Research ArticleOpen AccessGoogle Scholar indexed
Theories and Analyses Thick Hyperbolic Paraboloidal Composite Shells
Department of Mathematics, Tafila Technical University, Tafila, Jordan
Department of Mathematics, Tafila Technical University, Tafila, Jordan
Department of Mathematics, Tafila Technical University, Tafila, Jordan
- 1 Department of Mathematics, Tafila Technical University, Tafila, Jordan
- 2 Department of Mathematics, Tafila Technical University, Tafila, Jordan
- 3 Department of Mathematics, Tafila Technical University, Tafila, Jordan
American Journal of Computational Mathematics·Volume 05 (2015)·Pages 80–85·Published 13 May 2015·DOI10.4236/ajcm.2015.52006
Copy link · social · email
Abstract
This paper presents the stress resultants of hyperbolic paraboloidal shells using higher order shear deformation theory recently developed by Zannon [1]-[3]. The equilibrium equations of motion use Hamilton’s minimum energy principle for a simply supported cross-ply structure by Zannon (TSDTZ) [2] [3]. The results are calculated for orthotropic, two-ply unsymmetrical [90/0] shells. The extensional, bending and coupling stiffness parameters are calculated using MATLAB algorithm for laminated composite hyperbolic paraboloidal shells. A comparison of the present study with other researchers in the literature is given, and is in good agreement.
KeywordsStress ResultantsHyperbolic ParaboloidalHamilton PrinciplesThick ShellThird Order Shear DeformationCross-PlyStiffness Matrix
- Qatu, M., Zannon, M. and Mainuddin, G. (2013) Application of Laminated Composite Materials in Vehicle Design: Theories and Analyses of Composite Shells. SAE International Journal of Passenger Cars-Mechanical Systems, 6, 1347-1353. http://dx.doi.org/10.4271/2013-01-1989
- Zannon, M. and Qatu, M. (2014) Mathematical Modeling of Transverse Shear Deformation Thick Shell Theory. International Journal of Engineering Research and Management (IJERM), 1.
- Zannon, M. and Qatu, M. (2014) Free Vibration Analysis of Thick Cylindrical Composite Shells Using Higher Order Shear Deformation Theory. International Journal of Engineering Research and Management (IJERM), 1.
- Zannon, M. (2014) Free Vibration of Thin Film Cantilever Beam. International Journal of Engineering and Technical Research (IJETR), 2.
- Love, E. (1892) A Treatise on the Mathematical Theory of Elasticity. 4th Edition, Cambridge University Press, Cambridge; Dover Publishing, New York.
- Leissa, A.W. (1993) Vibration of Shells. US Government Printing Office, Washington DC. Reprinted by the Acoustical Society of America.
- Timoshenko, S. and Woinowsky-Krieger, S. (1959) Theory of Plates and Shells. New York.
- Lee, S.J. and Reddy, J.N. (2004) Vibration Suppression of Laminated Shell Structures Investigated Using Higher Order Shear Deformation Theory. Smart Materials and Structures, 13, 1176-1194. http://dx.doi.org/10.1088/0964-1726/13/5/022
- Qatu, M.S., Sullivan, R.W. and Wang, W. (2012) Review of Recent Literature on Static Analyses of Composite Shells: 2000-2010. Journal of Composite Materials, 2, 61-86. http://dx.doi.org/10.4236/ojcm.2012.23009
- Deana, C.E. and Werbya, M.F. (1992) Hamilton’s Principle and the Equations of Motion of an Elastic Shell with and without Fluid Loading. Computational and Applied Mathematics, 92, 131-140.
- Asadia, W., Wanga, W. and Qatu, M.S. (2012) Static and Vibration Analyses of Thick Deep Laminated Cylindrical Shells Using 3D and Various Shear Deformation Theories. Composite Structures, 94, 494-500. http://dx.doi.org/10.1016/j.compstruct.2011.08.011
- Qatu, M.S. (2004) Vibration of Laminated Shells and Plates. Elsevier, Oxford.