Efficient CUF-based FEM analysis of thin-wall structures with Lagrange polynomial expansion

Thin-walled structures have been widely adopted in engineering projects because of the advantages of good load-bearing capacity, light weight and low cost. In this paper, a refined finite element method (FEM) based on the Carrera Unified Formula (CUF) is performed to analyze the free vibration of thin-walled beams with the variables cross-section, length and boundary. The low-dimensional FEM method could improve the efficiency of numerical analysis and reduce the time consumption. The one-dimensional (1D) CUF is employed in which the models are assumed to be a beam-like axis-oriented structures. In this case, the geometry of the thin-walled beam can be discretized as a limited number of 1D beam elements along the axis, while the Lagrange polynomial expansion may be used to approximate the displacement field on the cross-beam surface. Thus, FEM matrices and vectors can be written in terms of fundamental nuclei whose forms are independent of beam theories. The validity and capabilities of the method presented are examined in some numerical examples, and a comparative study is carried out between the method proposed and the three-dimensional element method with and without warping solutions. The results obtained by CUF 1D models are in close agreement with the reference solutions. In addition, it has been argued that the innovative approach presented in this paper can be used as a precise tool for structural analysis for complex cross-section thin-walled beams to reduce computational costs.