Geodesic
Shell theories arising as low energy Γ-limit of 3d nonlinear elasticity
Lewicka, Marta1  ; Mora, Maria Giovanna2 ; Pakzad, Mohammad Reza3
1 University of Minnesota, Department of Mathematics, 206 Church St. S.E.,Minneapolis, MN 55455, USA
2 Scuola Internazionale Superiore di Studi Avanzati, via Beirut 2-4, 34014 Trieste, Italia
3 University of Pittsburgh, Department of Mathematics, 139 University Place, Pittsburgh, PA 15260, USA
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 2, pp. 253-295

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We discuss the limiting behavior (using the notion of Γ-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 h 4 , h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Kármán theory for plates.

Classification : 74K20, 74B20

Lewicka, Marta 1 ; Mora, Maria Giovanna 2 ; Pakzad, Mohammad Reza 3

1 University of Minnesota, Department of Mathematics, 206 Church St. S.E.,Minneapolis, MN 55455, USA
2 Scuola Internazionale Superiore di Studi Avanzati, via Beirut 2-4, 34014 Trieste, Italia
3 University of Pittsburgh, Department of Mathematics, 139 University Place, Pittsburgh, PA 15260, USA 
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     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},
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     zbl = {05791996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/item/ASNSP_2010_5_9_2_253_0/