Geodesic
Spline-interpolation solution of elasticity theory problems
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 4, pp. 24-41

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A spline-interpolation solution of static and dynamic elasticity theory problems is suggested. The method allows to solve the problems for solids with plane sections parallel to the plane $XOY$. We reduce space and dynamic problems to the series of plane boundary-value problems. The recursive formulas are obtained to determine the spline coefficients. The convergence of the constructed approximate solutions to the exact solutions is proved.
Mots-clés : spline interpolation
Keywords: elasticity theory, dynamic problem, polyharmonic functions. 
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     author = {P. N. Ivanshin},
     title = {Spline-interpolation solution of elasticity theory problems},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {24--41},
     publisher = {mathdoc},
     volume = {157},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2015_157_4_a1/}
}
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P. N. Ivanshin. Spline-interpolation solution of elasticity theory problems. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 4, pp. 24-41. http://geodesic.mathdoc.fr/item/UZKU_2015_157_4_a1/