THE GENERALIZED FINITE ELEMENT METHOD APPLIED IN FREE VIBRATION ANALYSIS UNDER PLANE STRESS

Ricardo Custódio¹; Marcos Arndt¹

¹ Program of Numerical Methods in Engineering, Federal University of Paraná

doi:10.20906/CPS/CILAMCE2017-0324

Resumo

The Generalized Finite Element Method can be defined as a generalization of the Finite Element Method. The main principle of this method consists in the enrichment of the finite element through construction of a subspace filled with shape functions, that not to be necessarily polynomial. Another characteristics of this method, it is the uses of concepts of the Partition of Unity, wherein the shape functions need to have that properties. However, the enrichment functions can often be defined through previously known boundary value problems. The aim of this paper is to investigate an enrichment with shape functions for a finite quadrilateral element and also to verify the response of its application in a problem of free vibration for a structure subjected to the plane stress, in order to check its convergence and precision when compared to conventional Finite Element Method.

Palavras-chave: Generalized Finite Element Method; Partition of Unity; Free Vibration; Plane Stress