Based on the classical laminated plate theory, a variational approach for the study of the statical and dynamical behaviour of arbitrary quadrilateral anisotropic plates with various boundary conditions is developed. The analytical formulation uses the Ritz method in conjunction with natural coordinates to express the geometry of general plates in a simple form. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the Gram–Schmidt procedure. The algorithm developed is quite general and can be used to study fibre reinforced composite laminates with symmetric lay-ups, which may have general anisotropy and any combinations of clamped, simply supported and free edge support conditions. Various numerical applications are presented and some results are compared with existing values in the literature to demonstrate the accuracy and flexibility of the present method. New results were also determined for plates with different geometrical shapes, combinations of boundary conditions, several stacking sequences and various angles of fibre orientation.
Abstract
Based on the classical laminated plate theory, a [...]
The formulation of an enriched macro element suitable to analyze the free vibration response of composite plate assemblies is presented in this article. Based on the Trigonometric Shear Deformation Theory (TSDT) and the use of Gram–Schmidt orthogonal polynomials as enrichment functions a finite macro element is developed. In the TSDT framework, shear stresses are vanished at the top and bottom surfaces of the plates and shear correction factors are no longer required. The Principle of Virtual Work is applied to derive the governing equations of motion. A special connectivity matrix is obtained; so that hierarchically enriched global stiffness matrix and mass matrix of general laminated plate structures are derived, allowing to study generally coplanar plate assemblies by combining two or more macro elements. This procedure gives a matrix-eigenvalue problem that can be solved with optimum efficiency. Results of free vibration analysis for symmetric laminated plates of different thickness ratios, geometrical planform shapes and boundary conditions are presented. The accuracy of the formulation is ensured by comparing some numerical examples with those available in the literature.
Abstract
The formulation of an enriched macro element suitable to analyze the free vibration response of composite plate assemblies is presented in this article. Based on the Trigonometric Shear Deformation Theory (TSDT) and the use of Gram–Schmidt orthogonal polynomials as enrichment [...]