Solution of boundary-value problems of plates by the Vekua method for approximations <Emphasis Type="Italic">N</Emphasis> = 1 and <Emphasis Type="Italic">N</Emphasis> = 2

In this paper, the problem of bending for an isotropic plate with constant thickness 2h is considered. Problems of bending for infinite plates with a circular hole in which a rigid body is placed in the cases of approximations N = 1 and N = 2 of the Vekua theory are solved. We consider the case where the body is soldered. Problems of bending of circular rings are also solved. The results obtained are compared to the corresponding results obtained by plane classical bending theory. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 51, Differential Equations and Their Applications, 2008.