Master's Dissertation
DOI
https://doi.org/10.11606/D.18.2008.tde-05022009-100510
Document
Author
Full name
Jesús Antonio García Sánchez
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2008
Supervisor
Committee
Laier, José Elias
Libardi, Walter
Title in Portuguese
Estudo do fenômeno da auto-intersecção em um anel anisotrópico
Keywords in Portuguese
Anisotropia
Auto-intersecção
Minimização com restrição
Abstract in Portuguese
Title in English
Study of the self-intersection anomaly in an anisotropic ring
Keywords in English
Anisotropy
Constrained minimization
Injectivity
Penalty method
Self-intersection
Abstract in English
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.