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 toBellows(Ⅱ)[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1241-1254.
 Citation: 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 toBellows(Ⅱ)[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1241-1254.

# Finite Element Displacement Perturbation Method for Geometric Nonlinear Behaviors of Shells of Revolution Overall Bending in a Meridional Plane and Application toBellows(Ⅱ)

• Rev Recd Date: 2002-05-20
• Publish Date: 2002-12-15
• The finite-element-displacement-perturbation method (FEDPM) for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first-order-perturbation solution (the linear solution) of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others. It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonliear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate, and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nomlinear solution they vary with respect to the convolutions of the bellows.Yet for most bellows, the linear solutions are valid in practice.
•  [1] 钱伟长,郑思梁.半圆弧波纹管的计算-环壳一般解的应用[J].应用数学和力学,1981,2(1):97-111. [2] 朱卫平,黄黔,郭平.柔性圆环壳在子午面内整体弯曲的复变量方程及细环壳的一般解[J].应用数学和力学,1999,20(9):889-895. [3] 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 Richard Liew,V Thevendran Eds.Thin-Walled Structures -Research and Development,2nd ICTWS 1998,Singapore[C].Oxford,UK:Elsevier Science Ltd,1998,477-484. [4] 朱卫平,黄黔.中细柔性圆环壳整体弯曲的一般解及在波纹管计算中的应用(Ⅲ)[J].应用数学和力学,2002,23(10):1025-1034. [5] 朱卫平.用初参数法解C型波纹管在子午面内整体弯曲[J].力学季刊,2000,21(3):311-315. [6] 朱卫平,郭平,黄黔.U型波纹管整体弯曲问题的一般解[J].应用数学和力学,2000,21(4):331-341. [7] Standards of the Expansion Joint Manufacturers Association(EJMA)[S].EJMA,INC,Seventh Edition,New York,1998. [8] 黎廷新,李天祥,胡坚,等.膨胀节的各种位移应力[J].华南理工大学学报(自然科学报),1994,22(3):94-102. [9] Skoczen B.Effect of shear deformation and relaxation of support conditions on elastic buckling of pressurized expansion bellows[J].Journal of Pressure Vessel Technology,Transaction of the ASME,1999,121(2):127-132. [10] 钱伟长,郑思梁.轴对称圆环壳的复变量方程和轴对称细环壳的一般解[J].清华大学学报,1979,19(1):27-47.

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