TY - EJOU
AU - Tsai, Chia-Cheng
TI - The Particular Solutions of Chebyshev Polynomials for Reissner Plates under Arbitrary Loadings
T2 - Computer Modeling in Engineering \& Sciences
PY - 2009
VL - 45
IS - 3
SN - 1526-1506
AB - 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 HÃ¶rmander 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.
KW - Particular solution
KW - Chebyshev polynomials
KW - Reissner plate
KW - HÃ¶rmander operator decomposition technique
KW - method of fundamental solutions
KW - method of particular solutions
DO - 10.3970/cmes.2009.045.249