A new spatial thin-walled beam finite element for tapered members

This paper presents the essentials of an original geometrically and materially non-linear 3-D tapered beam finite element. The theoretical bases of the element are described, with particular attention paid to the choice of an appropriate displacement field and to the corresponding non-linear axial strains. Specific numerical problems met in the development of the finite element are examined, concerning mainly shear and membrane locking and the handling of rigid body motions. Worked examples on isolated members are presented for various types of analyses: elastic linear, elastic critical and geometrically and materially non-linear analyses. Good accuracy with reference to numerical results is shown, as well as good convergence properties. It is also demonstrated – analytically and numerically – that the use of prismatic beam finite elements for the analysis of tapered beams (segmentation technique) may lead to significant discrepancies when the behaviour is influenced by torsional aspects.