Solutions of multiple crack problems of a circular region with free or fixed boundary condition in antiplane elasticity

Four cases of multiple crack problems in antiplane elasticity, circular region or an infinite region exterior to a circle with free or fixed boundary condition, are considered in this paper. For all these cases, the presented elementary solution is a particular solution of the circular region containing one crack. The solution consists of two parts and satisfies the following conditions: (a) The first part corresponds to a pair of longitudinal forces acting at a prescribed point on both edges of a single crack; (b) The second part corresponds to some distributed forces along both edges of the crack; (c) The elementary solution, i.e. the sum of the first and second parts, satisfies the above mentioned boundary value conditions along the circular boundary. As we have done in [1–3], the system of Fredholm integral equations for the undetermined densities of the elementary solutions can be easily estabished and the stress intensity factors at crack tips can also be evaluated.