The Solution of Large Deflection Problem of Thin Circular Plate by the Method of Composite Expansion

Chien Wei-zang; Chen Shan-lin

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Article Navigation > Applied Mathematics and Mechanics > 1985 > 6(2): 103-119

Chien Wei-zang, Chen Shan-lin. The Solution of Large Deflection Problem of Thin Circular Plate by the Method of Composite Expansion[J]. Applied Mathematics and Mechanics, 1985, 6(2): 103-119.

Citation:

Chien Wei-zang, Chen Shan-lin. The Solution of Large Deflection Problem of Thin Circular Plate by the Method of Composite Expansion[J]. Applied Mathematics and Mechanics, 1985, 6(2): 103-119.

Citation:

Chien Wei-zang, Chen Shan-lin. The Solution of Large Deflection Problem of Thin Circular Plate by the Method of Composite Expansion[J]. Applied Mathematics and Mechanics, 1985, 6(2): 103-119.

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The Solution of Large Deflection Problem of Thin Circular Plate by the Method of Composite Expansion

Chien Wei-zang¹,
Chen Shan-lin²

1.
Shanghai University of Technology, Shanghai;
2.
Chongqing Institute of Architectural Engineering, Chongqing

Received Date: 1984-07-30
Publish Date: 1985-02-15

Abstract

Abstract

In this paper, the method of composite expansion in perturbation theory is used for the solution of large deflection problem of thin circular plate. In this method. the outer field solution and the inner boundary layer solution are combined together to satisfy all the boundary conditions. In this paper, Hencky's membrane solution is used for the first approximation in outer field solution, and then the second approximate solution is obtained. The inner boundary layer solution is found on the bases of boundary layer coondinate. In this paper, the reciprocal ratio of maximum deflection and thickness of the plate is used as the small parameter. The results of this paper improves quite a bit in comparison with the results obtained in 1948 by Chien Wei-zang.

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References(7)

References

[1]	Chien Wei-zang,Asymptotic behavior of a thin clamped circular plate under uniform normal pressure at very large deflection,Science Reports(A) of National Tsing Hua University,5,1(1948),1-24.
[2]	Bromberg,E.,Nonlinear bending of a circular plate under normal pressure,Comm.Pure Appl.Math.,9(1956),633-659.
[3]	Срубшик Л.С.и В.И.Юдович,Асимлтоика уравнений болъшого лрогиба,круглой симметрично загуженней пластины,ПАН СССР,139,2(1961).
[4]	O'Malley,R.E.Jr.,Boundary layer methods for nonlinear initial value problems,SIAM Review,13(1971),425-434.
[5]	Chudov,L.A.,Some shortcomings of classical boundary layer theory,NASA(transl) TTF-360,TT65-50138(1966).
[6]	Latta,G.E.,Advanced Ordinary Differential Equations,Lecture Notes,Stanford University(1964).
[7]	周焕文,奇异摄动法在圆板大挠度问题中的应用,钱伟长主编《奇异摄动理论及其在力学中的应用》,科学出版社(1982), 310-338.