Inverse contact problem for an elastic half-space

This paper presents a system of integral equations for the determination of contact stresses on a part of the boundary of elastic half-space by measured data of displacements on the rest of the stress-free boundary. Inverse problems like this are refereed to as conditionally ill-posed with pronounced dependence of the solution from small perturbations in measured data. The 3D problem formulation is based on spatial harmonic functions. It is proposed to use a Trefftz-type method for the sought harmonic functions based on the radial basis functions to solve the system of integral equations. A synthetic example is presented to illustrate the proposed approach.