The problem of embedding a periodic continuous elastic gasket in a periodic cracked body is investigated by approaches using the singular integral equation (SIE) with the Hilbert kernel, the periodic solution in closed form of the SIE and analytical expressions of the stress intensity factors are obtained. Finally, some special examples are given.
1. BOUNDARY VALUE PROBLEM
IN MODERN engineering, periodic plane elastic problems are very important and useful, for example, in rock mechanics, concrete mechanics, solid mechanics and so on. Plane elastic problems of periodic holes and periodic cracks have been considered by many investigators in refs [l-6]. Periodic problems of the fracture of compound materials are more important in practical applications. In this paper, we investigate the problem of embedding a periodic continuous elastic gasket in a periodic cracked body.
The fundamental strip is denoted by P,, and it contains n cracks which lie on the x axis, rj = (a,, 6,) (j = 1,2, . . . , n). We denote Formulae ( 30) and ( 31) and formulae ( 33) and ( 34) show the direct linear relations between K,(b) and r, K,(c) and r, K,(b) and t;, and K,(c) and L in the periodic and non-periodic cases respectively [see Figs 2-5 where K = 1.6, ~1 = 0.2 and y = (2,3)].