)

Dynamic buckling analysis of functionally graded beam under thermal shock in Hamilton system

doi: 10.11883/1001-1455(2017)03-0431-08

1.
School of Sciences, Lanzhou University of Technology, Lanzhou 730050, Gansu, China
2.
School of Civil Science and Engineering, Yangzhou University, Yangzhou 225127, Jiangsu, China

Received Date: 2015-11-23
Rev Recd Date: 2016-06-20
Publish Date: 2017-05-25

Abstract

Abstract

Based on the Euler beam theory, the dynamic buckling of the functionally graded beam subjected to thermal shock was investigated in the Hamilton system. The material properties of the functionally graded beam were assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The transient temperature fields were solved analytically using the Laplace transform and power series method. It was shown that the dynamic buckling problem can be reduced to a zero-eigenvalue problem in the symplectic space, the buckling loading and the buckling mode of the FGM beam correspond to the generalized eigenvalue and eigen solution. The buckling mode and the buckling thermal axial forces can be obtained through bifurcation condition, and the buckling temperature rise of the FGM beam can be obtained by inverse solution. In this research, the solution process for dynamic buckling of the FGM beam subjected to thermal shock using the symplectic method were given, and the effects of the material constitution, geometric parameters and the parameters of thermal shock load on the critical temperature were discussed.
- functionally graded materials,
- Euler beam,
- thermal shock,
- symplectic method,
- dynamic buckling

FullText(HTML)

References(17)

