GBT-based cross-section deformation modes for curved thin-walled members with circular axis

This paper presents an improvement of the first-order Generalised Beam Theory (GBT) formulation proposed in [1], which was developed for naturally curved thin-walled members with deformable cross-section and whose undeformed axis is a circular arc with no pre-twist. In this paper, the restrictions on the cross-section shape are removed (in the previous paper only rather simple cross-sections were dealt with) by proposing and discussing a novel and systematic procedure to obtain the cross-section deformation modes for arbitrary flat-walled cross-sections (open, closed or “mixed”). The proposed procedure retains the nomenclature of the deformation mode subsets defined in [2], [3], even though the kinematic constraints employed to subdivide the modes are much more complex than for prismatic members. A set of representative illustrative examples is presented, involving complex local-distortional-global deformation, to show the efficiency of the proposed procedure when used together with a standard displacement-based GBT finite element. It is demonstrated that extremely accurate results are obtained with rather few DOFs and that the GBT modal solution provides in-depth insight into the structural behaviour of naturally curved members.