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

Abstract

A novel methodology for determining Stress Intensity Factor (SIF) sensitivities for plate bending problemsusing the Dual Boundary Element Method (DBEM) is presented. The direct derivatives of the DBEM integralequations for plate bending have been derived for the first time and are used as part of a DBEM-based ImplicitDifferentiation Method (IDM or DBEM-IDM) for calculating the sensitivities of SIFs to changes in differentgeometric parameters such as crack length and crack rotation angle. The SIFs and their sensitivities arecalculated using the J-integral and the derivative of the J-integral respectively. A numerical example featuringa thick plate subjected to membrane, bending, and pressure loads is presented. In the first half of the numericalexample, the SIF sensitivities from the IDM are compared with those obtained from the more common, butrelatively crude, Finite Difference Method (FDM or DBEM-FDM). Results show that the IDM is a significantlymore efficient and robust alternative to the FDM. The accuracy of the FDM showed significant dependence onthe step size used, necessitating a time-consuming optimization 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 halfof the numerical example, a demonstration of one possible application of the SIF sensitivities from the IDMis presented. This involved carrying out reliability analyses using the First-Order Reliability Method (FORM)with a large number of design variables.