Geodesic
The defining relations for nonlinear elastic bodies and their implementation in the calculation of the rotation shells subjected to axisymmetric loading based on the mixed FEM
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 2, pp. 28-39

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The relations between stresses and strains, stress and strain increments of a deformable body with nonlinear elastic properties were obtained on the basis of the hypotheses about the proportionality of the components of stress and strain deviators, as well as the components of stress and strain increment deviators. The obtained relations were implemented in a mixed version of the finite element method to calculate the nonlinear elastic deformable rotation shells subjected to axisymmetric loading.
Keywords: vector approximation, tensor approximation, vector field, tensor field, mixed formulation, variational principle. 
@article{UZKU_2015_157_2_a2,
     author = {N. A. Gureeva and Yu. V. Klotchkov and A. P. Nikolaev},
     title = {The defining relations for nonlinear elastic bodies and their implementation in the calculation of the rotation shells subjected to axisymmetric loading based on the mixed {FEM}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {28--39},
     publisher = {mathdoc},
     volume = {157},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2015_157_2_a2/}
}
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N. A. Gureeva; Yu. V. Klotchkov; A. P. Nikolaev. The defining relations for nonlinear elastic bodies and their implementation in the calculation of the rotation shells subjected to axisymmetric loading based on the mixed FEM. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 2, pp. 28-39. http://geodesic.mathdoc.fr/item/UZKU_2015_157_2_a2/