The topological asymptotic analysis provides the sensitivity of a given shape functional with respect to an infinitesimal domain perturbation, like the insertion of holes, inclusions, cracks. In this work we present the calculation of the topological derivative for a class of shape functionals associated to the Kirchhoff plate bending problem, when a circular inclusion is introduced at an arbitrary point of the domain. According to the literature, the topological derivative has been fully developed for a wide range of second-order differential operators. Since we are dealing here with a forth-order operator, we perform a complete mathematical analysis of the problem.

Classification: 35J30, 49Q10, 49Q12, 74K20, 74P15

Keywords: topological sensitivity, topological derivative, topology optimization, Kirchhoff plates

@article{COCV_2011__17_3_705_0, author = {Amstutz, Samuel and Novotny, Antonio A.}, title = {Topological asymptotic analysis of the Kirchhoff plate bending problem}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {17}, number = {3}, year = {2011}, pages = {705-721}, doi = {10.1051/cocv/2010010}, mrnumber = {2826976}, language = {en}, url = {http://www.numdam.org/item/COCV_2011__17_3_705_0} }

Amstutz, Samuel; Novotny, Antonio A. Topological asymptotic analysis of the Kirchhoff plate bending problem. ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 3, pp. 705-721. doi : 10.1051/cocv/2010010. http://www.numdam.org/item/COCV_2011__17_3_705_0/

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