Generalized Differential Quadrature Finite Element Method for Cracked Composite Structures of Arbitrary Shape

This paper investigates the dynamic behavior of moderately thick composite plates of arbitrary shape using the Generalized Differential Quadrature Finite Element Method (GDQFEM), when geometric discontinuities through the thickness are present. In this study a five degrees of freedom structural model, which is also known as the First-order Shear Deformation Theory (FSDT), has been used. GDQFEM is an advanced version of the Generalized Differential Quadrature (GDQ) method which can discretize any derivative of a partial differential system of equations. When the structure under consideration shows an irregular shape, the GDQ method cannot be directly applied. On the contrary, GDQFEM can always be used by subdividing the whole domain into several sub-domains of irregular shape. Each irregular element is mapped on a parent regular domain where the standard GDQ procedure is carried out. The connections among all the GDQFEM elements are only enforced by inter-element compatibility conditions. The equations of motion are written in terms of displacements and solved starting from their strong formulation. The validity of the proposed numerical method is checked up by using Finite Element (FE) results. Comparisons in terms of natural frequencies and mode shapes for all the reported applications have been performed.