A simplified-but-general nonlinear thin-walled beam finite element model with independent interpolated axial displacement

Abstract

This paper presents a study performed on the simplified thin-walled beam finite element model that takes into account the effects of shear deformation and higher-order axial displacement. Without using the torsion-related warping function derived from classical theories, the axial displacement field over the cross-section is constructed by using independent Langrage interpolation polynomials. Then, the effect of shear stress distribution can be reasonably included and the beam model is dedicated to thin-walled members with arbitrary cross-section. The expressions of the Green-Lagrange strain components are derived. The element elastic stiffness matrix and geometrical stiffness matrix are obtained to perform static and buckling analyses. Numerical examples are employed to demonstrate the effectiveness of the proposed model and discuss the probable accuracy-loss from different deformation assumptions and nonlinear strain definitions. As revealed by the results, the transverse shear deformation and higher-order axial displacement could exert significant effects on solution accuracy for static and buckling analyses under the circumstances of small slenderness and unsymmetrical cross-section. In addition, the nonlinear strain terms related to torsion and quadratic terms of the transverse shear deformation are found to be crucial to stability analysis, for which they ought to be included in a simplified strain definition. • A thin-walled beam finite element with interpolated axial displacements is developed. • The expressions of the Green-Lagrange strain components are derived. • Effects of shear deformation and higher-order axial displacement are discussed. • A simplified strain definition for flexural-torsional buckling analysis is suggested.