Eventos Anais de eventos
MecSol 2017
6th International Symposium on Solid Mechanics
GFEM STABILIZATION TECHNIQUES APPLIED TO DYNAMIC ANALYSIS OF NON-UNIFORM SECTION BARS
Submission Author:
Leticia Col Debella , PR
Co-Authors:
Paulo de Oliveira Weinhardt, Marcos Arndt, ROBERTO Dalledone Machado
Presenter: Paulo de Oliveira Weinhardt
doi://10.26678/ABCM.MecSol2017.MSL17-0117
Abstract
The Finite Element Method (FEM), although widely used as an approximate solution method, has some limitations when applied in dynamic analysis. As the loads excite the high frequency and modes, the method may lose precision and accuracy. To improve the representation of these high-frequency modes, we can use the Generalized Finite Element Method (GFEM) to enrich the approach space with appropriate functions according to the problem under study. However, there are still some aspects that limit the GFEM applicability in problems of dynamics of structures, as numerical instability associated with the process of enrichment. Due to numerical instability, the GFEM may lose precision and even result in numerically singular matrices. In this context, this paper presents the application of two proposals to minimize the problem of sensitivity of the GFEM: an adaptation of the Stable Generalized Finite Element Method for dynamic analysis and a stabilization strategy based on preconditioning of e¬nrichment. Examples of and one-dimensional modal and transient analysis are presented. Numerical results obtained are discussed analyzing the effects of the adoption of preconditioning techniques on the approximation and the stability of GFEM in dynamic analysis.
Keywords
GFEM, dynamic analysis, numerical stability
