Tesis Doctoral
DOI
https://doi.org/10.11606/T.18.2009.tde-15062009-092448
Documento
Autor
Nombre completo
Wesley Góis
Dirección Electrónica
Área de Conocimiento
Fecha de Defensa
Publicación
São Carlos, 2009
Director
Tribunal
Proença, Sergio Persival Baroncini (Presidente)
Assan, Aloísio Ernesto
Fancello, Eduardo Alberto
Savassi, Walter
Venturini, Wilson Sergio
Título en portugués
Elementos finitos híbridos e híbrido-mistos de tensão com enriquecimento nodal
Palabras clave en portugués
Estabilidade do método dos elementos finitos
Formulação híbrida e híbrido-mista de tensão
Método dos elementos finitos
Resumen en portugués
Título en inglés
Stress hybrid and hybrid-mixed finite elements with nodal enrichment
Palabras clave en inglés
Finite element method
Generalized finite element method
Stability of finite element method
Stress hybrid and hybrid-mixed formulations
Resumen en inglés
In the present work, the partition of unity enrichment concept is basically applied to non-conventional stress hybrid-mixed and hybrid formulations in plane elasticity. These formulations are referred to as non-conventional because no variational principles are explored. From these, triangular and quadrilateral finite elements with selective nodal enrichment are then derived. In the stress hybrid-mixed approach, three independent fields are approximated: stress and displacement fields in the domain and displacement fields on the static boundary. The partition of unity concept is then used to provide continuity to all the fields involved. Afterwards, the nodal enrichment feature is explored. Polynomial functions are employed to enrich each one of the approximation fields. Besides, some aspects concerning convergence and stability of the numerical solutions obtained are addressed. On the other hand, in the hybrid approach, two independent fields are approximated: stress fields in the domain and displacement fields on the static boundary. However, the approximation of the stress field must first satisfy the equilibrium condition in the domain without involving nodal values in its definition. Hence, the partition of unity concept is used to provide continuity of displacements between the boundaries of the elements. The partition of unity based nodal enrichment is then applied to the boundary displacement fields. Nevertheless, enrichment of the stress field can also be carried out with exploring a specific and original technique that permits applied the partition of unity concept but in such way as to preserve satisfaction of the equilibrium condition in the domain. Again, convergence and stability aspects of the hybrid approach are briefly addressed. Finally, some numerical examples are presented to illustrate the performance of both approaches derived, especially when combined possibilities of enrichment are explored.

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2009DO_WesleyGois.pdf (6.59 Mbytes)
Fecha de Publicación
2009-06-15