Analytical calculation of stress intensity factors for orthotropic plates containing cracks emanating from a circular hole using Schwarz integration

In this paper, a new analytical method is presented to determine the stress intensity factors (SIFs) of a generally orthotropic plate with cracks emanating from a circular hole. Therefore, using the Schwartz integration method, for the first time, the analytical solution is provided based on the complex variable method. In order to use the Schwartz's theorem in solving complex integrals, a new presentation of the mapping function has been presented, which leads to providing a simpler solution. After calculating the potential functions, the SIFs are determined for the circular hole with one and two cracks. Then, the effect of parameters such as fiber angle, different and unequal crack lengths, and different loadings are studied. To validate the results of the present analytical solution, some results have been compared with the results from other references. Comparing the results showed that the current solution has good accuracy and is reliable and the fiber angle has a significant effect on the mode II SIF. In the case that the fibers are along the crack length and the loading is perpendicular to the crack direction, the mode II SIF is zero, but if the fibers are not along the crack length, the value of the mode II SIF will not be zero. It is also shown that increasing the length of one crack increases the SIF of another crack as well. In this paper, a new analytical method is presented to determine the stress intensity factors (SIFs) of a generally orthotropic plate with cracks emanating from a circular hole. Therefore, using the Schwartz integration method, for the first time, the analytical solution is provided based on the complex variable method. In order to use the Schwartz's theorem in solving complex integrals, a new presentation of the mapping function has been presented, which leads to providing a simpler solution.…