New unified family of GBT deformation modes for the analysis of thin-walled cylinders

Generalised Beam Theory assumes the displacement field of a thin-walled member as a linear combination of deformation modes. The main family of deformation modes is constructed based on two simplifying assumptions: null membrane shear strain and null membrane transverse extension. If these modes are not sufficient for an accurate representation of the structural behaviour, two other families of modes are derived (from the main family) for which the two simplifying assumptions are eliminated. In this paper, for the special case of thin-walled cylinders, all three families of deformation modes are replaced by a new unified family, for which the membrane shear strain and transverse extension are not neglected. The derivation of the proposed modes is based on the stress equilibrium equations, and it involves the trigonometric series representation of the longitudinal modal amplitudes. The advantages of the proposed modes are highlighted throughout several linear buckling analyses with various loading and boundary conditions.