Contact Problems for Elastic Plates with Finite-Length Nonlinearly Deformable Stringers Glued to Their Boundaries

Abstract

The problem to determine the mechanical field in a homogeneous half-plane supported by a finite homogeneous stringer, material of which obeys the nonlinear Hooke’s law, is considered. The contact between the plate and stringer is realized by a thin glue layer. The posed problem is reduced to a nonlinear singular integrodifferential equation. Using the Schauder fixed-point principle, we prove the existence of a solution to this equation. The uniqueness of the solution of the problem is proved. Using the small-parameter method, we obtain a system of recurrence linear singular integral equations of the first kind.