Shell theories arising as low energy Γ-limit of 3d nonlinear elasticity
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 9 (2010) no. 2, p. 253-295

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
@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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 9},
     number = {2},
     year = {2010},
     pages = {253-295},
     zbl = {05791996},
     mrnumber = {2731157},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2010_5_9_2_253_0}
}
Shell theories arising as low energy $\mathbf{\Gamma }$-limit of 3d nonlinear elasticity. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 9 (2010) no. 2, pp. 253-295. http://www.numdam.org/item/ASNSP_2010_5_9_2_253_0/

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