Inelastic buckling of a layered conical shell

摘要

The purpose of the study is investigation of large displacement stability loss of a bilayered conical shell loaded by longitudinal forces and uniformly distributed external pressure. The shell under consideration is made of a material with exponential work-hardening. The physical relations used in the elastic-plastic analysis are those of the incremental Prandtl-Reuss plastic flow theory with the Huber-Mises yield condition. The virtual work principle is the basis to derive the strain energy expression. The analysis is based on the energy minimization, where the total strain ε in the shell can be expressed in terms of reference surface strains and changes in curvature and these reference surface quantities can then be expressed in terms of displacement vector components. The Ritz method is accepted in order to derive the stability equations for the considered shell. The final form of stability equation, being a flinction of deflection function parameter, makes possible to trace the equilibrium paths for the shell under consideration. An iterative computer algorithm was elaborated which makes it possible to analyze the shells in elastic, elastic-plastic or in totally plastic prebuckling state of stress. The numerical examples show the influence of principal geometrical and physical parameters of the shell on the stability loss at large deflections.