The investigation of singular integro-differential equations relating to adhesive contact problems of the theory of viscoelasticity

TL;DR

This paper develops methods to solve singular integro-differential equations in viscoelastic contact problems, providing exact and approximate solutions for elastic plates with creep properties using orthogonal polynomials and integral transformations.

Contribution

It introduces a novel approach combining orthogonal polynomials and integral transformations to analyze viscoelastic contact problems involving singular integro-differential equations.

Findings

Solutions for elastic plate contact problems with creep properties

Reduction of complex equations to boundary value problems of analytic functions

Asymptotic analysis of the integro-differential equations

Abstract

The exact and approximate solutions of singular integro-differential equations relating to the problems of interaction of an elastic thin finite or infinite non-homogeneous patch with a plate are considered, provided that the materials of plate and patch possess the creep property. Using the method of orthogonal polynomials the problem is reduced to the infinite system of Volterra integral equations, and using the method of integral transformations this problem is reduced to the different boundary value problems of the theory of analytic functions. An asymptotic analysis is also performed.