O método dos elementos finitos generalizados com elementos triangulares na análise dinâmica de estruturas em estado plano

Abstract

The dynamic analysis of structures is a relevant topic, given that advanced technology has allowed the execution of slender structures, which are more suitable to the dynamic effects. The in-plane vibration of structures can be approximated through Generalized Finite Element Method (GFEM). The purpose of this work is to present two triangular finite elements enriched with trigonometric functions, considering that oscillatory characteristic of this functions are common within these problems. The first methodology (it is called GFEM-D) is made from an enriched quadrilateral element. The second proposal (called GFEM-2) is done by generating new enrichment functions, based on the methodology of building enrichment functions for bar elements. To the in-plane vibration of plates, it is found that the GFEM-2 its better than GFEM-D. When compared to the traditional FEM, the GFEM-2 has a better approximation to the low natural frequency field. In this way, the method proves to be suitable for use in these types of problems.