On the solution of mode jumping phenomena in thin-walled shell structures

Riks, E.; Rankin, C.; Brogan, F. A.

doi:10.1016/0045-7825(95)00970-1

Cited by 110 publications

(82 citation statements)

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“…This is probably the best estimate of the true nonlinear response. It predicts that the cylinder undergoes a series of post-bucking bifurcations into modes with successively smaller numbers of circumferential waves, a mechanism that has been studied extensively elsewhere [40,46,48,49,50,52,54] and is not the focus of the present discussion. The sharp reversal in the slope of the load path at every bifurcation indicates that it is likely to be difficult to trace the unstable post-buckling path using a path-following method [48,53].…”

Section: Withmentioning

confidence: 99%

“…It predicts that the cylinder undergoes a series of post-bucking bifurcations into modes with successively smaller numbers of circumferential waves, a mechanism that has been studied extensively elsewhere [40,46,48,49,50,52,54] and is not the focus of the present discussion. The sharp reversal in the slope of the load path at every bifurcation indicates that it is likely to be difficult to trace the unstable post-buckling path using a path-following method [48,53]. Such algorithms often struggle to distinguish between closely-adjacent equilibrium paths and the analysis may either fail to converge, become stuck in an infinite loop that jumps back and forth between two paths or begin to trace a spurious load path due to accumulated round-off errors (especially deep in the post-buckling range after several thousand increments [42]).…”

Section: Withmentioning

confidence: 99%

“…Such a cylinder exhibits a discontinuous load path due to sudden bifurcation at buckling [40] which must be transformed into a smooth snapthrough response if it is to be followed by path-tracing methods. This is usually achieved by introducing a small mesh perturbation in the form of an eigenmode [48,49,50], though load-disturbance methods are also possible [51,52]. Using software such as ABAQUS or ANSYS, it is relatively simple to import an eigenmode from a linear bifurcation analysis as an initial imperfection, but only if the same mesh is retained.…”

Section: Verification Of Helical Meshing -Cylinder Under Axial Comprementioning

confidence: 99%

“…It is clear that even advanced commercial solvers currently struggle to trace such complex mode-jumping in thinwalled cylinders reliably using static analyses. Specialised methods for accurate detection of bifurcations and post-bifurcation paths have been devised in terms of hybrid static-dynamic procedures [48], catastrophe theory [63] and enhanced pathtracing using higher order derivatives of the tangent stiffness matrix or fold lines [64,65,66,67], amongst others, and have made much progress in overcoming this difficulty. Unfortunately, these highly specialised and complex procedures currently remain confined to the realm of personal custom-written finite element codes and are A damped static analysis using a 'rectangular' mesh (α = 0°) predicts that the cylinder will jump onto a stable equilibrium path (marked with an 'A'; see also …”

Section: Withmentioning

confidence: 99%

“…To characterise the mesh perturbation parametrically, the circumferential form of the eigenmode was expressed as a sine function while the meridional form was parametrised as a piecewise-continuous spline function S(z) using the Matlab Curve Fitting toolbox, though a Fourier series characterisation could also be used. For a 'rectangular' mesh, the nodal coordinates were generated directly using Eqs 3 to 5 assuming: It is well known that post-buckling deformations and bifurcations of this structure are strongly dependent on the mode into which the cylinder was initially perturbed [40,42,46,48,49,50,52,53]. However, the exact form of the eigenmode perturbation shown in Fig.…”

Section: Verification Of Helical Meshing -Cylinder Under Axial Comprementioning

confidence: 99%

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Modelling and behaviour of cylindrical shell structures with helical features

