October  2019, 12(6): 1535-1545. doi: 10.3934/dcdss.2019106

Existence theorem for a first-order Koiter nonlinear shell model

Département de Mathématiques, IRIMAS, Université de Haute-Alsace, 6 rue des Frères Lumière, 68093 Mulhouse Cedex, France

Received  January 2018 Revised  May 2018 Published  November 2018

We prove the existence of a minimizer for a nonlinearly elastic shell model which coincides to within the first order with respect to small thickness and change of metric and curvature energies with the Koiter nonlinear shell model.

Citation: Sylvia Anicic. Existence theorem for a first-order Koiter nonlinear shell model. Discrete & Continuous Dynamical Systems - S, 2019, 12 (6) : 1535-1545. doi: 10.3934/dcdss.2019106
References:
[1]

S. Anicic, Polyconvexity and existence theorem for nonlinearly elastic shells, J. Elasticity, 132 (2018), 161-173.  doi: 10.1007/s10659-017-9664-z.  Google Scholar

[2]

S. Anicic, A shell model allowing folds, in Numerical Mathematics and Advanced Applications, Springer Italia, (2003), 317-326.  Google Scholar

[3]

S. Anicic, From the Exact Kirchhoff-Love Shell Model to a Thin Shell Model and a Folded Shell Model, Ph.D thesis, Joseph Fourier University, France, 2001. Google Scholar

[4]

R. BunoiuPh.-G. Ciarlet and C. Mardare, Existence theorem for a nonlinear elliptic shell model, J. Elliptic Parabol. Equ., 1 (2015), 31-48.  doi: 10.1007/BF03377366.  Google Scholar

[5]

Ph.-G. Ciarlet and C. Mardare, A nonlinear shell model of Koiter's type, C. R. Math. Acad. Sci. Paris, 356 (2018), 227-234.  doi: 10.1016/j.crma.2017.12.005.  Google Scholar

[6]

Ph.-G. Ciarlet and C. Mardare, A mathematical model of Koiter's type for a nonlinearly elastic "almost spherical" shell, C. R. Math. Acad. Sci. Paris, 354 (2016), 1241-1247.  doi: 10.1016/j.crma.2016.10.011.  Google Scholar

[7]

W. T. Koiter On the nonlinear theory of thin elastic shells. Ⅰ, Ⅱ, Ⅲ, Nederl. Akad. Wetensch. Proc. Ser. B, 69 (1966), 1-17, 18-32, 33-54.  Google Scholar

show all references

References:
[1]

S. Anicic, Polyconvexity and existence theorem for nonlinearly elastic shells, J. Elasticity, 132 (2018), 161-173.  doi: 10.1007/s10659-017-9664-z.  Google Scholar

[2]

S. Anicic, A shell model allowing folds, in Numerical Mathematics and Advanced Applications, Springer Italia, (2003), 317-326.  Google Scholar

[3]

S. Anicic, From the Exact Kirchhoff-Love Shell Model to a Thin Shell Model and a Folded Shell Model, Ph.D thesis, Joseph Fourier University, France, 2001. Google Scholar

[4]

R. BunoiuPh.-G. Ciarlet and C. Mardare, Existence theorem for a nonlinear elliptic shell model, J. Elliptic Parabol. Equ., 1 (2015), 31-48.  doi: 10.1007/BF03377366.  Google Scholar

[5]

Ph.-G. Ciarlet and C. Mardare, A nonlinear shell model of Koiter's type, C. R. Math. Acad. Sci. Paris, 356 (2018), 227-234.  doi: 10.1016/j.crma.2017.12.005.  Google Scholar

[6]

Ph.-G. Ciarlet and C. Mardare, A mathematical model of Koiter's type for a nonlinearly elastic "almost spherical" shell, C. R. Math. Acad. Sci. Paris, 354 (2016), 1241-1247.  doi: 10.1016/j.crma.2016.10.011.  Google Scholar

[7]

W. T. Koiter On the nonlinear theory of thin elastic shells. Ⅰ, Ⅱ, Ⅲ, Nederl. Akad. Wetensch. Proc. Ser. B, 69 (1966), 1-17, 18-32, 33-54.  Google Scholar

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