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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


A Variational Problem on the Deformation Energy of an Elastic Medium

Discontinuity, Nonlinearity, and Complexity 8(3) (2019) 287--297 | DOI:10.5890/DNC.2019.09.005

Panayotis Vyridis

Department of Physics and Mathematics, Instituto Politécnico Nacional I.P.N. (National Polytechnic Institute), Campus Zacatecas P.C.098160, Zacatecas, Mexico

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The variational problem under consideration is a generalization to higher dimension (n > 2) of a free and constrained deformation of an elastic medium. In the case of the free body the existence of the minimizers of the corresponding energy functional is studied, using standard direct methods. When the elastic medium is subjected to a one parametric force field of the shell, the problem turns to the existence of bifurcation points, where the necessary conditions are also sufficient.


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