Geodesic
Triangulation method for approximate solving of variational problems in nonlinear elasticity
The Bulletin of Irkutsk State University. Series Mathematics, Tome 45 (2023), pp. 54-72

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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, finite element method.
Mots-clés : gradient descent method, Delaunay triangulation 
@article{IIGUM_2023_45_a3,
     author = {Vladimir A. Klyachin and Vladislav V. Kuzmin and Ekaterina V. Khizhnyakova},
     title = {Triangulation method for approximate solving of variational problems in nonlinear elasticity},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {54--72},
     publisher = {mathdoc},
     volume = {45},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2023_45_a3/}
}
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Vladimir A. Klyachin; Vladislav V. Kuzmin; Ekaterina V. Khizhnyakova. Triangulation method for approximate solving of variational problems in nonlinear elasticity. The Bulletin of Irkutsk State University. Series Mathematics, Tome 45 (2023), pp. 54-72. http://geodesic.mathdoc.fr/item/IIGUM_2023_45_a3/