International Journal for Numerical Methods in Engineering (Impact Factor: 2.06). 12/1998; 40(13):2369 - 2383. DOI: 10.1002/(SICI)1097-0207(19970715)40:13<2369::AID-NME168>3.0.CO;2-8

ABSTRACT 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: A new finite element formulation is presented for the non-linear analysis of elastic doubly curved segmented and branched shells of revolution subject to arbitrary loads. The circumferential variations of all quantities are described by truncated Fourier series with an appropriate number of harmonic terms. A coupled harmonics approach is employed, in which coupling between different harmonics is dealt with directly rather than by the use of pseudo-loads. Key issues in the formulation, such as non-linear coupling and growth of harmonic modes, are carefully and systematically explained. This coupled harmonics approach allows an easy implementation of the arc-length method. As a result, post-buckling load–deflection paths can be traced efficiently and accurately. The formulation also employs a non-linear shell theory more complete than existing classical theories. The results from the present study are independently verified using ABAQUS, while those from other studies are found to be inaccurate in general.
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    ABSTRACT: Cylinders, cones, spheres and tori are some of the common basic shell elements. Steel shell structures such as silos, tanks, pressure vessels, offshore platforms, chimneys and tubular towers generally consist of two or more of these basic shell elements. Axisymmetric intersections featuring meridional slope mismatches between the connected elements are common features in steel shell structures. High bending and circumferential membrane stresses are developed in these intersections, and their buckling and collapse strengths are a key design consideration. This paper presents a summary of recent research on the stress, stability and strength of axisymmetric steel shell intersections. Particular attention is paid to intersections formed from cylindrical and conical segments as these are more common and have been more extensively researched. A simple approximate method for extrapolating the knowledge gained on these intersections to those containing curved shell segments is also suggested.
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