On the interdependency of primary and initial secondary equilibrium paths in sensitivity analysis of elastic structures

On the influence of the prebuckling behavior of elastic structures on their initial postbuckling behavior

“…Bifurcation buckling from a membrane stress state is characterized by a subsidiary condition (see (8)) of the classic condition for loss of stability (see (1)). This condition is satisfied for, but not only for, linear prebuckling paths and linear stability problems which proves that these two special cases are not mutually conditional.…”

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Depending on whether or not bending and/or torsion are part of the prebuckling deformation state of elastic structures, the initial postbuckling behavior is either completely general or characterized by specific restrictions [1]. In this context, the term 'completely general' means (a) no restriction to monotonic improvement or deterioration of the initial postbuckling behavior in consequence of a monotonic change of a design parameter and (b) the impossibility of 'zero-stiffness postbuckling' characterized by a postbuckling path at a constant load level.

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Necessary and Sufficient Conditions for Zero‐stiffness Postbuckling

“…Non-zero-stiffness transitions from imperfection sensitivity to imperfection insensitivity are restricted to λ 4 (κ =κ) = 0 [7]. Hence, it is concluded that…”

Geometrically Non-Linear Finite Element Reliability Analysis of Steel Plane Frames With Initial Imperfections / Plieninių Rėmų Su Defektais Geometriškai Netiesinė Baigtinių Elementų Patikimumo Analizė

“…Different understanding of sensitivity analysis is used in different modelling communities, see, e.g., Edalat et al (2010), Keitel et al (2011). The imperfection sensitivity in buckling problems has been the subject of numerous investigations (Szymczak 2003;Mang et al 2009;Melcher et al 2009;Kala 2009;Mang et al 2011). The main motivation for these studies is the fact that initial imperfections often bring about a significant reduction of buckling resistance.…”