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Large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes

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Abstract

This paper deals with the nonlinear large deflection analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates and panels using a finite element method. Based on the first-order shear deformation theory (FSDT), the proposed model takes into account the transverse shear deformations and incorporates the geometrical nonlinearity type. A C0 isoparametric finite shell element is developed for the present nonlinear model with the description of large displacements and finite rotations. By adopting the extended rule of mixture, the effective material properties of FG-CNTRCs are approximated with the introduction of some efficiency parameters. Four carbon nanotube (CNT) distributions, labeled uniformly distributed (UD)-CNT, FG-V-CNT, FG-O-CNT, and FG-X-CNT, are considered. The solution procedure is carried out via the Newton-Raphson incremental technique. Various numerical applications in both isotropic and CNTRC composite cases are performed to trace the potential of the present model. The effects of the CNT distributions, their volume fractions, and the geometrical characteristics on the nonlinear deflection responses of FG-CNTRC structures are highlighted via a detailed parametric study.

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References

  1. GOHARDANI, O., ELOLA, M. C., and ELIZETXEA, C. Potential and prospective implementation of carbon nanotubes on next generation aircraft and space vehicles: a review of current and expected applications in aerospace sciences. Progress in Aerospace Sciences, 3, 42–68 (2014)

    Google Scholar 

  2. PAL, G. and KUMAR, S. Modeling of carbon nanotubes and carbon nanotubepolymer composites. Progress in Aerospace Sciences, 80, 33–58 (2016)

    Google Scholar 

  3. KWON, H., BRADBURY, C. R., and LEPAROUX, M. Fabrication of functionally graded carbon nanotube reinforced aluminum matrix composite. Advanced Engineering Materials, 13, 325–329 (2011)

    Google Scholar 

  4. LIEW, K. M., LEI, Z. X., and ZHANG, L. W. Mechanical analysis of functionally graded carbon nanotube reinforced composites: a review. Composite Structures, 120, 90–97 (2015)

    Google Scholar 

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

    Google Scholar 

  6. SHEN, H. S. and ZHANG, C. L. Non-linear analysis of functionally graded fiber reinforced composite laminated plates, part I: theory and solutions. International Journal of Nonlinear Mechanics, 47, 1045–1054 (2012)

    Google Scholar 

  7. SHEN, H. S. and XIANG, Y. Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments. Engineering Structures, 56, 698–708 (2013)

    Google Scholar 

  8. SHEN, H. S. and WANG, H. Nonlinear bending of FGM cylindrical panels resting on elastic foundations in thermal environments. European Journal of Mechanics: A/Solids, 49, 49–59 (2015)

    MathSciNet  MATH  Google Scholar 

  9. SHEN, H. S. and XIANG, Y. Nonlinear bending of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments. Engineering Structures, 80, 163172 (2014)

    Google Scholar 

  10. YANG, J. and SHEN, H. S. Non-linear analysis of functionally graded plates under transverse and in-plane loads. International Journal of Non-Linear Mechanics, 38(4), 467–482 (2003)

    MATH  Google Scholar 

  11. YANG, J. and SHEN, H. S. Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions. Composites Part B: Engineering, 34(2), 103–115 (2003)

    Google Scholar 

  12. ANSARI, R., HASRATI, E., SHAKOURI, A. H., BAZDID-VAHDATI, M., and ROUHI, H. Nonlinear large deformation analysis of shells using the variational differential quadrature method based on the six-parameter shell theory. International Journal of Non-Linear Mechanics, 106, 130–143 (2018)

    Google Scholar 

  13. ZHANG, L. W., LEI, Z. X., LIEW, K. M., and YU, J. L. Large deflection geometrically nonlinear analysis of carbon nanotube-reinforced functionally graded cylindrical panels. Computer Methods in Applied Mechanics and Engineering, 273, 1–18 (2014)

    MATH  Google Scholar 

  14. ZHANG, L. W., LIU, W. H., LIEW, K. M., and YU, J. L. Geometrically nonlinear large deformation analysis of triangular CNT-reinforced composite plates. International Journal of Non-Linear Mechanics, 86, 122–132 (2016)

