We discuss the limiting behavior (using the notion of -limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like , being the thickness of a shell, we derive a limiting theory which is a generalization of the von Kármán theory for plates.
@article{ASNSP_2010_5_9_2_253_0,
author = {Lewicka, Marta and Mora, Maria Giovanna and Pakzad, Mohammad Reza},
title = {Shell theories arising as low energy $\mathbf{\Gamma }$-limit of 3d nonlinear elasticity},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {253--295},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 9},
number = {2},
year = {2010},
mrnumber = {2731157},
zbl = {05791996},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2010_5_9_2_253_0/}
}
TY - JOUR
AU - Lewicka, Marta
AU - Mora, Maria Giovanna
AU - Pakzad, Mohammad Reza
TI - Shell theories arising as low energy $\mathbf{\Gamma }$-limit of 3d nonlinear elasticity
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2010
SP - 253
EP - 295
VL - 9
IS - 2
PB - Scuola Normale Superiore, Pisa
UR - http://www.numdam.org/item/ASNSP_2010_5_9_2_253_0/
LA - en
ID - ASNSP_2010_5_9_2_253_0
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%A Mora, Maria Giovanna
%A Pakzad, Mohammad Reza
%T Shell theories arising as low energy $\mathbf{\Gamma }$-limit of 3d nonlinear elasticity
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2010
%P 253-295
%V 9
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%I Scuola Normale Superiore, Pisa
%U http://www.numdam.org/item/ASNSP_2010_5_9_2_253_0/
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Lewicka, Marta; Mora, Maria Giovanna; Pakzad, Mohammad Reza. Shell theories arising as low energy $\mathbf{\Gamma }$-limit of 3d nonlinear elasticity. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 2, pp. 253-295. http://www.numdam.org/item/ASNSP_2010_5_9_2_253_0/
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