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This paper investigates the degenerate scale problem for plane elasticity in a multiply connected region with an outer elliptic boundary. Inside the elliptic boundary, there are many voids with arbitrary configurations. The problem is studied on the relevant homogenous boundary integral equation. The suggested solution is derived from a solution of a relevant problem. It is found that the degenerate scale and the non-trivial solution along the elliptic boundary in the problem are same as in the case of a single elliptic contour without voids. The present study mainly depends on integrations of several integrals, which can be integrated in a closed form. [ABSTRACT FROM AUTHOR]

This paper investigates the Zener–Stroh crack with curved configuration in plane elasticity. A singular integral equation is suggested to solve the problem. Formulae for evaluating the SIFs and T-stress at the crack tip are suggested. If the curve configuration is a product of a small parameter and a quadratic function, a perturbation method based on the singular integral equation is suggested. In the method, the singular integral equation can be expanded into a series with respect to the small parameter. Therefore, many singular integral equations can be separated from the same power order for the small parameter. These singular integral equations can be solved successively. The solution of the successive singular integral equations will provide results for stress intensity factors and T-stress at the crack tip. It is found that the behaviors for the solution of SIFs and T-stress in the Zener–Stroh crack and the Griffith crack are quite different. This can be seen from the presented comparison results. [ABSTRACT FROM AUTHOR]

In this paper, a hypersingular integral equation for the antiplane elasticity curved crack problems of circular regions is suggested. The original complex potential is formulated on a distribution of the density function along a curve, where the density function is the COD (crack opening displacement). The modified complex potential can also be established, provided the circular boundary is traction free or fixed. Using the proposed modified complex potential and the boundary condition, the hypersingular integral equation is obtained. The curve length method is suggested to solve the integral equation numerically. By using this method, the usual integration rule on the real axis can be used to the curved crack problems. In order to prove that the suggested method can be used to solve more complicated cases of the curved cracks, several numerical examples are given. [ABSTRACT FROM AUTHOR]