Structural dynamic analysis for time response of bars and trusses using the generalized finite element method

Torii, André Jacomel; Machado, Roberto Dalledone

doi:10.1590/s1679-78252012000300001

Cited by 26 publications

(25 citation statements)

References 25 publications

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“…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].…”

Section: Generalized Finite Element Methodsmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Shang

Machado

Filho

2016

Computers & Structures

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Section: Generalized Finite Element Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Shang

Machado

Filho

2016

Computers & Structures

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“…For the time response analysis, higher order polynomial finite elements were obtained using Lobatto's polynomials as shape functions, as described in details by [22]. These polynomials are different from Lagrange's polynomials that are commonly used in p-version of FEM.…”

Section: Figure 4: Error Evaluation According To Eq (16)mentioning

confidence: 99%

Generalized Finite Element Method for Vibration Analysis of Bars

Arndt¹,

Torii²,

Machado³

et al. 2014

Proceedings of 10th World Congress on Computational Mechanics

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“…The Timoshenko beam theory deals with two differential equations of motion in terms of deflection and cross-section rotation. The Timoshenko beam theory has come into focus with considerable developments of the finite element method and its application in practice [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Spectral element analysis of free - vibration of Timoshenko beam

Hamioud

Khalfallah

2018

IJEM

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The paper describes free vibration of Timoshenko beam by using spectral element method. Based on the partial differential equation of motion, the dynamic stiffness matrix in the frequency domain is formulated. In this case, natural frequencies for simply supported beam are obtained for each mode of vibration. In this study, three solutions are presented: (1) the analytical solution, (2) the finite element method, and (3) the spectral element method. In the last method, the beam is described by one element only, but in finite element modelling, the number of elements varies in order to improve the quality of the solution. Numerical results obtained by these three methods are collected. The spectral element method displays high performance compared to the finite element approach, and is considered as interesting tool in the structural dynamic field.

show abstract

Structural dynamic analysis for time response of bars and trusses using the generalized finite element method

Cited by 26 publications

References 25 publications

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

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

Generalized Finite Element Method for Vibration Analysis of Bars

Spectral element analysis of free - vibration of Timoshenko beam

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