Advanced variable kinematics Ritz and Galerkin formulations for accurate buckling and vibration analysis of anisotropic laminated composite plates

Accurate free-vibrations and linearized buckling analysis of anisotropic laminated plates with different lamination schemes and simply supported boundary condition are addressed in this paper. Approximation methods, such as Rayleigh-Ritz, Galerkin and Generalized Galerkin, based on Principle of Virtual Displacement are derived in the framework of Carrera’s Unified Formulation (CUF). CUF widely used in the analysis of composite laminate beams, plates and shells, have been here formulated both for the same and different expansion orders, for the displacement components, in the thickness layer-plate direction. An extensive assessment of advanced and refined plate theories, which include Equivalent single Layer (ESL), Zig-Zag (ZZ) and Layer-wise (LW) models, with increasing number of displacement variables is provided. Accuracy of the results is shown to increase by refining the theories. Convergence studies are made in order to demonstrate that accurate results are obtained examining thin and thick plates using trigonometric approximation functions. The effects of boundary terms, upon frequency parameters and critical loads are evaluated. The effects of the various parameters (material, number of layers, fiber orientation, thickness ratio, orthotropic ratio) upon the frequencies and critical loads are discussed as well. Numerical results are compared with 3D exact solution when available from the open literature.

► Refined plate theories show their accuracy when a 3D effects appear for thick plate analysis. ► Exact nonlinear strain-displacement relations give an higher accuracy than von Kàrmàn’s approximation for thick plates. ► When many terms are considered in the approximation methods the accuracy of the results is higher than the FEM. ► Is more convenient increase the order of the expansion for all the displacements than increasing only a component. ► Generalized Galerkin method becomes extremely useful when boundary terms are not zero.