This work presents a variational formulation of the material failure process, idealized as strain or displacement discontinuities, by weak, strong, or discrete embedded discontinuities into a continuum. It is shown that the solution of the proposed variational formulation may be approximated by different types of finite elements with embedded discontinuities. The developed displacement approximation of a finite element split by the discontinuity leads to a symmetric stiffness matrix, which considers not only the continuity of tractions but also the rigid body relative motions of the portions in which the element is split. The variational formulation of a continuum with more than one discontinuity in its interior is developed. It is shown that this formulation may lead to finite elements with embedded discontinuities that can be classified as displacement, force, mixed, and hybrid models. To show the effectiveness of the proposed formulation, the classical example of a bar under tension is solved using one and 2D finite element approximations.
El objetivo de esta investigación, fue determinar la prevalencia de forma de arcada dental, en adultos con maloclusión clase I,clase II y clase III. La muestra se constituyó por 106 modelos de estudio correspondiente a la arcada superior y 106 modelos de la arcada mandibular correspondientes a 29 hombres y 77 mujeres de 18 a 30 años con una media de edad de 19 años y que acudieron a solicitar tratamiento en la Clínica de Ortodoncia, de la División de Estudios de Posgrado de la UNAM en el periodo de julio de 2002 a diciembre de 2003. En los modelos se localizaron 12 puntos sobre superficies dentales sobreponiendo plantillas con formas de arco triangular, cuadrado y ovoide. Los resultados demostraron que la forma ovoide es la de mayor prevalencia en ambas arcadas, en 79 casos (49.3%) se encontró la misma forma de arco dental maxilar y mandibular y en 27 casos (16.8%) se presentó una combinación en la forma de arcada maxilar y mandibular, por lo que se evidencia que existe una variación en la forma de arco dental entre los individuos e inclusive entre la forma de arco maxilar y mandibular de un paciente.
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