Abstract
ABSTRACTIn 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.
Highlights
Vibration of slender bodies is an important topic in the design of aerospace, mechanical, and civil applications
The results by the present radial basis functions (RBFs) method are compared with reference solutions from the literature together with the results obtained from the finite element commercial code MSC Nastran
An higher-order beam formulation has been developed by using the Carrera Unified Formulation (CUF), which allows for the formulation of any-order beam theories by setting the expansion order as an input of the analysis
Summary
Vibration of slender bodies is an important topic in the design of aerospace, mechanical, and civil applications. Many refined beam theories have been proposed to overcome the limitation of classical beam modelling These approaches include the introduction of shear correction factors, the use of warping functions based on de Saint-Venant’s solution, the variational asymptotic solution (VABS), the generalized beam theory (GBT), and others. The generalized beam theory (GBT) probably was originated from the work of Schardt [23, 24] and it improves classical beam theories by using piece-wise beam description of thin-walled sections It has been widely employed and extended in various forms by Silvetre et al [25, 26] and a dynamic application has been presented by Bebiano et al [27]. The present work is focused on 1D higher-order theories based on the Carrera Unified Formulation (CUF) to carry out free vibration analysis of solid and thin-walled structures. Modal analyses of both solid and thin-walled structures are produced and compared by published literature and solid/shell models from the commercial code MSC Nastran
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