Analysis of Effect of InPlane and Transverse Loads on Static Performance of Plates

Abstract

Abstract: Abstract： Using the energy variation principle, the strain energy expression and static equilibrium differential equation for plates considering the effect of both initial inplane and transverse loads were proposed. Meanwhile, the finite plate element considering the effect of both initial inplane and transverse loads was presented. To verify the finite plate element, the approximate solutions of later transverse load displacement for three typical plates (clamped rectangular plate, clamped and simply supported circular plates) considering the effect of both initial inplane and transverse loads were derived by using the Galerkin method. The later transverse load displacements obtained by the finite plate element agreed well with the approximate solutions. The reliability and efficiency of the presented finite plate element and those later transverse load displacement approximate solutions were verified. Numerical examples show that the bending stiffness of plates are changed when the effect of both the effect of both initial inplane and transverse loads are considered, and that the key physical factors governing the effect of initial loads on the frequencies of plates are the initial loads (both inplane and transverse), thickness and boundary condition etc.

Key words: Key words： effect of both initial inplane and transverse loads, plate, static, finite plate element

CLC Number:

TU 313

LIU Degui, ZHOU Shijun, WANG Ning, YAO Yong. Analysis of Effect of InPlane and Transverse Loads on Static Performance of Plates[J]. Journal of Shanghai Jiao Tong University, 2016, 50(03): 336-344.

References

［1］TIMOSHENKO S, WOINOWSKYKRIEGER S. Theory of plates and shells［M］. 2nd ed. London: MeGrawHill Book Company, Inc, 1959. ［2］HERRMANN G, ARMENAKAS A E. Vibrations and stability of plates under initial stress ［J］. ASCE, 1962,127:458487. ［3］CRAWFORD J, ATLURI S. Nonlinear vibrations of a flat plate with initial stresses ［J］.Journal of Sound and Vibration, 1975, 43: 117129. ［4］YAMAKI N, OTOMO K, CHIBA M. Nonlinear vibration of a clamped circular plate with initial deflection and initial edge displacement. Part I:Theory［J］.Journal of Sound and Vibartion,1981,79(1):2342. ［5］YAMAKI N, OTOMO K, CHIBA M. Nonlinear vibration of a clamped circular plate with initial deflection and initial edge displacement. Part II: Experiment［J］.Journal of Sound and Vibartion,1981,79(1):4359. ［6］周又和.中心荷载作用下圆薄板的固有频率荷载关系曲线［J］.应用力学学报，1992，9(1)：119123. ZHOU Youhe. Natural frequencyload characteristic relation of circular plate under a central concentrated loads［J］.Journal of AppliedMechanics,1992,9(1):119123. ［7］王晋莹，陈科进.具有初始挠度的柔韧圆板的振动问题［J］.应用数学和力学,1993,14(2):165171. WANG Jinying,CHEN Kejin.Vibration problems of flexible circular plates with initial deflection［J］.Applied Mathematics and Mechanics, 1993,14(2):165171. ［8］杜国君，张秀礼，胡宇达.具有初挠度夹层圆形板非线性振动与解的稳定性［J］.振动与冲击，2007,26(11):156159. DU Guojun，ZHANG Xiuli,HU Yuda.Nonliner vibration and solution stability of circular sandwich plate with initial deflection［J］.Journal of Vibration and Shock,2007,26(11): 156159. ［9］TAKABATAKE H. Effects of dead loads in dynamic plate［J］. Journal of Structural Engineering, ASCE, 1992, 118(1): 3451. ［10］ZHOU Shijun.Loadinduced stiffness matrix of plates［J］. Canadian Journal of Civil Engineering，2002, 29(1):181184. ［11］周世军.板恒载效应的非线性分析的刚度法［J］.振动与冲击，2007,26（2）：3336. ZHOU Shijun. Stiffness method for nonlinear analysis of effect of dead loads on plate ［J］.Journal of Vibration and Shock, 2007,26(2): 3336. ［12］周世军，刘德贵.任意形状板考虑初始荷载效应的动力特性有限元分析［J］.振动与冲击，2014,33（12）：1523. ZHOU Shijun，LIU Degui. Finite element analysis for dynamic characteristic of arbitrary shape plate［J］. Journal of Vibration and Shock, 2014,33(12): 1523. ［13］刘德贵, 周世军. 几种典型板考虑初始荷载效应的基频近似［J］.应用数学与力学学,2013,34(12):12751284. LIU Degui, ZHOU Shijun. Approximate fundamental frequency solutions under initial load effect for 6 typical plates［J］.Applied Mathematics and Mechnics, 2013,34(12):12751284. ［14］刘德贵，周世军. 两种矩形板考虑初始横载效应的后期荷载位移伽辽金近似解［J］.土木建筑与环境工程,2013,35(6):5866. LIU Degui, ZHOU Shijun. Galerkin approximate solutions of displacement including the effect of dead loads for two kinds of rectangular plates［J］. Journal of Civil, Architectural & Environmental and Engineering, 2013,35(6):5866. ［15］ZIENKIEWICZ O C.The finite element method［M］.3rd ed. Blacklick, Ohio, USA:McGrwaHill Press,1977. ［16］SZILARD R.Theory and analysis of plates classical and numerical method［M］. Englewood Chiffs, New Jersey: PrenticeHall, Inc, 1974. ［17］吴家龙.弹性力学［M］.上海：同济大学出版社，1993.

