An adaptive generalized finite element method applied to free vibration analysis of straight bars and trusses

Dynamic analysis of Euler–Bernoulli beam problems using the Generalized Finite Element Method

“…Table 1 contains the trigonometric enrichment monomials for enriched dynamic analyses of bars, Eqs. (13a)-(13d) ( [20,22]) as well as the trigonometric enrichment monomials for dynamic analysis of Euler Bernoulli beams, Eqs. (14a)-(14f) [35].…”

“…Additionally, there are several researches concerning the development of error estimation in GFEM [18,19]. It has been shown that the enriched FE shape functions associated to trigonometric functions provide remarkable efficiency in free vibration analysis in bars and beams due to the fact that the trigonometric functions present similar profile to the vibration modes [20,21]. GFEM with trigonometric functions also has been applied by Torii and Machado [22] for free vibration analysis employing quadrilateral plane elements.…”

Generalized Finite Element Method for Vibration Analysis of Bars

“…Another refinement possible in the proposed GFEM is the adaptive refinement, which is presented below. The adaptive GFEM is an iterative approach presented first by [1] whose main goal is to increase the accuracy of the frequency (eigenvalue) related to a chosen vibration mode with order denoted by "target order". The flowchart with blocks A to H presented in Figure 3 represents the adaptive process.…”

The Generalized Finite Element Method Applied to Free Vibration of Framed Structures

“…Another possible refinement in the proposed GFEM is the adaptive one, which is presented below. The adaptive GFEM is an iterative approach presented first by Arndt et al (2010) whose main goal is to increase the accuracy of the frequency (eigenvalue) related to a chosen vibration mode with order denoted by "target order". The flowchart with blocks A to H presented in Fig.…”

“…Recently several studies have indicated the efficiency of the GFEM and others methods based on the Partition of Unity Method in problems such as analysis of cracks (Xiao & Karihaloo, 2007;Abdelaziz & Hamouine, 2008;Duarte & Kim, 2008;Nistor et al, 2008), dislocations based on interior discontinuities (Gracie et al, 2007), large deformation of solid mechanics (Khoei et al, 2008) and Helmholtz equation (Strouboulis et al, 2006a;Strouboulis et al, 2008). In structural dynamics, the Partition of Unity Method was applied by De Bel et al (2005), Hazard & Bouillard (2007) to numerical vibration analysis of plates and by Arndt et al (2010) to free vibration analysis of bars and trusses. Among the main challenges in developing the GFEM to a specific problem are: (a) choosing the appropriate space of functions to be used as local approximation and (b) the imposition of essential boundary conditions, since the degrees of freedom used in GFEM generally do not correspond to the nodal ones.…”