## Stress intensity sensitivities via hypersingular boundary integral equations.(English)Zbl 0967.74075

The paper deals with the derivation of weakly singular sensitivity boundary integral equations (BIE) and regularized hypersingular BIE for sensitivities. The authors utilize the fact that singularity is not increased by differentiation with respect to design parameters. Thus, differentiating the regularized BIE and/or HBIE, they obtain regularized integral equations for sensitivities without any additional regularization. The use of the HBIE is effective for some class of boundary value problems, e.g. crack problems, where the conventional BIE are insufficient for a unique formulation. The computation of sensitivities of a function is less expensive than the computation of values of this function, since the same coefficient matrix is utilized in both calculations. Having known the function values together with the derivative values, one can use Hermitian interpolation for an accurate construction of the dependence of solution on the design parameter. The derived sensitivity integral equations are employing in numerical examples concerning the stress intensity factor curves in dependence on the design parameter.

### MSC:

 74S15 Boundary element methods applied to problems in solid mechanics 74G70 Stress concentrations, singularities in solid mechanics 74R10 Brittle fracture
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