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

• Published in: Computational mechanics Vol. 39; no. 1; pp. 41 - 58
• Main Authors: Lee, Won-Hong, Han, Sung-Cheon
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.12.2006
• Subjects: Alliances; Composite structures; Constitutive equations; Constitutive relationships; Damping; Deformation effects; Elasticity; Exact solutions; Forced vibration; Laminates; Locking; Mindlin plates; Reissner theory; Resonant frequencies; Rotary inertia; Shear deformation; Shells; True strain; Vibration analysis
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-005-0007-8

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.