GBT formulation to analyse the buckling behaviour of isotropic conical shells

This paper presents a Generalised Beam Theory (GBT) formulation developed to analyse the elastic buckling behaviour of isotropic conical shells with constant thickness under axial compression. The GBT approach provides a general solution for 1st and 2nd order analysis using bar elements capable of describing the global and local deformations. The kinematic relations of the theory of thin shells are greatly simplified by the assumptions of null membrane shear strain and transverse extension before they are used for the evaluation of the strain energy variation. Because of the cross-section variation specific to conical shells, the mechanical and geometric properties are no longer constant along the bar axis as it is the case of cylinders and prismatic thin-walled structures. This formulation is validated by comparison between GBT results and values obtained by means of shell finite element analyses.

Research highlights
► First order analysis of isotropic conical shell under axial compression yields the pre-buckling stresses.
► First variation of strain energy is computed using shell theory kinematic relations and GBT methodology for the displacement functions.
► First variation of strain energy equation leads to a system of differential equations.
► Solution of the differential equation system yields the member bifurcation loads and corresponding buckling mode shapes.