A dual boundary element based implicit differentiation method for determining stress intensity factor sensitivities for plate bending problems

A novel methodology for determining Stress Intensity Factor (SIF) sensitivities for plate bending problems using the Dual Boundary Element Method (DBEM) is presented. The direct derivatives of the DBEM integral equations for plate bending have been derived for the first time and are used as part of a DBEM-based Implicit Differentiation Method (IDM or DBEM-IDM) for calculating the sensitivities of SIFs to changes in different geometric parameters such as crack length and crack rotation angle. The SIFs and their sensitivities are calculated using the J-integral and the derivative of the J-integral respectively. A numerical example featuring a thick plate subjected to membrane, bending, and pressure loads is presented. In the first half of the numerical example, the SIF sensitivities from the IDM are compared with those obtained from the more common, but relatively crude, Finite Difference Method (FDM or DBEM-FDM). Results show that the IDM is a significantly more efficient and robust alternative to the FDM. The accuracy of the FDM showed significant dependence on the step size used, necessitating a time-consuming optimisation procedure to determine the optimal step size. Once this optimal step size was found, both methods provided very similar results. As part of the second half of the numerical example, a demonstration of one possible application of the SIF sensitivities from the IDM is presented. This involved carrying out reliability analyses using the First-Order Reliability Method (FORM) with a large number of design variables.