Plastic Buckling of Initially Imperfect Stiffened Cylinders in Axial Compression

Abstract

The behavior in the plastic range of axially compressed stringer-stiffened cylinders is investigated. The shell under consideration is assumed to have an initial imperfection in the form of sinusoidal deviation both axially and circumferentially. The constitutive relation employed here is J2 deformation theory of plasticity. This relation, as well as kinematic assumptions regarding the behavior of the panels and stiffeners that constitute the stiffened shell, is used in the principle of virtual work to obtain a set of nonlinear algebraic equations whose solution provides complete information about the prebuckling equilibrium path. Bifurcation from the primary path is examined by making use of a functional whose first variation is zero when two solutions to the problem are possible. This leads to an eigenvalue problem, the eigenvalue being the critical compressive load and the eigenfunction being the corresponding buckling mode. Results are presented for shells of different geometries and material properties, and a comparison of results is made with results obtained by others. The imperfect shells analyzed all exhibit stable behavior, with sufficiently large imperfections having a beneficial effect. Results for bifurcation from these paths are also discussed.