Plate Bending Analysis

Abstract

Plate bending analysis concerns a plate subjected to transverse loadings and/or bending moments. Under this kind of loading conditions, the assumptions made in two-dimensional problems are not valid for plate bending problems which involve all three coordinate variables. Besides the two-dimensional problems, around 60 years ago Lekhnitskii also developed a complex variable formalism for the plate bending analysis (Lekhnitskii, 1938) and used his formalism to solve the problems of orthotropic plates containing circular holes or rigid inclusions (Lekhnitskii, 1968). After that, very few contributions can be found in the literature for the improvement of complex variable formulation in plate bending analysis. Through the connection between Stroh formalism and Lekhnitskii formalism for the two-dimensional problems, Hwu (2003a) developed a Stroh-like complex variable formalism for the bending theory of anisotropic plates, which can be applied directly to the symmetric laminates. Because the Stroh-like complex variable formalism developed by Hwu (2003a) possesses almost the same matrix form as Stroh formalism for two-dimensional linear anisotropic elasticity, almost all the mathematical techniques developed for two-dimensional problems can be employed to the plate bending analysis. By simple analogy, many problems that cannot be solved previously have the possibility to be solved even without detailed derivation if their counterparts in two-dimensional problems have been solved.