Buckling of Thin-Walled Cylinders from Three Dimensional Nonlinear Elasticity

Abstract The famous bifurcation analysis performed by Flügge on compressed thin-walled cylinders is based a series of simplifying assumptions, which allow to obtain the landscape, together with explicit expressions for limit behaviours: surface instability, wrinkling, and Euler rod buckling. most severe assumption introduced use an incremental constitutive equation, does not follow from any nonlinear hyperelastic law. This strong limitation applicability theory, becomes questionable when utilized material characterized different such as instance Mooney-Rivlin material. We re-derive entire Flügge’s formulation, thus obtaining framework where equation fits. two equations, referred compressible materials, leads reduce those derived under suitable simplifications. His results are confirmed, all now rigorously obtained, his theory extended. extension buckling thin shells allows computationally efficient determination landscapes laws, may be used model biomechanics arteries, or soft pneumatic robot arms.