Author
Abstract
In this study, nonlinear axisymmetric bending analysis of Functionally Graded Carbon Nanotube Reinforced Composite (FG-CNTRC) cylindrical shell is investigated. Four distribution types of carbon nanotubes along the thickness direction of shells are considered, including a uniform and three kinds of functionally graded distributions. The material properties of FG-CNTRC shells are determined according to the modified rule of mixture. The equilibrium equations are derived based on First-order Shear Deformation Shell Theory (FSDT) and nonlinear Donnell strains. The coupled nonlinear governing equations are solved by Dynamic Relaxation (DR) method combined with central finite difference technique for different combinations of simply supported and clamped boundary conditions. For this purpose, a FORTRAN computer program is provided to generate the numerical results. In order to verify the accuracy of the formulation and present method, the results are compared with those available in the literatures for ABAQUS finite element package, as well as a similar report for an isotropic function shell. The appropriate accordance of the results indicated the accuracy of employed numerical solution in the present study. Finally, a parametric study is carried out to study the effects of distribution of carbon nanotubes (CNTs), shell radius and width-to-thickness ratios, boundary conditions and volume fraction of CNTs on the deflection, stress and moment resultants in detail. The results show that with increase of CNTS volume fractions, the O and UD distributions have the most and the least decrease of deflection, respectively, in both clamped and simply supported boundary conditions.
Keywords
2. Dseldel, G. D., and Agodas, G. D. C., “Micromechanical Analysis of the Effective Elastic Properties of Carbon Nanotube Reinforced Composites, Mechanics of Material, Vol .38, pp. 884-907, 2006.
3. Han, Y., and Elliott, J., “Molecular Dynamics Simulations of the Elastic Properties of Polymer/Carbon Nanotube Composites”, Computation Materials Science, Vol. 39, pp. 315-323, 2007.
4. 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, Vol. 36, pp. 1555-1561, 2005.
5. Bower, C., Rosen, R., and Jin, L., “Deformation of Carbon Nanotubes in Nanotube-Polymer Composites”, Physics Letters, Vol. 74, No. 22, 1999.
6. Vodenitcharova, T., and Zhang, C., “Bending and Local Buckling of Nano-Composite Beam Reinforced by a Single-Walled Carbon Nanotube”, International Journal of Solids and Structures, Vol. 43, pp. 3006-3024, 2006.
7. Shen, H. S., “Postbuckling of Nanotube-Reinforced Composite Cylindrical Shells in Thermal Environments, Part I: Axially-Loaded Shells”, Composite Structures, Vol. 93, pp. 2096-2108, 2011.
8. Shen, H. S., “Nonlinear Bending of Functionally Graded Carbon Nanotube Reinforced Composite Plates in Thermal Environments”, Composite Structures, Vol. 91, pp. 9-19, 2009.
9. Sobhani Aragh, B., Barati, N., and Hedayati, H., “Eshelby-Mori Tanaka Approach for Vibrational Behavior of Continuously Graded Carbon Nanoube Reinforced Cylindrical Panels”, Composites: part B, Vol. 43, pp. 1943-1954, 2012.
10. Ghorbanpour Arani, A., Mozdianfar, M. R., Sadooghi, V., Mohammadimehr, M., and Kolahchi, R., “Magneto-Thermo-Tlastic Behavior of Cylinder Reinforced with FG-SWCNTs under Transient Thermal Field”, Journal of Solid Mechanics, Vol. 3, No. 1, pp. 9-18, 2011.
11. Ping, Z., Lei, Z. N., 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, 2011.
12. Wang, Z. X., and Hui shen, Sh., “Nonlinear Dynamic Response of Nanotube-Reinforced Composite Plates Resting on Elastic Foundations Thermal Environment”, Nonlinear Dynamics, Vol. 32, pp. 123-132, 2012.
13. Alibeigloo, A., and Liew, K. M., “Thermoelastic Analysis of Functionally Graded Carbon Nanotube-Reinforced Composite Plate using Theory of Elasticity”, Composite Structures, Vol. 106, pp. 873-881, 2013.
14. Dastjerdi, M., Foroutan, M. R., and Pourasghar, M. A., “Dynamic Analysis of Functionally Graded Nanocomposite Cylinders Reinforced by a Mesh-Free Method”, Material and Design, Vol. 44, pp. 258-266, 2013.
15. Aragh, B. S., and Hedayati, H., “Eshelby-Mori-Tanaka Approach for Vibrational Behavior of Continuously Graded Carbon Nanotube Reinforced Cylindrical Panels”, Composites: part B, Vol. 43, pp. 1943-54, 2012.
16. Obrush, D., and Almorth, B. O, Buckling of Bars Plates and Shells, New York, McGraw-Hill, 1975.
17. Dai, H. L., and Dai, T., “Analysis for the Thermoelastic Bending of a Functionally Graded Material Cylindrical Shell”, Meccanica, Vol. 49, pp. 1069-1081, 2013.
18. Golmakani, M. E., and Kadkhodayan, M., “Large Deflection Analysis of Circular and Annular FGM Plates under Thermo-Mechanical Loading with Temperature-Dependent Properties, Composites: Part B, Vol. 42, pp. 614-625, 2011
)