On the Problems of Buckling of an Annular Thin Plate

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1985 > 6(2): 175-190

Qin Sheng-li, Zhang Ai-shu. On the Problems of Buckling of an Annular Thin Plate[J]. Applied Mathematics and Mechanics, 1985, 6(2): 175-190.

Citation:

Qin Sheng-li, Zhang Ai-shu. On the Problems of Buckling of an Annular Thin Plate[J]. Applied Mathematics and Mechanics, 1985, 6(2): 175-190.

Citation:

Qin Sheng-li, Zhang Ai-shu. On the Problems of Buckling of an Annular Thin Plate[J]. Applied Mathematics and Mechanics, 1985, 6(2): 175-190.

Abstract

In this paper, problems of buckling of on annular thin plate under the action of in-plane pressure and transverse lood are studied by using the method of multiple scales. We obtain N-order uniformly valid asymptotic expansion of the solution. In the latter part of this paper we discuss a particular example, and calculate the critical value of in-plane pressure. We see that the asymptotic expansion obtained by the multiple scales is completely consistent with that of the exact solution.

[1]	江福汝.摄动方法在薄板弯曲问题中的某些应用.应用数学和力学,1 (1980),37-53.
[2]	Alzheimer,W.E.and R.T.Davis,Unsymmetrical bending of prestressed and annular plate,J.Eng.Mech.Div.Proc.ASCE,4(1968),905-917.
[3]	高汝熹,高阶双曲型方程的奇摄动问题,科学通报,20(1983). 1220-1223.
[4]	Reismann,Herbert and Peter S.Pawlik,Elasticity Theory and Applications.John Wiley Sons (1980),379-407.
[5]	Besjes,J.G.,Singular perturbation problems for linear elliptic differential operators of arbitrary order,Math.Anal.and Appl.,49,1(1975),24-46.
[6]	Timoshenko,S.,Theory of Elastic Stability.(1958),318-397.
[7]	江福汝,关于边界层方法.应用数学和力学,2, 5 (1981), 461-473.