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A thermoelastic half-plane with a functionally graded thermoelastic coating with arbitrary independently varying properties in depth is considered. The coating and the substrate are assumed to be imperfectly bonded (incomplete adhesion between the layers). Arbitrary distributed static thermomechanical loading is applied to the surface. The paper addresses to the construction and analysis of the compliance functions. These functions describing the linear correspondence between the Fourier transformations of the surface distribution of normal stresses, tangential stresses and heat flux on one side and displacements and temperature difference on the other side. Asymptotic analysis of the compliance functions is provided as well as the numerical results illustrating the difference between homogeneous and functionally graded coatings and the dependence at the coefficient describing the degree of imperfection of the coating-substrate bonding.

Compliance functions for a thermoelastic FGM coated half-plane with incomplete adhesion between the coating and substrate