A p-type solution for the bending of rectangular, circular, elliptic and skew plates

An energy method is presented in this paper for the linear static analysis of first order shear deformable plates of various shapes. In this method, the displacement fields are defined in terms of the shape functions, which correspond to a set of predefined points and are composed of significantly high order polynomials. The positions of these points are calculated by mapping the geometry using naturalized coordinates and the interpolating shape functions of second order to fourth order polynomials. The displacement degrees of freedom are assigned to each of the displacement nodes. The method is evaluated using the fully clamped and simply supported rectangular, circular and elliptic plates subjected to uniformly distributed transverse load as examples for which the exact results are given in the monograph of Timoshenko and Woinowsky-Krieger. Also presented in this paper is the analysis of the above three types of plates subjected to eccentric square and circular patch loadings. Plates with eccentric square and circular openings are analyzed by this method using the full plate model and the results compare extremely well with those obtained by finite element methods. The cutout part of the plate is accommodated in the solution by superposing negative stiffness and load over the area of the opening. Finally, skew plates with simply supported and clamped boundaries are analyzed and discussed.