Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-30T20:16:34.703Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  15 March 2003

Dominique Chapelle ,
Anca Ferent  and
Patrick Le Tallec
Dominique Chapelle
Affiliation:
INRIA-Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France. [email protected].
Anca Ferent
Affiliation:
INRIA-Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France. [email protected].
Patrick Le Tallec
Affiliation:
École Polytechnique, 91128 Palaiseau Cedex, France.
Get access

Abstract

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

Keywords

Numerical lockingshell finite elementsmixed formulation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 1 , January 2003 , pp. 143 - 158
Copyright
© EDP Sciences, SMAI, 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

K.J. Bathe, Finite Element Procedures. Prentice Hall (1996).
K.J. Bathe, A. Iosilevich and D. Chapelle, An evaluation of the MITC shell elements. Comput. & Structures 75 (2000) 1-30.
Bischoff, M. and Ramm, E., Shear deformable shell elements for large strains and rotations. Internat. J. Numer. Methods Engrg. 40 (1997) 4427-4449. 3.0.CO;2-9>CrossRef
Bischoff, M. and Ramm, E., On the physical significance of higher order kinematic and static variables in a three-dimensional shell. Internat. J. Solids Structures 37 (2000) 6933-6960. CrossRef
F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag (1991).
D. Chapelle, Towards the convergence of 3D and shell finite elements? Proceedings: Enumath 2001 (in press).
D. Chapelle and K.J. Bathe, Fundamental considerations for the finite element analysis of shell structures. Comput. & Structures 66 (1998) 19-36.
Chapelle, D. and Bathe, K.J., The mathematical shell model underlying general shell elements. Internat. J. Numer. Methods Engrg. 48 (2000) 289-313. 3.0.CO;2-8>CrossRef
D. Chapelle and K.J. Bathe, The Finite Element Analysis of Shells - Fundamentals. Springer-Verlag (2003).
D. Chapelle, A. Ferent and K.J. Bathe, 3D-shell finite elements and their underlying model. M3AS (submitted).
P.G. Ciarlet, The Finite Element Methods for Elliptic Problems. North-Holland (1978).
El-Abbasi, N. and Meguid, S.A., A new shell element accounting for through-thickness deformation. Comput. Methods Appl. Mech. Engrg. 189 (2000) 841-862. CrossRef
V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag (1986).
Hauptmann, R., Schweizerhof, K. and Doll, S., Extension of the `solid-shell' concept for application to large elastic and large elastoplastic deformations. Internat. J. Numer. Methods Engrg. 49 (2000) 1121-1141. 3.0.CO;2-F>CrossRef