Free and forced vibration analysis of laminated composite plates and shells using a 9-node assumed strain shell element

The natural frequencies of isotropic and composite laminates are presented. The forced vibration analysis of laminated composite plates and shells subjected to arbitrary loading is investigated. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To develop a laminated shell element for free and forced vibration analysis, the equivalent constitutive equation that makes the computation of composite structures efficient was applied. The Mindlin-Reissner theory which allows the shear deformation and rotary inertia effect to be considered is adopted for development of nine-node assumed strain shell element. The present shell element offers significant advantages since it consistently uses the natural co-ordinate system. Results of the present theory show good agreement with the 3-D elasticity and analytical solutions. In addition the effect of damping is investigated on the forced vibration analysis of laminated composite plates and shells.

[1]  P. Pinsky,et al.  An assumed covariant strain based 9‐node shell element , 1987 .

[2]  E. Hinton,et al.  A new nine node degenerated shell element with enhanced membrane and shear interpolation , 1986 .

[3]  Ki-Du Kim,et al.  Linear static and dynamic analysis of laminated composite plates and shells using a 4-node quasi-conforming shell element , 2005 .

[4]  O. C. Zienkiewicz,et al.  Analysis of thick and thin shell structures by curved finite elements , 1970 .

[5]  J. N. Reddy,et al.  Geometrically nonlinear transient analysis of laminated composite plates , 1983 .

[6]  J. C. Simo,et al.  On the Variational Foundations of Assumed Strain Methods , 1986 .

[7]  L. Donnell,et al.  Stability of Thin-Walled Tubes Under Torsion , 1934, Journal of Fluids Engineering.

[8]  Rolands Rikards,et al.  Analysis for buckling and vibrations of composite stiffened shells and plates , 2001 .

[9]  Worsak Kanok-Nukulchai,et al.  A simple and efficient finite element for general shell analysis , 1979 .

[10]  K. D. Kim,et al.  A resultant 8-node solid-shell element for geometrically nonlinear analysis , 2005 .

[11]  S. Srinivas,et al.  An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates , 1970 .

[12]  C. W. S. To,et al.  Transient responses of geometrically nonlinear laminated composite shell structures , 1998 .

[13]  S. J. Lee,et al.  A NINE-NODE ASSUMED STRAIN FINITE ELEMENT FOR LARGE-DEFORMATION ANALYSIS OF LAMINATED SHELLS , 1998 .

[14]  J. D. Day,et al.  Dynamic response of laminated anisotropic plates , 1995 .

[15]  Yang Xiang,et al.  Research on thick plate vibration: a literature survey , 1995 .

[16]  C. R. Hazell,et al.  Vibration studies on some integral rib-stiffened plates , 1977 .

[17]  Gilson R. Lomboy,et al.  A co-rotational 8-node assumed strain shell element for postbuckling analysis of laminated composite plates and shells , 2003 .

[18]  J. N. Reddy,et al.  Buckling and vibration of laminated composite plates using various plate theories , 1989 .

[19]  M. S. Qatu.  Review of shallow shell vibration research , 1992 .

[20]  Tarun Kant,et al.  Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory , 2001 .

[21]  J. N. Reddy,et al.  On the Solutions to Forced Motions of Rectangular Composite Plates , 1982 .

[22]  Donald W. White,et al.  Testing of shell finite element accuracy and robustness , 1989 .

[23]  E. Ventsel,et al.  Vibrations of Shells , 2001 .

[24]  Ted Belytschko,et al.  Assumed strain stabilization procedure for the 9-node Lagrange shell element , 1989 .

[25]  J. Z. Zhu,et al.  The finite element method , 1977 .

[26]  S. J. Lee,et al.  FREE-VIBRATION ANALYSIS OF PLATES AND SHELLS WITH A NINE-NODE ASSUMED NATURAL DEGENERATED SHELL ELEMENT , 2001 .

[27]  Worsak Kanok-Nukulchai,et al.  An element-based 9-node resultant shell element for large deformation analysis of laminated composite plates and shells , 2004 .

[28]  R. L. Harder,et al.  A proposed standard set of problems to test finite element accuracy , 1985 .

[29]  M. S. Qatu.  LITERATURE REVIEW analysis of the shock and vibration literature: Review of Shallow Shell Vibration Research , 1992 .