Non-symmetric bifurcation of geometrically nonlinear elastic-plastic axisymmetric shells under combined loads including torsion

A finite element formulation is presented for the non-symmetric bifurcation analysis of geometrically nonlinear elastic-plastic shells of revolution. The shell may be branched and segmented. The loads are axisymmetric but may include in-plane shears (non-uniform torsion). In place of the widely used relations of Donnell, Novozhilov and Sanders, a new nonlinear shell theory is adopted which includes nonlinear strains arising from in-plane displacements. For the determination of the non-linear prebuckling load deflection path, the J2flow theory of plasticity is used. For the non-symmetric bifurcation analysis, three theories are provided: J2flow theory, J2deformation theory and J2flow theory with the shear modulus predicted by J2deformation theory. A new efficient and automatic solution procedure is described to determine the critical buckling mode, and hence the critical buckling stress. Several example problems are analysed and the predictions of the present analysis are compared with available theoretical and experimental results. Very close agreement is achieved. The effect of using different plasticity theories in the stability analysis is also briefly discussed.