Sadowski

Rotter

2014

Computers & Structures

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Spiral welding or bonding is a particularly efficient and cost-effective method of constructing continuous tubes. However the understanding of the mechanics of such structures is not yet well developed. This is in no small part due to the difficulties involved in their computational analysis.Cylindrical shells are traditionally modelled using rectangular finite elements oriented parallel to the meridional and circumferential axes. However, spiral features are particularly challenging to model because such features are not orthogonal to the axes of the cylinder. Commercial finite element pre-processors often struggle to mesh these with anything other than a free triangulation. A superior mesh would consist of wellconditioned rectangular elements oriented orthogonally with respect to the axes of the helix, termed a 'helical mesh', but this requires significant programming effort. A helical mesh is particularly important if features of the shell such as geometric imperfections, residual stresses, weld material and heat affected zones, and bonding in systems using adhesives are required to follow the helical form. Helically wound structural forms are widely used in different applications that demand continuous cylindrical forms. The most common uses in structural engineering are in spiral wound tubes, piles, chimneys and pipelines. This paper describes a powerful computational procedure developed by the authors to generate high quality helical meshes. Special emphasis is placed on the modelling of geometric deviations defined relative to the helix, appropriate for the analysis of spiral welded and stiffened tubes. The effect of helical meshing is illustrated using benchmark examples of perfect and imperfect cylinders under axial compression.Published in: Computers and Structures, 133C,[90][91][92][93][94][95][96][97][98][99][100][101][102]

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Section: Withmentioning

confidence: 99%

Section: Withmentioning

confidence: 99%

Section: Verification Of Helical Meshing -Cylinder Under Axial Comprementioning

confidence: 99%

Section: Withmentioning

confidence: 99%

Section: Verification Of Helical Meshing -Cylinder Under Axial Comprementioning

confidence: 99%

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Modelling and behaviour of cylindrical shell structures with helical features

Sadowski

Rotter

2014

Computers & Structures

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Enhanced solution control for physically and geometrically non-linear problems. Part I?the subplane control approach

Geers

1999

Int. J. Numer. Meth. Engng.

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SUMMARYGeometrically or physically non-linear problems are often characterized by the presence of critical points with snapping behaviour in the structural response. These structural or material instabilities usually lead to ine ciency of standard numerical solution techniques. Special numerical procedures are therefore required to pass critical points. This paper presents a solution technique which is based on a constraint equation that is deÿned on a subplane of the degrees-of-freedom (dof 's) hyperspace or a hyperspace constructed from speciÿc functions of the degrees-of-freedom. This uniÿed approach includes many existing methods which have been proposed by various authors. The entire computational process is driven from only one control function which is either a function of a number of degrees-of-freedom (local subplane method) or a single automatically weighted function that incorporates all dof 's directly or indirectly (weighted subplane method). The control function is generally computed in many points of the structure, which can be related to the ÿnite element discretization. Each point corresponds to one subplane. In the local subplane method, the subplane with the control function that drives the load adaptation is selected automatically during the deformation process. Part I of this two-part series of papers fully elaborates the proposed solution strategy, including a fully automatic load control, i.e. load estimation, adaptation and correction. Part II presents a comparative analysis in which several choices for the control function in the subplane method are confronted with classical update algorithms. The comparison is carried out by means of a number of geometrically and physically non-linear examples. General conclusions are drawn with respect to the e ciency and applicability of the subplane solution control method for the numerical analysis of engineering problems.

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Buckling

Riks¹

2004

Encyclopedia of Computational Mechanics

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Although the first known solution of a buckling problem was given by the outstanding Swiss ‘natural philosopher’ Leonhard Euler (1744), buckling theory as an engineering subject is an outgrowth of a development that was established during the last century. The overview of the present knowledge regarding the computational analysis of buckling problems is here given in the context of the theory's most important historical developments.

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On the solution of mode jumping phenomena in thin-walled shell structures

Cited by 110 publications

References 11 publications

Modelling and behaviour of cylindrical shell structures with helical features

Modelling and behaviour of cylindrical shell structures with helical features

Enhanced solution control for physically and geometrically non-linear problems. Part I?the subplane control approach

Buckling

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