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

Dominique Chapelle; Anca Ferent; Patrick Le Tallec

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topChapelle, Dominique, Ferent, Anca, and Le Tallec, Patrick. "The treatment of “pinching locking” in 3D-shell elements." ESAIM: Mathematical Modelling and Numerical Analysis 37.1 (2010): 143-158. <http://eudml.org/doc/194150>.

@article{Chapelle2010,

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.
},

author = {Chapelle, Dominique, Ferent, Anca, Le Tallec, Patrick},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Numerical locking; shell finite elements; mixed formulation.; pinching locking; mixed formulation; quadratic displacements; thickness parameter; error estimates},

language = {eng},

month = {3},

number = {1},

pages = {143-158},

publisher = {EDP Sciences},

title = {The treatment of “pinching locking” in 3D-shell elements},

url = {http://eudml.org/doc/194150},

volume = {37},

year = {2010},

}

TY - JOUR

AU - Chapelle, Dominique

AU - Ferent, Anca

AU - Le Tallec, Patrick

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

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; mixed formulation; quadratic displacements; thickness parameter; error estimates

UR - http://eudml.org/doc/194150

ER -

## References

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