Flexural Analysis of Functionally Graded CNT-Reinforced Doubly Curved Singly Ruled Composite Truncated Cone
Publication: Journal of Aerospace Engineering
Volume 32, Issue 2
Abstract
The flexural analysis of functionally graded carbon nanotube (CNT)-reinforced doubly curved singly ruled composite truncated cone is studied. The mathematical model contains the expansion of Taylor’s series up to third degree of thickness coordinate and normal curvatures in in-plane displacement fields. Because the distribution of transverse shear strain across the thickness coordinate is parabolic, the need of shear correction factor is removed. The condition of zero-transverse shear strain at the upper and lower surface of the truncated cone is applied in the present formulation. The advancement in the present mathematical model is the simultaneous inclusion of normal curvatures in deformation field and twist curvature in strain-displacement equations. The proposed new mathematical model is implemented in finite-element code written in FORTRAN. The present results are in good agreement with the experimental results as well as results from other methods. After validation, a large number of flexural problems are presented by varying different boundary conditions, volume fraction, loading pattern, and geometric parameters.
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Acknowledgments
The authors gratefully acknowledge Science & Engineering Research Board (SERB) for the financial sanction of the research project File No. EMR/2016/004682.
References
Ansari, M. I., A. Kumar, D. Barnat-Hunek, Z. Suchorab, W. Andrzejuk, and D. Majerek. 2018. “Static and dynamic response of FG-CNT-reinforced rhombic laminates.” Appl. Sci. 8 (5): 834 https://doi.org/10.3390/app8050834.
Bakshi, K., and D. Chakravorty. 2014. “First ply failure study of thin composite conoidal shells subjected to uniformly distributed load.” Thin-Walled Struct. 76: 1–7. https://doi.org/10.1016/j.tws.2013.10.021.
Choi, C. K. 1984. “A conoidal shell analysis by modified isoparametric element.” Comput. Struct. 18 (5): 921–924. https://doi.org/10.1016/0045-7949(84)90037-3.
Civalek, Ö. 2017a. “Buckling analysis of composite panels and shells with different material properties by discrete singular convolution (DSC) method.” Compos. Struct. 161: 93–110. https://doi.org/10.1016/j.compstruct.2016.10.077.
Civalek, Ö. 2017b. “Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method.” Compos. Part B 111: 45–59. https://doi.org/10.1016/j.compositesb.2016.11.030.
Das, A. K., and J. N. Bandyopadhyay. 1993. “Theoretical and experimental studies on conoidal shells.” Comput. Struct. 49 (3): 531–536. https://doi.org/10.1016/0045-7949(93)90054-H.
Dey, A., J. N. Bandyopadhyay, and P. K. Sinha. 1992. “Finite element analysis of laminated composite conoidal shell structures.” Comput. Struct. 43 (3): 469–476. https://doi.org/10.1016/0045-7949(92)90281-4.
Duc, N. D., P. H. Cong, N. D. Tuan, P. Tran, and N. Thanh. 2017. “Thermal and mechanical stability of functionally graded carbon nanotubes (FG CNT)-reinforced composite truncated conical shells surrounded by the elastic foundations.” Thin Walled Struct. 115: 300–310. https://doi.org/10.1016/j.tws.2017.02.016.
Esawi, A. M. K., and M. M. Farag. 2007. “Carbon nanotube reinforced composites: Potential and current challenges.” Mater. Des. 28 (9): 2394–2401. https://doi.org/10.1016/j.matdes.2006.09.022.
Fidelus, J. D., E. Wiesel, F. H. Gojny, K. Schulte, and H. D. Wagner. 2005. “Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites.” Compos. Part A: Appl. Sci. Manufacturing 36 (11): 1555–1561. https://doi.org/10.1016/j.compositesa.2005.02.006.
García-Macías, E., R. Castro-Triguero, E. I. Saavedra, M. I. Friswell, and R. Gallego. 2016. “Static and free vibration analysis of functionally graded carbon nanotube reinforced skew plates.” Compos. Struct. 140: 473–490. https://doi.org/10.1016/j.compstruct.2015.12.044.
