Homogenization of an interface highly oscillating between two concentric ellipses
Do Xuan Tung, Pham Chi Vinh, Nguyen Kim Tung · Vietnam Journal of Mechanics · 2012
The main purpose of this paper is to find the homogenized equation and the associate continuity conditions in the explicit form of a boundary-value problem in a two-dimensional domain with an interface oscillating rapidly between two concentric ellipses. This boundary-value problem originates from various problems in practical applications. By the homogenization method and following the technique presented recently by Vinh and Tung [P. C. Vinh and D. X. Tung, Mech. Res.Comm. 37 (2010), 285-288; P. C. Vinh, D. X. Tung, ASME J. Appl. Mech., 78 (2011), 041014-1; P. C. Vinh and D. X. Tung, Acta Mech. 218 (2011), 333-348], the homogenized equation and the associate continuity conditions in the explicit form are derived.