Analyzing buckling mode interactions in elastic structures using an asymptotic approach; theory and experiments

Menken, CM Cees; Schreppers, G-Jma Gerd-Jan; Groot, WJ Wim; Petterson, R Rob

doi:10.1016/s0045-7949(96)00139-3

Cited by 21 publications

(14 citation statements)

References 9 publications

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“…This is akin to a Timoshenko beam formulation (Wang et al 2000); when q s = q t and q f = q t , shear strains are developed and allow the potential for modelling simultaneous LTB and local buckling. Previous work on this type of interactive buckling has included experimental work combined with the effective width theory (Cherry 1960), some phenomenological modelling using rigid links and springs along with experiments (Menken et al 1991), some numerical work using a finite strip formulation ) and a finiteelement formulation (Menken et al 1997). To model this analytically, however, two displacement functions to account for the extra in-plane displacement u and out-of-plane displacement w from local buckling, see figure 2c,d, need to be defined.…”

Section: Variational Formulation (A) Classical Critical Moment Derivamentioning

confidence: 99%

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Cellular buckling from mode interaction in I-beams under uniform bending

Wadee

Gardner

2011

Proc. R. Soc. A.

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Beams made from thin-walled elements, while very efficient in terms of the structural strength and stiffness to weight ratios, can be susceptible to highly complex instability phenomena. A nonlinear analytical formulation based on variational principles for the ubiquitous I-beam with thin flanges under uniform bending is presented. The resulting system of differential and integral equations are solved using numerical continuation techniques such that the response far into the post-buckling range can be portrayed. The interaction between global lateral-torsional buckling of the beam and local buckling of the flange plate is found to oblige the buckling deformation to localize initially at the beam midspan with subsequent cellular buckling (snaking) being predicted theoretically for the first time. Solutions from the model compare very favourably with a series of classic experiments and some newly conducted tests which also exhibit the predicted sequence of localized followed by cellular buckling.

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Section: Variational Formulation (A) Classical Critical Moment Derivamentioning

confidence: 99%

“…Experimental evidence, presented in Menken et al (1997), suggests that during interactive buckling, the significant local out-of-plane displacements within the flanges are confined to the vulnerable outstand. The component of additional strain energy stored in bending U bl is hence given by…”

Section: (I) Local Bending Energymentioning

confidence: 99%

Cellular buckling from mode interaction in I-beams under uniform bending

Wadee

Gardner

2011

Proc. R. Soc. A.

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“…Generally, numerical and experimental results for the reduced problem, as in [16,[18][19][20], suggest that a limited number of modes would suffice to describe correctly the buckling behaviour of plate structures. In the present investigation, it has been noticed that the estimate of buckling mode k deteriorates as k approaches the number of masters.…”

Section: Problem Reduction 231 Reduction Of Variables Strategymentioning

confidence: 99%

“…(19) The reduction of a single variable, say u r , can be speeded up considerably by setting up a vector {G} as follows: (20) and the back substitution is achieved by forming the vector {H} as follows:…”

Section: Frontal Solutionmentioning

confidence: 99%

Finite element analysis of linear plates buckling under in-plane patch loading

Ikhenazen

Saïdani

Chelghoum

2010

Journal of Constructional Steel Research

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“…[20][21][22][23]. In earlier studies using this perturbation approach for static buckling, often problems have been considered under the assumption of a linear pre-buckling state.…”

Section: Introductionmentioning

confidence: 99%

Dynamic buckling analysis of composite cylindrical shells using a finite element based perturbation method

Rahman¹,

Jansen

Gürdal

2011

Nonlinear Dyn

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In this paper a finite element formulation of a reduction method for dynamic buckling analysis of imperfection-sensitive shell structures is presented. The reduction method makes use of a perturbation approach, initially developed for static buckling and later extended to dynamic buckling analysis. The implementation of a single-mode dynamic buckling analysis in a general purpose finite element code is described. The effectiveness of the approach is illustrated by application to the dynamic buckling of composite cylindrical shells under axial and radial step loads. Results of the reduction method are compared with results available in the literature. The results are also compared with full model finite element explicit dynamic analysis, and a reasonable agreement is obtained.

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Analyzing buckling mode interactions in elastic structures using an asymptotic approach; theory and experiments

Cited by 21 publications

References 9 publications

Cellular buckling from mode interaction in I-beams under uniform bending

Cellular buckling from mode interaction in I-beams under uniform bending

Finite element analysis of linear plates buckling under in-plane patch loading

Dynamic buckling analysis of composite cylindrical shells using a finite element based perturbation method

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