A geometrically non-linear formulation of a three-dimensional beam element for solving large deflection multibody system problems

A beam finite element formulation for large deflection problems in the analysis of flexible multibody systems has been proposed. In this formulation, a set of independent discrete deformation modes are defined for each element which are related to conventional small deflection beam theory in a co-rotational frame. The paper examines the applicability of this formulation for a shear-deformable three-dimensional Timoshenko beam model, in which geometric non-linearities due to large deflections, buckling loads and post-buckling are included. The geometric non-linearities are accounted for by additional second-order terms in the expressions for the deformation modes. Some numerical examples including large deflections are presented and discussed in order to illustrate the influence of these terms on the accuracy and rate of convergence. The influence of these terms on the displacements is small, except for bifurcation points where the load–deflection characteristics change drastically. It is demonstrated, by comparison with available results in the literature, that highly accurate solutions can be obtained with the present beam finite element formulation. ► We propose a beam finite element formulation for large deflection problems. ► The beam element is based on the generalized deformation formulation. ► Geometric non-linearities due to large deflections and (post)buckling are included. ► Second-order terms are essential to describe the behaviour near bifurcation points.