POST‐COLLAPSE BIFURCATION ANALYSIS OF SHELLS OF REVOLUTION BY THE ACCUMULATED ARC‐LENGTH METHOD
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.
- SourceAvailable from: Ehab HamedJournal of Mechanics of Materials and Structures - J MECH MATER STRUCT. 01/2010; 5(1):107-128.
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ABSTRACT: In many practical applications, thin shells are in contact with soils or other solids. Such situations arise in cylindrical bulk solid storage silos, above-ground and underground liquid storage tanks, underground pipelines, ballistic missiles filled with solid propellants, and concrete-filled steel tubular columns. As a result, many studies have been carried out on the analysis and behavior of shells on elastic foundations. However, little has been done on shells on nonlinear elastic foundations, despite the fact that foundation behavior is generally nonlinear. This paper presents a finite element formulation for the buckling analysis of shells of revolution on nonlinear elastic foundations. To achieve a versatile foundation model, the foundation reaction–displacement relationship is represented by a number of discrete data points (referred to as the Discrete-Point or DP Model in this paper). Any specific nonlinear functions such as polynomials can be treated as special cases of this model and accurately represented by a sufficiently large number of data points. The validity and capability of the present analysis are demonstrated through numerical comparisons. The paper also presents the first set of verified numerical results for buckling of shells on nonlinear elastic foundations, which can be used to benchmark results from other sources in the future.Computers & Structures 01/1998; 69(4):499-511. · 2.18 Impact Factor
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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.Progress in Structural Engineering and Materials 06/2001; 2(4):459 - 471. · 0.55 Impact Factor