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Bulletin of Irkutsk State University. Series Mathematics, 2023, Volume 45, Pages 54–72
DOI: https://doi.org/10.26516/1997-7670.2023.45.54 (Mi iigum534) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Integro-differential equations and functional analysis

Triangulation method for approximate solving of variational problems in nonlinear elasticity

Vladimir A. Klyachinab, Vladislav V. Kuzminab, Ekaterina V. Khizhnyakovaba

a Volgograd State University, Volgograd, Russian Federation
b Novosibirsk State University, Novosibirsk, Russian Federation
Full-text PDF (1237 kB) Citations (4)
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DOI: https://doi.org/10.26516/1997-7670.2023.45.54
Abstract: A variational problem for the minimum of the stored energy functional is considered in the framework of the nonlinear theory of elasticity, taking into account admissible deformations. An algorithm for solving this problem is proposed, based on the use of a polygonal partition of the computational domain by the Delaunay triangulation method. Conditions for the convergence of the method to a local minimum in the class of piecewise affine mappings are found.
Keywords: stored energy functional, variational problem, gradient descent method, Delaunay triangulation, finite element method.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-282
The work is supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2022-282 from 05.04.2022 with the Ministry of Science and Higher Education of the Russian Federation.
Received: 10.05.2023
Revised: 16.06.2023
Accepted: 23.06.2023
Document Type: Article
UDC: 517.97
MSC: 49J35, 65K10
Language: Russian
Citation: Vladimir A. Klyachin, Vladislav V. Kuzmin, Ekaterina V. Khizhnyakova, “Triangulation method for approximate solving of variational problems in nonlinear elasticity”, Bulletin of Irkutsk State University. Series Mathematics, 45 (2023), 54–72
Citation in format AMSBIB
\Bibitem{KlyKuzKhi23}
\by Vladimir~A.~Klyachin, Vladislav~V.~Kuzmin, Ekaterina~V.~Khizhnyakova
\paper Triangulation method for approximate solving of variational problems in nonlinear elasticity
\jour Bulletin of Irkutsk State University. Series Mathematics
\yr 2023
\vol 45
\pages 54--72
\mathnet{http://mi.mathnet.ru/iigum534}
\crossref{https://doi.org/10.26516/1997-7670.2023.45.54}
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