ON EXACT SOLUTION OF KÁRMÁN’S EQUATIONS OF RIGID CLAMPED CIRCULAR PLATE AND SHALLOW SPHERICAL SHELL UNDER A CONCENTRATED LOAD

Applied Mathematics and Mechanics (English Edition) ›› 1987, Vol. 8 ›› Issue (11): 1057-1068.

ON EXACT SOLUTION OF KÁRMÁN’S EQUATIONS OF RIGID CLAMPED CIRCULAR PLATE AND SHALLOW SPHERICAL SHELL UNDER A CONCENTRATED LOAD

郑晓静, 周又和

Huazhong University of Science and Technology, Wuhan

收稿日期:1986-09-20 出版日期:1987-11-18 发布日期:1987-11-18
通讯作者: Yeh Kai-ynan

ON EXACT SOLUTION OF KÁRMÁN’S EQUATIONS OF RIGID CLAMPED CIRCULAR PLATE AND SHALLOW SPHERICAL SHELL UNDER A CONCENTRATED LOAD

Zheng Xiao-jing, Zhou You-he

Huazhong University of Science and Technology, Wuhan

Received:1986-09-20 Online:1987-11-18 Published:1987-11-18

摘要/Abstract

摘要： It is extremely difficult to obtain an exact solution of von Karman’s equations because the equations are nonlinear and coupled. So far many approximate methods have been used to solve the large deflection problems except that only a few exact solutions have been investigated but no strict proof on convergence is presented yet. In this paper, first of all, we reduce the von KÁrmÁn’s equations to equivalent integral equations which are nonlinear, coupled and singular. Secondly the sequences of continuous function with general form are constructed using iterative technique. Based on the sequences to be uniformly convergent, we obtain analytical formula of exact solutions to von Karman’s equations related to large deflection problems of circular plate and shallow spherical shell with clamped boundary subjected to a concentrated load at the centre.

关键词: Mori-Tanaka model, effective modulus, coating, syntactic foam

Abstract: It is extremely difficult to obtain an exact solution of von Karman’s equations because the equations are nonlinear and coupled. So far many approximate methods have been used to solve the large deflection problems except that only a few exact solutions have been investigated but no strict proof on convergence is presented yet. In this paper, first of all, we reduce the von KÁrmÁn’s equations to equivalent integral equations which are nonlinear, coupled and singular. Secondly the sequences of continuous function with general form are constructed using iterative technique. Based on the sequences to be uniformly convergent, we obtain analytical formula of exact solutions to von Karman’s equations related to large deflection problems of circular plate and shallow spherical shell with clamped boundary subjected to a concentrated load at the centre.

Key words: Mori-Tanaka model, effective modulus, coating, syntactic foam

郑晓静;周又和. ON EXACT SOLUTION OF KÁRMÁN’S EQUATIONS OF RIGID CLAMPED CIRCULAR PLATE AND SHALLOW SPHERICAL SHELL UNDER A CONCENTRATED LOAD[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(11): 1057-1068.

Zheng Xiao-jing;Zhou You-he. ON EXACT SOLUTION OF KÁRMÁN’S EQUATIONS OF RIGID CLAMPED CIRCULAR PLATE AND SHALLOW SPHERICAL SHELL UNDER A CONCENTRATED LOAD[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(11): 1057-1068.

参考文献

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[3] Liu Ren-huai and Shi Yun-fang, Exact solution for circular sandwich plate with large deflection, Appl. Math. and Mech. (English Edition), 3, 1 (1982), 11-24.
[4] Vincent,J.J, The bending of a thin circular plate, Phil, Mag, 12 (193l), 185-196.
[5] Chien, W.Z, Large deflection of a circular clampled plate under uniform pressure, The Chinese Journal of Physics, 7, 2 (1947), 102-113.
[6] Hu Hai-chang, On the large deflection of a circular plate under combined action of uniformly distributed load and concentrated load at the centre, (in Chinese), Acta Physica Sinica, 10, 4(1954), 383-392. (in Chinese).
[7] DaDeppo, D.A. and R. Schmidt, Moderately large deflections of a loosely clamped circular plate under a uniformly distributed load, Indus. Math. 25,1(1975),17-28.
[8] Chen Shan-lin and Kuang Ji-chang, The perturbation parameter in the problem of large deflection of clamped circular plates, Appl. Math. and Mech. (English Edition), 2, 1 (1981),137-154.
[9] Yeh Kai-yuan and Zhou You-he, On solving high-order solutions of chuen’s perturbation method to study convergence by computer, Appl. Math. and Mech, 7, 4 (1986), 285-293.
[10] Yeh Kai-yuan and Liu Ke-huai,etc.,Nonlinear stabilitico of thin circular shallow shells under actions of axisymmetrical uniformly distributed line loads,Journal of Lanzhou University(Natural Sciences),18,2(1965),10-33. (in Chinese).
[11] Keller,M.B.and E.L.Reiss,Iterative solutions for the nonlinear bending of circular plates,Comm.,on Pure and Appl.Math.,XI(1958),273-292.
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ON EXACT SOLUTION OF KÁRMÁN’S EQUATIONS OF RIGID CLAMPED CIRCULAR PLATE AND SHALLOW SPHERICAL SHELL UNDER A CONCENTRATED LOAD

ON EXACT SOLUTION OF KÁRMÁN’S EQUATIONS OF RIGID CLAMPED CIRCULAR PLATE AND SHALLOW SPHERICAL SHELL UNDER A CONCENTRATED LOAD

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