Buckling Analysis of Functionally Graded Carbon Nanotube-reinforced Composite Plates using Incremental Loading and Dynamic Relaxation Methods
Authors
Abstract
In this paper, buckling behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates is studied in line with the plates thikness. All governing equations are presented incrementally, based on a First-order Shear Deformation Theory (FSDT) of plates and von Karman strain field. In order to find the critical buckling load, the axial load is applied to the plate incrementally and the equilibrium equations are solved by Dynamic Relaxation (DR) method. Parametric study of the effects of volume fraction of Carbon Nanotubes (CNTs), CNTs distribution, plate width-to-thickness ratio and aspect ratio of nano composite plates is done in detail. The results show that functionally graded distribution of CNTs causes a significant increase of critical buckling load.
Keywords
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2. Lijima, S., “Helical Microtubules of Graphitic Carbon”, Nature, Vol. 354, pp. 56-58, 1991.
3. Han, Y., and Elliott, J., “Molecular Dynamics Simulations of the Elastic Properties of Polymer/Carbon Nanotube Composites”, Computational Materials Science, Vol. 39, pp. 315-323, 2007.
4. Esawi, A. M. K., and Farag M. M., “Carbon Nanotube Reinforced Composites: Potential and Current Challenges”, Materials & Design, Vol. 28, pp. 2394-2401, 2007.
5. Ruoff, R. S., Qian, D., and Liu, W. K., “Mechanical Properties of Carbon Nanotubes: Theoretical Predictions and Experimental Measurements”, Comptes Rendus Physique, Vol. 4, pp. 993-1003, 2003.
6. Thostenson, E. T., Ren, Zh., and Chou, T. W., “Advances in the Science and Technology of Carbon Nanotubes and their Composites: a Review”, Composites Science and Technology, Vol. 61, pp. 1899-1912, 2001.
7. Griebel, M., and Hamaekers, J., “Molecular Dynamics Simulations of the Elastic Moduli of Polymer-Carbon Nanotube Composites”, Computer Methods in Applied Mechanics and Engineering, Vol. 193, pp. 1773-1788, 2004.
8. Fidelus, J. D., Wiesel, E., Gojny, F. H.,Schulte, K., and Wagner, H. D., “Thermo-Mechanical Properties of Randomly Oriented Carbon/Epoxy Nanocomposites”, Composites Part A: Applied Science and Manufacturing, Vol. 36, pp. 1555-1561, 2005.
9. Ming, Li., Kang. Z. H.,Yang, P., Meng, X., and Lu, Y., “Molecular Dynamics Study on Carbon/Epoxy Buckling of Single-Wall Carbon Nanotube-Based Intramolecular Junctions and Influence Factors”, Computational Materials Science, Vol. 67, pp. 390-396, 2013.
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12. Shen, H. S., “Nonlinear Bending of Functionally Graded Carbon Nanotube-Reinforced Composite Plates in Thermal Environments”, Composite Structures, Vol. 91, pp. 9-19, 2009.
13. Shen, H. S., and Zhang, C. L., “Thermal Buckling and Postbuckling Behavior of Functionally Graded Carbon Nanotube-Reinforced Composite Plates”, Materials & Design, Vol. 31, pp. 3403-3411,
2010.
14. Wang, Z. X., and Shen, H. S., “Nonlinear Vibration of Nanotube-Reinforced Composite Plates in Thermal Environments”, Computational Materials Science, Vol. 50, pp. 2319-2330, 2011.
15. Shen, H. S., “Postbuckling of Nanotube-Reinforced Composite Cylindrical Shells in Thermal Environments, Part I: Axially-Loadedshells”, Composite Structures, Vol. 93, pp. 2096-2108,
2011.
16. Shen, H. S., “Postbuckling of Nanotube-Reinforced Composite Cylindrical Shells in Thermal Environments, Part II: Pressure-Loaded Shells”, Composite Structures, Vol. 93, pp. 2496-2503,
2011.
17. Shen, H. S., “Thermal Buckling and Postbuckling Behavior of Functionally Graded Carbon Nanotube Reinforced Composite Cylindrical Shells”, Composites Part B: Engineering, Vol. 43, pp. 1030-1038, 2012.
18. Shen, H. S., and Xiang, Y., “Nonlinear Vibration of Nanotube-Reinforced Composite Cylindrical Shells Inthermal Environments”, Computer Methods in Applied Mechanics and Engineering, Vol. 213-216, pp. 196-205, 2012.
19. Zhu, P., Lei, Z. X., and Liew K. M., “Static and
Free Vibration Analyses of Carbon Nanotube-Reinforced Composite Plates using Finite Element Method with First Order Shear Deformation Plate Theory”, Composite Structures, Vol. 94, pp. 1450-1460, 2012.
20. Sobhani Aragh, B., Nasrollah Barati A. H., and Hedayati H., “Eshelby-Mori-Tanaka Approach for Vibrational Behavior of Continuously Graded Carbon Nanotube-Reinforced Cylindrical Panels”, Composites Part B: Engineering, Vol. 43, pp. 1943-1954, 2012.
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22. Wang, Z. X., and Shen H. S., “Nonlinear Dynamic Response of Nanotube-Reinforced Composite Plates Resting on Elastic Foundations in Thermal Environments”, Nonlinear Dynamics, Vol. 70, pp. 735-754, 2012.
23. Alibeigloo, A., “Static Analysis of Functionally Graded Carbon Nanotube-Reinforced Composite Plate Embedded in Piezoelectric Layers by using Theory of Elasticity”, Composite Structures, Vol. 95, pp. 612-622, 2013.
24. Lei, Z. X., Leiw, K. M., and Yu, J. K., “Buckling Analysis of Functionally Graded Carbon Nanotube-Reinforced Composite Plates using the Element-Free kp-Ritz Method”, Composite Structures, Vol. 98, pp. 160-168, 2013.
25. Shen, H. S., and Zhu, Z. H., “Postbuckling of Sandwich Plates with Nanotube-Reinforced Composite Face Sheets Resting on Elastic Foundations”, European Journal of Mechanics -A/Solids, Vol. 35, pp. 10-21, 2012.
26. Wang, Z. X., and Shen, H. S., “Nonlinear Vibration and Bending of Sandwich Plates with Nanotube-Reinforced Composite Face Sheets”, Composites Part B: Engineering, Vol. 43, pp. 411-421, 2012.
27. Reddy , J. N., “Mechanics of Laminated Composite Plates and Shells: Theory and Analysis”, Boca Raton (FL): CRC Press, 2004.
28. Rezaee Pajand, M., and Alamatian, J., “The Dynamic Relaxation Method using New Formulation for Fictitious Mass and Damping”, Structural Engineering and Mechanics, Vol. 34, pp. 109-133, 2010.
29. Zhang, L. C., Kadkhodayan, M., and Mai, Y. W., “Development of the maDR method”, Computers & Structures, Vol.52, pp.1-8, 1994.
30. Underwood, P., “Dynamic Relaxation, in: Computational Method for Transient Analysis”, Elsevier, Amsterdam, 1983.
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