Improving the efficiency of GBT displacement-based finite elements

This paper focuses on computational efficiency aspects related to Generalised Beam Theory (GBT) displacement-based finite elements. In particular, a cross-section node-based DOF approach is proposed, which makes it possible to (i) deal, straightforwardly, with discrete variations of the thickness of the walls (including holes) in the longitudinal direction and (ii) achieve significant computational savings in non-linear problems, with respect to the conventional GBT approach (based on cross-section deformation modes). The proposed approach leads to a beam-like finite element that is equivalent to an assembly of flat quadrilateral shell elements and, therefore, (i) much smaller matrices are handled and (ii) the resulting element stiffness matrix is significantly sparse. The deformation mode participations, which are the trademark of GBT, are recovered through post-processing. Several numerical examples are provided, involving both linear and non-linear (static) problems, to highlight the capabilities and efficiency of the proposed approach.