Buckling of Thick Laminated Composite Plates Based on Zigzag and Third order Shear Deformation Theories using the Finite Strip Method
Authors
Abstract
A semi-analytical finite strip method was developed for the buckling analysis of laminated composite plates based on zigzag and third order shear deformation theories. The displacement functions of the plates were evaluated using a continuous harmonic function series in the longitudinal direction that satisfied the simply supported boundary conditions and a piecewise interpolation polynomial in the transverse direction. By considering the displacement-strain relations and strain-stress relations, the standard and geometric matrices were evaluated using the virtual work principle. The numerical results related to the buckling of single-layer and multi-layer plates were presented based on two different plate theories. The effects of different boundary conditions, length to thickness ratio, fiber orientation and modulus of elasticity were also investigated through numerical examples.
Keywords
1. Reissner, E., “The Effect of Transverse Shear Deformation on The Bending of Elastic Plates”, Journal of Applied Mechanics (American Society of Mechanical Engineers: ASME), Vol. 12, pp. 69-77, 1945.
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8. Zenkour, A., “Analytical Solution for Bending of Cross-ply Laminated Plates under Thermo-mechanical Loading”, Composite Structures, Vol. 65, pp. 367-379, 2004.
9. Zhong, H., and Gu, C., “Buckling of Symmetrical Cross-ply Composite Rectangular Plates under A Linearly Varying In-Plane Load”, Composite Structures, Vol. 80, pp. 42-48, 2007.
10. Kulkarni, S., and Kapuria, S., “Free Vibration Analysis of Composite and Sandwich Plates using An Improved Discrete Kirchhoff Quadrilateral Element Based on Third-order Zigzag Theory”, Computational Mechanics, Vol. 42, pp. 803-824, 2008.
11. Kim, S. E., Thai, H. T., and Lee, J., “A Two Variable Refined Plate Theory for Laminated Composite Plates”, Composite Structures, Vol. 89, pp. 197-205, 2009.
12. Thai, H. T., and Kim, S. E., “Free Vibration of Laminated Composite Plates using Two Variable Refined Plate Theory”, International Journal of Mechanical Sciences, Vol. 52, pp. 626-633, 2010.
13. Kumar, J. S., Raju, T. D., and Reddy, K. V. K., “Vibration Analysis of Composite Laminated Plates using Higher-order Shear Deformation Theory With Zig-Zag Function”, Indian Journal of Science and Technology, Vol. 4, pp. 960-966, 2011.
14. Sahoo, R., and Singh, B., “A New Shear Deformation Theory for the Static Analysis of Laminated Composite and Sandwich Plates”, International Journal of Mechanical Sciences, Vol. 75, pp. 324-336, 2013.
15. Sayyad, A. S., and Ghugal, Y. M., “Flexure of Cross-ply Laminated Plates using Equivalent Single Layer Trigonometric Shear Deformation Theory”, Structural Engineering and Mechanics, Vol. 51, pp. 867-891, 2014.
16. Sayyad, A. S., and Ghugal, Y. M., “On the Buckling of Isotropic, Transversely Isotropic and Laminated Composite Rectangular Plates”, International Journal of Structural Stability and Dynamics, Vol. 14, p. 1450020, 2014.
17. Akhras, G., and Li, W., “Spline Finite Strip Analysis of Composite Plates Based on Higher-order Zigzag Composite Plate Theory”, Composite Structures, Vol. 78, pp. 112-118, 2007.
18. Zenkour, A., “Buckling of Fiber-Reinforced Viscoelastic Composite Plates Using Various Plate Theories”, Journal of Engineering Mathematics, Vol. 50, pp. 75-93, 2004.
19. Reddy, J. N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed., CRC Press, 2004.
2. Mindlin, R. D., “Influence of Rotary Inertia and Shear on Flexural Motions of Isotropic Elastic Plates”, Journal of Applied Mechanics (American Society of Mechanical Engineers: ASME), Vol. 18, pp. 31-38, 1951.
3. Reddy, J. N., “A Simple Higher-order Theory for Laminated Composite Plates”, Journal of Applied Mechanics, Vol. 51, pp. 745-752, 1984.
4. Cho, M., and Parmerter, R., “Efficient Higher order Composite Plate Theory for General Lamination Configurations”, AIAA Journal, Vol. 31, pp. 1299-1306, 1993.
5. Xiaoping, S., and Liangxin, S., “An Improved Simple Higher-order Theory for Laminated Composite Plates”, Computers & Structures, Vol. 50, pp. 231-236, 1994.
6. Zenkour, A., and Fares, M., “Buckling and Free Vibration of Non-homogeneous Composite Cross-Ply Laminated Plates with Various Plate Theories”, Composite Structures, Vol. 44, pp. 279-287, 1999.
7. Topdar, P., Sheikh, A., and Dhang, N., “Finite Element Analysis of Composite and Sandwich Plates using a Continuous Inter-laminar Shear Stress Model”, Journal of Sandwich Structures and Materials, Vol. 5, pp. 207-231, 2003.
8. Zenkour, A., “Analytical Solution for Bending of Cross-ply Laminated Plates under Thermo-mechanical Loading”, Composite Structures, Vol. 65, pp. 367-379, 2004.
9. Zhong, H., and Gu, C., “Buckling of Symmetrical Cross-ply Composite Rectangular Plates under A Linearly Varying In-Plane Load”, Composite Structures, Vol. 80, pp. 42-48, 2007.
10. Kulkarni, S., and Kapuria, S., “Free Vibration Analysis of Composite and Sandwich Plates using An Improved Discrete Kirchhoff Quadrilateral Element Based on Third-order Zigzag Theory”, Computational Mechanics, Vol. 42, pp. 803-824, 2008.
11. Kim, S. E., Thai, H. T., and Lee, J., “A Two Variable Refined Plate Theory for Laminated Composite Plates”, Composite Structures, Vol. 89, pp. 197-205, 2009.
12. Thai, H. T., and Kim, S. E., “Free Vibration of Laminated Composite Plates using Two Variable Refined Plate Theory”, International Journal of Mechanical Sciences, Vol. 52, pp. 626-633, 2010.
13. Kumar, J. S., Raju, T. D., and Reddy, K. V. K., “Vibration Analysis of Composite Laminated Plates using Higher-order Shear Deformation Theory With Zig-Zag Function”, Indian Journal of Science and Technology, Vol. 4, pp. 960-966, 2011.
14. Sahoo, R., and Singh, B., “A New Shear Deformation Theory for the Static Analysis of Laminated Composite and Sandwich Plates”, International Journal of Mechanical Sciences, Vol. 75, pp. 324-336, 2013.
15. Sayyad, A. S., and Ghugal, Y. M., “Flexure of Cross-ply Laminated Plates using Equivalent Single Layer Trigonometric Shear Deformation Theory”, Structural Engineering and Mechanics, Vol. 51, pp. 867-891, 2014.
16. Sayyad, A. S., and Ghugal, Y. M., “On the Buckling of Isotropic, Transversely Isotropic and Laminated Composite Rectangular Plates”, International Journal of Structural Stability and Dynamics, Vol. 14, p. 1450020, 2014.
17. Akhras, G., and Li, W., “Spline Finite Strip Analysis of Composite Plates Based on Higher-order Zigzag Composite Plate Theory”, Composite Structures, Vol. 78, pp. 112-118, 2007.
18. Zenkour, A., “Buckling of Fiber-Reinforced Viscoelastic Composite Plates Using Various Plate Theories”, Journal of Engineering Mathematics, Vol. 50, pp. 75-93, 2004.
19. Reddy, J. N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed., CRC Press, 2004.
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