Imperfections, a main contributor to scatter in experimental values of buckling load

Horton, W.H.; Durham, S. C.

doi:10.1016/0020-7683(65)90015-6

Cited by 34 publications

(13 citation statements)

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“…Such a situation could occur if, e.g., the cylinder were manufactured by rolling up a naturally planar elastic sheet into a tube and joining the ends (as is done in [25]). If instead the cylinder were manufactured as a naturally curved elastic shell (as is done in [15] via electroforming), then the case of vanishing displacement should achieve zero elastic energy. In such a setting, one could substitute in the bending term a difference of second fundamental forms (or, keeping with our simplification, of second partial derivative matrices) between that of the deformed and that of the natural state.…”

Section: A Nonlinear Model Of Elasticitymentioning

confidence: 99%

“…In many controlled experiments involving the axial compression of thin elastic cylinders, one observes complex folding patterns (see, e.g., [9,15,23,25]). It is natural to wonder if such patterns are required to minimize elastic energy, or if they are instead due to loading history.…”

Section: Introductionmentioning

confidence: 99%

“…Since the work of Horton and Durham [15], it is a common experimental practice to place the elastic cylinder about a hard inner core that stabilizes its deformation during loading. In this paper, we consider the minimum energy of a compressed thin elastic cylinder fit about a hard cylindrical core (which we also refer to as the "mandrel").…”

Section: Introductionmentioning

confidence: 99%

“…This has been exploited in experiments that explore both the incipient buckling load [15], as well as buckled states deep into the bifurcation diagram [25]. This has been exploited in experiments that explore both the incipient buckling load [15], as well as buckled states deep into the bifurcation diagram [25].…”

Section: Introductionmentioning

confidence: 99%

“…The presence of the mandrel core in the cylinder-mandrel setup has a stabilizing effect. This has been exploited in experiments that explore both the incipient buckling load [15], as well as buckled states deep into the bifurcation diagram [25]. In practice, there is a gap between the cylinder and the core (we call this the "small mandrel" case).…”

Section: Introductionmentioning

confidence: 99%

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Axial Compression of a Thin Elastic Cylinder: Bounds on the Minimum Energy Scaling Law

Tobasco

2017

Comm Pure Appl Math

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We consider the axial compression of a thin elastic cylinder placed about a hard cylindrical core. Treating the core as an obstacle, we prove upper and lower bounds on the minimum energy of the cylinder that depend on its relative thickness and the magnitude of axial compression. We focus exclusively on the setting where the radius of the core is greater than or equal to the natural radius of the cylinder. We consider two cases: the "large mandrel" case, where the radius of the core exceeds that of the cylinder, and the "neutral mandrel" case, where the radii of the core and cylinder are the same. In the large mandrel case, our upper and lower bounds match in their scaling with respect to thickness, compression, and the magnitude of pre-strain induced by the core. We construct three types of axisymmetric wrinkling patterns whose energy scales as the minimum in different parameter regimes, corresponding to the presence of many wrinkles, few wrinkles, or no wrinkles at all. In the neutral mandrel case, our upper and lower bounds match in a certain regime in which the compression is small as compared to the thickness; in this regime, the minimum energy scales as that of the unbuckled configuration. We achieve these results for both the von Kármán-Donnell model and a geometrically nonlinear model of elasticity.

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Section: A Nonlinear Model Of Elasticitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%