ISOGEOMETRIC ANALYSIS APPLIED TO FREE VIBRATION ANALYSIS OF PLANE STRESS AND PLANE STRAIN STRUCTURES

Autores

  • Mateus Rauen Universidade Federal do Paraná
  • Roberto Dalledone Machado
  • Marcos Arndt

DOI:

https://doi.org/10.26512/ripe.v2i14.21367

Palavras-chave:

Isometric Analysis. Free Vibration. Plane Stress.

Resumo

Actually Isogeometric Analysis (IGA) have proven high accuracy and efficacy in dynamical problems, openning possibilities to improve the traditional FEM models. The aim of this paper is to test the response of IGA for free vibration problems of plane stress and structures. Based on numerical applications, IGA models have their convergence and accuracy checked and compared with those developed in FEM and GFEM. The results shows high accuracy for IGA models, and reinforce its way as a promising tool.

Downloads

Não há dados estatísticos.

Referências

Arndt, M. (2009), O M´etodo dos Elementos Finitos Generalizados Aplicado `A An´alise de Vibrac¸ ˜oes Livres de Estruturas Reticuladas, PhD thesis, Programa de P´os-Graduac¸ ˜ao em M´etodos Num´ericos em Engenharia, Curitiba. Doutorado em M´etodo Num´ericos em Engenharia.

Arndt, M., Machado, R. D. & Scremin, A. (2010), ‘An adaptive generalized finite element method applied to free vibration analysis of straight bars and trusses’, Journal of Sound and Vibration 329, 659”“672.

Arndt, M., Machado, R. D. & Scremin, A. (2011), Enriched methods for vibration analysis of framed structures, in ‘21st International Congress of Mechanical Engineering - COBEM 2011’, Natal, Brazil.

Babuˇska, I. & Banerjee, U. (2012), ‘Stable generalized finite element method (sgfem)’, Computer Methods in Applied Mechanics and Engineering 201, 91”“111.

Cottrell, J. A., Bazilevs, Y. & Hughes, T. J. R. (2009), Isogeometric Analysis: Toward Integration of CAD and FEA, 1st edition edn, John Wiley & Sons, USA.

Cottrell, J. A., Hughes, A. T. J. R. & Reali, A. (2007), ‘Studies of refinement and continuity in isogeometric structural analysis’, Computer Methods in Applied Mechanics and Engineering 196, 4160”“4183.

Cottrell, J. A., Reali, A., Bazilevs, Y. & Hughes, T. J. R. (2006), ‘Isogeometric analysis of structural vibrations’, Computer Methods in Applied Mechanics and Engineering 195, 5257”“ 5196.

Cox, M. G. (1972), ‘The numerical evaluation of b-splines’, IMA Journal of Applied Mathematics 10(2), 134”“149.

De-Boor, C. (1972), ‘On calculation of b-splines’, Journal of Approximation Theory 6, 50”“62.

Hughes, T. J. R., Cottrell, J. A. & Bazilevs, Y. (2005), ‘Isogeometric analysis: Cad, finite elements, nurbs, exact geometry and mesh refinement’, Computer Methods in Applied Mechanics and Engineering 194, 4135”“4195.

Melenk, J. M. & Babuska, I. (1996), ‘The partition of unity finite element method: Basic theory and applications’, Computer Methods in Applied Mechanics and Engineering 139(1- 4), 289”“314.

Piegl, L. & Tiller, W. (1997), The NURBS Book (2Nd Ed.), Springer-Verlag New York, Inc., New York, NY, USA.

Rauen, M. (2014), An´alise isogeom´etrica aplicada ao problema de vibrac¸ ˜ao livre na mecˆanica das estruturas, Master’s thesis, Universidade Federal do Paran´a.

Rauen, M., Machado, R. D. & Arndt, M. (2013), Comparison between the isogeometric analysis and the enriched methods to the problem of free vibration of bars, in ‘Proceedings of the XXXIV Ibero-Latin American Congress on Computational Methods in Engineering’, XXXIV Ibero-Latin American Congress on Computational Methods in Engineering, Piren´oopolis, Brazil.

Reddy, J. N. (1993), An Introduction to the Finite Element Method, McGraw-Hill, New York.

Sillem, A., Simone, A. & Sluys, L. (2014), ‘The orthonormalized generalized finite element method”“ogfem: Efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions’, Computer Methods in Applied Mechanics and Engineering

Torii, A. J. (2012), An´alise Dinˆamica de Estruturas com oM´etodo dos Elementos Finitos Generalizado, PhD thesis, Programa de P´os-Graduac¸ ˜ao em M´etodos Num´ericos em Engenharia, Curitiba. Doutorado em M´etodo Num´ericos em Engenharia.

Torii, A. & Machado, R. D. (2012), ‘Structural dynamic analysis for time response of bars and trusses using the generalized finite element method’, Latin American Journal of Solids and Structures 9(3), 309”“338.

Zeng, P. (1998a), ‘Composite element method for vibration analysis of structures, part i: principle and c0 element (bar)’, Journal of Sound and Vibration 218(4), 619”“658.

Downloads

Publicado

2017-01-30

Como Citar

Rauen, M., Machado, R. D., & Arndt, M. (2017). ISOGEOMETRIC ANALYSIS APPLIED TO FREE VIBRATION ANALYSIS OF PLANE STRESS AND PLANE STRAIN STRUCTURES. Revista Interdisciplinar De Pesquisa Em Engenharia, 2(14), 146–155. https://doi.org/10.26512/ripe.v2i14.21367