The GDQ method for the free vibration analysis of arbitrarily shaped laminated composite shells using a NURBS-based isogeometric approach

A numerical procedure based on the Generalized Differential Quadrature (GDQ) method is presented to solve the strong form of the differential equations that govern the free vibration problem of some structural elements. The dynamic behavior of several laminated composite doubly-curved shells with arbitrary shape is investigated comparing the results achieved through different Higher-order Shear Deformation Theories (HSDTs) based on an Equivalent Single Layer (ESL) approach. The theoretical framework of the well-known Carrera Unified Formulation (CUF) represents the starting point to develop easily different higher-order models. Starting from regular domains described in principal curvilinear coordinates, a completely arbitrary shape is obtained by means of Non-Uniform Rational B-Splines (NURBS) due to the advantages shown in the well-known isogeometric analysis (IGA). The mapping technique based on the use of blending functions is illustrated to twist the original domain into the distorted one without subdividing the reference domain into sub-elements or finite element (FE). The procedure is extremely general and allows to deal with different boundary condition combinations and stacking sequences. Its validity is proven by the comparison with the results available in the literature concerning arbitrarily shaped plates or obtained through three-dimensional FE models.