# A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry

ESAIM: Control, Optimisation and Calculus of Variations (2011)

- Volume: 17, Issue: 2, page 493-505
- ISSN: 1292-8119

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topLewicka, Marta. "A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry." ESAIM: Control, Optimisation and Calculus of Variations 17.2 (2011): 493-505. <http://eudml.org/doc/276328>.

@article{Lewicka2011,

abstract = {
We prove that the critical points of the 3d nonlinear elasticity functional
on shells of small thickness h and around the mid-surface S of
arbitrary geometry, converge as h → 0
to the critical points of the von
Kármán functional on S, recently proposed in [Lewicka et al.,
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (to appear)].
This result extends the statement in [Müller and Pakzad, Comm. Part. Differ.
Equ.33 (2008) 1018–1032], derived for the case
of plates when $S\subset\mathbb\{R\}^2$.
The convergence holds provided the elastic energies of the 3d deformations scale
like h4 and the external body forces scale like h3.
},

author = {Lewicka, Marta},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Shell theories; nonlinear elasticity; Gamma convergence; calculus of
variations; shell theories; gamma convergence; calculus of variations},

language = {eng},

month = {5},

number = {2},

pages = {493-505},

publisher = {EDP Sciences},

title = {A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry},

url = {http://eudml.org/doc/276328},

volume = {17},

year = {2011},

}

TY - JOUR

AU - Lewicka, Marta

TI - A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2011/5//

PB - EDP Sciences

VL - 17

IS - 2

SP - 493

EP - 505

AB -
We prove that the critical points of the 3d nonlinear elasticity functional
on shells of small thickness h and around the mid-surface S of
arbitrary geometry, converge as h → 0
to the critical points of the von
Kármán functional on S, recently proposed in [Lewicka et al.,
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (to appear)].
This result extends the statement in [Müller and Pakzad, Comm. Part. Differ.
Equ.33 (2008) 1018–1032], derived for the case
of plates when $S\subset\mathbb{R}^2$.
The convergence holds provided the elastic energies of the 3d deformations scale
like h4 and the external body forces scale like h3.

LA - eng

KW - Shell theories; nonlinear elasticity; Gamma convergence; calculus of
variations; shell theories; gamma convergence; calculus of variations

UR - http://eudml.org/doc/276328

ER -

## References

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