Contact Interaction of a Plate with a Nonlinear Elastic Stringer

Abstract

A problem for determining the mechanical field in a homogeneous half-plane supported by a finite homogeneous stringer, material of which obeys the nonlinear Hooke law, is considered. The posed problem is reduced to a nonlinear singular integro-differential equation. Using the Schauder fixed-point theorem, the existence of a solution for this equation is proved. Using the small parameter method, a system of recurrence linear singular integral equations of the first kind is obtained.