Shape sensitivity analysis of stress intensity factors by the scaled boundary finite element method

The scaled boundary finite element method (SBFEM) is extended for shape sensitivity analysis of stress intensity factors (SIFs) with respect to the crack geometry. The procedure combines the finite element formulations with the boundary discretization. The original equations of the SBFEM are reformulated as functions of the so-called scaling centre, synonymous to the crack tip. The variation in crack geometry is modelled without remeshing. Sensitivity is analyzed by direct differentiation. Following the computation of the displacement field sensitivity, the SIF sensitivity is evaluated directly from the present SIF definition. Numerical examples are presented.