Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Lychev S. A., Mark A. V. field, action, least action principle, field equations, transformation group, Lie group, infinitesimal generator, variation, varied domain, constraint.. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 2, pp. 209-227. DOI: 10.18500/1816-9791-2014-14-2-209-227

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field, action, least action principle, field equations, transformation group, Lie group, infinitesimal generator, variation, varied domain, constraint.

Lychev Sergei Aleksandrovich, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Mark Alexander Victorovich, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences

The finite deformations of the growing cylinder fabricated of an incompressible elastic material of Mooney–Rivlin type are under consideration. We assume that the deformations are axisymmetric and constant along the cylinder axis. The discrete and continuous types of growing are studied. The analytical solutions of the corresponding boundary-value problems are derived. The computational examples show the convergence of solutions obtained for the discrete growth to corresponding solutions for continuous growth under the following conditions: the number of discrete plies increases while their thickness decreases such that the final volume of growing solid is fixed.

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