Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
권호 표지
DOI QR코드

DOI QR Code

Dynamic Analysis of Plates using a Improved Assumed Natural Strain Shell Element

개선된 자연변형률 쉘 요소를 이용한 판의 진동해석

  • Lee, Won-Hong (Department of Civil Engineering, Jinju National University) ;
  • Han, Sung-Cheon (Department of Civil & Railroad Engineering, Daewon College) ;
  • Park, Weon-Tae (Division of Construction and Environmental Engineering, Kongju National University)
  • 이원홍 (진주산업대학교 토목공학과) ;
  • 한성천 (대원과학대학 철도건설과) ;
  • 박원태 (공주대학교 건설환경공학부)
  • Received : 2010.04.20
  • Accepted : 2010.06.18
  • Published : 2010.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we investigate the vibration analysis of plates, using an 8-node shell element that accounts for the transverse shear strains and rotary inertia. The forced vibration analysis of plates subjected to arbitrary loading is investigated. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To improve an 8-node shell element for forced vibration analysis, the new combination of sampling points for assumed natural strain method was applied. The refined first-order shear deformation theory based on Reissner-Mindlin theory which allows the shear deformation without shear correction factor and rotary inertia effect to be considered is adopted for development of 8-node assumed strain shell element. In order to validate the finite element numerical solutions, the reference solutions of plates are presented. Results of the present theory show good agreement with the reference solution. In addition the effect of damping is investigated on the forced vibration analysis of plates.

본 논문에서는 회전관성과 전단변형이 고려된 8절점 쉘 요소를 이용한 판의 진동해석을 연구하였다. 면내 잠김과 전단 잠김 현상을 극복하기 위하여 가정자연변형률 방법을 이용하였다. 8절점 쉘 요소의 성능 향상을 위해 새로운 보간점의 조합을 이용한 가정변형률 방법을 사용하였다. Reissner-Mindlin 이론에 근거한 개선된 1차 전단변형이론을 적용하여 회전관성을 고려하였으며 전단보정계수를 사용하지 않았다. 본 연구의 결과를 검증하기 위해 참고문헌의 직사각형 판의 동적 해석결과를 제시하였다. 해석결과는 참고문헌의 결과와 잘 일치하였다. 또한 감쇄효과가 고려된 판의 진동해석을 수행하였다.

