摄动初参数法解轴对称壳几何非线性问题

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

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

摘要: 作者在文[7]中提出轴对称壳任意大挠度问题的一阶微分方程组和以载荷变量为尺度的变特征无量纲化方法。在此基础上,本文选取挠角非线性偏差的加权均方根作摄动参数,给出该问题的无量纲摄动微分方程组。从而把非线性问题转化为n个线性问题来解决。本文采用数值积分的初参数方法对摄动后的各阶线性问题进行了计算。摄动结果与实验^[4]相符合。

Abstract: 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.