    Google Scholar 

  15. ZHANG, L. W. and LIEW, K. M. Large deflection analysis of FG-CNT reinforced composite skew plates resting on Pasternak foundations using an element-free approach. Composite Structures, 132, 974–983 (2015)

    Google Scholar 

  16. MEHAR, K. and PANDA, S. K. Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field. Composite Structures, 143, 336–346 (2016)

    Google Scholar 

  17. MEHAR, K. and PANDA, S. K. Numerical investigation of nonlinear thermomechanical deflection of functionally graded CNT reinforced doubly curved composite shell panel under different mechanical loads. Composite Structures, 161, 287–298 (2017)

    Google Scholar 

  18. MEHAR, K., PANDA, S. K., and MAHAPATRA, T. R. Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure. European Journal of Mechanics-A/Solids, 85, 384–396 (2017)

    MathSciNet  MATH  Google Scholar 

  19. MEHAR, K., PANDA, S. K., and MAHAPATRA, T. R. Large deformation bending responses of nanotube-reinforced polymer composite panel structure: numerical and experimental analyses. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 233(5), 1695–1704 (2018)

    Google Scholar 

  20. ZGHAL, S., FRIKHA, A., and DAMMAK, F. Static analysis of functionally graded carbon nanotube-reinforced plate and shell structures. Composite Structures, 176, 1107–1123 (2017)

    MATH  Google Scholar 

  21. ZGHAL, S., FRIKHA, A., and DAMMAK, F. Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures. Applied Mathematical Modelling, 53, 132–155 (2018)

    MathSciNet  MATH  Google Scholar 

  22. FRIKHA, A., ZGHAL, S., and DAMMAK, F. Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element. Aerospace Science and Technology, 78, 438–451 (2018)

    MATH  Google Scholar 

  23. ZGHAL, S., FRIKHA, A., and DAMMAK, F. Non-linear bending analysis of nanocomposites reinforced by graphene-nanotubes with finite shell element and membrane enhancement. Engineering Structures, 158, 95–109 (2018)

    Google Scholar 

  24. ZGHAL, S., FRIKHA, A., and DAMMAK, F. Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels. Composites Part B: Engineering, 150, 165–183 (2018)

    MATH  Google Scholar 

  25. FRIKHA, A., ZGHAL, S., and DAMMAK, F. Finite rotation three and four nodes shell elements for functionally graded carbon nanotubes-reinforced thin composite shells analysis. Computer Methods in Applied Mechanics and Engineering, 329, 289–311 (2018)

    MathSciNet  MATH  Google Scholar 

  26. TRABELSI, S., FRIKHA, A., ZGHAL, S., and DAMMAK, F. Thermal post-buckling analysis of functionally graded material structures using a modified FSDT. International Journal of Mechanical Sciences, 144, 74–89 (2018)

    Google Scholar 

  27. TRABELSI, S., FRIKHA, A., ZGHAL, S., and DAMMAK, F. A modified FSDT-based four nodes finite shell element for thermal buckling analysis of functionally graded plates and cylindrical shells. International Journal of Mechanical Sciences, 144, 74–89 (2018)

    Google Scholar 

  28. FRIKHA, A. and DAMMAK, F. Geometrically non-linear static analysis of functionally graded material shells with a discrete double directors shell element. Computer Methods in Applied Mechanics and Engineering, 150, 1–24 (2017)

    MathSciNet  MATH  Google Scholar 

  29. REINOSO, J. and BLAZQUEZ, A. Geometrically nonlinear analysis of functionally graded power-based and carbon nanotubes reinforced composites using a fully integrated solid shell element. Composite Structures, 152, 277–294 (2016)

    Google Scholar 

  30. DUNG, D. V., HOA, L. K., THUYET, B. T., and NGA, N. T. Buckling analysis of functionally graded material (FGM) sandwich truncated conical shells reinforced by FGM stiffeners filled inside by elastic foundations. Applied Mathematics and Mechanics (English Edition), 37(7), 879–902 (2016) https://doi.org/10.1007/s10483-016-2097-9

