奇异摄动法应用于扁球壳的非线性稳定问题(Ⅱ)

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

The Singular Perturbation Method Applied to The Nonlinear Stability Problem of A Shallow Spherical Shell (Ⅱ)

摘要: 本文对边缘固定夹紧在均布载荷作用下弹性圆底扁薄球壳的非线性稳定性问题进行了研究.利用奇异摄动法求出几何参数k较大时的一致有效的渐近解,并导得决定中心挠度和临界载荷的解析公式,作出了稳定性曲线.这篇文章是作者文章[11]的继续.

Abstract: In this paper we consider the nonlinear stability of a thin elastic circular shallow spherical shell under the action of uniform normal pressure with a clamped edge. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained by means of the singular perturbation method. In addition, we give the analytic formula for determining the centre deflection and the critical load, and the stability curve is also derived. This paper is a continuation of the author's previous paper[11].

[1]	Simons,R.M.,A power series solution of the nonlinear equations for axisymmetrical bending of shallow spherical shells,J.Math.phys.,35,2(1956),164-176.
[2]	Reiss,E.L.,H.J.Greenberg and H.B.Keller,Nonlinear deflections of shallow spherical shells,J.Aero.Sci.,24,7(1957),533-543.
[3]	Weinitschke,H.,On the stability problem for shallow spherical shells,J.Math.phys.,38,4(1960),209-231.
[4]	Kaplan,A.and Y.C,Fung,A nonlinear theory of bending and buckling of thin elastic shallow spherical shells,NACA TN,3213(1954).
[5]	Срубщик Л,С.,Докритическодравновесие тонкой пологой оболочки враменля и его устойчивость,ПММ,44,2(1980).
[6]	叶开沅、刘人怀、张传智、徐一帆,弹性圆底扁球壳在边缘均布力矩作用下的非线性稳定问题,应用数学和力学,1,1 (1980),71-87.
[7]	江福汝,关于椭圆型方程的奇摄动,复旦学报,2(1978),29-37.
[8]	钱伟长、叶开沅,圆薄板大挠度问题,中国科学,3,4 (1954),405-436.
[9]	胡海昌,球面扁薄圆壳的跳跃问题,物理学报,10,2(1954),105-36.
[10]	Chen,Jye and R.E.O'Malley Jr.,On the Asymptotic solution of a two-parameter boundary value problem of chemical reactor theory,SIAM J.Appl.Math.,26,4,(1974).
[11]	康盛亮,奇异摄动方法应用于扁球壳的非线性稳定问题(I),同济大学学报,16(1988),377-384.

点击查看大图