Stiffness Matrix for Plates by Galerkin's Method

Abstract

The master stiffness matrix is derived from the biharmonic plate equation. The application of Galerkin's method to the biharmonic plate equation results in a system of algebraic equations. These equations contain area integrals which must be evaluated over the plate domain. It is shown that by considering the domain of these integrals as a collection of polygonal sub-domains and approximating the displacement function with polynomial spline functions over each sub-domain, the original set of simultaneous algebraic equations can be approximated by a new set, the coefficient matrix of which is identical to the master stiffness matrix of the Finite Element Method. Criteria are postulated for best plate elements and development of an 18 degree-of-freedom plate element, conforming with these criteria, is outlined.