Free vibration analysis of curved Bernoulli-Euler beam using isogeometric approach
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Isogeometric analysis (IGA) is based on a concept that uses the same base functions for representing both the model geometry and the solution space. The most common base functions used in the IGA are NURBS (Non-Uniform Rational B-Splines) functions for their capability to analytically represent various geometries. In this paper, the IGA is applied in the free vibration analysis of rotation-free plane curved Bernoulli-Euler beam. The stiffness and mass matrices have been developed using basic concepts of continuum mechanics and the principle of virtual work. Geometry of the undeformed and deformed beam is defined using convective coordinates and cross section basis vectors. Results of the free vibration analysis for beam with arbitrary curvature are compared with the results obtained from the conventional finite element method (FEM) software. The significant advantages of the IGA approach over the FEM are shown and discussed.
Keywords:
isogeometric analysis / free vibration / rotation-free Bernoulli-Euler beamSource:
Proceedings / The 6th International Congress of Serbian Society of Mechanics, Tara, June 19-21, 2017, 2017, 134-134Publisher:
- Serbian Society of Mechanics ; Faculty of Mechanical Engineering, University of Belgrade,Belgrade, Beograd
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GraFarTY - CONF AU - Jočković, Miloš AU - Baitsch, Matthias AU - Nefovska-Danilović, Marija PY - 2017 UR - https://grafar.grf.bg.ac.rs/handle/123456789/1573 AB - Isogeometric analysis (IGA) is based on a concept that uses the same base functions for representing both the model geometry and the solution space. The most common base functions used in the IGA are NURBS (Non-Uniform Rational B-Splines) functions for their capability to analytically represent various geometries. In this paper, the IGA is applied in the free vibration analysis of rotation-free plane curved Bernoulli-Euler beam. The stiffness and mass matrices have been developed using basic concepts of continuum mechanics and the principle of virtual work. Geometry of the undeformed and deformed beam is defined using convective coordinates and cross section basis vectors. Results of the free vibration analysis for beam with arbitrary curvature are compared with the results obtained from the conventional finite element method (FEM) software. The significant advantages of the IGA approach over the FEM are shown and discussed. PB - Serbian Society of Mechanics ; Faculty of Mechanical Engineering, University of Belgrade,Belgrade, Beograd C3 - Proceedings / The 6th International Congress of Serbian Society of Mechanics, Tara, June 19-21, 2017 T1 - Free vibration analysis of curved Bernoulli-Euler beam using isogeometric approach EP - 134 SP - 134 UR - https://hdl.handle.net/21.15107/rcub_grafar_1573 ER -
@conference{ author = "Jočković, Miloš and Baitsch, Matthias and Nefovska-Danilović, Marija", year = "2017", abstract = "Isogeometric analysis (IGA) is based on a concept that uses the same base functions for representing both the model geometry and the solution space. The most common base functions used in the IGA are NURBS (Non-Uniform Rational B-Splines) functions for their capability to analytically represent various geometries. In this paper, the IGA is applied in the free vibration analysis of rotation-free plane curved Bernoulli-Euler beam. The stiffness and mass matrices have been developed using basic concepts of continuum mechanics and the principle of virtual work. Geometry of the undeformed and deformed beam is defined using convective coordinates and cross section basis vectors. Results of the free vibration analysis for beam with arbitrary curvature are compared with the results obtained from the conventional finite element method (FEM) software. The significant advantages of the IGA approach over the FEM are shown and discussed.", publisher = "Serbian Society of Mechanics ; Faculty of Mechanical Engineering, University of Belgrade,Belgrade, Beograd", journal = "Proceedings / The 6th International Congress of Serbian Society of Mechanics, Tara, June 19-21, 2017", title = "Free vibration analysis of curved Bernoulli-Euler beam using isogeometric approach", pages = "134-134", url = "https://hdl.handle.net/21.15107/rcub_grafar_1573" }
Jočković, M., Baitsch, M.,& Nefovska-Danilović, M.. (2017). Free vibration analysis of curved Bernoulli-Euler beam using isogeometric approach. in Proceedings / The 6th International Congress of Serbian Society of Mechanics, Tara, June 19-21, 2017 Serbian Society of Mechanics ; Faculty of Mechanical Engineering, University of Belgrade,Belgrade, Beograd., 134-134. https://hdl.handle.net/21.15107/rcub_grafar_1573
Jočković M, Baitsch M, Nefovska-Danilović M. Free vibration analysis of curved Bernoulli-Euler beam using isogeometric approach. in Proceedings / The 6th International Congress of Serbian Society of Mechanics, Tara, June 19-21, 2017. 2017;:134-134. https://hdl.handle.net/21.15107/rcub_grafar_1573 .
Jočković, Miloš, Baitsch, Matthias, Nefovska-Danilović, Marija, "Free vibration analysis of curved Bernoulli-Euler beam using isogeometric approach" in Proceedings / The 6th International Congress of Serbian Society of Mechanics, Tara, June 19-21, 2017 (2017):134-134, https://hdl.handle.net/21.15107/rcub_grafar_1573 .