Free vibration analysis of curved metallic and composite beam structures using a novel variable-kinematic DQ method

The present paper investigates the 3 D free vibration behavior of curved metallic and composite beams via a novel beam theory. The refined beam theory is constructed within the framework of the Carrera Unified Formulation (CUF), which expands 3 D displacement fields as 1 D generalized displacement unknowns over the cross-section. As a novelty, a set of improved hierarchical Legendre polynomials called the improved hierarchical Legendre expansion (IHLE) is used to describe the cross-sectional deformation. In this way, displacements at shared sides between piles can be interpolated by Lagrange polynomials, while displacements at the rest of the cross-section remain to be defined by hierarchical Legendre polynomials. Such determined cross-sectional kinematics not only retain the hierarchical properties of HLE in part but also facilitate the implementation of the Layer-Wise approach without paying much attention to the order that expansion terms appear over the cross-section. Due to the absence of the mesh generation and the convenience of collocation techniques, the differential quadrature based-meshless method is employed for the approximate solution of strong form governing equations derived by the principle of virtual displacements. Several numerical cases, including curved beams with various material properties and boundary conditions, are proposed to illustrate the optimized computational efficiency of this novel model over the 3 D finite element method and consistent convergence properties over the previous CUF-HLE model.