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.
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.
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
\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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This publication is cited in the following 2 articles:
V. A. Klyachin, “Otsenki kusochno-lineinoi approksimatsii proizvodnykh funktsii klassov Soboleva”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 49 (2024), 78–89
Vladislav Kuzmin, “Calculation of 3D Shape of a Hyperelastic Body for Nonlinear Elasticity Models Using the Newton Method”, Mathematical Physics and Computer Simulation, 27:2 (2024), 80
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