Imperfection sensitivity due to coupled local instability: a non‐convex QP solution algorithm

Abstract

SUMMARYThe paper deals with the collapse safety of slender elastic structures subjected to local buckling interaction. Using Koiter's asymptotic approach, the mechanical problem is reduced to the search for all the local minima of an indefinite quadratic form over the unit simplex. An efficient recursive branch-and-cut algorithm is proposed for solving this non-convex QP problem, allowing a numerical procedure providing statistical information about the collapse load for a given distribution of random imperfections to be set up.

Nonlinear FEM analysis for beams and plate assemblages based on the implicit corotational method

“…Moreover, once the preprocessor phase of the analysis has been performed (Steps (1)-(4)), the presence of small loading imperfections or geometrical defects can be taken into account in the postprocessing phase (Step (5)), by adding some additional imperfection terms in the expression of µ k [λ], with a negligible computational extra cost, so allowing an inexpensive imperfection sensitivity analysis (for example, see [Lanzo and Garcea 1996;]). From (6h) we can also extract information about the worst imperfection shapes [Salerno and Casciaro 1997;Salerno and Uva 2006] we can use to improve the imperfection sensitivity analysis or for driving more detailed investigations through specialized pathfollowing analysis (see [Casciaro 2005;Casciaro and Mancusi 2006] and references therein).…”

Imperfection sensitivity analysis of laminated folded plates

“…6 in terms of nodal displacements. Loss of stability in the post-critical range and the presence of attractive paths [20,22] can be seen in the figures. Even if the random imperfections generate different behavior within a range, the imperfect paths manifest a convergent behavior to some particular paths (i.e., attractive paths).…”

“…From Eq. (1h) we can also extract information about the worst imperfection shapes [20,21] that we can use to improve the imperfection sensitivity analysis or for driving more detailed investigations through specialized path-following analysis [22].…”

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“…Moreover, once the preprocessor phase of the analysis has been performed (Steps (1)-(4)), the presence of small loading imperfections or geometrical defects can be taken into account in the postprocessing phase (Step (5)), by adding some additional imperfection terms in the expression of µ k [λ], with a negligible computational extra cost, so allowing an inexpensive imperfection sensitivity analysis (for example, see [Lanzo and Garcea 1996;]). From (6h) we can also extract information about the worst imperfection shapes [Salerno and Casciaro 1997;Salerno and Uva 2006] we can use to improve the imperfection sensitivity analysis or for driving more detailed investigations through specialized pathfollowing analysis (see Casciaro and Mancusi 2006] and references therein).…”