Efficient XFEM approach for the analysis of thin-walled beams

Abstract

This paper presents a new approach to the analysis of thin-walled beams. The proposed model is developed by utilizing the eXtended Finite Element Method (XFEM). Global enrichment functions are added to a standard 3D Finite Element (FE) coarse mesh to enhance its performance and reduce the number of degrees of freedom. These analytical functions provide an approximate solution in the longitudinal direction of the beam. The resulting model bridges the gap between the Finite Prism Method (FPM), which provides an efficient approximation to beam bending with analytical functions but has also well-known limitations, and a detailed 3D FE model, which can accurately resolve thin-walled structures but is computationally demanding.Our method can be easily extended for beams with non-prismatic cross-sections (e.g., tapered beams) or with perforations, which makes it more general than other semi-analytical methods, such as the FPM. However, these extensions are not in the scope of this paper. Additionally, one can improve the solution by sectional and/or longitudinal mesh refinements.The performance of the model is investigated on two benchmark problems. The results show that the proposed method captures different global and sectional deformation modes of thin-walled beams when subjected to torsion, including shear-lag and distortion cross-section. Furthermore, convergence studies demonstrate the superior performance of the proposed method as compared to the FPM, and a 3D FE model with a coarse mesh.