Analytic 3-D p-element for vibration analyses of plates, Part 2: Laminated plates

An analytic 3-D p-version arbitrary quadrilateral plate element is applied to solve the free vibration of laminated plates. The computational accuracy is considerably improved due to the additional hierarchical shape functions and analytic integration. The study on a single layer orthotropic plate with simply supported boundary conditions shows the fast convergence and great accuracy of the present element. Then the analyses of rectangular plates with simply supported, cantilevered and fully clamped boundary conditions are carried out. Because of the great fitness to all kinds of geometry shapes, the present element is easily applied to various polygonal plates.