Optimal Shells Formed on a Sphere. The Topological Derivative Method
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 measure...
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ftunivnantes:oai:HAL:inria-00073191v1 2023-05-15T17:39:53+02:00 Optimal Shells Formed on a Sphere. The Topological Derivative Method Lewinski, Tomasz Sokolowski, Jan Mathematical Analysis and Numerical Simulation of Non-Linear Models (NUMATH) INRIA Lorraine Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria) INRIA 1998 https://hal.inria.fr/inria-00073191 https://hal.inria.fr/inria-00073191/document https://hal.inria.fr/inria-00073191/file/RR-3495.pdf en eng HAL CCSD Report N°: RR-3495 inria-00073191 https://hal.inria.fr/inria-00073191 https://hal.inria.fr/inria-00073191/document https://hal.inria.fr/inria-00073191/file/RR-3495.pdf info:eu-repo/semantics/OpenAccess https://hal.inria.fr/inria-00073191 [Research Report] RR-3495, INRIA. 1998, pp.62 shape optimization shape derivative topological derivative asymptotic expansion inverse problem [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH] info:eu-repo/semantics/report Reports 1998 ftunivnantes 2023-02-08T00:23:51Z 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. Report North Pole Université de Nantes: HAL-UNIV-NANTES North Pole |
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Open Polar |
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Université de Nantes: HAL-UNIV-NANTES |
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ftunivnantes |
language |
English |
topic |
shape optimization shape derivative topological derivative asymptotic expansion inverse problem [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH] |
spellingShingle |
shape optimization shape derivative topological derivative asymptotic expansion inverse problem [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH] Lewinski, Tomasz Sokolowski, Jan Optimal Shells Formed on a Sphere. The Topological Derivative Method |
topic_facet |
shape optimization shape derivative topological derivative asymptotic expansion inverse problem [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH] |
description |
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. |
author2 |
Mathematical Analysis and Numerical Simulation of Non-Linear Models (NUMATH) INRIA Lorraine Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria) INRIA |
format |
Report |
author |
Lewinski, Tomasz Sokolowski, Jan |
author_facet |
Lewinski, Tomasz Sokolowski, Jan |
author_sort |
Lewinski, Tomasz |
title |
Optimal Shells Formed on a Sphere. The Topological Derivative Method |
title_short |
Optimal Shells Formed on a Sphere. The Topological Derivative Method |
title_full |
Optimal Shells Formed on a Sphere. The Topological Derivative Method |
title_fullStr |
Optimal Shells Formed on a Sphere. The Topological Derivative Method |
title_full_unstemmed |
Optimal Shells Formed on a Sphere. The Topological Derivative Method |
title_sort |
optimal shells formed on a sphere. the topological derivative method |
publisher |
HAL CCSD |
publishDate |
1998 |
url |
https://hal.inria.fr/inria-00073191 https://hal.inria.fr/inria-00073191/document https://hal.inria.fr/inria-00073191/file/RR-3495.pdf |
geographic |
North Pole |
geographic_facet |
North Pole |
genre |
North Pole |
genre_facet |
North Pole |
op_source |
https://hal.inria.fr/inria-00073191 [Research Report] RR-3495, INRIA. 1998, pp.62 |
op_relation |
Report N°: RR-3495 inria-00073191 https://hal.inria.fr/inria-00073191 https://hal.inria.fr/inria-00073191/document https://hal.inria.fr/inria-00073191/file/RR-3495.pdf |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1766140658418974720 |