Browse > Article

A New Higher-Order Hybrid-Mixed Element for Curved Beam Vibrations  

Kim Jin-Gon (대구가톨릭대학교 기계자동차공학부)
Park Yong-Kuk (대구가톨릭대학교 기계자동차공학부)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.19, no.2, 2006 , pp. 151-160 More about this Journal
Abstract
In this study, we propose a new efficient 2-noded hybrid-mixed element for curved beam vibrationshaving a uniform and non-uniform cross section. The present element considering transverse shear strain is based on Hellinger-Reissner variational principle and introduces additional nodeless degrees for displacement field interpolation in order to enhance the numerical performance. The stress parameters are eliminated by the stationary condition and then the nodeless degrees are condensed out by the Guyan reduction. In the performance evaluation process of the present field-consistent higher-order element, we carefully examine the effects of field consistency and the role of higher-order interpolation functions on the hybrid-mixed formulation. Several benchmark tests confirm e superior behavior of the present hybrid-mixed element for curved beam vibrations.
Keywords
2-noded curved beam element; Hybrid-mixed formulation; Nodeless degrees; Free vibration analysis; Guyan reduction;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Saleeb, A.F., Chang. T.Y. (1987) On the Hybrid-Mixed Formulation $C^0$ Curved Beam Elements, Computer Methods in Applied Mechanics and Engeering, 60, pp.95-121   DOI   ScienceOn
2 Leung, A.Y.T., Zhu, B. (2004) Fourier p-Elements for Curved Beam Vibrations, Thin-Walled Structures, 42. pp.39-57
3 Rossi, R.E., Laura, P.A.A. (1990) Dynamic Stiffening of an Arch Clamped at One End Free at the Other, Journal of Sound and Vibration. 160, pp.190-192
4 이병구, 박광규, 모정만, 이재만 (1998) 변단면 수평 곡선보의 자유진동에 관한 연구, 한국전산구조공학회논문집, 11(3), pp.155-164
5 Tessler. A., Spiridigliozzi, L. (1986) Curved Beam Elements with Penalty Relaxation, International Journal for Numerical Method in Engeering, 23, pp.2245-2262   DOI   ScienceOn
6 Dawe, D.J. (1974) Numerical Studies Using Circular Arch Finite Elements. Computers and. Structures., 4. pp.729-740   DOI   ScienceOn
7 Raveendranath, P., Singh, G., Pradhan, B. (1999) A Two-Noded Locking-Free Shear Flexible Curved Beam Element, International Journal for Numerical Method in Engeering, 44, pp.265-280   DOI   ScienceOn
8 서광진, 민병철, 김문영 (2000) 곡률이 변하는 박벽 곡선보의 3차원 자유진동 및 좌굴해석, 한국전산구조공학회 논문집, 13(3), pp.321-328
9 Noor, A.K.. Peters, J.M. (1981) Mixed Models and Reduced/Selective Integration Displacement Models for Nonlinear Analysis of Curved Beams, International Journal for Numerical Method in Engeering, 17, pp.615-631   DOI   ScienceOn
10 김진곤, 노병국 (2003) 혼합 유한요소를 이용한 축대칭 셸의 정동적해석, 한국전산구조공학회논문집, 16(2), pp.165-172
11 Kim, J.G.. Kim, Y.Y. (1998) A New Higher-Order Hybrid-Mixed Curved Beam Element, International Journal for Numerical Method in Engeering, 43, pp.925-940   DOI   ScienceOn
12 Stolarski, H., Belytschko, T. (1982) Membrane Locking and Reduced Integration for Curved Elements, Journal of Applied Mechanics, 49, pp.172-176   DOI
13 유하상, 신효철 (1997) 곡선보 요소의 고유치 해석에서 질량 행렬의 영향, 대한기계학회논문집, 21(2), pp.288-296
14 Rao. S.S. (2004) Mechanical Vibrations. 4th Edition, Pearson Prentice Hall, p.1078
15 이병구, 오상진 (1996) 원호형 곡선보의 면외 자유진동에 관한 수치해석적 연구, 한국전산구조공학회논문집, 8(1), pp.133-139
16 Babu, C.R., Prathap, G. (1986) A Linear Thick Curved Beam Element. International Journal for Numerical Method in Engeering, 23. pp.1313-1328   DOI   ScienceOn
17 Cook, R.D., Malkus, D.S., Plesha, M.E. (1989) Concepts and Applications of Finite Element Analysis, JohnWiely & Sons, New York, p.630
18 Stolarski. H., Belvtschko, T. (1983) Shear and Membrane Locking in Curved $C^0$ Elements. Computer Methods in Applied Mechanics and Engeering, 41. pp.279-296   DOI   ScienceOn
19 Prathap, G., Babu, C.R. (1986) An Isoparametric Quadratic Thick Curved Beam Element, International Journal for Numerical Method in Engeering, 23, pp .1583-1600   DOI   ScienceOn