Higher-order theories and radial basis functions applied to free vibration analysis of thin-walled beams

In this article, the efficiency of the radial basis functions (RBFs) method when applied to higher-order beam theories is investigated. The displacement field of the generic-order beam model is expressed by making use of the Carrera Unified Formulation (CUF). The strong form of the principle of virtual displacements (PVD) is used to obtain the equations of motion of beams in free vibration. The hierarchical capability of the CUF, in conjunction with the PVD, allows to write the governing equations and the natural boundary conditions in terms of fundamental nuclei. The nuclei can be automatically expanded depending on the theory order N, which is a free parameter of the formulation. Locally supported Wendland’s C6 radial basis functions are subsequently used to approximate the derivatives of the generalized displacements, which are collocated on a number of points (centers) along the beam axis. Several numerical results are proposed including solid structures as well as open and closed thin-walled sections. The solutions by the proposed method are compared both by published literature and by solid/shell models from the commercial code MSC Nastran.