A shear locking-free spatial beam element with general thin-walled closed cross-section

• The proposed model can be applied to general closed thin-walled beams.
• Effects of Shear deformation and warping shear stress are included.
• Influence of flexural–torsional coupling is considered.
• Shear locking is avoided by the consistent interpolation.
• Mixed Hermitian and Lagrangian interpolation is adopted.

A new shear locking-free spatial beam element with general closed thin-walled cross-section is presented in this paper. Based on the Timoshenko beam theory and Benscoter thin-walled beam theory, the proposed element considers the effects of shear deformation, coupled flexure and torsion, and warping shear stress. The shear locking is avoided by introducing an interior node to the element and adopting two-node Hermitian interpolation functions for transverse displacements and torsional rotation and three-node Lagrangian interpolation functions for the flexural rotations and warping function. Several examples are analyzed to validate the accuracy and convergent efficiency of the proposed beam element, and the results are compared with theoretical and numerical solutions. The comparisons demonstrate that the proposed element is applicable to the analysis of a thin-walled beam with an arbitrary closed cross-section.