The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the isotropic and anisotropic composite material. The effect of the coupling term between the bending strain and displacement has been investigated in the warping problem. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. In composite plates and shells, the transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. The results showed very good agreement compared with well-established formulations in the literature.
Ahmad, S., Irons, B.M. and Zienkiewicz, O.C. (1970), "Analysis of thick and thin shell structures by curved finite elements", Int. J. Num. Meth. Eng., 2, 419-451.
Huang, H.C. and Hinton, E. (1986), "A new nine node degenerated shell element with enhanced membrane and shear interpolation", Int. J. Num. Meth. Eng., 22, 73-92.
Jang, J. and Pinsky, P.M. (1987), "An assumed covariant strain based 9-node shell element", Int. J. Num. Meth. Eng., 24, 2389-2411.
Lee, S.W. and Pian, T.H.H. (1978), "Improvement of plate and shell finite elements by mixed formulation", AIAA J., 16, 29-34.
Liu, W.K., Lam, D., Law, S.E. and Belytschko, T. (1986), "Resultant stress degenerated shell element", Comput. Meth. Appl. Mech. Eng., 55, 259-300.
Rolfes, R. and Rohwer, K. (1997), "Improved transverse shear stress in composite finite element based on first order shear deformation theory", Int. J. Num. Meth. Eng., 40, 51-60.
Simo, J.C. and Hughes, T.J.R. (1986), "On the variational formulations of assumed strain methods", J. Appl. Mech., ASME, 53, 51-54.
Simo, J.C. (1993), "On a stress resultant geometrically exact shell model. Part VII: Shell intersections with 5/6- DOF finite element formulations", Comput. Meth. Appl. Mech. Eng., 108, 319-339.
White, D.W. and Abel, J.F. (1989), "Testing of shell finite element accuracy and robustness", Finite Element Method in Analysis and Design, 6, 129-151.
Chaisomphob, T., Kanok-Nuculchai, W. and Nishino, F. (1988), "An automatic arc length algorithm for tracing equilibrium paths of nonlinear structures", Proc. of JSCE, Struct. Eng./Earthq. Eng., 5, 205-208.
Ramm, E. (1977), "A plate/shell element for large deflections and rotations", Nonlinear Finite Element Analysis in Structural Mechanics, Wunderlich, W., Stein, E., Bathe, K.J. (eds.), M.I.T. Press, NY.
Saigal, S., Kapania, R.K. and Yang, Y.T. (1986), "Geometrically nonlinear finite element analysis of imperfect laminated shells", J. Compos. Mater., 20, 197-214.
XFINAS (2003), Nonlinear Structural Dynamic Analysis System, School of Civil Engineering, A.I.T., Thailand.
Kim, K.D. and Park, T.H. (2002), "An 8-node assumed strain element with explicit integration for isotropic and laminated composite shells", Struct. Eng. Mech., 13(4), 387-410.
Kim, K.D., Park, T. and Voyiadjis, G.Z. (1998), "Postbuckling analysis of composite panels with imperfection damage", Comput. Mech., 22, 375-387.
MacNeal, R.H. (1982), "Derivation of element stiffness matrices by assumed strain distributions", Nicl. Enggr. Design, 33, 1049-1058.
Wong, Wai-Kong (1984), "Pseudo Lagrangian formulation for large deformation analysis of continua and structures", Master Thesis, School of Civil Engineering, A.I.T.
Belytschko, T., Wong, B.L. and Stolarski, H. (1989), "Assumed strain stabilization procedure for the 9-node Lagrange shell element", Int. J. Num. Meth. Eng., 28, 385-414.
Kim, K.D. and Voyiadjis, G.Z. (1999), "Non-linear finite element analysis of composite panels", Composites Part B: Engineering, 30(4), 365-381.
Ma, H. and Kanok-Nukulchai, W. (1989), "On the application of assumed strained methods", Structural Engineering and Construction, Achievements, Trends and Challenges, Kanok-Nukulchai et al. (eds.), AIT, Bankok.
Crisfield, M.A. (1981), "A fast incremental/iterative solution procedure that handles snap-through", Comput. Struct., 13, 55-62.
Kim, K.D., Lomboy, G.R. and Han, S.C. (2003), "A co-rotational 8-node assumed strain shell element for postbuckling analysis of laminated composite plates and shells", Comput. Mech., 30(4), 330-342.
Noor, A.K. and Mathers, M.D. (1976), "Anisotropy and shear deformation in laminated composite plates", AIAA, 14, 282-285.
Fontes Valente, R.A., Natal Jorge, R.M., Cardoso, R.P.R., Cesar de Sa, J.M.A. and Gra´cio, J.J.A. (2003), "On the use of an enhanced transverse shear strain shell element for problems involving large rotations", Comput. Mech., 30, 286-296.
Kanok-Nukulchai, W. and Wong, W.K. (1988), "Element-based Lagrangian formulation for large-deformation analysis", Comput. Struct., 30, 967-974.
Yoo, S.W. and Choi, C.K. (2000), "Geometrically nonlinear analysis of laminated composites by an improved degenerated shell element", Struct. Eng. Mech., 9(1), 123-456.
Hughes, T.J.R. and Liu, W.K. (1981), "Nonlinear finite element analysis of shells: Part I. Three-dimensional shells", Comput. Meth. Appl. Mech. Eng., 26, 331-362.
Lee, S.J. and Kanok-Nukulchai, W. (1998), "A nine-node assumed strain finite element for large deformation analysis of laminated shells", Int. J. Num. Meth. Eng., 42, 777-798.
Lee, Won-Hong ; Han, Sung-Cheon ; Park, Weon-Tae 2010. "Buckling Analysis of Laminated Composite Plates under the In-plane Compression and Shear Loadings" 한국산학기술학회논문지 = Journal of the Korea Academia-Industrial cooperation Society, 11(12): 5199~5206
Han, Sung-Cheon ; Park, Weon-Tae ; Lee, Won-Hong 2010. "Non-linear Analysis of Laminated Composite Plates with Multi-directional Stiffness Degradation" 한국산학기술학회논문지 = Journal of the Korea Academia-Industrial cooperation Society, 11(7): 2661~2669
2010. "" Structural engineering and mechanics : An international journal, 34(1): 97~107
2011. "" Structural engineering and mechanics : An international journal, 40(2): 191~213
Han, Sung-Cheon 2012. "Geometrically Nonlinear Analysis of Hinged Cylindrical Laminated Composite Shells" 복합신소재구조학회 논문집 = Journal of the Korean Society for Advanced Composite Structures, 3(2): 1~10