The treatment of “pinching locking” in 3D-shell elements
Chapelle, Dominique ; Ferent, Anca ; Tallec, Patrick Le1
1 Ecole Polytechnique, 91128 Palaiseau Cedex, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 1, pp. 143-158.

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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.

DOI : 10.1051/m2an:2003015
Classification : 65N30, 74K25
Mots-clés : numerical locking, shell finite elements, mixed formulation

Chapelle, Dominique  ; Ferent, Anca  ; Tallec, Patrick Le 1

1 Ecole Polytechnique, 91128 Palaiseau Cedex, France. 
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     title = {The treatment of {\textquotedblleft}pinching locking{\textquotedblright} in $3D$-shell elements},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {143--158},
     publisher = {EDP-Sciences},
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Chapelle, Dominique; Ferent, Anca; Tallec, Patrick Le. The treatment of “pinching locking” in $3D$-shell elements. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 1, pp. 143-158. doi : 10.1051/m2an:2003015. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003015/

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