Vibration of laminated composites and sandwich shells based on higher order zigzag theory

Published Date
November 2013, Vol.56:880–888, doi:10.1016/j.engstruct.2013.06.014

Author

• Ajay Kumar ^,
• Anupam Chakrabarti
• Pradeep Bhargava

• Department of Civil Engineering, IIT Roorkee, Roorkee 247 667, India

Received 28 March 2013. Revised 10 June 2013. Accepted 12 June 2013. Available online 17 July 2013. 

Highlights

• The cross curvature effect included in formulation help to analyze hypar shells.
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  This is first FE of the HOZT in shells incorporating all three radii of curvatures.
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  Present 2D HOZT static results are quite close to 3D elasticity results.
• •
  Present model predicts shell vibration results more accurately than HSDT/FSDT.
• •
  New results of composite/sandwich shells will serve as benchmark for researchers.

Abstract

Free vibration response of laminated composite and sandwich shell is studied by using an efficient 2D FE (finite element) model based on higher order zigzag theory (HOZT). This is the first finite element implementation of the HOZT to solve the vibration problem of shells incorporating all three radii of curvatures including the effect of cross curvature in the formulation using Sanders’ approximations. The proposed finite element model satisfies the inter-laminar shear stress continuity at the interfaces in addition to higher order theory features, hence most suitable to model sandwich shells along with composite shells. The C₀ finite element formulation has been done efficiently to overcome the problem of C₁ continuity associated with the HOZT. The present model can also analyze shells with cross curvature like hypar shells, etc., besides normal curvature shells like cylindrical, and spherical shells. The numerical studies show that the present 2D FE model is more accurate than existing FE models based on first and higher order theories for predicting results close to those obtained by 3D elasticity solutions for laminated composite and sandwich shallow shells. Many new results are presented by varying different parameters which should be useful for future research.

Keywords

Composite

Sandwich

Shell

Finite element method

Free vibration

Higher order zigzag theory

Boundary condition

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• ⁎ 
  Corresponding author. Tel.: +91 1332 285844; fax: +91 1332 275568.

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