Analytical Solution of the Frictional Contact Problem of a Semi-circular Punch Sliding Over a Homogeneous Orthotropic Half-plane

Abstract

An analytical solution to the frictional sliding contact problem for homogeneous orthotropic materials indented by a semi-circular punch is developed.The principal axes of orthotropy are assumed to be parallel and perpendicular to the contact. Coulomb friction assumption is used to model the friction between the punch and the orthotropic medium. The mixed boundary value problem is reduced into a Fredholm integral equation of the second kind by using Fourier transform technique. The singular integral equation is solved analytically using Jacobi Polynomials for the unknown surface contact stresses. Numerical results show the effect of the orthotropic material parameters, coefficient of friction on the contact stress distribution and load vs. contact length behavior.