GBT deformation modes for curved thin-walled cross-sections based on a mid-line polygonal approximation

• A rational and efficient procedure for calculating the GBT deformation modes of curved cross-sections is proposed.
• The geometry is approximated independently of the cross-section DOFs considered.
• The procedure can handle rounded corners efficiently.

This paper addresses the determination of deformation modes for curved thin-walled cross-sections through the polygonal approximation of the cross-section mid-line, in the framework of Generalised Beam Theory (GBT). A new GBT cross-section analysis procedure is proposed, which discretises the geometry independently of the number of cross-section DOFs considered to obtain the deformation modes. This procedure is more efficient than the classic GBT one, since curved geometries may be accurately described without increasing the number of deformation modes. In particular, polygonal sections with rounded corners can be easily handled. For illustrative purposes, the procedure is applied to several cross-sections with curved walls and it is shown that it leads to accurate results with coarse cross-section DOF discretisations.