Contact problems for functionally graded materials of complicated structure
- 74 Downloads
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).
Keywordscontact 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.
- 3.I. N. Sneddon, “The Reissner–Sagoci problem,” in: Proc. Glasgow Math. Assoc., 7 (1966), pp. 136–144.Google Scholar
- 4.D. V. Grilitskii, “Torsion of a two-layer elastic medium,” Prikl. Mekh., 7, Iss.1, 89–94 (1961).Google Scholar
- 5.S. M. Aizikovich, “Torsion of an inhomogeneous half-space by a round stamp,” in: Raschet Obol. Plast., RISI, Rostovon-Don (1978), pp. 156–169.Google Scholar
- 11.J. Rokne, B. M. Singh, R. S. Dhaliwal, and J. Vrbik, “The Reissner–Sagoci-type problem for a non-homogeneous elastic cylinder embedded in an elastic non-homogeneous half-space,” J. Appl. Math., 69, 159–173 (2004).Google Scholar
- 12.S. M. Aizikovich, V. M. Aleksandrov, I. S. Trubchik, and L. I. Krenev, “Penetration of a spherical indenter into a half-space with a functionally gradient elastic covering,” Dokl. Ross. Akad. Nauk. Mekhanika, 418, No. 2, 188–192 (2008).Google Scholar
- 13.S. M. Aizikovich, “Asymptotic solutions of contact problems of the theory of elasticity for media inhomogeneous in depth,” Priklad. Mat. Mekh., 46, Iss. 1, 148–158 (1982).Google Scholar