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Generalized periodic problem of elasticity theory for a cracked half-plane

Authors
Journal
Journal of Applied Mathematics and Mechanics
0021-8928
Publisher
Elsevier
Publication Date
Volume
49
Issue
2
Identifiers
DOI: 10.1016/0021-8928(85)90103-0
Disciplines
  • Mathematics

Abstract

Abstract The state of stress of an Isotropie half-plane weakened by a regular system of rectilinear cracks perpendicular to its edge is studied. The formulation of the problem is different from that used in /1/ in that the load on the crack does not generally possess any periodic properties. This circumstance makes utilization of the approaches proposed in /1/ for the solution impossible in practice. As is well-known, the problem reduces to infinite systems of singular integral equations in unknown jumps which the derivatives of the displacements undergo during the passage through each crack. To simplify the system obtained, a scheme of analytic accounting of the symmetry of the elastic geometric characteristics of the medium is used /2/, according to which the generalized periodic problems are studied first. As is shown in the paper, a system of four singular integral equations in the desired jumps on the fundamental crack corresponds to them. These jumps are determined by the method of orthogonal polynomials, and by using elementary algebraic relationships on the other cracks.

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