Selected closed-form algebraic solutions for linear stress and buckling analyses of elastic shear-flexible axisymmetric cylindrical shells

This paper presents a systematic analytical treatment of finite transverse shear strains in cylindrical shells using first-order shear deformation theory (FSDT), applied as an extension to classical thin shell elastic bending theory. The theory is illustrated on linear stress and, in particular, linear bifurcation buckling analyses of two fundamental reference load cases (axisymmetric cylinders under uniform meridional compression and uniform external pressure), with the stability analysis including non-shallow terms in addition to the transverse shear strains. Excellent agreement with FE solutions is demonstrated in a series of examples, with thick shell results characterised by increased flexibility compared against classical thin shell theories while also tending to the latter in the appropriate limit. The closed-form algebraic results presented in this paper will be particularly useful for developers of buckling design formulae, such as those which figure in the capacity curve framework of EN 1993-1-6 (2025), who currently resort to ad-hoc empirical modifications to classical ‘thin’ shell reference results to account for finite thickness effects even in shells of low relative slenderness which buckle with significant plastification. Detailed Excel and Python implementations are provided via GitHub.