Abstract
An exact solution of a four part mixed boundary value problem representing a three colinear crack system connected with specified crack opening displacements between the cracks is obtained. The three cracks thus become one with pressure and/or opening displacement prescribed on the crack face. From considerations of dual symmetry and a formulation based on Papkovich-Neuber harmonic functions, the boundary value problem is reduced to solving a quadruple set of integral equations. An exact solution of these equations is derived using a modified finite Hilbert transform technique. The closed form results for the stress distributions and the crack-tip stress intensity factors are presented. Limiting cases of the solution yield results which agree with well known solutions.
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Nagar, A.K., Fu, L.S. & Mendelsohn, D.A. On quadruple integral equations related to a certain crack problem. J Elasticity 16, 163–177 (1986). https://doi.org/10.1007/BF00043583
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DOI: https://doi.org/10.1007/BF00043583