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

Dominique Chapelle; Anca Ferent; Patrick Le Tallec^{[1]}

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

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

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topChapelle, 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

top- [1] K.J. Bathe, Finite Element Procedures. Prentice Hall (1996). Zbl0994.74001
- [2] K.J. Bathe, A. Iosilevich and D. Chapelle, An evaluation of the MITC shell elements. Comput. & Structures 75 (2000) 1–30.
- [3] M. Bischoff and E. Ramm, Shear deformable shell elements for large strains and rotations. Internat. J. Numer. Methods Engrg. 40 (1997) 4427–4449. Zbl0892.73054
- [4] M. Bischoff and E. Ramm, On the physical significance of higher order kinematic and static variables in a three-dimensional shell. Internat. J. Solids Structures 37 (2000) 6933–6960. Zbl1003.74045
- [5] F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag (1991). Zbl0788.73002MR1115205
- [6] D. Chapelle, Towards the convergence of 3D and shell finite elements? Proceedings: Enumath 2001 (in press). Zbl1179.74137
- [7] D. Chapelle and K.J. Bathe, Fundamental considerations for the finite element analysis of shell structures. Comput. & Structures 66 (1998) 19–36. Zbl0934.74073
- [8] D. Chapelle and K.J. Bathe, The mathematical shell model underlying general shell elements. Internat. J. Numer. Methods Engrg. 48 (2000) 289–313. Zbl0991.74067
- [9] D. Chapelle and K.J. Bathe, The Finite Element Analysis of Shells - Fundamentals. Springer-Verlag (2003). Zbl1103.74003MR2143259
- [10] D. Chapelle, A. Ferent and K.J. Bathe, 3D-shell finite elements and their underlying model. M3AS (submitted). Zbl1058.74078
- [11] P.G. Ciarlet, The Finite Element Methods for Elliptic Problems. North-Holland (1978). Zbl0999.65129
- [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] V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag (1986). Zbl0585.65077MR851383
- [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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