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.
Mots clés : 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},
pages = {705--721},
publisher = {EDP-Sciences},
volume = {17},
number = {3},
year = {2011},
doi = {10.1051/cocv/2010010},
mrnumber = {2826976},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2010010/}
}
TY - JOUR AU - Amstutz, Samuel AU - Novotny, Antonio A. TI - Topological asymptotic analysis of the Kirchhoff plate bending problem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 705 EP - 721 VL - 17 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2010010/ DO - 10.1051/cocv/2010010 LA - en ID - COCV_2011__17_3_705_0 ER -
%0 Journal Article %A Amstutz, Samuel %A Novotny, Antonio A. %T Topological asymptotic analysis of the Kirchhoff plate bending problem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 705-721 %V 17 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2010010/ %R 10.1051/cocv/2010010 %G en %F 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, Tome 17 (2011) no. 3, pp. 705-721. doi : 10.1051/cocv/2010010. http://www.numdam.org/articles/10.1051/cocv/2010010/
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