Kang Sheng-liang. The Singular Perturbation Method Applied to The Nonlinear Stability Problem of A Shallow Spherical Shell (Ⅱ)[J]. Applied Mathematics and Mechanics, 1990, 11(3): 267-273.
 Citation: Kang Sheng-liang. The Singular Perturbation Method Applied to The Nonlinear Stability Problem of A Shallow Spherical Shell (Ⅱ)[J]. Applied Mathematics and Mechanics, 1990, 11(3): 267-273.

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

• Publish Date: 1990-03-15
• 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.

Catalog

通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142