Mechanics of Composite Materials

, Volume 47, Issue 5, pp 539–548 | Cite as

Contact problems for functionally graded materials of complicated structure

  • S. M. AizikovichEmail author
  • A. S. Vasil’ev
  • L. I. Krenev
  • I. S. Trubchik
  • N. M. Seleznev

An approximate analytical method allowing one to efficiently solve, to a preassigned accuracy, contact problems for materials with properties arbitrarily varying in depth is developed. Its possibilities are illustrated with the example of torsion of an elastic half-space, having a coating inhomogeneous across its thickness, by a circular stamp. All the results obtained are rigorously substantiated. For the approximate solutions constructed, their error is analyzed. The asymptotic properties of the solutions are investigated. The cases of a nonmonotonic change in the elastic properties are considered. In particular, the analytical solutions are examined in the case where the variation gradient of the elastic properties changes its sign many times. The results derived allow one to solve the inverse problems of elasticity theory of inhomogeneous media (e.g., the problem on controlling the variation in the elastic properties of a covering across its thickness).


contact problems functionally graded materials approximate analytical solution 


This study was financially supported by the Russian Fund for Basic Research (08-01-00003a, 09-08-011410a, 10-08-01296-a, 10-08-90025-Bel_a) and GK No. 02.740.11.0413, No. 02.740.11.5193, No. P1107, and ABTsP 2.1.2/5729.


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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • S. M. Aizikovich
    • 1
    Email author
  • A. S. Vasil’ev
    • 1
  • L. I. Krenev
    • 1
  • I. S. Trubchik
    • 1
  • N. M. Seleznev
    • 1
  1. 1.Don State Technical University, Management of Scientific ResearchRostov-on-DonRussia

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