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Large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes. (English) Zbl 1457.74159

Summary: 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 \(C^0\) 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.

MSC:

74M25 Micromechanics of solids
74A40 Random materials and composite materials
74S05 Finite element methods applied to problems in solid mechanics
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[1] Gohardani, O.; Elola, M. C.; 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)
[2] Pal, G.; Kumar, S., Modeling of carbon nanotubes and carbon nanotubepolymer composites, Progress in Aerospace Sciences, 80, 33-58 (2016)
[3] Kwon, H.; Bradbury, C. R.; Leparoux, M., Fabrication of functionally graded carbon nanotube reinforced aluminum matrix composite, Advanced Engineering Materials, 13, 325-329 (2011)
[4] Liew, K. M.; Lei, Z. X.; Zhang, L. W., Mechanical analysis of functionally graded carbon nanotube reinforced composites: a review, Composite Structures, 120, 90-97 (2015)
[5] Shen, H. S., Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments, Composite Structures, 91, 9-19 (2009)
[6] Shen, H. S.; 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)
[7] Shen, H. S.; Xiang, Y., Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments, Engineering Structures, 56, 698-708 (2013)
[8] Shen, H. S.; 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) · Zbl 1406.74259
[9] Shen, H. S.; Xiang, Y., Nonlinear bending of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments, Engineering Structures, 80, 163172 (2014)
[10] Yang, J.; 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) · Zbl 1346.74116
[11] Yang, J.; 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)
[12] Ansari, R.; Hasrati, E.; Shakouri, A. H.; Bazdid-Vahdati, M.; 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)
[13] Zhang, L. W.; Lei, Z. X.; Liew, K. M.; 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) · Zbl 1296.76116
[14] Zhang, L. W.; Liu, W. H.; Liew, K. M.; Yu, J. L., Geometrically nonlinear large deformation analysis of triangular CNT-reinforced composite plates, International Journal of Non-Linear Mechanics, 86, 122-132 (2016)
[15] Zhang, L. W.; 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)
[16] Mehar, K.; 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)
[17] Mehar, K.; 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)
[18] Mehar, K.; Panda, S. K.; Mahapatra, T. R., Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure, European Journal of Mechanics-A/Solids, 85, 384-396 (2017) · Zbl 1406.74182
[19] Mehar, K.; Panda, S. K.; 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)
[20] Zghal, S.; Frikha, A.; Dammak, F., Static analysis of functionally graded carbon nanotube-reinforced plate and shell structures, Composite Structures, 176, 1107-1123 (2017)
[21] Zghal, S.; Frikha, A.; Dammak, F., Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures, Applied Mathematical Modelling, 53, 132-155 (2018) · Zbl 1480.74137
[22] Frikha, A.; Zghal, S.; 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) · Zbl 1439.74412
[23] Zghal, S.; Frikha, A.; 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)
[24] Zghal, S.; Frikha, A.; 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) · Zbl 1439.74412
[25] Frikha, A.; Zghal, S.; 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) · Zbl 1439.74412
[26] Trabelsi, S.; Frikha, A.; Zghal, S.; Dammak, F., Thermal post-buckling analysis of functionally graded material structures using a modified FSDT, International Journal of Mechanical Sciences, 144, 74-89 (2018)
[27] Trabelsi, S.; Frikha, A.; Zghal, S.; 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)
[28] Frikha, A.; 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) · Zbl 1439.74174
[29] Reinoso, J.; 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)
[30] Dung, D. V.; Hoa, L. K.; Thuyet, B. T.; 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) · Zbl 1345.74075
[31] Dung, D. V.; 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) · Zbl 1358.74031
[32] Dung, D. V.; Nga, N. T.; 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) · Zbl 1365.74112
[33] Mohammadimehr, M.; 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) · Zbl 1382.74085
[34] Bathe, K. J.; 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) · Zbl 0551.73072
[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)
[36] Shen, H. S.; Zhang, C. L., Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates, Materials and Design, 31, 3403-3411 (2010)
[37] Han, Y.; Elliot, J., Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites, Computational Materials Science, 39, 315-323 (2007)
[38] Zhang, C. L.; Shen, H. S., Temperature-dependent elastic properties of single-walled carbon nanotubes: prediction from molecular dynamics simulation, Applied Physics Letters, 89, 081904 (2006)
[39] Lei, Z. X.; Liew, K. M.; 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) · Zbl 1352.74165
[40] Gorgi, M., On large deflection of symmetric composite plates under static loading, Journal of Mechanical Engineering Science, 200, 13-19 (1986)
[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)
[42] Buechter, N.; 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) · Zbl 0760.73041
[43] Buechter, N.; Ramm, E., On implementation of a nonlinear four node shell finite element for thin multilayered elastic shells, Computational Mechanics, 16, 341-359 (1995) · Zbl 0848.73060
[44] Brendel, B.; Ramm, E., Linear and nonlinear stability analysis of cylindrical shells, Computational Mechanics, 12, 549-558 (1980) · Zbl 0443.73025
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