Non-symmetric bifurcation of geometrically nonlinear elastic-plastic axisymmetric shells under combined loads including torsion. (English) Zbl 0701.73024

Summary: A finite element formulation is presented for the nonsymmetric 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 [e.g.: J. L. Sanders, Q. J. Appl. Math. 20, 21-36 (1963)], a new nonlinear shell theory is adapted which includes nonlinear strains arising from in-plane displacements. For the determination of the nonlinear prebuckling load deflection path, the \(J_ 2\) flow theory of plasticity is used. For the nonsymmetric bifurcation analysis, three theories 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.


74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74C20 Large-strain, rate-dependent theories of plasticity
74S05 Finite element methods applied to problems in solid mechanics
74G60 Bifurcation and buckling
74K15 Membranes


Full Text: DOI