On the use of polynomial series with the Rayleigh-Ritz method

摘要

Extensive literature emphasising the use of special sets of polynomials for Rayleigh-Ritz solutions to plate problems exists. It is commonly suggested that convergence can be improved by the use of special sets of polynomials, which are often orthogonal over the plate domain. This paper shows analytically that the polynomial series chosen does not affect convergence directly. It is shown that the only effect of the choice of set (for given polynomial degree) is on the numerical stability of the solution. These assertions are supported by numerical results for bending and vibration of laminated composite plates.