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

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 analyt...

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Bibliographic Details
Published in:Composite structures 1997-11, Vol.39 (3), p.191-196
Main Authors: Brown, R.E., Stone, M.A.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Vibrations and mechanical waves
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Summary: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.
ISSN:0263-8223
1879-1085
DOI:10.1016/S0263-8223(97)00113-X