References

[1]	仲政, 吴林志, 陈伟球.功能梯度材料与结构的若干力学问题研究进展[J].力学进展, 2010, 40(5):528-541. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK201002077615 Zhong Zheng, Wu Linzhi, Chen Weiqiu.Pregress in the study on mechanics problems of functionally graded materials and structures[J].Advances in Mechanics, 2010, 40(5):528-541. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK201002077615
[2]	张靖华, 潘双超, 李世荣.热冲击下功能梯度圆板的动力屈曲[J].应用力学学报, 2015, 32(6):901-907. http://d.old.wanfangdata.com.cn/Periodical/yylxxb201506003 Zhang Jinghua, Pan Shuangchao, Li Shirong.Dynamic buckling of functionally graded circular plate under thermal shock[J].Chinese Journal of Applied Mechanics, 2015, 32(6):901-907. http://d.old.wanfangdata.com.cn/Periodical/yylxxb201506003
[3]	Mehrian S M N, Naei M H.Two dimensional analysis of functionally graded partial annular disk under radial thermal shock using hybrid Fourier-Laplace transform[J].Applied Mechanics and Materials, 2013, 436:92-99. doi: 10.4028/www.scientific.net/AMM.436
[4]	Mirzavand B, Eslami M R, Shakeri M.Dynamic thermal postbuckling analysis of piezoelectric functionally graded cylindrical shells[J].Journal of Thermal Stresses, 2010, 33(7):646-660. doi: 10.1080/01495731003776010
[5]	Mirzavand B, Eslami M R, Reddy J N.Dynamic thermal postbuckling analysis of shear deformable piezoelectric FGM cylindrical shells[J].Journal of Thermal Stresses, 2013, 36(3):189-206. doi: 10.1080/01495739.2013.768443
[6]	Ma L S, Wang T J.Relationships between the solutions of axisymmetric bending and buckling of functionally graded circular plates based on the third-order plate theory and the classical solutions for isotropic circular plates[J].International Journal of Solids and Structures, 2004, 41(1):85-101. doi: 10.1016/j.ijsolstr.2003.09.008
[7]	Li S R, Zhang J H, Zhao Y G.Thermal post-buckling of functionally graded material Timoshenko beams[J].Applied Mathematics and Mechanics, 2006, 27(6):803-811. doi: 10.1007/s10483-006-0611-y
[8]	Li S R, Zhang J H, Zhao Y G.Nonlinear thermo-mechanical post-buckling of circular FGM plate with geometric imperfection[J].Thin Walled Structures, 2007, 45(5):528-536. doi: 10.1016/j.tws.2007.04.002
[9]	Shegokar N L, Lal A.Thermo-electromechanically induced stochastic post buckling response of piezoelectric functionally graded beam[J].International Journal of Mechanics and Materials in Design, 2014, 10(3):329-349. doi: 10.1007/s10999-014-9246-1
[10]	Shariyat M.Dynamic thermal buckling of suddenly heated temperature-dependent FGM cylindrical shells under combined axial compression and external pressure[J].International Journal of Solids and Structures, 2008, 45(9):2598-2612. doi: 10.1016/j.ijsolstr.2007.12.015
[11]	Sohn K J, Kim J H.Structural stability of functionally graded panels subjected to aero-thermal loads[J].Composite Structure, 2007, 82(3):317-325. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=11f85b2888164944f65097acd729e1bc
[12]	徐新生, 段政, 马源, 等.辛方法和弹性圆柱壳在内外压和轴向冲击下的动态屈曲[J].爆炸与冲击, 2007, 27(6):509-514. doi: 10.3321/j.issn:1001-1455.2007.06.005 Xu Xinsheng, Duan Zheng, Ma Yuan, et al.A symplectic method and dynamic buckling of elastic cylindrical shells under both axial impact and internal or external pressure[J].Explosion and Shock Waves, 2007, 27(6):509-514. doi: 10.3321/j.issn:1001-1455.2007.06.005
[13]	谈梅兰, 吴光, 王鑫伟.矩形薄板面内非线性分布载荷下的辛弹性力学解[J].工程力学, 2008, 25(10):50-53. http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX200810012.htm Tan Meilan, Wu Guang, Wang Xinwei.Symplectic elasticity solutions for thin rectangular plates subjected to nonlinear distributed in plane loadings[J].Engineering Mechanics, 2008, 25(10):50-53. http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX200810012.htm
[14]	刘淼.功能梯度材料结构的非传统Hamilton变分原理及其有限元法[D].上海: 同济大学, 2008. http://cdmd.cnki.com.cn/Article/CDMD-10247-2008049158.htm
[15]	褚洪杰, 徐新生, 林志华, 等.弹性梁非线性热屈曲行为与辛本征解展开方法[J].大连理工大学学报, 2011, 51(1):1-6. doi: 10.3969/j.issn.1008-407X.2011.01.001 Chu Hongjie, Xu Xinsheng, Ling Zhihua, et al.Nonlinear thermal buckling of elastic beams and expanding method of symplectic eigensolutions[J].Journal of Dalian University of Technology, 2011, 51(1):1-6. doi: 10.3969/j.issn.1008-407X.2011.01.001
[16]	Sun J B, Xu X S, Lim C W.Buckling of functionally graded cylindrical shells under combined thermal and compressive loads[J].Journal of Thermal Stresses, 2014, 37(3):340-362. doi: 10.1080/01495739.2013.869143
[17]	Zhang J H, Li G Z, Li S R.DQM based thermal stresses analysis of a FG cylindrical shell under thermal shock[J].Journal of Thermal Stresses, 2015, 38(9), 959-982. doi: 10.1080/01495739.2015.1038488

