Geodesic
Multigrid finite element method in calculation of 3D homogeneous and composite solids
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 4, pp. 530-543

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In the present paper, a method of multigrid finite elements to calculate elastic three-dimensional homogeneous and composite solids under static loading has been suggested. The method has been developed based on the finite element method algorithms using homogeneous and composite three-dimensional multigrid finite elements (MFE). The procedures for construction of MFE of both rectangular parallelepiped and complex shapes have been shown. The advantages of MFE are that they take into account, following the rules of the microapproach, heterogeneous and microhomogeneous structures of the bodies, describe the three-dimensional stress-strain state (without any simplifying hypotheses) in homogeneous and composite solids, as well as generate small dimensional discrete models and numerical solutions with a high accuracy.
Mots-clés : composites
Keywords: elasticity, three-dimensional solids, multigrid finite elements, microapproach, high accuracy. 
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     author = {A. D. Matveev},
     title = {Multigrid finite element method in calculation of {3D} homogeneous and composite solids},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {530--543},
     publisher = {mathdoc},
     volume = {158},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2016_158_4_a5/}
}
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A. D. Matveev. Multigrid finite element method in calculation of 3D homogeneous and composite solids. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 4, pp. 530-543. http://geodesic.mathdoc.fr/item/UZKU_2016_158_4_a5/