GFEM STABILIZATION TECHNIQUES APPLIED TO DYNAMIC ANALYSIS OF NON-UNIFORM SECTION BARS

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 enrichment. Examples of one-dimensional modal and transient analysis are presented as bars with cross section area variation. 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.