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The main purpose of this paper is to find the homogenized equation and the associate continuity condition in the explicit form of a boundary-value problem in two-dimensional domains separated by an interface oscillating rapidly between two concentric ellipses. This boundary-value problem originates from various mechanical problems. By the homogenization method and following the techniques presented recently by these authors the homogenized equation and the associate continuity condition in the explicit form are derived. Since the obtained homogenized equation is totally explicit it is convenient to use.
Czasopismo
Rocznik
Tom
Strony
461--476
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
autor
- Faculty of Mathematics, Mechanics and Informatics Hanoi University of Science 334, Nguyen Trai Str., Thanh Xuan, Hanoi,Vietnam, pcvinh@vnu.edu.vn
Bibliografia
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- 2. J.R.S. Talbot, J.B. Tichener, J.R. Willis, The reflection of electromagnetic waves from very rough interface, Wave Motion, 12, 245–260, 1990.
- 3. S.S. Singh, S.K. Tomar, Quassi-P-waves at a corrugated interface between two dissimilar monoclinic elastic half-spaces, Int. J. Solids Struct., 44, 197–228, 2007.
- 4. S.S. Singh, S.K. Tomar, qP-wave at a corrugated interface between two dissimilar prestressed elastic half-spaces, J. Sound Vibr., 317, 687–708, 2008.
- 5. K.T. Cheng, N. Olhoff, An investigation concerning optimal design of solid elastic plates, Int. J. Solids Struct., 17, 795–810, 1981.
- 6. Y. Achdou, O. Pironneau, F. Valentin, Effective boundary conditions for laminar flows over rough boundaries, J. Comput. Phys., 147, 187–218, 1998.
- 7. A. Bensoussan, J.B. Lions, J. Papanicolaou, Asymptotic analysis for periodic structures, North-Holland, Amsterdam 1978.
- 8. E. Sanchez-Palencia, Non-homogeneous media and vibration theory, in Lecture Notes in Phys., 127, Springer, Heidelberg 1980.
- 9. J. Nevard, J.B. Keller, Homogenization of rough boundaries and interface, SAM J. Appl. Math., 57 (6), 1660–1686, 1997.
- 10. P.C. Vinh, D.X. Tung, Homogenized equations of the linear elasticity in two-dimensional domains with very rough interfaces, Mech. Res. Comm., 37, 285–288, 2010.
- 11. P.C. Vinh, D.X. Tung, Homogenization of rough two-dimensional interfaces separating two anisotropic solids, ASME J. Appl. Mech., 78, 041014-1 (7 pages), 2011.
- 12. P.C. Vinh, D.X. Tung, Homogenized equations of the linear elasticity theoryin two-dimensional domains with interfaces highly oscillating between two circles, Acta Mech., 218, 333–348, 2011.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0013-0008