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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.

### Keywords

Particular solution, Chebyshev polynomials, Reissner plate, Hörmander operator decomposition technique, method of fundamental solutions, method of particular solutions

### Cite This Article

Tsai, C. (2009). The Particular Solutions of Chebyshev Polynomials for Reissner Plates under Arbitrary Loadings. CMES-Computer Modeling in Engineering & Sciences, 45(3), 249–272.

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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