A nonlinear cross-section deformable thin-walled beam finite element model with high-order interpolation of warping displacement

Abstract

In this paper, a new finite element model is developed for nonlinear analysis of thin-walled beams by introducing a high-order interpolation for the warping displacement field to better simulate actual cross-section deformation. It is discovered that, due to the significant coupling between bending and membrane deformations in each wall, it is crucial for a nonlinear thin-walled beam finite element to be capable to describe complex warping displacement distribution over the cross-section. In the geometrically exact beam element model developed, the warping displacement is expressed by using a higher-order interpolation scheme, while the distortion displacements are independently described by using a number of cross-section in-plane deformation modes. Numerical results are presented to demonstrate the effectiveness of the proposed model and investigate possible impacts of interpolation schemes for the warping displacement distribution on the solution accuracy under different problem settings. The results show that with an appropriate high-order warping displacement interpolation scheme, the proposed beam model can produce very accurate results even in the case of small wall thickness, outperforming many of the existing models. It is therefore concluded that special attention is needed on the warping displacement field for a finite element model to accurately simulate the cross-section distortional deformation of thin-walled beams. • A geometrically exact cross-section deformable thin-walled beam finite element model is developed. • The distortion and warping displacements are described by distortion modes and high-order interpolation, respectively. • Numerical examples are presented for a comprehensive investigation of the present finite element model. • The importance of warping displacement field for ensuring solution accuracy is pointed out.