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

• The SBFEM is extended for shape sensitivity analysis of the SIF.
• Sensitivity of the SIF with respect to the crack size and orientation is computed.
• A normalization procedure makes stress modes insensitive to crack location.
• Only first-order displacement field and stiffness matrix sensitivities required.

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.