On the solvability of one boundary-value problem using a refined theory of Vekua

In the present paper, a boundary-value problem of plates for St. Venant-Kirchhoff materials is considered. This three-dimensional problem is reduced to a two-dimensional problem by Vekua's method for the geometrical nonlinear theory. In the case of N = 0 approximation, using the small-parameter method of Signorini and the theory of complex-variable functions, we solve boundary-value problems either for infinity plates that include a circle or concentrated circular rings. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 51, Differential Equations and Their Applications, 2008.