Topological asymptotic analysis of the Kirchhoff plate bending problem
ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 3, p. 705-721

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.

DOI : https://doi.org/10.1051/cocv/2010010
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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