Biaxial loading of a plate containing a hole and two co-axial through cracks

The paper presents the solution linear elasticity problem for an isotropic plate weakened by a hole and two co-axial cracks. The plate is exerted by uniform traction at infinity. The corresponding 2D problem is solved by the method of Kolosova-Muskhelishvili complex potentials. The method implies reduction of the problem to simultaneous singular integral equations (SIE) for the functions defined the region of the cracks and hole. For particular case the solution the SIE is obtained analytically in a closed form. A thorough analysis of the stress intensity factors (SIF) is carried out for various cases of the hole shape: penny-shaped, elliptical and rectangular.