Meshless analysis of metallic and composite beam structures by advanced hierarchical models with layer-wise capabilities

This paper proposes radial basis function (RBF)-based meshless solutions for static and dynamic analyses of metallic and laminated beam-like structures with various boundary conditions. Making use of the Carrera Unified Formulation (CUF), the three-dimensional displacement field can be reduced to one-dimensional displacements related to the axial direction multiplied by cross-sectional kinematics. Locally supported Wendland's C-6 RBF is employed to interpolate the displacements in the axial domain and Hierarchical Legendre Expansion (HLE) is used to expand the kinematic unknowns over the cross-section domain, being endowed with Layer-Wise (LW) ability. The principle of virtual displacements (PVD) is adopted to derive the governing equation in a strong form, accompanied by the advent of fundamental nuclei, which are independent of the transverse assumptions in the cross section domain. Different numerical assessments on metallic and laminated structures are addressed to show the performance of RBF-based HLE models in terms of displacements, stresses and vibration modes. 3D accuracy of the obtained results is demonstrated by comparison with 3D FEM solutions provided by well-known commercial softwares (Ansys and Abaqus).