Hwang Chien. Perturbation Initial Parameter Method for Solving the Geometrical Nonlinear Problem of Axisymmetrical Shells[J]. Applied Mathematics and Mechanics, 1986, 7(6): 533-543.
 Citation: Hwang Chien. Perturbation Initial Parameter Method for Solving the Geometrical Nonlinear Problem of Axisymmetrical Shells[J]. Applied Mathematics and Mechanics, 1986, 7(6): 533-543.

# Perturbation Initial Parameter Method for Solving the Geometrical Nonlinear Problem of Axisymmetrical Shells

• Publish Date: 1986-06-15
• In the previous paper[7], the author presented a System of First-Order Differential Equations for the problem of axisynrm'trically loaded shells of revolution with small elastic. strains and arbitrarily large axial deflections, and a Method of Variable-Characteristic Nondimensionization with a Scale of Load Parameter. On this basis, by taking the weighted root-mean-square deviation of angular deflection from linearity as perturbation parameter, this paper pressents a perturbation system of nondimensional differential equations for the problem, thus transforms the geometrical nonlinear problem into several linear problems. This paper calculates these linear problems by means of the initial parameter method of numerical integration. The numerical results agree quite well with the experiments[4].
•  [1] Chien Wei-zang, Large deflection of a circular clamped plate under uniform pressure, Chinese J. of Physics,7(1947).102-113. [2] 钱伟长、叶开沅,圆薄板大挠度问题,物理学报,10 (1954),209-238. [3] Schmidt, R. and D.A. DaDeppo, A new approach to the analysis of shells, plates and membranes with finite deflections,Inter.J.of Nonlinear Mech.,9(1974),409-419. [4] Wildhack,W.A.,R.F.Dressler and E. C. Lloyd, Investigations of the properties of corrugated diaphragms,ASME(1957). [5] 黄黔,用数值积分的初参数法解波纹管,应用数学和力学.3, 1 (1982), 101-112.. [6] Gill.S.,A process for step-by-step integration of differential equations in the automatic digital computing machinc,Proc.Cambridge Phil.Soc.,47(1951);96-108. [7] 黄黔,轴对称壳任意大挠度问题的一阶微分方程组、最小位能原理、广义变分原理及奇异无量纲化方法.

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