Free vibration analysis of variable stiffness composite laminate plate with circular cutout

Abstract

This paper presents the free vibration analysis of a variable stiffness composite laminate (VSCL) square plate with circular cutout. Although the h-version of the finite element method is quite attractive, it could not be used in the VSCL plate. This is due to the difficulties associated with the inter-element continuity for the curvilinear fibre and the fact that the circular cutout cannot be represented accurately. To overcome this problem, a new C0 enriched curved quadrilateral p-element is developed based on the first-order shear deformation theory, in which the transformed reduced stiffness elements are computed exactly within the stiffness matrix, and the curved edges are represented accurately using the blending function method. The convergence properties of the proposed p-version and the results of the numbers of test problems are in good agreement with the results of the literature. The natural frequencies are examined by considering the parabolic fibre orientation, radius of the circular cutout, the plate thickness and the boundaries conditions. It is found that the variation of the fibre orientation have significant effect on natural frequencies, especially for plates with large circular cutout.