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Analysis of the low velocity impact response of functionally graded carbon nanotubes reinforced composite spherical shells

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Abstract

The low velocity impact analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) spherical shells including the contact force and indentation of the shell surface center was presented. The material properties were set according to the rule of mixture. The fibers and polymeric matrix were temperature-dependent. Timoshenko-Midlin assumption was used to establish the dimensionless nonlinear governing equations of the axis-symmetric transverse isotropy spherical shells. The Hertz contact theory was established to obtain the force and displacement between the spherical shell and impactor. Seven species of comparison analyses including grading profiles and volume fraction were mentioned to investigate the influence on the low velocity impact response of the FG-CNTRC spherical shells. The results revealed that the contact force was determined by the material properties of both contact surface and noncontact surface collectively. Furthermore, the increase of volume fraction can result in the larger contact force and shorter contact time.

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References

  1. S. Iijima, Helical microtubules of graphitic carbon, Nature, 354 (1991) 56–58.

    Article  Google Scholar 

  2. C. H. Sun, F. Li, H. M. Cheng and G. Q. Lu, Axial Young's modulus prediction of single-walled carbon nanotube arrays with diameters from nanometer to meter scales, Applied Physics Letters (2005) 87.

    Google Scholar 

  3. K. T. Lau and D. Hui, The revolutionary creation of new advanced materials -carbon nanotube composites, Composites Part B-Engineering, 33 (2002) 263–277.

    Article  Google Scholar 

  4. E. T. Thostenson, Z. Ren and T. Chou, Advances in the science and technology of carbon nanotubes and their composites: A review, Composites Science and Technology, 61 (2001) 1899–1912.

    Article  Google Scholar 

  5. S. Hui-Shen, Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments, Composite Structures, 91 (2009) 9–19.

    Article  Google Scholar 

  6. H. Kwon, C. R. Bradbury and M. Leparoux, Fabrication of functionally graded carbon nanotube-reinforced aluminum matrix composite, Advanced Engineering Materials, 13 (2011) 325–329.

    Article  Google Scholar 

  7. H. Shen, Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axiallyloaded shells, Composite Structures, 93 (2011) 2096–2108.

    Google Scholar 

  8. S. Hui-Shen, Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part II: Pressureloaded shells, Composite Structures, 93 (2011) 2496–2503.

    Google Scholar 

  9. H. Shen, Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells, Composites Part B-Engineering, 43 (2012) 1030–1038.

    Article  Google Scholar 

  10. H. Shen and Y. Xiang, Nonlinear bending of nanotubereinforced composite cylindrical panels resting on elastic foundations in thermal environments, Engineering Structures, 80 (2014) 163–172.

    Article  Google Scholar 

  11. H. Shen and Y. Xiang, Postbuckling of nanotube-reinforced composite cylindrical shells under combined axial and radial mechanical loads in thermal environment, Composites Part B-Engineering, 52 (2013) 311–322.

    Article  Google Scholar 

  12. H. Shen and Y. Xiang, Nonlinear vibration of nanotubereinforced composite cylindrical shells in thermal environments, Computer Methods in Applied Mechanics and Engineering, 213 (2012) 196–205.

    Article  MathSciNet  MATH  Google Scholar 

  13. R. Moradi-Dastjerdi, M. Foroutan, A. Pourasghar and R. Sotoudeh-Bahreini, Static analysis of functionally graded carbon nanotube-reinforced composite cylinders by a meshfree method, Journal of Reinforced Plastics and Composites, 32 (2013) 593–601.

    Article  MATH  Google Scholar 

  14. R. Moradi-Dastjerdi, M. Foroutan and A. Pourasghar, Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method, Materials & Design, 44 (2013) 256–266.

    Article  MATH  Google Scholar 

  15. S. M. Hosseini, Application of a hybrid mesh-free method based on generalized finite difference (GFD) method for natural frequency analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotubes, CMES-Computer Modeling in Engineering & Sciences, 95 (2013) 1–29.

    MathSciNet  MATH  Google Scholar 

  16. M. R. Bidgoli, M. S. Karimi and A. G. Arani, Nonlinear vibration and instability analysis of functionally graded CNT-reinforced cylindrical shells conveying viscous fluid resting on orthotropic Pasternak medium, Mechanics of Advanced Materials and Structures, 23 (2016) 819–831.

    Article  Google Scholar 

  17. H. Ghayoumizadeh, F. Shahabian and S. M. Hosseini, Elastic wave propagation in a functionally graded nanocomposite reinforced by carbon nanotubes employing meshless local integral equations (LIEs), Engineering Analysis with Boundary Elements, 37 (2013) 1524–1531.

    Article  MathSciNet  MATH  Google Scholar 

  18. S. Ghouhestani, F. Shahabian and S. M. Hosseini, Dynamic analysis of a layered cylinder reinforced by functionally graded carbon nanotubes distributions subjected to shock loading using MLPG method, CMES-Computer Modeling in Engineering & Sciences, 100 (2014) 295–321.

    MathSciNet  MATH  Google Scholar 

  19. R. Ansari, T. Pourashraf, R. Gholami and A. Shahabodini, Analytical solution for nonlinear postbuckling of functionally graded carbon nanotube-reinforced composite shells with piezoelectric layers, Composites Part B-Engineering, 90 (2016) 267–277.

    Article  Google Scholar 

  20. Y. Heydarpour, M. M. Aghdam and P. Malekzadeh, Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells, Composite Structures, 117 (2014) 187–200.

    Article  MATH  Google Scholar 

  21. J. E. Jam and Y. Kiani, Buckling of pressurized functionally graded carbon nanotube reinforced conical shells, Composite Structures, 125 (2015) 586–595.

