GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅰ)-GOVERNING EQUATION AND GENERAL SOLUTION

Abstract

Abstract: The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed. The derivation of the equations was based upon the theory of flexible shells generalized by E.L. Axelrad and the assumption of the moderately slender ratio less than 1/3 (i.e., ratio between curvature radius of the meridian and distance from the meridional curvature center to the axis of revolution). The present general solution is an analytical one convergent in the whole domain of the shell and with the necessary integral constants for the boundary value problems. It can be used to calculate the stresses and displacements of the related bellows. The whole work is arranged into four parts: (Ⅰ) Governing equation and general solution; (Ⅱ) Calculation for Omega-shaped bellows; (Ⅲ) Calculation for C-shaped bellows; (Ⅳ) Calculation for U-shaped bellows. This paper is the first part.

2010 MSC Number:

O343.2

ZHU Wei-ping;HUANG Qian . GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅰ)-GOVERNING EQUATION AND GENERAL SOLUTION. Applied Mathematics and Mechanics (English Edition), 2002, 23(8): 889-897.

TrendMD

References

[1] Axelrad E L.Flexible Shells[M].Moscow:Science,1976.
[2] Axelrad E L.Theory of Flexible Shells[M].New York:Elsevier Science Publishing Company,Inc,1987.
[3] CHIEN Wei-zang,ZHENG Si-liang.Equations of axisymmetrical shells in complex quantities andtheir general solution for slender ring shells[J].Journal of Tsinghua University,1979,19(1):27-47.(in Chinese)
[4] CHIEN Wei-zang,ZHENG Si-liang.General solution for axisymmetrical circular ring shells[J].Applied Mathematics and Mechanics(English Ed),1980,1(3):305-318.
[5] CHIEN Wei-zang.Calculation for C-shaped bellows)an application of the theory of slender ringshells[J].Journal of Tsinghua University,1979,19(1):84-99.(in Chinese)
[6] CHIEN Wei-zang,ZHENG Si-liang.Calculation for C-shaped bellows)an application of the general solution for ring shells[J].Applied Mathematics and Mechanics(English Ed),1981,2(1):103-116.
[7] CHEN Shan-lin.General solution of the bending of ring shells with equations in complex[A].In:Yeh K Y Ed.Progress in Applied Mechanics[C].Dordrecht:Martinus Nijhoff Publishers,1987,181-192.
[8] ZHU Wei-ping,HUANG Qian,GUO Ping.Complex equations of flexible circular ring shellsoverall-bending in a meridian plane and general solution for the slender ring shells[J].AppliedMathematics and Mechanics(English Ed),1999,20(9):952-959.
[9] ZHU Wei-ping,HUANG Qian,GUO Ping,et al.General solution for C-shaped bellows overall-bending problems[A].In:N E Shanmugam,J Y Kichard,V Thevendran Eds.Thin-WalledStructures)Research and Development,Proc 2nd ICTWS.1998,Singapore[C].Oxford,UK:Elsevier Science Ltd,1998,477-484.
[10] ZHU Wei-ping,GUO Ping,HUANG Qian.General solution for U-shaped bellows overall-bendingproblems[J].Applied Mathematics and Mechanics(English Ed),2000,21(4):371-382.
[11] ZHU Wei-ping.Numerical solution for C-shaped bellows overall-bending in a meridian plane byinitial parameter method[J].Chinese Quarterly of Mechanics,2000,21(3):311-315.(in Chi2nese)
[12] CHIEN Wei-zang.On convergence problems of series solution for ring shells and on the conver2gence theorems[J].Journal of Lanzhou University,1979,(Special Edition for Mechanics):1-38.(in Chinese)

[1]	Haitao LIU, Zhengong ZHOU. Dynamic behavior of rectangular crack in three-dimensional orthotropic elastic medium by means of non-local theory [J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(2): 173-190.
[2]	Yanzheng WANG, Weiqiu CHEN, Xiangyu LI. Statics of FGM circular plate with magneto-electro-elastic coupling: axisymmetric solutions and their relations with those for corresponding rectangular beam [J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(5): 581-598.
[3]	Xiang-rong FU;Ming-wu YUAN;Song CEN;Ge TIAN . Characteristic equation solution strategy for deriving fundamental analytical solutions of 3D isotropic elasticity [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(10): 1253-1264.
[4]	Ying-song YU . Substrate elastic deformation due to vertical component of liquid-vapor interfacial tension [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(9): 1095-1114.
[5]	QING Guang-hui;XU Jian-xin;QIU Jia-jun. State-vector equation with damping and vibration analysis of laminates [J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(2): 253-259 .
[6]	LIU Yan-hong;ZHANG Hui-ming. Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation [J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(2): 193-200 .
[7]	QING Guang-hui;QIU Jia-jun;LIU Yan-hong. Hamiltonian parametric element and semi-analytical solution for smart laminated plates [J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(1): 51-58 .
[8]	HOU Peng-fei;DING Hao-jiang;Leung Andraw-YT. THREE-DIMENSION INTERACTIONS OF CIRCULAR CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES [J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(11): 1439-1449 .
[9]	SUI Yun-kang;DU Jia-zheng;GUO Ying-qiao. METHOD BASED ON DUAL-QUADRATIC PROGRAMMING FOR FRAME STRUCTURAL OPTIMIZATION WITH LARGE SCALE [J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(3): 383-391 .
[10]	XIAO Yong-gang;FU Yi-ming;ZHA Xu-dong. NONLINEAR VIBRATION FOR MODERATE THICKNESS RECTANGULAR CRACKED PLATES INCLUDING COUPLED EFFECT OF ELASTIC FOUNDATION [J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(8): 963-972 .
[11]	QING Guang-hui;QIU Jia-jun;LIU Yan-hong. MODIFIED H-R MIXED VARIATIONAL PRINCIPLE FOR MAGNETOELECTROELASTIC BODIES AND STATE-VECTOR EQUATION [J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(6): 722-728 .
[12]	ZHU Wei-ping;HUANG Qian. FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ) [J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(12): 1374-1389.
[13]	ZHU Wei-ping;HUANG Qian. FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ) [J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(12): 1390-1406.
[14]	ZHU Wei-ping;HUANG Qian . GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅲ)-CALCULATION FOR C-SHAPED BELLOWS [J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(10): 1153-1163.
[15]	ZHU Wei-ping;HUANG Qian . GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅳ)-CALCULATION FOR U-SHAPED BELLOWS [J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(10): 1164-1169.