Free Vibration Analysis of Elastic Bars using Isogeometric Approach

• Journal title : Architectural research
• Volume 13, Issue 3,  2011, pp.41-47
• Publisher : Architectural Institute of Korea
• DOI : 10.5659/AIKAR.2011.13.3.41
Title & Authors
Free Vibration Analysis of Elastic Bars using Isogeometric Approach
Lee, Sang-Jin; Park, Kyoung-Sub;

Abstract
A study on the free vibration analysis of elastic bar is described in this paper. In order to determine the natural frequencies of bars, a bar element is developed by using isogeometric formulation. The B-spline is introduced to represent the geometry of bar and the same geometric definition is also used to define its unknown displacement field in isogeometric formulation. Therefore, the stiffness and mass matrices are derived by the order-free B-spline basis function. The efficiency and accuracy of the present isogeometric bar elementis demonstrated by using several numerical tests. From numerical results, it is found to be that the present isogeometric element produces very accurate natural frequencies of bars. Finally, the present isogeometric solutions are provided as future reference solutions.
Keywords
Isogeometric Analysis;Elastic bar;Free Vibration;NURBS;Knot Vector;Control Point;
Language
English
Cited by
1.
Isogeometric Analysis of Laminated Plates under Free Vibration,;

Architectural research, 2014. vol.16. 3, pp.121-129
2.
등기하해석법을 적용한 평면구조물의 위상최적화,박경임;이상진;

대한건축학회논문집:구조계, 2016. vol.32. 2, pp.3-10
1.
Isogeometric Analysis of Laminated Plates under Free Vibration, Architectural research, 2014, 16, 3, 121
2.
Topology Optimization for Plane Structures using Isogeometric Approach, Journal of the Architectural Institute of Korea Structure & Construction, 2016, 32, 2, 3
References
1.
Cottrell, J.A., Bazilevs, Y. and Hughes, T.J.R. (2009) Isogeometric Analysis: Towards Integration of CAD and FEA.Wiley.

2.
De Boor, C. (1978)A Practical Guide to Splines. Springer

3.
Hughes, T.J.R. (2000)The Finite Element Method: Linear Static and Dynamic Finite ElementAnalysis. Dover Publications.

4.
Hughes,T. J.R . Cott rel l , J. A . and Ba z i le vs, Y. (2005) Isogeometricanalysis: CAD,finiteelements,NURBS,exact geometry andmesh refinement.Comput. Methods Appl. Mech. Eng., vol. 194, no. 39-41, pp. 4135-4195.

5.
Hughes, T.J.R. and Evans J.A. (2010) Isogeometric analysis.ICES Report 10-18, The Institute of Computational Engineering and Science, University of Texas Austin

6.
Rogers,D. (2001) An Introduction to NURBS: With Historical Perspective.Academic Press, London, UK.