Geodesic
Convergence of power series in the method of initial functions
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2012), pp. 41-51
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An algorithm for constructing basic equations of the method initial functions (MIF) for plane problems of elasticity theory for anisotropic solids in an orthogonal Cartesian coordinate system in matrix-operator form using a general solution of elasticity theory equations in displacements through two arbitrary functions is presented. Displacements and stresses at an arbitrary point of an elastic body are obtained as a result of an impact of MIF operators to displacements and stresses (initial functions) defined on a coordinate line. The MIF operators are obtained in the form of power operator series in which the operator acts as a differentiation operator with respect to one of the independent variables. Regularity of MIF operators for an arbitrary anisotropic body is shown. Convergence of power series in the MIF solution in the case of the initial functions definition in terms of trigonometric sines and cosines is proved.
Keywords: plane problem of elasticity theory, anisotropic body, method of initial functions. 
@article{VSPUI_2012_1_a5,
     author = {A. V. Matrosov},
     title = {Convergence of power series in the method of initial functions},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {41--51},
     year = {2012},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2012_1_a5/}
}
TY  - JOUR
AU  - A. V. Matrosov
TI  - Convergence of power series in the method of initial functions
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2012
SP  - 41
EP  - 51
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2012_1_a5/
LA  - ru
ID  - VSPUI_2012_1_a5
ER  - 
%0 Journal Article
%A A. V. Matrosov
%T Convergence of power series in the method of initial functions
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2012
%P 41-51
%N 1
%U http://geodesic.mathdoc.fr/item/VSPUI_2012_1_a5/
%G ru
%F VSPUI_2012_1_a5
A. V. Matrosov. Convergence of power series in the method of initial functions. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2012), pp. 41-51. http://geodesic.mathdoc.fr/item/VSPUI_2012_1_a5/

[1] Maliev A. S., “O vybore funktsii v obschikh resheniyakh zadachi ravnovesiya izotropnogo uprugogo tela”, Trudy LETIIZhTa, no. 4, Transzheldorizdat, M., 1952, 180–244

[2] Vlasov V. Z., Leontev N. N., Balki, plity i obolochki na uprugom osnovanii, Gos. izd-vo fiz.-mat. lit., M., 1960, 491 pp.

[3] Vlasov V. V., Metod nachalnykh funktsii v zadachakh teorii uprugosti i stroitelnoi mekhaniki, Stroiizdat, M., 1975, 223 pp.

[4] Elpatevskii A. N., Zimakov N. N., “Metod nachalnykh funktsii v ploskoi zadache teorii uprugosti dlya tela s pryamolineinoi ortotropiei”, Izv. AN SSSR. Mekhanika tverdogo tela, 1973, no. 1, 127–134 | MR

[5] Lekhnitskii S. G., Anizotropnye plastinki, Izd. 2-e, Gos. izd-vo tekhn.-teor. lit., M., 1957, 464 pp.

[6] Lekhnitskii S. G., Teoriya uprugosti anizotropnogo tela, Izd. 2-e, Nauka, Gl. red. fiz.-mat. lit., M., 1977, 416 pp.

[7] Galileev S. M., Matrosov A. V., “Method of initial functions in the computation of sandwich plates”, International Applied Mechanics, 31:6 (1995), 413–500 | DOI | MR

[8] Lure A. I., Prostranstvennye zadachi teorii uprugosti, Gos. izd-vo tekhn.-teor. lit., M., 1955, 491 pp.

[9] Matrosov A. V., “Chislenno-analiticheskoe reshenie granichnoi zadachi deformirovaniya lineino-uprugogo anizotropnogo pryamougolnika”, Vestn. S.-Peterb. un-ta. Ser. 10: Prikladnaya matematika, informatika, protsessy upravleniya, 2007, no. 2, 55–65

[10] Galileev S. M., Matrosov A. V., Verizhenko V. E., “Method of initial functions for layered and continuously inhomogeneous plates and shells”, Mechanics of Composite Materials, 30:4 (1995), 313–415 | DOI

[11] Chashkin A. V., Lektsii po diskretnoi matematike, Izd-vo Mosk. un-ta, M., 2007, 260 pp.

[12] Agarev V. A., Metod nachalnykh funktsii dlya dvumernykh kraevykh zadach teorii uprugosti, Izd-vo AN USSR, Kiev, 1963, 203 pp.