Eventos Anais de eventos
MecSol 2017
6th International Symposium on Solid Mechanics
COMPUTATIONAL SIMULATIONS USING THE HIGHER ORDER STABLE GENERALIZED FINITE ELEMENT METHOD
Submission Author:
Sergio Persival Proenca , SP
Co-Authors:
Fernando Sato, Dorival Piedade
Presenter: Sergio Persival Proenca
doi://10.26678/ABCM.MecSol2017.MSL17-0036
Abstract
The Stable Generalized Finite Element Method (SGFEM) is essentially an improved version of the Generalized Finite Element Method (GFEM). Besides of retaining the good flexibility for constructing local enriched approximations, the SGFEM has the advantage of presenting much better conditioning than that of the conventional GFEM. Actually, bad conditioning is well known as one of the main drawbacks of the GFEM, while affecting severely the precision of the numerical scheme used for solving the associated linear system. Despite of its consistent mathematical basis, the numerical experiments so far conducted on using SGFEM are not yet clearly conclusive, especially regarding the robustness of the method. Therefore, the main purpose of the present paper is to give a contribution in this direction, through further investigating the SGFEM accuracy and stability. In particular, the recent proposed version of the method, called higher order SGFEM, is hereby considered. Some computational aspects, as the ones related to the implementation and integration of a flat-top partition of unit for constructing the augmented approximation space with polynomial enrichments are emphasized. The numerical experiments consist essentially of two-dimensional linear analysis of solids with internal cracks and corners on its boundaries. Our findings from the numerical tests are highly relevant regarding conditioning control and order of convergence provided by the SGFEM compared to the conventional GFEM.
Keywords
Generalized/Stable Finite Element Method, numerical stability, system conditioning
