NON-SYMETRIC BIFURCATION OF GEOMETRICALLY NON-LINEAR ELASTIC-PLASTIC AXISYMMETRIC SHELLS UNDER COMBINED LOADS INCLUDING TORSION.

A finite element formation is presented for the non-symmetric bifurcation analysis of geometrically non-linear elastic-plastic shells of revolution. In place of the widely used relations of Donnel, Novozhilov and Sanders, a new non-linear shell theory is adopted which includes non-linear strains prebuckling load deflection path, the J//2 flow theory of plasticity is used. For the non-symmetric bifurcation analysis, three alternatives are provided: J//2 flow theory, J//2 deformation theory and J//2 flow theory with the shear modulus predicted by J//2 deformation 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 analyzed 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.