Partial slip problem in frictional contact of orthotropic elastic half-plane and rigid punch

Planar partial-slip contact problem of a rigid indenter with flat end and an orthotropic elastic material is analytically and numerically investigated. In the analytical way, the coupled singular equations of this problem are reduced to a Fredholm integral equation with a regular kernel. The analytical solutions are derived in the forms of the Goodman's and Spence's approximations. In the numerical way, a linear complementarity formulation is developed by reformulating the governing equations are as coupled Volterra integral equations. And, a Newton-based optimization algorithm based on smoothing approximation is used to solve the problem. The validness of both the Goodman and Spence approximate solutions is verified by comparing with the numerical results for different orthotropic elastic materials.