GFEM STABILIZATION TECHNIQUES APPLIED TO TRANSIENT DYNAMIC ANALYSIS - Weinhardt, Paulo de Oliveira (2017)
In the context of dynamic analysis of structures, one of the limitations of the Finite Element Method (FEM) is the difficulty of approaching the high frequencies. This lack of precision becomes more significant as the loading excite modes with higher frequencies. Aiming at address this problem one may use the Finite Element Method Generalized / Extended (GFEM /XFEM) to enrich the approximation space and better represent these high frequency modes. Despite the excellent properties of GFEM / XFEM as high accuracy, application versatility and excellent convergence rates, there are aspects that still limit its applicability as the numerical instability associated with this enrichment process even in well-placed boundary value problems. GFEM/XFEM matrices may be ill-conditioned, which may result in a accuracy loss, and even resulting in numerically singular matrices. In this work two proposals are presented to circumvent the GFEM sensitivity problem. Examples of one-dimensional transient analysis are presented and results are discussed analyzing the effects of adopting the preconditioning of enrichment functions strategy.