Solution methods for the growth of a repeating imperfection in the line of a strut on a nonlinear foundation

Lagrange, Romain; Averbuch, Daniel

doi:10.1016/j.ijmecsci.2012.06.010

Cited by 21 publications

(11 citation statements)

References 22 publications

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“…Consistent deformation-dependent resistance force models were incorporated into the analyses of lateral buckling by Taylor and Gan (Taylor and Gan, 1986a) and Zhu et al (Zhu et al, 2015). Bi-linear and tri-linear restoring force models were employed to obtain the analytical solutions of an axially loaded strut (Lagrange and Averbuch, 2012) and an axially loaded subsea pipeline (Karampour et al, 2015), respectively. Furthermore, a nonlinear lateral soil resistance model, which contained cubic and quintic nonlinear terms, was used by Zeng and Duan (Zeng and Duan, 2014) to obtain localised solutions with an intricate bifurcation structure.…”

Section: Soil Resistancementioning

confidence: 99%

“…As to the soil modelling, different soil resistance models have been incorporated into the localised lateral buckling problem. Lagrange and Averbuch (Lagrange and Averbuch, 2012) have studied the periodic solutions of a strut on a nonlinear elastic Winkler-type foundation with imperfection in the form of a sine shape. The nonlinear restoring force of the foundation was either a bi-linear or an exponential profile.…”

Section: Introductionmentioning

confidence: 99%

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Localised lateral buckling of partially embedded subsea pipelines with nonlinear soil resistance

Wang

Heijden

2017

Thin-Walled Structures

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Unburied partially embedded subsea pipelines under high temperature conditions tend to relieve their axial compressive force by forming localised lateral buckles. This phenomenon is traditionally studied as a kind of imperfect column buckling problem. We study lateral buckling as a genuinely localised buckling phenomenon governed by a different static instability, with a different critical load. No ad hoc assumptions need to be made. We combine this buckling analysis with a detailed state-of-the-art nonlinear pipe-soil interaction model that accounts for the effect of lateral breakout resistance. This allows us to investigate the effect of initial embedment of subsea pipelines on their load-deflection behaviour. Parameter studies reveal a limit to the temperature difference for safe operation of the pipeline, in the sense that for higher temperature differences a localised buckling mode has lower total energy than the straight unbuckled pipe. Localised lateral buckling may then occur if the pipe is sufficiently imperfect or sufficiently dynamically perturbed.

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Section: Soil Resistancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Localised lateral buckling of partially embedded subsea pipelines with nonlinear soil resistance

Wang

Heijden

2017

Thin-Walled Structures

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“…In addition, the mechanical behavior of a beam, initially straight or with an initial curvature, lying on a nonlinear elastic foundation, have been the subject of many studies, see e.g. [7][8][9][10][11][12][13][14][15][16]. An important point to notice is that the equilibrium curves may exhibit in this case a limit point, i.e.…”

Section: Introductionmentioning

confidence: 99%

Compression-induced stiffness in the buckling of a one fiber composite

Lagrange

2021

Preprint

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We study the buckling of a one fiber composite whose matrix stiffness is slightly dependent on the compressive force. We show that the equilibrium curves of the system exhibit a limit load when the induced stiffness parameter gets bigger than a threshold. This limit load increases when increasing the stiffness parameter and is related to a possible localized path in the post-buckling domain. Such a change in the maximum load may be very desirable from a structural stand point.

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“…on this maximum load. The papers on deterministic imperfection sensitivity include those of [4,5,11,15,[20][21][22][23][24] and extensive references for the stochastic imperfection sensitivity are compiled in [25]. As a general rule, the maximum load at which the beam becomes unstable diminishes with increasing imperfection size.…”

Section: Introductionmentioning

confidence: 99%

“…As a general rule, the maximum load at which the beam becomes unstable diminishes with increasing imperfection size. Considering a finite beam on a bilinear/exponential foundation, [24] has shown the existence of a critical imperfection size A 0c such that: if A 0 < A 0c , then the maximum load diminishes with the imperfection size, from the critical buckling load predicted by the classical linear analysis [see 10], for A 0 = 0, to the Euler load for A 0 = A 0c . In this case, the decay rate is sensitive to the restoring force model.…”

Section: Introductionmentioning

confidence: 99%

Limit point buckling of a finite beam on a nonlinear foundation

Lagrange

2021

Preprint

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In this paper, we consider an imperfect finite beam lying on a nonlinear foundation, whose dimensionless stiffness is reduced from 1 to k as the beam deflection increases.Periodic equilibrium solutions are found analytically and are in good agreement with a numerical resolution, suggesting that localized buckling does not appear for a finite beam. The equilibrium paths may exhibit a limit point whose existence is related to the imperfection size and the stiffness parameter k through an explicit condition. The limit point decreases with the imperfection size while it increases with the stiffness parameter. We show that the decay/growth rate is sensitive to the restoring force model. The analytical results on the limit load may be of particular interest for engineers in structural mechanics.

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Solution methods for the growth of a repeating imperfection in the line of a strut on a nonlinear foundation

Cited by 21 publications

References 22 publications

Localised lateral buckling of partially embedded subsea pipelines with nonlinear soil resistance

Localised lateral buckling of partially embedded subsea pipelines with nonlinear soil resistance

Compression-induced stiffness in the buckling of a one fiber composite

Limit point buckling of a finite beam on a nonlinear foundation

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