Post-collapse bifurcation analysis of shells of revolution by the accumulated arc-length method

International Journal for Numerical Methods in Engineering (Impact Factor: 2.06). 07/1997; 40(13):2369 - 2383. DOI: 10.1002/(SICI)1097-0207(19970715)40:13<2369::AID-NME168>3.0.CO;2-8


Shells of revolution subject to axisymmetric loads often fail by non-symmetric bifurcation buckling after non-linear axisymmetric deformations. A number of computer programmes have been developed in the past decades for these problems, but none of them is capable of bifurcation analysis on the descending branch of the primary load–deflection path following axisymmetric collapse/snap-through. This paper presents the first finite element formulation of post-collapse bifurcation analysis of axisymmetric shells in which a modified arc-length method, the accumulated arc-length method, is developed to effect a new automatic bifurcation solution procedure. Numerical examples are presented to demonstrate the validity and capability of the formulation as well as the practical importance of post-collapse bifurcation analysis. The accumulated arc-length method proposed here can also be applied to the post-collapse bifurcation analysis of other structural forms. © 1997 by John Wiley & Sons, Ltd.

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    ABSTRACT: The paper describes different computational approaches and solution methodologies that can be used in nonlinear structural analysis, in particular, the so called path–following anal-ysis, the linearized stability analysis, the asymptotic analysis, the imperfection sensitivity analysis and the transient dynamic analysis, for each showing the main problems, peculiar aspects, possible failures and computational convenience. Nonlinear solutions are, by their nature, sensitive to small variations in data, so a performance–based analysis must include an extensive investigation, which takes into account all possible loading imperfections and geometrical defects. Great care has to be taken to assure the reliability of the results and, if possible, any analysis should be repeated using an alternative approach.
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