Plate Deflections Using Orthogonal Polynomials

Abstract

Bending deflection of plates under static loading has been determined using beam characteristic orthogonal polynomials in Rayleigh‐Ritz formulation. The first member of the orthogonal polynomial set was constructed as the simplest polynomial that satisfies all the boundary conditions of the corresponding beam problems accompanying the plate problem. The rest of the set was generated using the Gram Schmidt orthogonalization process. Results are obtained for plates with all edges clamped and those with three edges clamped and one edge free. Two types of loadings, uniform and hydrostatic, are considered. The results are found to agree closely with those obtained by previous methods. Since the Gram Schmidt orthogonalization process can include a weight function also, even plates with nonuniform properties can be studied using this method.