In fracture mechanics, due to singularity existing on the crack tip, the corresponding sensitivity analysis of Stress Intensity Factor (SIF) is not clear whether the overall finite difference (OFD) or Semi-analytical Method (SAM) can obtain accurate sensitivities. The paper proposes the Semi-analytical Complex Variable Method (SACVM) to compute sensitivities of SIF and compares the sensitivities computed by the SACVM with those computed by the OFD and SAM in Center Cracked Tension (CCT) specimen and Single Edge Notched Tension (SENT) specimen. The results reveal that the OFD obtains oscillated sensitivities because of the ill-conditioned linear system. The sensitivities computed by the OFD and SAM are sensitive to the perturbation size out of a certain range. However, this certain range varies with different variable, and is not known a priori. The proposed SACVM can always obtain accurate, consistent sensitivities with little extra computational cost than the SAM. The SACVM is not sensitive to the perturbation size and is not affected by the ill-conditioned linear system. Therefore, the SACVM is recommended to deal with sensitivity analysis in the fracture mechanics.
Complex Variable Solutions for Forces and Displacements of Circular Lined Tunnels