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

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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 : 10.1051/cocv/2010010
Classification : 35J30, 49Q10, 49Q12, 74K20, 74P15
Keywords: topological sensitivity, topological derivative, topology optimization, Kirchhoff plates 
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     title = {Topological asymptotic analysis of the {Kirchhoff} plate bending problem},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {705--721},
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Amstutz, Samuel; Novotny, Antonio A. Topological asymptotic analysis of the Kirchhoff plate bending problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 3, pp. 705-721. doi: 10.1051/cocv/2010010

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