A geometrically exact thin-walled beam element with simplified strain definition

This paper presents a study of the formulation of nonlinear beam elements for spatial thin-walled frame structures. A formulation based on the geometrically exact beam theory is developed first, which includes transverse shear deformation, torsion-related warping and all major nonlinear strain terms. A comprehensive investigation is then made on different terms in the nonlinear strain expressions and their effects on the solution accuracy in nonlinear stability and post-buckling analyses. It is found that some nonlinear terms in the strain expression for the Wagner effect, quadratic shear deformation and torsion-shear coupling may have a significant impact on the solution accuracy, and hence must be included in an element formulation. A simplified strain expression is proposed, and a new thin-walled beam element is developed for physically and geometrically nonlinear analyses by using the proposed expression and formulation. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed formulation and element.