ABSTRACT
The partial differential equations governing composite laminates (see Section 4.3) of arbitrary geometries and boundary conditions cannot be solved in closed form. Analytical solutions of plate theories are available (see Reddy [4–8]) mostly for rectangular plates with all edges simply supported (i.e., the Navier solutions) or with two opposite edges simply supported and the remaining edges having arbitrary boundary conditions (i.e., the Lévy solutions). The Rayleigh–Ritz and Galerkin methods can also be used to determine approximate analytical solutions, but they too are limited to simple geometries because of the difficulty in constructing the approximation functions for complicated geometries. The use of numerical methods facilitates the solution of these equations for problems of practical importance. Among the numerical methods available for the solution of differential equations defined over arbitrary domains, the finite element method is the most effective one [9,14,15].
