Nonlinear stability analysis of elastic-plastic conical shells with shape imperfections

The paper presents the theoretical background for elastic-plastic stability problem of a conical shell with the assumption that the shell has initial shape imperfections of the order of shell thickness. Physical relations follow Prandtl-Reuss incremental plastic flow theory of plasticity associated with Huber-Mises yield condition. The stability problem is reduced to a set of two nonlinear partial differential equations of the fourth order with the two unknown functions: deflection function, and stress function. As a result of solution the nonlinear relation between the external load and deflection function parameter is obtained. The equations are solved by Galerkin method and with the help of a numerical algorithm. The approximate functions satisfy the boundary conditions of free-supported shell edges. An iterative software code was elaborated to get numerical results for elastic-plastic shells.