Relative Articles

[1]	CHEN Jianliang, YANG Pu, LI Jicheng, CHEN Gang, DENG Hongjian, FAN Zhigeng. Numerical simulation on the deflection behavior of large caliber conical nose projectile at oblique high-speed water entry[J]. Explosion And Shock Waves, 2024, 44(7): 073301. doi: 10.11883/bzycj-2023-0398
[2]	QIAN Bingwen, ZHOU Gang, LI Mingrui, YIN Lixin, GAO Pengfei, CHEN Chunlin, MA Kun. Rigid-body critical transformation velocity of a high-strength steel projectile penetrating concrete targets at high velocities[J]. Explosion And Shock Waves, 2024, 44(10): 103301. doi: 10.11883/bzycj-2022-0309
[3]	FANG Houlin, LU Qiang, GUO Quanshi, LI Guoliang, LIU Cunxu, TAO Sihao, ZHANG Dezhi. Experimental research on the free surface effect of shock wave and bubble behavior of small yield underwater explosion[J]. Explosion And Shock Waves, 2024, 44(8): 081444. doi: 10.11883/bzycj-2024-0003
[4]	MA Chenyang, WU Li, SUN Miao. Influence of free surface numbers on the energy distribution and attenuation of vibration signals of underwater drilling blasting[J]. Explosion And Shock Waves, 2022, 42(1): 015201. doi: 10.11883/bzycj-2020-0436
[5]	LI Ming, WANG Kehui, ZOU Huihui, DUAN Jian, GU Renhong, DAI Xianghui, YANG Hui. Crater morphology of a projectile penetrating a thick concrete target[J]. Explosion And Shock Waves, 2022, 42(8): 083302. doi: 10.11883/bzycj-2021-0294
[6]	WANG Yuntian, ZENG Xiangguo, CHEN Huayan, YANG Xin, WANG Fang, QI Zhongpeng. Multi-scale simulation study on characteristics of free surface velocity curve in ductile metal spallation[J]. Explosion And Shock Waves, 2021, 41(8): 084202. doi: 10.11883/bzycj-2020-0467
[7]	LIU Xiangyu, GONG Min, WU Haojun, AN Di. Determination method of tunnel blasting parameters using electronic detonator under changing condition of free surface[J]. Explosion And Shock Waves, 2021, 41(10): 105202. doi: 10.11883/bzycj-2020-0428
[8]	GAO Weitao, PENG Kefeng, ZHANG Yongliang, ZHENG Hang, ZHAO Kai, ZHENG Zhijun. On ballistic performance of a metal target with crescent-shaped cavity structure[J]. Explosion And Shock Waves, 2021, 41(5): 053303. doi: 10.11883/bzycj-2020-0473
[9]	GUO Hu, HE Liling, CHEN Xiaowei, CHEN Gang, LI Jicheng. Penetration mechanism of a high-speed projectile into a shelter made of spherical aggregates[J]. Explosion And Shock Waves, 2020, 40(10): 103301. doi: 10.11883/bzycj-2019-0428
[10]	DUAN Zhuoping, LI Shurui, MA Zhaofang, OU Zhuocheng, HUANG Fenglei. Analytical model for attitude deflection of rigid projectile during oblique perforation of concrete targets[J]. Explosion And Shock Waves, 2019, 39(6): 063302. doi: 10.11883/bzycj-2018-0411
[11]	JIN Yunsheng, SUN Chengwei, ZHAO Jianheng, LUO Binqiang, WANG Guiji, TAN Fuli. Direct calculation method for free surface data processing of step target in ICE[J]. Explosion And Shock Waves, 2019, 39(4): 044201. doi: 10.11883/bzycj-2017-0294
[12]	HONG yong, MA Honghao, SHEN Zhaowu, REN Lijie, CUI Yu, ZHAO Kai. Research and application on efficient rock blasting based on circular free surface[J]. Explosion And Shock Waves, 2018, 38(1): 98-105. doi: 10.11883/bzycj-2016-0176
[13]	Deng Yongjun, Chen Xiaowei, Yao Yong, Yang Tao. On ballistic trajectory of rigid projectile normal penetration based on a meso-scopic concrete model[J]. Explosion And Shock Waves, 2017, 37(3): 377-386. doi: 10.11883/1001-1455(2017)03-0377-10
[14]	MINGFu-ren, ZHANGA-man, YANG Wen-shan. Three-dimensionalsimulationsonexplosiveloadcharacteristicsof underwaterexplosionnearfreesurface[J]. Explosion And Shock Waves, 2012, 32(5): 508-514. doi: 10.11883/1001-1455(2012)05-0508-07
[15]	GONG Bai-lin, LU Fang-yun, LI Xiang-yu. Atheoreticalmodelforforecastingdeformationshapes ofdeformablewarheads[J]. Explosion And Shock Waves, 2010, 30(1): 65-69. doi: 10.11883/1001-1455(2010)01-0065-05
[16]	WANG Cheng-hua, CHEN Pei-yin, XU Xiao-cheng. Filtering of penetration deceleration data and determining of penetration deceleration on the rigid-body[J]. Explosion And Shock Waves, 2007, 27(5): 416-419. doi: 10.11883/1001-1455(2007)05-0416-04

Supplements(0)