Ghosh, B., and J. N. Bandyopadhyay. 1989. “Bending analysis of conoidal shells using curved quadratic isoparametric element.” Comput. Struct. 33 (3): 717–728. https://doi.org/10.1016/0045-7949(89)90245-9.
Ghosh, B., and J. N. Bandyopadhyay. 1990. “Approximate bending analysis of conoidal shells using the Galerkin method.” Comput. Struct. 36 (5): 801–805. https://doi.org/10.1016/0045-7949(90)90150-Z.
Ghosh, B., and J. N. Bandyopadhyay. 1994. “Bending analysis of conoidal shells with cut-outs.” Comput. Struct. 53 (1): 9–18. https://doi.org/10.1016/0045-7949(94)90124-4.
Hadid, H. A. 1964. “An analytical and experimental investigation into the bending theory of elastic conoidal shell.” Ph.D. dissertation, Univ. of Southampton.
Han, Y., and J. Elliott. 2007. “Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites.” Comput. Mater. Sci. 39 (2): 315–323. https://doi.org/10.1016/j.commatsci.2006.06.011.
Heydarpour, Y., M. M. Aghdam, and P. Malekzadeh. 2014. “Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells.” Compos. Struct. 117 (1): 187–200. https://doi.org/10.1016/j.compstruct.2014.06.023.
Huang, B., Y. Guo, J. Wang, J. Du, Z. Qian, T. Ma, and L. Yi. 2016. “Bending and free vibration analyses of antisymmetrically laminated carbon nanotube-reinforced functionally graded plates.” J. Compos. Mater. 51 (22): 3111–3125. https://doi.org/10.1177/0021998316685165.
Iijima, S. 1991. “Helical microtube of graphitic carbon.” Nature 354 (6348): 56–58. https://doi.org/10.1038/354056a0.
Jooybar, N., P. Malekzadeh, and A. Fiouz. 2016. “Vibration of functionally graded carbon nanotubes reinforced composite truncated conical panels with elastically restrained against rotation edges in thermal environment.” Compos. Part B: Eng. 106: 242–261. https://doi.org/10.1016/j.compositesb.2016.09.030.
Kumari, S., and D. Chakravorty. 2010. “Finite element bending behaviour of discretely delaminated composite conoidal shell roofs under concentrated load.” Int. J. Eng. Sci. Technol. 2 (4): 54–70. https://doi.org/10.4314/ijest.v2i4.59199.
Kumari, S., and D. Chakravorty. 2011. “Bending of delaminated composite conoidal shells under uniformly distributed load.” J. Eng. Mech. 137 (10): 660–668. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000275.
Lei, Z. X., K. M. Liew, and J. L. Yu. 2013. “Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment.” Compos. Struct. 106: 128–138. https://doi.org/10.1016/j.compstruct.2013.06.003.
Malekzadeh, P., and A. R. Zarei. 2014. “Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers.” Thin Walled Struct. 82: 221–232. https://doi.org/10.1016/j.tws.2014.04.016.
Mayandi, K., and P. Jeyaraj. 2015. “Bending, buckling and free vibration characteristics of FG-CNT polymer composite beam under non-uniform thermal load.” Proc. IMechE Part L: J. Mater.: Des. Appl. 229 (1): 13–28.
Mehar, K., and S. K. Panda. 2017. “Nonlinear static behavior of FG-CNT reinforced composite flat panel under thermomechanical load.” J. Aerosp. Eng. 30 (3): 04016100. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000706.
Mehri, M., H. Asadi, and M. A. Kouchakzadeh. 2017. “Computationally efficient model for flow-induced instability of CNT reinforced functionally graded truncated conical curved panels subjected to axial compression.” Comput. Methods Appl. Mech. Eng. 318: 957–980. https://doi.org/10.1016/j.cma.2017.02.020.
Mehri, M., H. Asadi, and Q. Wang. 2016a. “Buckling and vibration analysis of a pressurized CNT reinforced functionally graded truncated conical shell under an axial compression using HDQ method.” Comput. Methods Appl. Mech. Eng. 303: 75–100. https://doi.org/10.1016/j.cma.2016.01.017.
Mehri, M., H. Asadi, and Q. Wang. 2016b. “On dynamic instability of a pressurized functionally graded carbon nanotube reinforced truncated conical shell subjected to yawed supersonic airflow.” Compos. Struct. 153: 938–951. https://doi.org/10.1016/j.compstruct.2016.07.009.