[1]	CHEN Changxiong, PENG Zilong, SONG Hao, XUE Yaqiang, ZHOU Fulin. Prediction Method of the Low-Frequency Multistatic Scattering Sound Field for Underwater Spherical Targets Based on Limited Data [J]. Journal of Shanghai Jiao Tong University, 2024, 58(7): 1006-1017.
[2]	CHEN Hongting, ZHAO Yanjie, ZHOU Hongyu, WANG Deyu. Crashworthiness of.pngfened Plate Under Wedge Impact [J]. Journal of Shanghai Jiao Tong University, 2024, 58(7): 1057-1066.
[3]	TANG Qianyu. Experimental Study on Platform Vortex Induced Motion Considering Wave Current Coupling Effect [J]. Ocean Engineering Equipment and Technology, 2024, 11(4): 75-84.
[4]	LENG Junjie¹ (冷俊杰), DI Xinjie^,2*1 (邸新杰), LI Chengning^1,2 (利成宁), CHENG Shanghua³ (程尚华). Toughening Mechanism of Large Heat Input Weld Metal for Marine Engineering Extra-Thick Plate [J]. J Shanghai Jiaotong Univ Sci, 2024, 29(2): 349-360.
[5]	HAN Xueyang, WU Lin, LIU Zhibing, YU Dongwei, KONG Xiangyi, ZHANG Dayong. Influence of Convection Heat Transfer of Tread Plate in Polar Environment [J]. Journal of Shanghai Jiao Tong University, 2024, 58(11): 1687-1697.
[6]	CHEN Gang(陈刚), LIU Hongyue(刘宏月), GAO Ruiriang(高瑞翔). Calibration Technology of Optical Fiber Strain Sensor [J]. J Shanghai Jiaotong Univ Sci, 2023, 28(5): 551-559.
[7]	HUANG Huaizhou, WANG Hailong, YUAN Yujie, HOU Tao, SHI Rui, YE Maosheng. A Simplified Calculation of Doubler Plate Reinforced Tubular T Joints [J]. Ocean Engineering Equipment and Technology, 2023, 10(4): 64-69.
[8]	ZHU Kai, (祝楷), XIONG Baiqing, ∗ (熊柏青), YAN Hongwei, (闫宏伟), ZHANG Yongan, (张永安), LI Zhihui, (李志辉), LI Xiwu, (李锡武), LIU Hongwei, (刘红伟), WEN Kai, (温凯), YAN Lizhen, (闫丽珍). Numerical Simulation on the Effect of Conveyor Velocity of the Roller Table on Stress Distribution and Evolution in Large Aluminum Alloy Thick Plates [J]. J Shanghai Jiaotong Univ Sci, 2023, 28(2): 255-263.
[9]	WANG Jue∗ (王珏), LI Peng (李朋), SONG Shiyao (宋诗瑶). Mechanical Analysis Methods of Cantilever Gearbox Housing [J]. J Shanghai Jiaotong Univ Sci, 2023, 28(2): 233-242.
[10]	JIANG Peng (江鹏), LI Zhibin (李志彬), ZHANG Long (张龙), LI Jing (李敬), ZHANG Qun (张群), GUAN Zhenqun∗ (关振群). Calculation of Electrostatic/Magnetic Adhesion Force Between Adjacent Objects Considering Thin Gap Effect [J]. J Shanghai Jiaotong Univ Sci, 2023, 28(2): 213-219.
[11]	Huang Jun, LI Shaojie, KANG Zhuang. Analysis of J-Lay Laying of Large Diameter Submarine Pipeline [J]. Ocean Engineering Equipment and Technology, 2023, 10(2): 145-151.
[12]	WANG Qian, DING Xiaohong, ZHANG Heng. Stiffener Layout Optimization of Thin-Walled Structures Through Thick/Thin Generic Quadrilateral Shell Elements [J]. Air & Space Defense, 2023, 6(2): 55-61.
[13]	JI Pengxiang, AI Wanzheng, DING Tianming. Quantitative Factors of Recovery Length of Flow Pressure Behind Orifice Plate [J]. Journal of Shanghai Jiao Tong University, 2022, 56(8): 1051-1056.
[14]	GAO Zihang (高梓航), WANG Xin (王鑫) ZHAO Yifan (赵一帆), JIN Zhehui (金哲慧), WANG Gang (王刚), GAO Shuo∗ (高硕). Piezoelectric-Based Smart Bone Plate for Fracture Healing Progress Monitoring [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(4): 561-569.
[15]	HUANG Fenghua, CHENG Bin, TENG Nianguan. Influence of Structural Pseudo-Static Components on Seismic Responses of Low-Medium Speed Maglev Vehicle-Bridge System [J]. Journal of Shanghai Jiao Tong University, 2022, 56(4): 486-497.