This paper addresses an axisymmetric quasi-static contact problem on both thermal and mechanical interactions of a circular punch and a nonhomogeneous elastic half-space whose mechanical and thermophysical properties are assumed to be arbitrary functions of the depth coordinate. To solve the formulated boundary value problem, the technique of Hankel's integral transformation is used. Using the bilateral asymptotic method, an approximate analytical-numerical solution is constructed for the heat flux, boundary displacements of the half-space, and contact stress under the punch. Numerical implementation is performed for different dependences of the material properties on the depth of the half-space.
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