    MathSciNet  MATH  Google Scholar 

  31. DUNG, D. V. and THIEM, H. T. Mechanical and thermal postbuckling of FGM thick circular cylindrical shells reinforced by FGM stiffener system using higher-order shear deformation theory. Applied Mathematics and Mechanics (English Edition), 38(1), 73–98 (2017) https://doi.org/10.1007/s10483-017-2159-6

    MathSciNet  MATH  Google Scholar 

  32. DUNG, D. V., NGA, N. T., and HOA, L. K. Nonlinear stability of functionally graded material (FGM) sandwich cylindrical shells reinforced by FGM stiffeners in thermal environment. Applied Mathematics and Mechanics (English Edition), 38(5), 647–670 (2017) https://doi.org/10.1007/s10483-017-2198-9

    MathSciNet  MATH  Google Scholar 

  33. MOHAMMADIMEHR, M. and ROSTAMI, R. Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields. Applied Mathematics and Mechanics (English Edition), 39(2), 219–240 (2018) https://doi.org/10.1007/s10483-018-2301-6

    MathSciNet  MATH  Google Scholar 

  34. BATHE, K. J. and DVORKIN, E. A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation. International Journal for Numerical Methods in Engineering, 21, 367–383 (1985)

    MATH  Google Scholar 

  35. SHEN, H. S. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, part I: axially-loaded shells. Composite Structures, 93, 2096–2108 (2011)

    Google Scholar 

  36. SHEN, H. S. and ZHANG, C. L. Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates. Materials and Design, 31, 3403–3411 (2010)

    Google Scholar 

  37. HAN, Y. and ELLIOT, J. Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Computational Materials Science, 39, 315–323 (2007)

    Google Scholar 

  38. ZHANG, C. L. and SHEN, H. S. Temperature-dependent elastic properties of single-walled carbon nanotubes: prediction from molecular dynamics simulation. Applied Physics Letters, 89, 081904 (2006)

    Google Scholar 

  39. LEI, Z. X., LIEW, K. M., and YU, J. L. Large deflection analysis of functionally graded carbon nanotube-reinforced composite plates by the element-free kp-Ritz method. Computer Methods in Applied Mechanics and Engineering, 256, 189–199 (2013)

    MathSciNet  MATH  Google Scholar 

  40. GORGI, M. On large deflection of symmetric composite plates under static loading. Journal of Mechanical Engineering Science, 200, 13–19 (1986)

    Google Scholar 

  41. SHEN, H. S. Nonlinear bending of shear deformable laminated plates under transverse and inplane loads and resting on elastic foundations. Composites Structures, 50, 131–142 (2000)

    Google Scholar 

  42. BUECHTER, N. and RAMM, E. Shell theory versus degeneration — a comparison in large rotation finite element analysis. International Journal for Numerical Methods in Engineering, 50, 39–59 (1992)

    MATH  Google Scholar 

  43. BUECHTER, N. and RAMM, E. On implementation of a nonlinear four node shell finite element for thin multilayered elastic shells. Computational Mechanics, 16, 341–359 (1995)

    Google Scholar 

  44. BRENDEL, B. and RAMM, E. Linear and nonlinear stability analysis of cylindrical shells. Computational Mechanics, 12, 549–558 (1980)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Laboratory of Electromechanical Systems, National Engineering School of Sfax, University of Sfax, B. P W3038, Sfax, Tunisia

    S. Zghal, A. Frikha & F. Dammak

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  1. S. Zghal
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  2. A. Frikha
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  3. F. Dammak
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Correspondence to S. Zghal.

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Zghal, S., Frikha, A. & Dammak, F. Large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes. Appl. Math. Mech.-Engl. Ed. 41, 1227–1250 (2020). https://doi.org/10.1007/s10483-020-2633-9

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  • DOI: https://doi.org/10.1007/s10483-020-2633-9

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