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The Particular Solutions of Chebyshev Polynomials for Reissner Plates under Arbitrary Loadings

Chia-Cheng Tsai1

Department of Marine Environmental Engineering, National Kaohsiung Marine University, Kaohsiung City, 81143, Taiwan, E-mail: tsaichiacheng@ntu.edu.tw

Computer Modeling in Engineering & Sciences 2009, 45(3), 249-272. https://doi.org/10.3970/cmes.2009.045.249

Abstract

Analytical particular solutions of Chebyshev polynomials are obtained for problems of Reissner plates under arbitrary loadings, which are governed by three coupled second-ordered partial differential equation (PDEs). Our solutions can be written explicitly in terms of monomials. By using these formulas, we can obtain the approximate particular solution when the arbitrary loadings have been represented by a truncated series of Chebyshev polynomials. In the derivations of particular solutions, the three coupled second-ordered PDE are first transformed into a single six-ordered PDE through the Hörmander operator decomposition technique. Then the particular solutions of this six-ordered PDE can be found in the author's previous study. These formulas are further implemented to solve problems of Reissner plates under arbitrary loadings in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). Numerical experiments are carried out to validate these particular solutions. Due to the exponential convergence of both Chebyshev interpolation and the MFS, our numerical results are extremely accurate.

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Cite This Article

APA Style
Tsai, C. (2009). The particular solutions of chebyshev polynomials for reissner plates under arbitrary loadings. Computer Modeling in Engineering & Sciences, 45(3), 249-272. https://doi.org/10.3970/cmes.2009.045.249
Vancouver Style
Tsai C. The particular solutions of chebyshev polynomials for reissner plates under arbitrary loadings. Comput Model Eng Sci. 2009;45(3):249-272 https://doi.org/10.3970/cmes.2009.045.249
IEEE Style
C. Tsai, “The Particular Solutions of Chebyshev Polynomials for Reissner Plates under Arbitrary Loadings,” Comput. Model. Eng. Sci., vol. 45, no. 3, pp. 249-272, 2009. https://doi.org/10.3970/cmes.2009.045.249



cc Copyright © 2009 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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