Abstract
It is well known that classical, exact methods of analytical solution cannot be applied to the plate bending problem in cases of irregular boundary shape and arbitrary transverse loading and constraint. The paper summarizes and compares results obtained from using nine approximate analytical methods: point matching, boundary point least squares, TrefftzMorley, interior collocation, interior least squares, subdomain, Galerkin, Ritz, and Kantorovich. For purposes of concrete comparison, each of the methods is applied to two problems for which exact, although intricate, solutions are known: 1) a uniformly loaded, simply supported elliptical plate; 2) a square plate having free edges, supported at four asymmetrically located interior points, and loaded by its own weight. Comparative results are presented. Each technique is rated good, fair, or poor according to 11 important technical criteria and the underlying rationale is explained.
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