The singular integro‐differential equations and its applications in the contact problems of elasticity theory

Abstract

The problems of constructing an exact or approximate solution of system of singular integro‐differential equations related to the problems of adhesive interaction between elastic thin finite or infinite nonhomogeneous patch and elastic plate are investigated. For the patch loaded with horizontal and vertical forces, the usual model of beam bending in combination with the uniaxial stress state model is valid. Using the methods of theory of analytic functions, integral transformation, or orthogonal polynomials, the singular integro‐differential equations reduced to the different boundary value problems (Karleman type problem with displacements and Riemann problem) of the theory of analytic functions or to the infinite system of linear algebraic equations. The asymptotic analysis of problem is carried out.