Postbuckling equilibrium of axially compressed circular cylindrical shells.

Hoff, N. J.; Madsen, Wayne A.; Mayers, J.

doi:10.2514/3.3395

Cited by 53 publications

(20 citation statements)

References 6 publications

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“…Under increasing end-shortening, the response restabilizes, undergoes a mode jump to 10 circumferential waves, restabilizes and jumps to 9 waves and so on, with each successive curve reaching a minimum at a lower load than before. This is strongly reminiscent of the argument of Hoff et al [19], who effectively destroyed the search for the minimum possible post-buckling load by arguing that in the limit it drops to zero. Numerical solutions of the von Kármán-Donnell equations, showing the resulting tangle of possible equilibrium paths involving different circumferential wavenumbers, are given here in Figure 14.…”

Section: The Axially-compressed Cylindrical Shellmentioning

confidence: 91%

“…The Koiter circle waves are known to interact in classical two or three mode symmetry-breaking combinations [17,24], each linked to a specific circumferential wavenumber n. Experiments [18,25] show clearly that the cylinder length affects the selection of circumferential wavenumber and hence the first minimum load. The linear eigenvalue information leading to (19) offers no direct means of determining which value of n would be preferred. However, the following mechanism for the selection of n, prompted by the phenomenological difference between localized and distributed buckling that is the theme of this paper, has recently been proposed [23].…”

Section: Koiter Circle Prediction For Circumferential Wavenumber Nmentioning

confidence: 98%

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Buckling in Space and Time

Hunt

2006

Nonlinear Dyn

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A personal overview of the buckling process is given, based on more than 30 years research experience. A fundamental distinction is drawn between structures that tend to distribute their pattern of buckling over the entire available length, and those that favour limiting it to a localized portion. Difficulties are compounded by the fact that localized solutions typically are shadowed by distributed counterparts. The difference is found to depend primarily on the stability of the system at the point of buckling.When an unstable localized form shows a tendency to restabilize, a pattern known as cellular buckling can develop, taking place sequentially in both space and time. The paper focuses particularly on the buckling of the axially-compressed cylindrical shell, and shows how the circumferential periodicity coupled with axial localization has special but hidden characteristics. In particular, the circumferential wavenumber is picked at an early stage of buckling and remains locked, while localization in the axial sense permits extensive change to the post-buckling shape.

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Section: The Axially-compressed Cylindrical Shellmentioning

confidence: 91%

Section: Koiter Circle Prediction For Circumferential Wavenumber Nmentioning

confidence: 98%

Buckling in Space and Time

Hunt

2006

Nonlinear Dyn

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“…Kempner (1954) [6], for example, re®ned the Ka Ârma Ân±Tsien theory for postbuckling analysis and Almroth (1963) [7] successively increased the number of free constants involved in the displacement functions for the total potential energy until no signi®cant change occurred in the magnitude of the minimum postbuckling load of a cylinder of suf®cient length. Hoff et al (1966) [8] also extended earlier numerical solutions of the Ka Ârma Ân± Donnell large-displacement equations by considering the larger number of terms in the double Fourier series to accurately represent the radial displacement ®eld of the buckled con®guration (Yoshimura buckle pattern [5] used). An increase in the number of trigonometric series lowered signi®cantly the equilibrium load-shortening curve below that presented by Almroth [7].…”

Section: Introductionmentioning

confidence: 97%

Static path jumping to attain postbuckling equilibria of a compressed circular cylinder

Fujii

Noguchi

Ramm

2000

Computational Mechanics

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The postbuckling behavior of an axially compressed circular cylindrical shell is exceedingly complicated due to an in®nite number of closely spaced postbuckling branches and bifurcation points. The minimum strength existing in the deep bottom of the postbuckling region may serve as a design limit. The primary concern in this present paper is to compute this stable postbuckling equilibrium solution by two different approaches: One is to repeat the procedures of tracing unstable branches, pinpointing bifurcation points and branch-switching in order to carefully approach to the target. The other is to trigger a static jump to the target by two-parametric loading. As a numerical example, a perfect circular cylindrical panel is analyzed to show that a direct jump from the undeformed state to a stable postbuckling solution is possible with a proper choice of the load perturbation.

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“…[ 325] seem to indicate that with increasing shortening of the cylinder the postbuckling load asymptotically approaches zero or, if more accurate basic equations had been used, a value that is dependent cn the radius-to-thickness ratio of the shell but which for practical dimensions is very small. As a result of these studies it has been determined that the mini- Some of the papers [ 326,327] retain the assumption common to most previous shell-buckling analyses that the prebuckling conditions can Le sufficiently accurately described by use of a nonlinear membrane solution.…”

mentioning

confidence: 99%