Differentiability of strongly singular and hypersingular boundary integral formulations with respect to boundary perturbations.

Marc Bonnet (1)

1 LMS - Laboratoire de mécanique des solides

In this paper, we establish that the Lagrangian-type material differentiation formulas, that allow to express the first-order derivative of a (regular) surface integral with respect to a geometrical domain perturbation, still hold true for the strongly singular and hypersingular surface integrals usually encountered in boundary integral formulations. As a consequence, this work supports previous investigations where shape sensitivities are computed using the so-called direct differentiation approach in connection with singular boundary integral equation formulations.

Domaines: Mécanique des solides [physics.class-ph]

Marc Bonnet. Differentiability of strongly singular and hypersingular boundary integral formulations with respect to boundary perturbations.. Computational Mechanics, 1997, 19, pp.240-246. ⟨10.1007/s004660050172⟩. ⟨hal-00111249⟩