Abstract
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.
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Communicated by T. Cruse, 6 September 1996
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Bonnet, M. Differentiability of strongly singular and hypersingular boundary integral formulations with respect to boundary perturbations. Computational Mechanics 19, 240–246 (1997). https://doi.org/10.1007/s004660050172
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DOI: https://doi.org/10.1007/s004660050172