A variational formulation and analysis of polar orthotropic circular plates using an energy principle, part I: Thin plates

This paper concerns the bending analysis of an axisymmetric polar orthotropic thin circular plate (solid or annular) subjected to thermal or mechanical loading. Direct variational methods such as the Rayleigh-Ritz, the Galerkin, the Kantorovich and the Treftz have usually been employed to solve plate problems. In this study, the variational (energy) principle is used to derive the governing differential equations and the boundary conditions of the plate by using the rules of the calculus of variations. The set of differential equations derived from the variational process are solved simultaneously. The accuracy of the present formulation is demonstrated by the problems for which exact solutions are available, and the problems whose isotropic solutions are available while polar orthotropic solutions are not available. It is shown that the principle is useful to get solutions easily compared with the direct variational methods. © Freund Publishing House Ltd