Numerical convergence of simple and orthogonal polynomials for the unilateral plate buckling problem using the Rayleigh–Ritz method
✍ Scribed by S. T. Smith; M. A. Bradford; D. J. Oehlers
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 158 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0029-5981
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✦ Synopsis
Unilateral buckling is a contact problem whereby buckling is confined to take place in only one lateral direction. For plate structures, this can occur when a thin steel plate is juxtaposed with a rigid concrete medium and the steel may only buckle locally away from the concrete core. This paper investigates the use of simple and orthogonal polynomials in the Rayleigh-Ritz method for unilateral plate buckling. The orthogonal polynomials used are the classical Chebyshev types 1 and 2, Legrende, Hermite and Laguerre. The study presents a comparison between the efficiency of the polynomial-based displacement functions with regard to elastic bilateral and unilateral plate buckling, where efficiency is measured as a function of their convergence characteristics. Some buckling solutions for plates with varying boundary conditions and in-plane shear loads are also provided as an illustration.