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Periodic group edge crack problem of half-plane in antiplane elasticity. (English) Zbl 1147.74042

Summary: Using complex variable function, we obtain an elementary solution of a single-edge crack problem for half-plane. The elementary solution is obtained by distributing the dislocation density along the prospective place of crack, and it is composed of the principal part and the complementary part. Based on the elementary solution and the principle of superposition, we formulate a system of Cauchy singular integral equations for periodic group edge crack problems in half-plane in antiplane elasticity. In the solution of the singular integral equation, the influence of many neighbouring groups on the central group is evaluated exactly. In addition, the influence on the central group by many remote groups is considered approximately. By using a semi-open quadrature rule, the singular integral equations are solved and the stress intensity factors at the crack tips are evaluated. Several numerical examples are given.

MSC:

74R10 Brittle fracture
74G70 Stress concentrations, singularities in solid mechanics
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References:

[1] Savruk, Two-dimensional Problems of Elasticity for Body with Crack (1981) · Zbl 0478.73086
[2] Chen, An infinite plate weakened by periodic cracks, Journal of Applied Mechanics 69 pp 552– (2002) · Zbl 1110.74383
[3] Wang, A complex boundary integral method for multiple circular holes in an infinite plane, Engineering Analysis with Boundary Elements 27 pp 789– (2003)
[4] Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity (1953) · Zbl 0052.41402
[5] Boiko, On some numerical methods for the solution of the plane elasticity problem for bodies with cracks by means of singular integral equation, International Journal of Fracture 17 pp 381– (1981)
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