Shape sensitivity method for computation of stress intensity factors sensitivity in functionally graded materials

摘要

This paper presents a method for computing the derivatives of stress intensity factors of a crack in an isotropic, linear-elastic functionally graded material. The present work is based on nonequilibrium formulation. The proposed' method involves the material derivative concept from continuum mechanics, domain integral representation of interaction integrals, known as the M-integral, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed to calculate the sensitivity of stress-intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations are independent of approximate numerical techniques, such as the meshless method, finite element method, boundary element method or others. Three numerical examples are presented to calculate the first-order derivative of the stress-intensity factors. The results show that first-order sensitivities of stress intensity factors obtained using the proposed method are in excellent agreement with the reference solutions obtained using the finite-difference method for the structural and crack geometries considered in this study.