GBT-based FE formulation to analyse the buckling behaviour of isotropic conical shells with circular cross-section.

Abstract The following paper presents a Finite Element formulation based on the Generalized Beam Theory (GBT), to analyse the buckling behaviour of isotropic conical shells under various loading and boundary conditions. The formulation offers the solution of the 1st order analysis from which the pre-buckling stresses are computed, including stress concentrations, and the linear (bifurcation) buckling solution. Due to the variable cross-section of conical shells, the mechanical and geometrical properties are no longer constant along the bar's axis as they are in the case of cylindrical structures and thin-walled prismatic bars. Special focus is given to the effect of the pre-buckling stress concentrations and non-conventional cross-section deformation modes. The proposed formulation is validated by comparing results obtained from GBT and Shell Finite Element Analyses. Highlights • 1st variation of strain energy is computed using conical shell theory and GBT. • GBT-based bar Finite Elements are used for conical shells. • 1st order analysis yields the pre-buckling stresses. • Linear buckling analysis yields the bifurcation loads and mode shapes. • The effect of the pre-buckling stress concentrations is assessed. [ABSTRACT FROM AUTHOR]