    Article  Google Scholar 

  22. M. Mirzaei and Y. Kiani, Thermal buckling of temperature dependent FG-CNT reinforced composite conical shells, Aerospace Science and Technology, 47 (2015) 42–53.

    Article  MATH  Google Scholar 

  23. H. Shiuh-Chuan and L. Ching-Chun, Impact analysis of composite laminate shell structures, Applied Mechanics and Materials, 764–765 (2015) 1185–1188.

    Article  Google Scholar 

  24. Y. Q. Mao, S. G. Ai, C. P. Chen and D. N. Fang, Nonlinear dynamic response and damage analysis for functionally graded metal shallow spherical shell under low-velocity impact, Archive of Applied Mechanics, 85 (2015) 1627–1647.

    Article  Google Scholar 

  25. K. M. Fard, A. V. Ghorghabad, A. H. Azarnia and F. A. Ghasemi, High order impact elastic analysis of circular thick cylindrical sandwich panels subjected to multi-mass impacts, Latin American Journal of Solids and Structures, 12 (2015) 2281–2310.

    Article  Google Scholar 

  26. M. Kharazan, M. H. Sadr and M. Kiani, Delamination growth analysis in composite laminates subjected to low velocity impact, Steel and Composite Structures, 17 (2014) 387–403.

    Article  Google Scholar 

  27. S. Dey and A. Karmakar, Dynamic analysis of delaminated composite conical shells under low velocity impact, Journal of Reinforced Plastics and Composites, 32 (2013) 380–392.

    Article  Google Scholar 

  28. Z. Wang, J. Xu and P. Qiao, Nonlinear low-velocity impact analysis of temperature-dependent nanotube-reinforced composite plates, Composite Structures, 108 (2014) 423–434.

    Article  Google Scholar 

  29. J. E. Jam and Y. Kiani, Low velocity impact response of functionally graded carbon nanotube reinforced composite beams in thermal environment, Composite Structures, 132 (2015) 35–43.

    Article  Google Scholar 

  30. P. Malekzadeh and M. Dehbozorgi, Low velocity impact analysis of functionally graded carbon nanotubes reinforced composite skew plates, Composite Structures, 140 (2016) 728–748.

    Article  Google Scholar 

  31. D. L. Shi, X. Q. Feng, Y. Huang, K. C. Hwang and H. J. Gao, The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites, Journal of Engineering Materials and Technology-Transactions of the ASME, 126 (2004) 250–257.

    Article  Google Scholar 

  32. G. D. Seidel and D. C. Lagoudas, Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites, Mechanics of Materials, 38 (2006) 884–907.

    Article  Google Scholar 

  33. X. Li et al., Reinforcing mechanisms of single-walled carbon nanotube-reinforced polymer composites, Journal of Nanoscience and Nanotechnology, 7 (2007) 2309–2317.

    Article  Google Scholar 

  34. J. D. Fidelus, E. Wiesel, F. H. Gojny, K. Schulte and H. D. Wagner, Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites, Composites Part AApplied Science and Manufacturing, 36 (2005) 1555–1561.

    Article  Google Scholar 

  35. A. M. K. Esawi and M. M. Farag, Carbon nanotube reinforced composites: Potential and current challenges, Materials & Design, 28 (2007) 2394–2401.

    Article  Google Scholar 

  36. L. Librescu, S. Oh and O. Song, Thin-walled beams made of functionally graded materials and operating in a high temperature environment: Vibration and stability, Journal of Thermal Stresses, 28 (2005) 649–712.

    Article  Google Scholar 

  37. B. Thomas and T. Roy, Vibration analysis of functionally graded carbon nanotube-reinforced composite shell structures, Acta Mechanica, 227 (2016) 581–599.

    Article  MathSciNet  MATH  Google Scholar 

  38. S. Abrate, Impact engineering of composite structures, Springer Vienna (2011).

    Book  MATH  Google Scholar 

  39. H. Shen and Y. Xiang, Nonlinear analysis of nanotubereinforced composite beams resting on elastic foundations in thermal environments, Engineering Structures, 56 (2013) 698–708.

    Article  Google Scholar 

  40. M. Shariyat and R. Jafari, Nonlinear low-velocity impact response analysis of a radially preloaded two-directionalfunctionally graded circular plate: A refined contact stiffness approach, Composites Part B: Engineering, 45 (2013) 981–994.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

    Chun-Hao Yang, Wu-Ning Ma, Da-Wei Ma & Jian-Lin Zhong

  2. Department of Mechanical Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212003, China

    Qiang He

Authors
  1. Chun-Hao Yang
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  2. Wu-Ning Ma
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  3. Da-Wei Ma
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  4. Qiang He
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  5. Jian-Lin Zhong
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Corresponding author

Correspondence to Qiang He.

Additional information

Chun-Hao Yang is currently a doctoral candidate in Nanjing University of Science and Technology in Nanjing City, Jiangsu. He obtained the B.S. from the Nanjing University of Science and Technology, all in Mechanical Engineering. His research interests include impact dynamics and mechanical properties of composites.

He Qiang is currently an lecturer in School of Mechanical Engineering, Jiangsu University of Science and Technology in Zhenjiang City, Jiangsu. He obtained the B.S. from Xuzhou Institute of Technology, M.S. and Ph.D. from the Nanjing University of Science and Technology, all in Mechanical Engineering. His research interests include impact dynamics and mechanical properties of composites.

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Yang, CH., Ma, WN., Ma, DW. et al. Analysis of the low velocity impact response of functionally graded carbon nanotubes reinforced composite spherical shells. J Mech Sci Technol 32, 2681–2691 (2018). https://doi.org/10.1007/s12206-018-0525-x

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  • DOI: https://doi.org/10.1007/s12206-018-0525-x

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