Geodesic
The contact problems for the elastic foundation with the functionally graded coatings of the complicated structure
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 4, pp. 3-8.

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The contact problemfor the impression of axisymmetrical indenter into a functional graded elastic half-space is considered. Analytical methods for solving this problem have been developed. It is assumed that the indenter has a parabolic shape and contact between the indenter and the coating is smooth. The used method make it possible to find the analytical asymptotically exact problem solution. The stress-strain state of the coating is analyzed due to numerical experiment with the coatings which elastic modula are described with continuously smooth non-monotonic function with the changing of derivation sight is finite into the coating. 
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S. M. Aizikovich; L. I. Krenev; I. S. Trubchik. The contact problems for the elastic foundation with the functionally graded coatings of the complicated structure. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 4, pp. 3-8. http://geodesic.mathdoc.fr/item/ISU_2009_9_4_a0/

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[2] Aizikovich S. M., Krenev L. I., Trubchik I. S., “Asimptoticheskoe reshenie zadachi o vnedrenii sfericheskogo indentora v neodnorodnoe po glubine poluprostranstvo”, Izv. RAN. Mekhanika tverdogo tela, 2000, no. 5, 107–117