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The authors (see below) write: “For slender structures, a stability analysis is all the more complex that they are often very sensitive to imperfections. A small defect can significantly reduce their critical buckling load, causing the collapse for a smaller value than in the perfect case (without imperfection). A simple way for carrying a sensitivity analysis consists in introducing an imperfection in the definition of the structure and in solving problem for this “imperfect” structure. Doing so, an equilibrium branch is obtained for each value of the imperfection amplitude Λ, as represented in figure 1, and the limit point on each of them gives the “imperfect” buckling load. This type of analysis is very simple to implement and the previously described algorithms can be used.”
This and the next 2 images are from:
Sébastien Baguet and Bruno Cochelin (Laboratory of Mechanics and Acoustics, Marseille, France), “Stability of thin-shell structures and imperfection sensitivity analysis with the asymptotic numerical method”, Revue Européenne des Eléments Finis, Hermès, 2002, 11/2-3-4, pp.493-509. <10.3166/reef.11.493-509>.
ABSTRACT: This paper is concerned with stability behaviour and imperfection sensitivity of thin elastic shells. The aim is to determine the reduction of the critical buckling load as a function of the imperfection amplitude. For this purpose, the direct calculation of the so-called fold line connecting all the limit points of the equilibrium branches when the imperfection varies is performed. This fold line is the solution of an extended system demanding the criticality of the equilibrium. The Asymptotic Numerical Method is used as an alternative to Newton-like incremental-iterative procedures for solving this extended system. It results in a very robust and efficient path-following algorithm that takes the singularity of the tangent stiffness matrix into account. Two specific types of imperfections are detailed and several numerical examples are discussed.
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