Accurate Stress Analysis of Laminated Plates Combining a Two-Dimensional Theory with the Exact Three-Dimensional Solution for Simply Supported Edges

Abstract

This paper proposes a method for improving the performance of two-dimensional, higher order theories of homogeneous and laminated composite plates. The method is based on the appropriate specification of through-thickness shape functions which are suitable for the accurate stress analysis of plates, on the basis of a general six-degrees-of-freedom plate theory (G6DOFPT). G6DOFPT takes both transverse shear and transverse normal deformation effects into consideration using three shape functions, each of which is associated with one of the three unknown displacement components. Specification of these three shape functions is achieved by solving the corresponding equations of three-dimensional elasticity for a simply supported plate. Thus, the shape functions correspond to the exact elasticity solution presented in previous work. Hence, no results are shown for simply supported plates because, in that case, the present method will yield the results of the exact elasticity analysis. Instead, new results are presented and discussed. These deal with the cylindrical bending of homogeneous orthotropic and two-layered laminates which have both edges rigidly clamped. The new method is considered as the appropriate match of the new shape functions with the equations of G6DOFPT. This is a very promising combination because it employs through-thickness displacement and stress distributions having an "exact" shape away from the edge boundaries. In addition, it takes advantage of the relative ease with which solutions are obtained from the governing equations of a two-dimensional theory, especially in cases which involve complicated edge boundary conditions.