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.
Mots clés : numerical locking, shell finite elements, mixed formulation
@article{M2AN_2003__37_1_143_0,
author = {Chapelle, Dominique and Ferent, Anca and Tallec, Patrick Le},
title = {The treatment of {\textquotedblleft}pinching locking{\textquotedblright} in $3D$-shell elements},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {143--158},
publisher = {EDP-Sciences},
volume = {37},
number = {1},
year = {2003},
doi = {10.1051/m2an:2003015},
zbl = {1031.74046},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2003015/}
}
TY - JOUR AU - Chapelle, Dominique AU - Ferent, Anca AU - Tallec, Patrick Le TI - The treatment of “pinching locking” in $3D$-shell elements JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 143 EP - 158 VL - 37 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2003015/ DO - 10.1051/m2an:2003015 LA - en ID - M2AN_2003__37_1_143_0 ER -
%0 Journal Article %A Chapelle, Dominique %A Ferent, Anca %A Tallec, Patrick Le %T The treatment of “pinching locking” in $3D$-shell elements %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 143-158 %V 37 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2003015/ %R 10.1051/m2an:2003015 %G en %F M2AN_2003__37_1_143_0
Chapelle, Dominique; Ferent, Anca; Tallec, Patrick Le. The treatment of “pinching locking” in $3D$-shell elements. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 1, pp. 143-158. doi : 10.1051/m2an:2003015. http://archive.numdam.org/articles/10.1051/m2an:2003015/
[1] , Finite Element Procedures. Prentice Hall (1996).
[2] , and, An evaluation of the MITC shell elements. Comput. & Structures 75 (2000) 1-30.
[3] and, Shear deformable shell elements for large strains and rotations. Internat. J. Numer. Methods Engrg. 40 (1997) 4427-4449. | Zbl
[4] and, On the physical significance of higher order kinematic and static variables in a three-dimensional shell. Internat. J. Solids Structures 37 (2000) 6933-6960. | Zbl
[5] and, Mixed and Hybrid Finite Element Methods. Springer-Verlag (1991). | MR | Zbl
[6] , Towards the convergence of 3D and shell finite elements? Proceedings: Enumath 2001 (in press).
[7] and, Fundamental considerations for the finite element analysis of shell structures. Comput. & Structures 66 (1998) 19-36. | Zbl
[8] and, The mathematical shell model underlying general shell elements. Internat. J. Numer. Methods Engrg. 48 (2000) 289-313. | Zbl
[9] and, The Finite Element Analysis of Shells - Fundamentals. Springer-Verlag (2003). | MR | Zbl
[10] , and, 3D-shell finite elements and their underlying model. M3AS (submitted).
[11] , The Finite Element Methods for Elliptic Problems. North-Holland (1978). | Zbl
[12] and, A new shell element accounting for through-thickness deformation. Comput. Methods Appl. Mech. Engrg. 189 (2000) 841-862. | Zbl
[13] and, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag (1986). | MR | Zbl
[14] , and, Extension of the ‘solid-shell' concept for application to large elastic and large elastoplastic deformations. Internat. J. Numer. Methods Engrg. 49 (2000) 1121-1141. | Zbl
Cité par Sources :
