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A perturbation solution in the nonlinear theory of circular plates

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Abstract

In this paper, we analyzed some problems of nonlinear circular plates by means of perturbation method. The perturbation parameters chosen here are obtained from solving the equations and are not certain mechanical quantities given precedently. This is an extension of W. Z. Chien's perturbation method, which uses the central deflection as the perturbation parameter.

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References

  1. Chien, W. Z., Large deflection of a circular clamped plate under uniform pressure, Chinese Journal of Physics, 7, 2, (1947), 102–113.

    Google Scholar 

  2. Schmidt, R., Finite deflections of a loosely clamped circular plate loaded at its center, Industrial Mathematics, 23, part 1, (1973), 45–51.

    Google Scholar 

  3. Schmidt, R., Moderately large deflection of a loosely clamped circular plate under a uniformly distributed load, Industrial Mathematics, 25, part I, (1975), 17–28.

    Google Scholar 

  4. Chien Wei-zang, Lin Hong-sun, Hu Hai-chang and Yeh Kai-yuan, The large deflection problem of the circular thin plate (in Chinese), (1954).

  5. Chien Wei-zang and Yeh Kai-yuan, On the large deflections of a circular thin plate, Chinese Journal of Physics, 10, 3, (1954).

    Google Scholar 

  6. Timoshenko, S. and Woinowsky-Krieger, S., Theory of Plates and Shells, (1959).

  7. Schmidt, R., Several perturbation solutions in the nonlinear theory of circular plates and membranes, Industrial Mathematics, 25, part 2, (1975).

  8. Yeh Kai-yuan, Liu Zen-huai, Chang Chuan-dzi and Shue Ih-fan, Nonlinear stability of thin elastic circular shallow spherical shell under the action of uniform edge moment. Applied Mathematics and Mechanics, 1, 1, (1980), 71–90.

    Google Scholar 

  9. Chien Wei-zang, Singular Perturbation Theory (to be published).

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Authors and Affiliations

  1. Wuhan University, Wuhan

    Chou Huan-wen

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  1. Chou Huan-wen
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Huan-wen, C. A perturbation solution in the nonlinear theory of circular plates. Appl Math Mech 2, 519–528 (1981). https://doi.org/10.1007/BF01895455

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  • DOI: https://doi.org/10.1007/BF01895455

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