The treatment of “pinching locking” in $3D$-shell elements
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 1, p. 143-158

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 : https://doi.org/10.1051/m2an:2003015
Classification:  65N30,  74K25
Keywords: 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 pinching locking'' in $3D$-shell elements},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {37},
number = {1},
year = {2003},
pages = {143-158},
doi = {10.1051/m2an:2003015},
zbl = {1031.74046},
language = {en},
url = {http://www.numdam.org/item/M2AN_2003__37_1_143_0}
}
Chapelle, Dominique; Ferent, Anca; Tallec, Patrick Le. The treatment of “pinching locking” in $3D$-shell elements. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 1, pp. 143-158. doi : 10.1051/m2an:2003015. http://www.numdam.org/item/M2AN_2003__37_1_143_0/

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