Topological asymptotic analysis of the Kirchhoff plate bending problem

Samuel Amstutz; Antonio A. Novotny

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 3, page 705-721
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Amstutz, Samuel, and Novotny, Antonio A.. "Topological asymptotic analysis of the Kirchhoff plate bending problem." ESAIM: Control, Optimisation and Calculus of Variations 17.3 (2011): 705-721. <http://eudml.org/doc/221927>.

@article{Amstutz2011,
abstract = { 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. },
author = {Amstutz, Samuel, Novotny, Antonio A.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Topological sensitivity; topological derivative; topology optimization; Kirchhoff plates; topological sensitivity; topology optimization},
language = {eng},
month = {8},
number = {3},
pages = {705-721},
publisher = {EDP Sciences},
title = {Topological asymptotic analysis of the Kirchhoff plate bending problem},
url = {http://eudml.org/doc/221927},
volume = {17},
year = {2011},
}

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
DA - 2011/8//
PB - EDP Sciences
VL - 17
IS - 3
SP - 705
EP - 721
AB - 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.
LA - eng
KW - Topological sensitivity; topological derivative; topology optimization; Kirchhoff plates; topological sensitivity; topology optimization
UR - http://eudml.org/doc/221927
ER -

References

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