Edge-wave buckling of rolled elastic strips: asymptotic results

Coman, Ciprian D.

doi:10.1007/s00707-009-0227-7

Cited by 13 publications

(5 citation statements)

References 19 publications

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“…It is not difficult to see that such additional terms must have the structure already recorded in (20) but, unfortunately, the answer to the above question is negative -simply because a closed-form solution of (21) is not available. The same hurdle was encountered in a couple of recent works involving residual stresses (Coman, , 2010, where further details about the origin of this difficulty may be found. The absence of higher-order terms in (22) places some limitation on its range of accuracy, mostly because the original eigenproblems (9) and (10) depend on ' but our results do not.…”

Section: Approximations For L; ' ¼ Oð1þ and K )mentioning

confidence: 79%

Global asymptotic approximations for wrinkling of polar orthotropic annular plates in tension

Coman

2010

International Journal of Solids and Structures

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a b s t r a c tThe role of polar orthotropy is investigated in relation to an elastic wrinkling problem for annular thin plates in tension. An appealing feature of this generalised constitutive framework is the possibility of allowing the radial and circumferential directions to have different bending stiffnesses. By suitably rescaling the buckling equation, three main parameters are identified as being responsible for the behaviour of the linear wrinkling mechanism. We conduct a number of singular-perturbation analyses in order to capture the dependence of the critical loads and mode numbers on the various physical parameters that enter in the description of the problem.

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Section: Approximations For L; ' ¼ Oð1þ and K )mentioning

confidence: 79%

Global asymptotic approximations for wrinkling of polar orthotropic annular plates in tension

Coman

2010

International Journal of Solids and Structures

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“…In general, there is no quarantee that such particular solutions will represent minimum energy configurations for the buckled web (a moot point in the work of our predecessors). We have carried out additional numerical work in which we explored the more general expression w(x, y) = f (y) sin(mπx), where m ∈ N represents the so-called axial mode number, a quantity that has to be determined as part of the solution as explained, for instance, in [5,14,29]. For the physical/geometrical parameter values used by Banichuk et al [10,11], the critical mode number is indeed m = 1.…”

Section: Discussionmentioning

confidence: 99%

“…Comparison of (2.5) with other classical buckling equations in related scenarios (e.g., [5,6]) indicates that the axial translation acts only to modify the effective tension in the plate. In this sense, identifying the critical speed at which the plate becomes unstable is entirely analogous to a study of the classical plate buckling problem.…”

Section: The Key Equationsmentioning

confidence: 93%

“…There are several possible factors associated with the compressive forces mentioned above. For example, in metal forming applications residual stresses are known to have a detrimental effect that could be responsible for the buckling instabilities frequently encountered in rolling and levelling processes (e.g., see [5,6,7] and the references therein). The misalignment of the rollers that support the moving web (and over which it passes) can also play a destabilising role.…”

Section: Introductionmentioning

confidence: 99%

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Divergence instabilities of nonuniformly prestressed travelling webs

Coman

2024

J. Mech. Mater. Struct.

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The phenomenon of edge-buckling in an axially moving stretched thin elastic web is described as a non-standard singularly-perturbed bifurcation problem, which is then explored through the application of matched asymptotic techniques. Previous numerical work recently reported in the literature is re-evaluated in this context by approaching it through the lens of asymptotic simplifications. This allows us to identify two distinct regimes characterised by qualitative differences in the corresponding eigen-deformations; some simple approximate formulae for the critical eigenvalues are also proposed. The obtained analytical results capture the intricate relationship between the critical speeds, the background tension, and other relevant physical and geometric parameters that feature in the mathematical model.

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“…Mathieu et al [5] made an in-depth research on the deformation of strip shape and its generation mechanism using finite element (FE) simulation. A number of works [6][7][8][9][10] have been conducted on strip shape defects in detail such as edge wave and central buckling. Peng et al [11] introduced the mechanism of shape modeling and design strategy of shape setup model (SSM).…”

Section: Introductionmentioning

confidence: 99%

A Study on Potential Strip Shape Control of High‐Strength Steel during Hot Pinch Rolling Process

Kong

Zhao

Cao

et al. 2020

steel research int.

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Hot‐rolled high‐strength steel (HSS) strips always present side‐camber after they are cut into subsections along the rolling direction. To deal with the potential strip shape defect of hot‐rolled HSS, the nonlinear finite element (FE) software is applied to establish a 3D model of pinch roll and strips to simulate the pinch rolling process before the hot rolling coiler. The effects of temperature distribution, roll wear, friction coefficient, initial strip flatness defects, and tension on the strip longitudinal extension distribution are studied along the width direction. The results indicate that the pinch roll wear presents a great influence on both the tendency and quantitative value of the strip longitudinal extension distribution. The maximum unevenness value is 178%, and the maximum differences of longitudinal strain between the center and edge of the strips reach to 51.43%. A newly pinch roll contour is proposed to improve the potential strip shape defects. After the industrial application, the average pinch roll wear thickness decreases from 180 to 120 μm. The hot rolled strips are cut into substrips and the maximum side‐camber value decreases from 12 to 3 mm, which meets the requirement from the auto part manufacturers.

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Edge-wave buckling of rolled elastic strips: asymptotic results

Cited by 13 publications

References 19 publications

Global asymptotic approximations for wrinkling of polar orthotropic annular plates in tension

Global asymptotic approximations for wrinkling of polar orthotropic annular plates in tension

Divergence instabilities of nonuniformly prestressed travelling webs

A Study on Potential Strip Shape Control of High‐Strength Steel during Hot Pinch Rolling Process

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