Abstract
In this paper, we present a perturbation-iterative method for solving certain boundary value problems encountered in the nonlinear theory of elastic circular thin plates. At the same time, with this method, we strictly prove the convergence of the solutions for the large deflection equations of circular plates subjected to certain distributed loads.
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References
Keller, H.B. and E.L. Reiss, Iterative solution for the nonlinear bending of circular plates,Communications on Pure and Applied Mathematics,11 (1958), 273–292.
Chien, W.Z., Large deflection of a circular clamped plate under uniform pressure,Chinese J. Phys.,7 (1947), 102–114.
Way, S., Bending of circular plates with large deflection,Trans. ASME,56 (1934), 627–636.
Chien, W.Z., Asymptotic behavior of a thin clamped circular plate under uniform normal pressure at verylarge deflection.Sci. Rep. Nat. Tsinghua University, Ser. A,5 (1948), 71–94.
Bromberg, E., Non-linear bending of a circular plate under normal pressure,Communications on Pure and Applied Mathematics,9 (1956), 633–659.
Chou Huan-wen, Some applications of the singular perturbation method to the bending probmems of thin plates and shells,Applied Mathematics and Mechanics,5, 4 (1984), 1449–1457.
Caratheodory, C.,Theory of Functions of a Complex Variable,1 (1985), 251–255. (Chinese version)
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Huan-wen, C., Chuan-yan, Y. The perturbation-iterative method applied to the problems of the large deflection of the elastic circular thin plates. Appl Math Mech 9, 327–334 (1988). https://doi.org/10.1007/BF02456113
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DOI: https://doi.org/10.1007/BF02456113