Deformation Modes and Dual Stress Resultants of Spatial Beam Elements in Large Deflection Multibody System Analyses

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 deformation modes are defined for each element that do not change if the element is subjected to rigid body motions. The paper examines the applicability of this deformation mode formulation for a shear-deformable three-dimensional Timoshenkolike beam model. In particular, the influence of the second-order terms in the expressions for the deformation modes on the results is shown. Some numerical examples including large deflections are presented and discussed in order to illustrate their effect on the accuracy and rate of convergence. Comparisons are made with analytical solutions of the large deflection of a cantilever beam and with numerical results obtained with the absolute nodal coordinate and geometrically exact beam formulations of a 45 degree cantilever bend. Finally, the vibration mode frequencies and buckling loads of a simple parallel leaf spring guidance subject to misalignment are analysed.