Doctoral Thesis
DOI
10.11606/T.18.2009.tde-15062009-092448
Document
Author
Full name
Wesley Góis
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2009
Supervisor
Committee
Proença, Sergio Persival Baroncini (President)
Assan, Aloísio Ernesto
Fancello, Eduardo Alberto
Savassi, Walter
Venturini, Wilson Sergio
Title in Portuguese
Elementos finitos híbridos e híbrido-mistos de tensão com enriquecimento nodal
Keywords in Portuguese
Estabilidade do método dos elementos finitos
Formulação híbrida e híbrido-mista de tensão
Método dos elementos finitos
Abstract in Portuguese
Title in English
Stress hybrid and hybrid-mixed finite elements with nodal enrichment
Keywords in English
Finite element method
Generalized finite element method
Stability of finite element method
Stress hybrid and hybrid-mixed formulations
Abstract in English
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.