Eventos Anais de eventos
MECSOL 2019
7th International Symposium on Solid Mechanics
Stability Investigation of GFEM and SGFEM Applying the inf-sup Test
Submission Author:
Wesley Góis , SP
Co-Authors:
Wesley Góis, Sergio Persival Proenca
Presenter: Wesley Góis
doi://10.26678/ABCM.MECSOL2019.MSL19-0011
Abstract
The stability issue of the numerical solutions of two-dimensional elasticity problems analyzed through the Generalized/Stable Finite Element Method (GFEM/SGFEM) is hereby addressed. An Inf-Sup Test for the GFEM/SGFEM is proposed aiming the numerical evaluation of the Babuška-Brezzi Condition. Both the GFEM and the SGFEM preserve the conventional structure of the Finite Element Method (FEM). In addition, the resource of the so called nodal enrichment available by those methods conceptually enlarges the approximation bases of the conventional FEM, without the need to introduce new nodal points in the domain. In this work, polynomial functions are exclusively explored for enrichment. The essential difference between SGFEM and GFEM is precisely the previous modification of the enrichment function aiming to improve the conditioning of the solving system. However, even in the SGFEM numerical stability problems can be induced when polynomial enrichment is arbitrarily explored. Therefore, focusing the goal of efficiently exploiting nodal enrichment possibilities, the present investigation on the solvability and convergence of the GFEM/SGFEM numerical responses for plane problems was conceived. Two reference problems in linear elasticity are selected for conducting the investigation, being both discretized by several meshes of four node quadrilateral elements and three node linear triangle elements. In each problem, the issue of solvability is treated through the computation of the condition number of the stiffness matrix. The issue of convergence is then addressed through a numerical evaluation of the Babuška-Brezzi Condition - Inf-Sup Test. The results obtained from the numerical analyzes done have validated the numerical inf-sup test as a consistent tool for investigation of the stability aspects of the numerical solutions, as well as for pointing out good combinations of polynomial functions to be used for nodal enrichment in the GFEM/SGFEM.
Keywords
Generalized Finite Element Method, Stable Generalized Finite Element Method, Babuška-Brezzi condition, Inf-Sup Test, Condition Number
