An indentation contact problem of a stamp and a bonded thin elastic layer

Abstract

This paper concerns an indentation contact problem between a cylinder stamp and a bonded elastic layer. Basing on the Navier equation and boundary conditions, the contact problem is transformed to a singular integral equation of the first kind through Fourier transform techniques. Applying properties of Chebyshev polynomials, the singular integral equation is then reduced to a system of linear algebraic equations of the first Chebyshev polynomial. Numerical solution for contact pressure is finally obtained by solving the coefficient matrix of the algebraic equations with least-squares algorithm. The reliability of the solution is testified, and the contact pressure turns into a Hertz type when the layer thickness increases.