Mirzaei, M., and Y. Kiani. 2016. “Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels.” Compos. Struct. 142: 45–56. https://doi.org/10.1016/j.compstruct.2015.12.071.
Moradi-Dastjerdi, R., M. Foroutan, A. Pourasghar, and R. Sotoudeh-Bahreini. 2013. “Static analysis of functionally graded carbon nanotube-reinforced composite cylinders by a mesh-free method.” J. Reinf. Plast. Compos. 32 (9): 593–601. https://doi.org/10.1177/0731684413476353.
Nayak, A. N., and J. N. Bandyopadhyay. 2002. “Free vibration analysis and design aids of stiffened conoidal shells.” J. Eng. Mech. 128 (4): 419–427. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:4(419).
Nejati, M., A. Asanjarani, R. Dimitri, and F. Tornabene. 2017. “Static and free vibration analysis of functionally graded conical shells reinforced by carbon nanotubes.” Int. J. Mech. Sci. 130: 383–398. https://doi.org/10.1016/j.ijmecsci.2017.06.024.
Sankar, A., S. Natarajan, and M. Ganapathi. 2016. “Dynamic instability analysis of sandwich plates with CNT reinforced facesheets.” Compos. Struct. 146: 187–200. https://doi.org/10.1016/j.compstruct.2016.03.026.
Selim, B. A., L. W. Zhang, and K. M. Liew. 2016. “Vibration analysis of CNT reinforced functionally graded composite plates in a thermal environment based on Reddy’s higher-order shear deformation theory.” Compos. Struct. 156: 276–290. https://doi.org/10.1016/j.compstruct.2015.10.026.
Shahrbabaki, E. A., and A. Alibeigloo. 2014. “Three-dimensional free vibration of carbon nanotube-reinforced composite plates with various boundary conditions using Ritz method.” Compos. Struct. 111: 362–370. https://doi.org/10.1016/j.compstruct.2014.01.013.
Shen, H. S. 2009. “Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments.” Compos. Struct. 91 (1): 9–19. https://doi.org/10.1016/j.compstruct.2009.04.026.
Song, Z. G., L. W. Zhang, and K. M. Liew. 2016. “Vibration analysis of CNT-reinforced functionally graded composite cylindrical shells in thermal environments.” Int. J. Mech. Sci. 115–116: 339–347. https://doi.org/10.1016/j.ijmecsci.2016.06.020.
Thomas, B., and T. Roy. 2016. “Vibration analysis of functionally graded carbon nanotube-reinforced composite shell structures.” Acta Mech. 227 (2): 581–599. https://doi.org/10.1007/s00707-015-1479-z.
Yas, M. H., A. Pourasghar, S. Kamarian, and M. Heshmati. 2013. “Three-dimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube.” Mater. Des. 49: 583–590. https://doi.org/10.1016/j.matdes.2013.01.001.
Zghal, S., A. Frikha, and F. Dammak. 2017. “Static analysis of functionally graded carbon nanotube-reinforced plate and shell structures.” Compos. Struct. 176: 1107–1123. https://doi.org/10.1016/j.compstruct.2017.06.015.
Zhang, L. W., W. C. Cui, and K. M. Liew. 2015. “Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges.” Int. J. Mech. Sci. 103: 9–21. https://doi.org/10.1016/j.ijmecsci.2015.08.021.
Zhang, L. W., and B. A. Selim. 2017. “Vibration analysis of CNT-reinforced thick laminated composite plates based on Reddy’s higher-order shear deformation theory.” Compos. Struct. 160: 689–705. https://doi.org/10.1016/j.compstruct.2016.10.102.
Zhu, P., Z. X. Lei, and K. M. Liew. 2012. “Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory.” Compos. Struct. 94 (4): 1450–1460. https://doi.org/10.1016/j.compstruct.2011.11.010.
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©2018 American Society of Civil Engineers.
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Received: Feb 6, 2018
Accepted: Aug 31, 2018
Published online: Dec 28, 2018
Published in print: Mar 1, 2019
Discussion open until: May 28, 2019
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