The aim of this work is the application of Radial Basis Function (RBF) method to a General Higher-order Equivalent Single Layer (GHESL) formulation for the free vibrations of doubly-curved laminated composite shells and panels. The theoretical development of the present paper is based on the well-known Carrera Unified Formulation. In particular, the fundamental nuclei of a multi-layered doubly-curved shell structure are deducted and explicitly defined. The Differential Geometry (DG) tool has been used to geometrically define each of the structures under consideration: doubly-curved, singly-curved and degenerate shells. The 2D free vibration shell problems are numerically solved using RBFs, where the shape parameters have been optimized using two different algorithms. In fact, the shape parameters of RBFs depend not only on the choice of the radial basis functions, but also on how the points are located on the given computational domain. Modifying the positions of such points, the shape parameters change too. It has been discovered that, once the shape parameters have been optimized for a given grid distribution, they can be rounded off and used for every kind of structure. This is a very important aspect because when, using a fixed parameter, the RBF method becomes a “parameter free” numerical technique. In order to demonstrate the accuracy, stability and reliability of the present methodology, many comparisons are presented with reference to literature results, that are obtained by using Generalized Differential Quadrature method. The above numerical applications of this study are also compared with finite element method solutions.
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