Keywords

References

  1. Ahmad, S. Irons, B. M, and Zienkiewicz, O. C., Analysis of thick and thin shell structures by curved finite elements, Int. J. Num. Meth. Eng. Vol. 2, pp. 419-451, 1970. https://doi.org/10.1002/nme.1620020310
  2. Bathe, K. J. and Dvorkin, E. N. A formulation of general shell elements-The use of mixed interpolation of tensorial components, Int. J. Num.Meth. Eng. Vol. 22, pp. 697-722, 1986. https://doi.org/10.1002/nme.1620220312
  3. Bathe, K. J., Ozdemir, H. and Wilson, E. L. Static and dynamic geometric and material nonlinear analysis, UC SESM 74-4, (University of California, Berkeley, California), 1974.
  4. Belytschko, T., Wong, B. L., and Stolarski, H. Assumed strain stabilization procedure for the 9-node Lagrange shell element, Int. J. Num.Meth .Eng. Vol. 28, pp. 385-414, 1989. https://doi.org/10.1002/nme.1620280210
  5. Bucalem, M. L. and Bathe, K. J. Higher-order MITC general shell elements, Int. J. Num. Meth.Eng. Vol. 36, pp. 3729-3754, 1993. https://doi.org/10.1002/nme.1620362109
  6. Donell, L. H. Stability of thin-walled tubes under torsion. NASA Report 479, Washington, DC, 1933.
  7. Huang, H. C., and Hinton, E. A new nine node degenerated shell element with enhanced membrane and shear interpolation, Int. J. Num. Meth. Eng. Vol. 22, pp. 73-92, 1986. https://doi.org/10.1002/nme.1620220107
  8. Hughes, T. J. R., and Liu, W. K. Nonlinear finite element analysis of shells: Part I. Three-dimensional shells. Comput. Methods Appl. Mech. Eng. Vol. 26, pp. 331-362, 1981. https://doi.org/10.1016/0045-7825(81)90121-3
  9. Jang, J., and Pinsky, P. M. An assumed covariant strain based 9-node shell element, Int. J. Num. Meth. Eng. Vol. 24, pp. 2389-2411, 1987. https://doi.org/10.1002/nme.1620241211
  10. Kim, K. D., Lomboy, G. R. and Han, S. C. A co-rotational 8-node assumed strain shell element for postbuckling analysis of laminated composite plates and shells, Comput. Mech, Vol. 30(4), pp. 330-342, 2003. https://doi.org/10.1007/s00466-003-0415-6
  11. Kim, K. D. and Park, T. H. An 8-node assumed strain element with explicit integration for isotropic and laminated composite shells, Struct. Eng. Mech. Vol. 13, pp. 1-18, 2002. https://doi.org/10.12989/sem.2002.13.1.001
  12. Lakshminarayana, H. V. and Kailash, K. A shear deformable curved shell element of quadrilateral shape, Comput. Struct. Vol. 33, pp. 987-1001, 1989. https://doi.org/10.1016/0045-7949(89)90434-3
  13. Lee, W. H. and Han, S. C. Free and forced vibration analysis of laminated composite plates and shells using a 9-node assumed strain shell element, Comput. Mech. Vol. 39, pp. 41-58, 2006. https://doi.org/10.1007/s00466-005-0007-8
  14. Leissa, A. W. Vibrations of shells. NASA PA-288, Washington, DC, 1973.
  15. Liew, K. M. Research on thick plate vibration: a literature survey, J. Sound Vib. Vol. 180, pp. 163-176, 1995. https://doi.org/10.1006/jsvi.1995.0072
  16. Liu, W. K., Lam, D., Law, S. E., and Belytschko, T. Resultant stress degenerated shell element, Comput. Meth. Appl. Mech. Eng. Vol. 55, pp. 259-300, 1986. https://doi.org/10.1016/0045-7825(86)90056-3
  17. Love, A. E. H. The small vibrations and deformations of thin elastic shell, Philosophical Transactions of the Royal Society Vol. 179, pp. 527-546, 1888.
  18. Ma, H. and Kanok-Nukulchai, W. On the application of assumed strained methods (eds.) Kanok-Nukulchai et al., Structureal Engineering and Construction, Achievements, Trend and Challenges, AIT, Thailand, 1989.
  19. MacNeal, R. H. and Harder, R. L. A proposed standard set of problems to test finite element accuracy, Finite Elements in Analysis and Design Vol. 1, pp. 3-20, 1985. https://doi.org/10.1016/0168-874X(85)90003-4
  20. Park, T. H., Kim, K. D. and Han, S. C. Linear static and dynamic analysis of laminated composite plates and shells using a 4-node quasi-conforming shell element, Compos. Part B-Eng. Vol. 37(2-3), pp. 237-248, 2006.
  21. Qatu, M. S. Review of shallow shell vibration research, Shock and Vibration Digest Vol. 24, pp. 3-15, 1992.
  22. Ramm, E. A plate/shell element for large deflections and rotations. Nonlinear finite element analysis in structural mechanics, W. Wunderlich, E. Stein, and K. J. Bathe, eds., M.I.T. Press, New York, 1977.
  23. Reddy, J. N. Mechanics of composite plates and shells: Theory and Analysis, 2nd edn. CRC press, Boca Raton, 2004.
  24. Simo, J. C., and Hughes, T. J. R. On the variational formulations of assumed strain methods, J. Appl. Mech. Vol. 53, pp. 51-54, 1986. https://doi.org/10.1115/1.3171737
  25. Srinivas, C. V., Rao, J. and Rao, A. K. An exact analysis for vibration of simply supported homogeneous and laminated, thick rectangular plates. J. Sound Vib. Vol. 12, pp. 187-199, 1970. https://doi.org/10.1016/0022-460X(70)90089-1
  26. Yunqian, Q., Norman, F. and Knight, J. A refined first-order shear-deformation theory and its justification by plane-strain bending problem of laminated plates, Int. J. Solids Struct. Vol. 33(1), pp. 49-64, 1996. https://doi.org/10.1016/0020-7683(95)00010-8
  27. 이원홍, 한성천, 박원태, 점진기능재료(FGM) 판의 휨, 진동 및 좌굴 해석, 한국산학기술학회논문집 제9권 제4호, pp. 1043-1049, 2008. https://doi.org/10.5762/KAIS.2008.9.4.1043
  28. 한성천, 이창수, 김기동, 박원태 (2007) 4절점 준적합 쉘요소를 이용한 점진기능재료(FGM) 판과 쉘의 구조적 안정 및 진동연구, 한국방재학회논문집 제7권 제5호, pp. 47-60.