Natural boundary conditions in the bending of anisotropic laminated plates

Natural boundary conditions in the bending of anisotropic plates can never be exactly satisfied by a solution in a variables separable form. This creates difficulties for classic solution methods such as Ritz and finite elements, both of which are based on a variables separable approach. Solutions utilizing both of these methods are obtained for deflection, moment resultant, and shear force resultants for simply supported, clamped, and mixed (clamped-simply supported) boundary conditions. A comparison is made between the solutions from these two approaches with emphasis on convergence and how closely each method satisfies natural boundary conditions. Balanced-symmetric angle-ply, special orthotropic, and general anisotropic lay-ups are considered.