Periodic Crack Systems in an Elastic Wedge

Abstract

We investigate three-dimensional periodic problems of the theory of elasticity for a wedge in the case where an infinite system of identical cracks of normal separation (mathematical cuts) is located in the middle half-plane of a wedge along the rib (at an equal distance from the rib for equal intervals between neighboring cracks). Three types of boundary-value conditions on the wedge faces are considered: the absence of tensions, the sliding sealing, and the rigid sealing. The problems are reduced to an integrodifferential equation such that the principal part is selected from its kernel; that principal part corresponds to one crack in an elastic space. To solve it, the regular asymptotical method is used. The intensity coefficients for tensions are computed at different wedge angles.