Stress intensity sensitivities via Hypersingular boundary integral equations

In sensitivity analysis for problems involving thin domains or cracks, conventional boundary integral equations must be supplemented and/or replaced by hypersingular ones. Hypersingular boundary integral equations for sensitivity analysis are developed here in two forms, using both a global and a local regularization. These regularizations are easily implemented, since the singularity order of the sensitivity BIE formulae are no stronger than those of the ordinary BIEs. A justification for this work is that obtaining stress intensity factor versus crack size curves is made easier using sensitivity analysis, since the computation of a function value and a derivative is less expensive than that for two function values. Examples of a circular bar with an embedded penny-shaped crack under tension, bending, and torsion loads are shown to be accurate and verify the formulation and the computer codes developed in this paper.