Mémoire de Maîtrise
DOI
10.11606/D.18.2008.tde-05022009-100510
Document
Auteur
Nom complet
Jesús Antonio García Sánchez
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Carlos, 2008
Directeur
Jury
Laier, José Elias
Libardi, Walter
Titre en portugais
Estudo do fenômeno da auto-intersecção em um anel anisotrópico
Mots-clés en portugais
Anisotropia
Auto-intersecção
Minimização com restrição
Resumé en portugais
Titre en anglais
Study of the self-intersection anomaly in an anisotropic ring
Mots-clés en anglais
Anisotropy
Constrained minimization
Injectivity
Penalty method
Self-intersection
Resumé en anglais
This work concerns a numerical study of a homogeneous circular plate with a centered hole that is under a state of plane strain. The plate is fixed at its inner surface and is under uniform radial compression at its outer surface. The plate is linear, elastic, and anisotropic. An analytical solution for this problem, which satisfies the governing equations of equilibrium, is presented in the context of classical linear elasticity. This solution predicts the spurious behavior of self-intersection in a central region of the plate. To avoid this behavior, a constrained minimization theory is used. This theory concerns the search for a displacement field that minimizes the total potential energy of the body, which is a quadratic functional from the classical linear theory, subjected to the constraint of local injectivity for the associated deformation field. This theory together with an interior penalty method and a standard finite element methodology yield a numerical solution, which is radially symmetric, that preserves injectivity. Here, it is investigated the possibility of finding a rotationally symmetric solution to the constrained problem; one for which the associated displacement field has radial and tangential components, which are both functions of the radius only. The numerical results show, however, that the tangential component is zero. It is also shown that, as the radius of the hole tends to zero, the corresponding sequence of solutions tends to the solution of a solid disk.

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Date de Publication
2009-02-18

AVERTISSEMENT: Le matériau se réfère à des documents provenant de cette thèse ou mémoire. Le contenu de ces documents est la responsabilité de l'auteur de la thèse ou mémoire.
• AGUIAR, A. R., FOSDICK, R. L., and SÁNCHEZ, Jesus Antonio García. A Study of Penalty Formulations Used in the Numerical Approximation of a Radially Symmetric Elasticity Problem [doi:10.2140/jomms.2008.3.1403]. Journal of Mechanics of Materials and Structures [online], 2008, vol. 3, p. 1403-1427.
• AGUIAR, A. R., FOSDICK, R. L., e SÁNCHEZ, Jesus Antonio García. Recent Advances on the Theoretical and Numerical Investigations of the Constrained Aeolotropic Pipe Problem. In XXIX CILAMCE - Congresso Ibero Latino Americano de Métodos Computacionais em Engenharia, Maceió, AL, 2008. Anais do XXIX CILAMCE - Congresso Ibero Latino Americano de Métodos Computacionais em Engenharia., 2008. Dispon?vel em: http://www.acquacon.com.br/cilamce2008/.
• AGUIAR, A. R., e SÁNCHEZ, Jesus Antonio García. Investigação da Convergência de Soluções Aproximadas de Problemas Singulares em Elasticidade Anisotrópica. In 13º Simpósio Internacional de Iniciação Científica da Universidade de São Paulo, São Carlos, SP, 2005. São Carlos, 2005. Resumo. Dispon?vel em: http://www.usp.br/siicusp/13osiicusp/aprovados/index01.htm.
• AGUIAR, A. R., FOSDICK, R. L., and SÁNCHEZ, Jesus Antonio García. Self-Intersection in an Anisotropic Solid in the Absence of Singularity - Part II: Computational Results. In Tenth Pan American Congress of Applied Mechanics - PACAM X, Cancún, 2008. Proceedings of PACAM X., 2008.
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