New GBT Formulation for the Stability Analysis of Thin‐Walled Cylinders

Abstract Standard Generalised Beam Theory (GBT) represents the displacement field of a thin‐walled member as a linear combination of deformation modes classified in three main families: Vlasov (which neglects the membrane shear and the transverse extension), Shear and Transverse Extension modes. Recently the author proposed a unified family of deformation modes for the first‐order (pre‐buckling) analysis and linear buckling analysis of thin‐walled cylinders using variable pre‐buckling stresses. 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 main advantage of a single family of deformation modes is the reduced number of degrees of freedom which can be decreased up to three times. To validate the proposed formulation and to illustrate its advantages, the results are compared with values obtained by shell finite element analyses.