COMPARATIVE ANALYSIS OF TRIGONOMETRIC ENRICHMENTS USED IN DYNAMIC ANALYSIS OF TIMOSHENKO BEAMS BY THE GENERALIZED FINITE ELEMENT METHOD

Resumo

The Finite Element Method (FEM) is widely used in the dynamic analysis of structures, how-
ever it has some limitations. In order to improve the numerical response, enriching functions can be

incorporated to FEM approximation space using the Generalized Finite Element Method (GFEM) pro-
cedure. Several studies have already been carried out to prove the efficiency of GFEM in the dynamic

analysis of bars, Euler-Bernoulli beams, trusses, among other structural elements, but few studies have
investigated the application of GFEM in the dynamic analysis of Timoshenko beams. The present work
aims to contribute to this field presenting modal and transient analyses of Timoshenko beams using the
GFEM technique. Three different trigonometric enrichments are used to perform modal and transient
analyses of Timoshenko clamped-free beams without damping and the results are compared with those

obtained by FEM. The normalized spectrum is obtained by the modal analysis and displacements, ve-
locities and accelerations of the beam along the time are also calculated by transient analysis. In that

manner the efficiency of each GFEM enrichment in modal and transient analysis of Timoshenko beams
is discussed.