Non-linear stability of elastic-plastic conical shell under combined load

The paper presents stability analysis of an elastic-plastic sandwich open conical shell of a circular cross section under combined external load in the form of lateral pressure, longitudinal forces, and shear. The shell consists of two load-carrying faces made of an isotropic, compressible work-hardening material, and they are of different thicknesses and made of different material properties; the core material is of a soft type and it resists transversal forces only. It is also assumed that the shell can be deformed into plastic range before buckling. The flexural stiffness of the faces is taken into account, the Kirchhoff-Love hypotheses hold for the faces, and the active deformation processes are considered. The constitutive relations used in the analysis are those of the incremental Prandtl-Reuss plastic flow theory associated with the Huber-Mises yield condition. The virtual work principle is the basis to obtain the governing stability equations and the Ritz method is used to derive differential equations of the considered problem. An iterative computer algorithm was elaborated to analyse the shells both in the elastic or elastic-plastic prebuckling state of stress.