# Optimal Shells Formed on a Sphere. The Topological Derivative Method

Abstract : The subject of the paper is the analysis of sensitivity of a thin elastic spherical shell to the change of its shape associated with forming a small circular opening, far from the loading applied. The analysis concerns the elastic potential of the shell. The sensitivity of this functional is measured as a topological derivative, introduced for the plane elasticity problem by Sokolowski and $\buildrel . \over {\hbox{Z}}$ochowski (1997) and extended here to the case of a spherical shell. A proof is given that : i) the first derivative of the functional with respect to the radius of the opening vanishes, and : ii) the second derivative does not blow up. A partially constructive formula for the second derivative or for the topological derivative is put forward. The theoretical considerations are confirmed by the analysis of a special case of a shell loaded rotationally symmetric, weakened by an opening at its north-pole. The whole treatment is based on the Niordson-Koiter theory of spherical shells, belonging to the family of correct first order shell models of Love.
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Type de document :
Rapport
[Research Report] RR-3495, INRIA. 1998, pp.62
Domaine :

https://hal.inria.fr/inria-00073191
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 12:07:36
Dernière modification le : samedi 17 septembre 2016 - 01:06:49
Document(s) archivé(s) le : dimanche 4 avril 2010 - 21:44:07

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• HAL Id : inria-00073191, version 1

### Citation

Tomasz Lewinski, Jan Sokolowski. Optimal Shells Formed on a Sphere. The Topological Derivative Method. [Research Report] RR-3495, INRIA. 1998, pp.62. 〈inria-00073191〉

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