Membrane locking in the finite element computation of very thin elastic shells

Choi, Daniel S.; Palma, Francisco; Sanchez‐Palencia, E.; Vilariño, M. A.

doi:10.1051/m2an/1998320201311

Cited by 24 publications

(13 citation statements)

References 10 publications

(14 reference statements)

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“…The specific difficulty with shells is that, unlike for beams or plates, the pathological situation expressed by (3.40) is the common rule, as illustrated in the following result, for which we also give the proof because it is simple and illuminating as to how the geometry influences the asymptotic properties (cf. also Choï, Palma, Sanchez-Palencia and Vilarino (1998) and Sanchez-Hubert and Sanchez-Palencia (1997) for other results concerning (3.40)).…”

Section: Asymptotic Reliability Of Shell Finite Elementsmentioning

confidence: 68%

Some new results and current challenges in the finite element analysis of shells

Chapelle

2001

Acta Numerica

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International audienceThis article, a companion to the article by Philippe G. Ciarlet on the mathematical modelling of shells also in this issue of Acta Numerica, focuses on numerical issues raised by the analysis of shells. Finite element procedures are widely used in engineering practice to analyse the behaviour of shell structures. However, the concept of 'shell finite element' is still somewhat fuzzy, as it may correspond to very different ideas and techniques in various actual implementations. In particular, a significant distinction can be made between shell elements that are obtained via the discretization of shell models, and shell elements - such as the general shell elements - derived from 3D formulations using some kinematic assumptions, without the use of any shell theory. Our first objective in this paper is to give a unified perspective of these two families of shell elements. This is expected to be very useful as it paves the way for further thorough mathematical analyses of shell elements. A particularly important motivation for this is the understanding and treatment of the deficiencies associated with the analysis of thin shells (among which is the locking phenomenon). We then survey these deficiencies, in the framework of the asymptotic behaviour of shell models. We conclude the article by giving some detailed guidelines to numerically assess the performance of shell finite elements when faced with these pathological phenomena, which is essential for the design of improved procedures

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Section: Asymptotic Reliability Of Shell Finite Elementsmentioning

confidence: 68%

Some new results and current challenges in the finite element analysis of shells

Chapelle

2001

Acta Numerica

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“…We may refer to [8,10] for these features. As a result, the situation in the present case, of inhibited shells, is analogous to that of non-inhibited ones where the non-uniformity of the convergence is a consequence of the phenomenon of locking which appears for any conformal approximation with piecewise polynomial finite elements [3].…”

Section: Introductionmentioning

confidence: 83%

A model problem for boundary layers of thin elastic shells

Karamian¹,

Sanchez-Hubert

Palencia³

2000

ESAIM: M2AN

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Abstract. We consider a model problem (with constant coefficients and simplified geometry) for the boundary layer phenomena which appear in thin shell theory as the relative thickness ε of the shell tends to zero. For ε = 0 our problem is parabolic, then it is a model of developpable surfaces. Boundary layers along and across the characteristic have very different structure. It also appears internal layers associated with propagations of singularities along the characteristics. The special structure of the limit problem often implies solutions which exhibit distributional singularities along the characteristics. The corresponding layers for small ε have a very large intensity. Layers along the characteristics have a special structure involving subspaces; the corresponding Lagrange multipliers are exhibited. Numerical experiments show the advantage of adaptive meshes in these problems.Résumé. Nous considérons un problème modèle (avec coefficients constants et géométrie simplifiée) pour l'étude des couches limites qui apparaissent en théorie des coquesélastiques minces lorsque l'épaisseur relative ε tend vers zéro. Pour ε = 0, notre problème est parabolique, c'est donc un problème modèle pour les surfaces développables. Les couches limites le long et transversalement aux caractéristiques ont des structures très différentes. Il apparaît aussi des couches internes associéesà la propagation des singularités le long des caractéristiques. Dans certains cas,à cause de sa structure particulière, le problème limite a des solutions qui présentent des singularités faisant intervenir des distributions le long des caractéristiques. Pour ε petit, les couches correspondantes sont de très grande intensité. Les couches le long des caractéristiques ont une structure particulière incluant des sousespaces ; les multiplicateurs de Lagrange correspondants sont mis enévidence. Les calculs numériques montrent l'avantage de l'utilisation de maillages adaptés dans ce type de problèmes.Mathematics Subject Classification. 73K15, 35B25.

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“…The shear locking, induced by the Kirchhoff constraint in the limit case, has been extensively discussed and a variety of shear locking free plate and shell elements have been proposed. For membrane locking, also called inextensional locking, where the (curved) elements fail to represent pure bending, only little analysis has been done [1,23,19,14] and mostly reduced integration schemes are used in practice [43,36,37]. There, the membrane constraints are weakened due to underintegration.…”

Section: Introductionmentioning

confidence: 99%

Avoiding Membrane Locking with Regge Interpolation

Neunteufel,

Schöberl

2019

Preprint

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In this paper a novel method to overcome membrane locking of thin shells is presented. An interpolation operator into the so-called Regge finite element space is inserted in the membrane energy term to weaken the implicitly given kernel constraints. Due to the tangential-tangential continuity of Regge elements, the number of constraints is asymptotically halved on triangular meshes compared to reduced integration techniques. Provided the interpolant, this approach can be incorporated easily to any shell element. The performance of the proposed method is demonstrated by means of several benchmark examples.

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Membrane locking in the finite element computation of very thin elastic shells

Cited by 24 publications

References 10 publications

Some new results and current challenges in the finite element analysis of shells

Some new results and current challenges in the finite element analysis of shells

A model problem for boundary layers of thin elastic shells

Avoiding Membrane Locking with Regge Interpolation

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