Cited By

Cited by

Periodical cited type(23)

1.	赵越宸，庞维强，苏昌银，龙杰才，郑荣耀，李锡文. 复合固体推进剂混合工艺参数推算方法. 固体火箭技术. 2024(06): 851-858 .
2.	沈飞，王辉，王金涛，余文力，王煊军. 基于圆筒试验的DNTF基叠层复合装药的爆轰驱动释能特性. 爆炸与冲击. 2023(11): 58-66 . 本站查看
3.	李昂，钱江，褚恩义，韩克华，朱朋，沈瑞琪. 爆炸箔起爆器热烤试验与数值模拟研究. 火工品. 2023(06): 33-38 .
4.	肖游，智小琦，王琦，范兴华. 多种复合炸药装药的慢烤特性及其机理. 高压物理学报. 2022(02): 166-175 .
5.	叶青，余永刚. 含能材料热安全性研究进展. 装备环境工程. 2022(03): 1-10 .
6.	刘静，赵非玉. 不同升温速率下模块装药的烤燃特性分析. 装备环境工程. 2022(03): 11-16 .
7.	方远德，姜春兰，毛亮，王在成，王新宇，卢士伟. 聚能装药战斗部烤燃响应的数值模拟研究. 兵器装备工程学报. 2022(07): 121-127 .
8.	王茂，韩志伟，李亚宁，李宏伟，陈坤，王伯良. 基于虚拟仪器的慢速烤燃系统的设计及应用. 爆破器材. 2020(03): 37-42 .
9.	刘子德，智小琦，周捷，王帅. 药量和升温速率对DNAN基熔铸炸药烤燃特性的影响. 爆炸与冲击. 2019(01): 20-24 . 本站查看
10.	蒋超，闻泉，王雨时，张志彪，王光宇. 不敏感弹药烤燃试验技术综述. 探测与控制学报. 2019(02): 1-9 .
11.	王新颖，卢熹. 温升对水雷主装药安全性影响的数值模拟. 科学技术与工程. 2019(15): 125-129 .
12.	屈可朋，李亮亮，肖玮. 高低温循环及对称冲击耦合加载下炸药的安全性研究. 爆破器材. 2019(04): 43-46+53 .
13.	徐洪涛，金朋刚. 炸药缓慢加热条件实验技术进展. 装备环境工程. 2019(09): 5-17 .
14.	常天笑，闻泉，王雨时，王光宇，蒋超，闫丽. 引信内部装药对烤燃试验响应的影响. 探测与控制学报. 2019(05): 17-24 .
15.	邓海，沈飞，梁争峰，王辉. 不同约束条件下B炸药的慢烤响应特性. 火炸药学报. 2018(05): 465-470 .
16.	刘子德，智小琦. DNAN熔铸混合炸药的慢烤试验与模拟. 兵器装备工程学报. 2018(12): 178-181 .
17.	袁俊明，张林炎，唐鑫，刘玉存，张喜亮，陈银刚，李硕. 小型传爆装置慢燃实验及数值计算. 兵工学报. 2017(08): 1541-1546 .
18.	李文凤，余永刚，叶锐，杨后文. 不同升温速率下AP/HTPB底排装置慢速烤燃的数值模拟. 爆炸与冲击. 2017(01): 46-52 . 本站查看
19.	杨筱，智小琦. 炸药烤燃特性的隔热层效应研究. 科学技术与工程. 2016(35): 198-202 .
20.	吴世永，王伟力，苗润，吕鹏博，刘晓夏. 不同尺寸装药烤燃特性的数值模拟研究. 中国测试. 2016(10): 85-89 .
21.	姚奎光，钟敏，代晓淦，吕子剑. 缓慢热作用下PBX-9炸药的响应特性. 火炸药学报. 2015(06): 56-60 .
22.	陈科全，黄亨建，路中华，蒋治海，聂少云，陈红霞. 一种弹体排气缓释结构设计方法与试验研究. 弹箭与制导学报. 2015(04): 15-18 .
23.	杨后文，余永刚，叶锐. AP/HTPB复合固体推进剂慢烤燃特性的数值模拟. 含能材料. 2015(10): 924-929 .