Discontinuous mappings and the limit load in boundary value problems of nonlinear elasticity

Authors

  • Igor A. Brigadnov St Petersburg Mining University, 2, 21-ya liniya V.O., St Petersburg, 199106, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2023.108

Abstract

The article discusses a boundary value problem of nonlinear elasticity for mapping (deformation) in two weak formulations: in the form of a variational equilibrium equation and in the form of minimization of a multidimensional integral functional. Some questions of a mathematical correctness of the nonlinear elasticity BVP are discussed. Using methods of calculus of variations, by the example of two simple problems, it is proved that for some nonlinear elastic models in the corresponding boundary value problems there can be mappings that have discontinuities of the slip type, as well as there is the limit load - such a finite value of external forces, above which the boundary value problem has no solution at all.

Keywords:

nonlinear elasticity, variational formulations, discontinuous mappings, limit load

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Published

2023-03-03

How to Cite

Brigadnov, I. A. (2023). Discontinuous mappings and the limit load in boundary value problems of nonlinear elasticity. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(1), 86–98. https://doi.org/10.21638/spbu01.2023.108

Issue

Vol. 10 No. 1 (2023)

Section

Mechanics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.