Journal of the Architectural Institute of Korea Structure & Construction (대한건축학회논문집:구조계)

Architectural Institute of Korea (대한건축학회)
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Geometrically Nonlinear Analysis of Plates and Shells with Reissner-Mindlin Isogeometric Degenerated Shell Element

등기하 퇴화쉘 요소를 이용한 판과 쉘의 기하학적 비선형해석

  • 박경섭 (경상대학교 건축공학과 계산역학연구실) ;
  • 이상진 (경상대학교 건축공학과)
  • Received : 2014.11.26
  • Accepted : 2015.07.15
  • Published : 2015.07.30
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Abstract

In this study, geometrically nonlinear analysis of plate and shell structures is carried out by using a degenerated shell element. The present shell element is formulated by using the isogeometric concept. Reissner-Mindlin assumption is adopted in the element formulation where total Lagrange formulation is used. In particular, the positions of control points is consistently used to create the normal vector for the mapping between control points and associated points on real surface. The arc-length method is employed to handle the snap-through behaviour of shells. Several benchmark tests are tackled to verify the performance of the present shell element. From numerical tests, the present shell element can remove locking phenomena with the only use of refinement technique and it performs satisfactorily for both thin and thick plate and shell structures under geometrically nonlinear situations.

Keywords

References

  1. Ahmad, S., Irons, B. M., & Zienkiewicz, O. C. (1970). Analysis of thick and thin shell structures by curved finite elements. Int. J. Num. Meth. Engng., 2, 419-451. https://doi.org/10.1002/nme.1620020310
  2. Benson, D. J., Bazilevs, Y., Hsu, M. C., & Hughes, T. J. R. (2010). Isogeometric shell analysis: The Reissner-Mindlin shell. Comput. Methods Appl. Mech. Engrg., 199, 276-289. https://doi.org/10.1016/j.cma.2009.05.011
  3. Bogner, F. K., Fox, R. L., & Schmit, L. A. (1965). The generation of inter-element compatible stiffness and mass matrices by the use of interpolation formulae. Proc. Conf. Matrix Melh. Srruct. Anal. Wright-Patterson AFB.
  4. Chattopadhyay, B., Sinha, P. K., & Mukhopadhyay, M. (1995). Geometrically nonlinear analysis of composite stiffened plates using finite elements. Composite Structures, 31, 107-118. https://doi.org/10.1016/0263-8223(95)00004-6
  5. Cottrell, J. A., Hughes, T. J. R., & Bazilevs, Y. (2009). Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, Chichester.
  6. Crisfield, M. A. (1981). A fast incremental/iterative solution procedure that handles snap-through. Computers and Structures, 13, 55-62. https://doi.org/10.1016/0045-7949(81)90108-5
  7. Dornisch, W., Klinkela, S., & Simeon, B. (2013). Isogeometric Reissner-Mindlin shell analysis with exactly calculated director vectors. Comput. Methods Appl. Mech. Engrg., 253, 491-504. https://doi.org/10.1016/j.cma.2012.09.010
  8. Figueiras, J. A. (1983). Ultimate load analysis of anisotropic and reinforced concrete plates and shells. Ph.D. Thesis, Department of Civil Engineering, University College of Swansea.
  9. Hinton, E., & Owen, D. R. J. (1984). Finite element software for plates and shells. Swansea, UK, Pineridge Press, 235-273.
  10. Horrigmoe, G., & Bergan, P. G. (1978). Nonlinear analysis of free-form shells by flat finite elements. Comput. Methods Appl. Mech. Eng., 16, 11-35. https://doi.org/10.1016/0045-7825(78)90030-0
  11. Hughes, T. J. R., Cottrell, J. A., & Bazilevs, Y. (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Engrg., 194, 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008
  12. Lee, S. J., & Kim, H. R. (2012). Analysis of plates using isogeometric approach based on Reissner-Mindlin Theory. J. of Atchitectual Institute of Korea, Structure & Consttuction, 28(9), 75-82.
  13. Levy, S. (1972). Square plate with clamped edges under normal pressure producing large deflection. NACA, Tech. Note 847.
  14. Parisch, H. (1981). Large displacement of shells including material nonlinearities. Comput. Methods Appl. Mech. Eng., 27, 183-214. https://doi.org/10.1016/0045-7825(81)90149-3
  15. Park, K. S., & Lee, S. J. (2014). Linear Aanalysis of Continuum Shells Using Isogeometric Degenerated Shell Element. J. of Atchitectual Institute of Korea, Structure & Consttuction, 30(10), 3-10.
  16. Pica, A., Wood, R. D., & Hinton, E. (1980). Finite Element Analysis of geometrically non-linear plate bending behaviour using a Mindlin formulation. Comput Struct., 11, 203-215. https://doi.org/10.1016/0045-7949(80)90160-1
  17. Piegel, L., & Tiller, W. (1995). The NURBS Book. Springer-Verlag.
  18. Ramesh, G., & Krishnamoorthy, C. S. (1995). Geometrically non-linear analysis of plates and shallow shells by dynamic relaxation. Comput. Methods Appl. Mech. Engrg., 123, 15-32. https://doi.org/10.1016/0045-7825(94)00761-B
  19. Razzaque, R. (1973). Program for triangular bending element with derivative smoothing. Int. J. Num. Meth. Engng., 5, 588-589. https://doi.org/10.1002/nme.1620050415
  20. Reissner, E. (1945). The effect of transverse shear deformation on the bending of elastic plate. ASME, J. Appl. Mech., 12, 69-76.
  21. Rushton, K. R. (1970). Large deflection of plates with initial curvature. Int. J. Mech. Sci., 12, 1037-1051. https://doi.org/10.1016/0020-7403(70)90031-7
  22. Sheikh, A.H. & Mukhopadhyay, M. (2000). Geometric nonlinear analysis of stiffened plate by the spline finite strip method. Computers and Structures, 76, 765-785. https://doi.org/10.1016/S0045-7949(99)00191-1
  23. Singh, A. V., & Elaghabash, Y. (2003). On the finite displacement analysis of quadrangular plates, International Journal of Non-Linear Mechanics, 38, 1149-1162. https://doi.org/10.1016/S0020-7462(02)00060-4
  24. Stricklin, J. A., Haisler, W. E., Tisdale, P. R., & Gunderson, R. (1969). A rapidly converging triangular plate element. AIAA J., 7, 180-181. https://doi.org/10.2514/3.5068
  25. Taylor, R. L. (1998). FEAP - A Finite Element Analysis Program. Ver. 7.4.
  26. Thankam, V. S., Singh, G., Rao, G. V., & Rath, A. K. (2003). Shear flexible element based on coupled displacement eld for large deflection analysis of laminated plates. Computers and Structures, 81, 309-320. https://doi.org/10.1016/S0045-7949(02)00450-9
  27. Uhm, T. K., & Youn, S. K. (2009). T-spline finite element method for the analysis of shell structures. Int. J. Numer. Meth. Engng., 80, 507-536. https://doi.org/10.1002/nme.2648
  28. Weil, N. A., & Newmark, N. M. (1956). Large deflections of elliptical plates. J. Appl. Mech., 23, 21-26.
  29. Zhang, Y. X., & Cheung, Y. K. (2003). Geometric nonlinear analysis of thin plates by a refined nonlinear non-conforming triangular plate element. Thin-Walled Structures, 41, 403-418. https://doi.org/10.1016/S0263-8231(02)00114-3