MLSDQ based on RBFs for the free vibrations of laminated composite doubly-curved shells

A Moving Least Squares Differential Quadrature (MLSDQ) method based on Radial Basis Functions (RBFs) is employed in this paper for solving doubly-curved shells made of composite materials. DQ method can easily approximate partial derivatives of any order by choosing proper basis functions. RBFs are functions that vary according to the radial distance from a current point and its neighborhood. The MLS method is implemented for the approximation of the shape functions used as basis functions. These shape functions depend on some weight functions that in this case are chosen as RBFs. Generally, numerical approaches based on the radial distance work very well on flat surfaces, such as plates, and on curves with constant curvature, such as spheres and cylinders, because the distance between two points can be easily measured. On the contrary, doubly-curved structures with variable radii of curvature which are defined by parametric curvilinear lines do not have a one-to-one (mutual) relationship between a curvilinear distance (defined by using curvilinear coordinates s1, s2) and the location of two points on the same surface (identified by two parameters α1, α2). Therefore, this work aims to show when it is possible to apply the MLSDQ method for solving doubly-curved laminated composite structures.