Transient Dynamic Structural Analysis of Bars and Trusses Using the Generalized Finite Element Method

Abstract

The Generalized Finite Element Method (GFEM) can be viewed as a standard Finite Element Method (FEM) enriched by a family of shape functions appropriately chosen. Many applications of the GFEM can be found in literature, mostly when some information about the solution is known a priori. This paper presents the application of the GFEM to the problem of transient dynamic analysis of bars and trusses. Since the analytical solution of this problem leads, in most cases, to a trigonometric series, the enrichment used in this paper is composed of sine and cosine functions. The method of Newmark is used for the time integration procedure. The results and implementation issues are then compared to the ones obtained with a standard FEM using linear elements, and a Hierarchical Finite Element Method (HFEM) using higher order elements.