Finite Deflection of Skew Sandwich Plates on Elastic Foundations by the Galerkin Method

ABSTRACT

Application of the Galerkin method to various fluid and structural mechanics problems that are governed by a single linear or nonlinear differential equation is well known 1-5]. Recently, the method has been extended to finite element formulations 6-10], In this paper the suitability of the Galerkin method for solution of large deflection problems of plates is studied. The method is first applied to investigate large deflection behavior of clamped isotropic plates on elastic foundations. After validity of the method is established, it is then extended to analyze problems of large deflection of clamped skew sandwich plates, both with and without elastic foundations. The plates are considered to be subjected to uniformly distributed loads. The governing differential equations for the sandwich plate in terms of displacements in Cartesian coordinates are first established and then transformed into skew coordinates. The nonlinear differential equations of the plates are then transformed into nonlinear algebraic equations, using the Galerkin method. These equations are solved using a Newton-Raphson iterative procedure. The parameters considered herein for large deflection behavior of skew sandwich plates are the aspect ratio of the plate, Poisson's ratio, skew angle, shearing stiffnesses of the core, and foundation moduli. Numerical results are presented for skew sandwich plates for various skew angles and aspect ratios. Simplicity and quick convergence are the advantages of the method, in comparison with other much more laborious numerical methods that require extensive computer facilities.