Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahmad S, Irons BM, Zienkiewicz OC (1970) Analysis of thick and thin shell structures by curved finite elements. Int J Num Meth Eng 2:419–451
Belytschko T, Wong BL, Stolarski H (1989) Assumed strain stabilization procedure for the 9-node lagrange shell element. Int J Num Meth Eng 28:385–414
Donell LH (1933) Stability of thin-walled tubes under torsion. NASA Report 479, Washington, DC.
Han SC, Choi S (2004) Linear static and free vibration analysis of laminated composite plates and shells using a 9-node shell element with strain interpolation. J Comput Struct Eng Inst Korea 17(3):279–293 (in Korean)
Han SC, Kim KD, Kanok-Nukulchai W (2004) An element-based 9-node resultant shell element for large deformation analysis of laminated composite plates and shells. Struct Eng Mech 18(6):807–829
Huang HC, 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, Pinsky PM (1987) An assumed covariant strain based 9-node shell element. Int J Num Meth Eng 24:2389–2411
Kant T, Swaminathan K (2001) Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory. Compos Struct 53:73–85
Kim KD, Liu GZ, Han SC (2005) A resultant 8-node solid-shell element315–331.
Kim (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
Lee SJ, Han SE (2001) Free-vibration analysis of plates and shells with a nine-node assumed natural degenerated shell element. J Sound Vib 241(4):601–633
Lee SJ, 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 WH, Han SC, Chun KS, Chang SY (2003) Buckling and vibration analysis of antisymmetric angle-ply laminated composite plates using a three-dimensional higher-order theory. J Korean Soc Steel Constr 15(2):97–107
Leissa AW (1973) Vibrations of shells. NASA PA-288, Washington, DC
Liew KM (1995) Research on thick plate vibration: a literature survey. J Sound Vib 180:163–176
Love AEH. (1888). The small vibrations and deformations of thin elastic shell. Philos Trans Royal Soc 179:527–546
MacNeal RH, Harder RL. (1985). A proposed standard set of problems to test finite element accuracy. Finite Elem Anal Des 1:3–20
Meimaris C, Day JD. (1995) Dynamic response of laminated anisotropic plates. Comput Struct. 55(2):269–278
Olson MD, Hazell CR. (1977) Vibration studies on some integral rib-stiffened plates. J Sound Vib 50:43–61
Park T, Kim KD, Han SC (2005) Linear static and dynamic analysis of laminated composite plates and shells using a 4-node quasi-conforming shell element. Composites Part B Eng (Accepted)
Qatu MS. (1992) Review of shallow shell vibration research. Shock Vib Dig 24:3–15
Reddy JN. (1982) On the solutions to forced motions of rectangular composite plates. J App Mech ASME 49:403–408
Reddy JN. (1983) Geometrically nonlinear transient analysis of laminated composite plates. AIAA 21(4):621–629
Reddy JN. (1997) Mechanics of laminated composite plates. Florida, CRC Press
Reddy JN, Khdeir AA (1989). Buckling and vibration of laminated composite plates using various plate theories. AIAA 27(12):1808–1817
Rikards R, Chate A, Ozolinsh O. (2001). Analysis for buckling and vibrations of composite stiffened shells and plates. Composite Struct 51:361–370
Simo JC, Hughes TJR. (1986) On the variational formulations of assumed strain methods. J Appl Mech ASME 53:51–54
Srinivas CV, Rao J, Rao AK. (1970) An exact analysis for vibration of simply supported homogeneous and laminated, thick rectangular plates. J Sound Vib 12:187–199
White DW, Abel JF. (1989) Testing of shell finite element accuracy and robustness. Finite Elem Anal Des 6:129–151
XFINAS. (2003) Nonlinear structural dynamic analysis system. School of Civil Engineering, AIT, Thailand
Zienkiewicz OC, Taylor RL. (1989) The finite element method. McGraw-Hill, London
Zienkiewicz OC, Taylor RL. (2000). The Finite Element Method. Butterworth-Heinemann, London
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lee, WH., Han, SC. Free and forced vibration analysis of laminated composite plates and shells using a 9-node assumed strain shell element. Comput Mech 39, 41–58 (2006). https://doi.org/10.1007/s00466-005-0007-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-005-0007-8