The treatment of “pinching locking” in 3 D -shell elements

Dominique Chapelle; Anca Ferent; Patrick Le Tallec[1]

  • [1] Ecole Polytechnique, 91128 Palaiseau Cedex, France.

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

  • Volume: 37, Issue: 1, page 143-158
  • ISSN: 0764-583X

Abstract

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We consider a family of shell finite elements with quadratic displacements across the thickness. These elements are very attractive, but compared to standard general shell elements they face another source of numerical locking in addition to shear and membrane locking. This additional locking phenomenon – that we call “pinching locking” – is the subject of this paper and we analyse a numerical strategy designed to overcome this difficulty. Using a model problem in which only this specific source of locking is present, we are able to obtain error estimates independent of the thickness parameter, which shows that pinching locking is effectively treated. This is also confirmed by some numerical experiments of which we give an account.

How to cite

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Chapelle, Dominique, Ferent, Anca, and Tallec, Patrick Le. "The treatment of “pinching locking” in $3D$-shell elements." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.1 (2003): 143-158. <http://eudml.org/doc/245479>.

@article{Chapelle2003,
abstract = {We consider a family of shell finite elements with quadratic displacements across the thickness. These elements are very attractive, but compared to standard general shell elements they face another source of numerical locking in addition to shear and membrane locking. This additional locking phenomenon – that we call “pinching locking” – is the subject of this paper and we analyse a numerical strategy designed to overcome this difficulty. Using a model problem in which only this specific source of locking is present, we are able to obtain error estimates independent of the thickness parameter, which shows that pinching locking is effectively treated. This is also confirmed by some numerical experiments of which we give an account.},
affiliation = {Ecole Polytechnique, 91128 Palaiseau Cedex, France.},
author = {Chapelle, Dominique, Ferent, Anca, Tallec, Patrick Le},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {numerical locking; shell finite elements; mixed formulation; pinching locking; quadratic displacements; thickness parameter; error estimates},
language = {eng},
number = {1},
pages = {143-158},
publisher = {EDP-Sciences},
title = {The treatment of “pinching locking” in $3D$-shell elements},
url = {http://eudml.org/doc/245479},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Chapelle, Dominique
AU - Ferent, Anca
AU - Tallec, Patrick Le
TI - The treatment of “pinching locking” in $3D$-shell elements
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 1
SP - 143
EP - 158
AB - We consider a family of shell finite elements with quadratic displacements across the thickness. These elements are very attractive, but compared to standard general shell elements they face another source of numerical locking in addition to shear and membrane locking. This additional locking phenomenon – that we call “pinching locking” – is the subject of this paper and we analyse a numerical strategy designed to overcome this difficulty. Using a model problem in which only this specific source of locking is present, we are able to obtain error estimates independent of the thickness parameter, which shows that pinching locking is effectively treated. This is also confirmed by some numerical experiments of which we give an account.
LA - eng
KW - numerical locking; shell finite elements; mixed formulation; pinching locking; quadratic displacements; thickness parameter; error estimates
UR - http://eudml.org/doc/245479
ER -

References

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  9. [9] D. Chapelle and K.J. Bathe, The Finite Element Analysis of Shells - Fundamentals. Springer-Verlag (2003). Zbl1103.74003MR2143259
  10. [10] D. Chapelle, A. Ferent and K.J. Bathe, 3D-shell finite elements and their underlying model. M3AS (submitted). Zbl1058.74078
  11. [11] P.G. Ciarlet, The Finite Element Methods for Elliptic Problems. North-Holland (1978). Zbl0999.65129
  12. [12] N. El-Abbasi and S.A. Meguid, A new shell element accounting for through-thickness deformation. Comput. Methods Appl. Mech. Engrg. 189 (2000) 841–862. Zbl1011.74068
  13. [13] V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag (1986). Zbl0585.65077MR851383
  14. [14] R. Hauptmann, K. Schweizerhof and S. Doll, Extension of the ‘solid-shell’ concept for application to large elastic and large elastoplastic deformations. Internat. J. Numer. Methods Engrg. 49 (2000) 1121–1141. Zbl1048.74041

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