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Finite rotation three and four nodes shell elements for functionally graded carbon nanotubes-reinforced thin composite shells analysis. (English) Zbl 1439.74412

Summary: In this paper, we address the extension of the Kirchhoff shell model to non-linear analysis of functionally graded carbon nanotubes-reinforced thin composite shells (FG-CNTRCs). The present model can bring up two levels of analysis: geometrically non-linearities and nanostructures with the possibilities of two type of discretization. Either, three and four nodes finite shell elements are implemented to analyze as well as predict the non-linear bending behavior of FG-CNTRC shell structures. Uniform (UD) and three graded distributions of carbon nanotubes (CNTs) which are FG-V, FG-O and FG-X are considered. These distributions are uniaxially aligned in the axial direction of the shell and functionally graded along the thickness direction. The material properties of CNTs are estimated using the modified rule of mixture and the size dependence of these CNTs is taken into account via the introduction of some efficiency parameters. Three numerical examples of FG-CNTRC plates, hyperboloidal and cylindrical shells are presented to highlight the applicability and effectiveness of the present finite element model notably for thin structures. The effect of CNT profiles, CNT volume fractions and others geometrical parameters on non-linear behavior of such structures are also examined.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74K25 Shells

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[1] Reddy, J. N.; Liu, C. F., A higher-order shear deformation theory of laminated elastic shells, Internat. J. Engrg. Sci., 23, 319-330 (1985) · Zbl 0559.73072
[2] Murthy, S. S., On the use of the Trigonometric Ritz method for general vibration analysis of rectangular Kirchhoff plates, Comput. Methods Appl. Mech. Engrg., 54, 197-222 (1986) · Zbl 0575.73091
[3] Reddy, J. N.; Robbins, D. H., Theories and computational models for composite laminates, Appl. Mech. Rev., 47, 147-169 (1994)
[4] Ferreira, A. J.M.; Fasshauer, G. E.; Batra, R. C.; Rodrigues, J. D., Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter, Compos. Struct., 86, 328-343 (2008)
[5] Carrera, E.; Brischetto, S.; Nali, P., Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis (2011), John Wiley & Sons, Ltd · Zbl 1241.74001
[6] Cinefra, M.; Carrera, E.; Croce, L. Della; Chinosi, C., Refined shell elements for the analysis of functionally graded structures, Compos. Struct., 94, 415-422 (2012)
[7] Viola, E.; Tornabene, F.; Fantuzzi, N., Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories, Compos. Struct., 101, 59-93 (2013)
[8] Viola, E.; Tornabene, F.; Fantuzzi, N., General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels, Compos. Struct., 95, 639-666 (2013)
[9] Tornabene, F.; Viola, E., Static analysis of functionally graded doubly-curved shells and panels of revolution, Meccanica, 48, 901-930 (2013) · Zbl 1293.74300
[10] Reddy, J. N.; Srinivasa, A. R., Non-linear theories of beams and plates accounting for moderate rotations and material length scales, Int. J. Non-Linear Mech., 66, 43-53 (2014)
[11] Tang, Y. Q.; Zhou, Z. H.; Chan, S. L., Geometrically nonlinear analysis of shells by quadrilateral flat shell element with drill, shear, and warping, Internat. J. Numer. Methods Engrg., 108, 1248-1272 (2016)
[12] Miehe, C., A theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains, Comput. Methods Appl. Mech. Engrg., 155, 193-233 (1998) · Zbl 0970.74043
[13] Klinkel, S.; Gruttmann, F.; Wagner, W., A robust non-linear solid shell element based on a mixed variational formulation, Comput. Methods Appl. Mech. Engrg., 195, 197-201 (2006) · Zbl 1106.74058
[14] Schwarze, M.; Reese, S., A reduced integration solid-shell finite element based on the EAS and the ANS concept-Large deformation problems, Internat. J. Numer. Methods Engrg., 85, 289-329 (2011) · Zbl 1217.74135
[15] Rah, K.; Paepegem, W. Van; Habraken, A. M.; Degrieck, J.; de Sousa, R. J. Alves; Valente, R. A.F., Optimal low-order fully integrated solid-shell elements, Comput. Methods Appl. Mech. Engrg., 51, 309-326 (2013) · Zbl 1398.74393
[16] Hajlaoui, A.; Jarraya, A.; Kallel-Kamoun, I.; Dammak, F., Buckling analysis of a laminated composite plate with delaminations using the enhanced assumed strain solid shell element, J. Mech. Sci. Technol., 26, 3213-3221 (2012)
[17] Hajlaoui, A.; Jarraya, A.; Bikri, K. El; Dammak, F., Buckling analysis of functionally graded materials structures with enhanced solid-shell elements and transverse shear correction, Compos. Struct., 132, 87-97 (2015)
[18] Koizumi, M., Functionally gradient materials the concept of FGM, Ceram. Trans., 34, 3-10 (1993)
[19] Koizumi, M., FGM activities in Japan, Composites B, 28, 1-4 (1997)
[20] Iijima, S., Helical microtubules of graphitic carbon, Nature, 354, 56-58 (1991)
[21] Liew, K. M.; Lei, Z. X.; Zhang, L. W., Mechanical analysis of functionally graded carbon nanotube reinforced composites: a review, Compos. Struct., 120, 90-97 (2015)
[22] Wuite, J.; Adali, S., Deflection and stress behavior of nanocomposite reinforced beams using a multiscale analysis, Compos. Struct., 71, 388-396 (2005)
[23] Shen, H. S., Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments, Compos. Struct., 91, 9-19 (2009)
[24] Zafarmand, H.; Kadkhodayan, M., Nonlinear analysis of functionally graded nanocomposite rotating thick disks with variable thickness reinforced with carbon nanotubes, Aerosp. Sci. Technol., 41, 47-54 (2015)
[25] Alinaghizadeh, F.; Kadkhodayan, M., Large deflection analysis of moderately thick radially functionally graded annular sector plates fully and partially rested on two-parameter elastic foundations by GDQ method, Aerosp. Sci. Technol., 39, 260-271 (2014)
[26] Kadkhodayan, M.; Golmakani, M. E., Non-linear bending analysis of shear deformable functionally graded rotating disk, Int. J. Non-Linear Mech., 58, 41-56 (2014)
[27] 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, Comput. Methods Appl. Mech. Engrg., 256, 189-199 (2013) · Zbl 1352.74165
[28] 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, Comput. Methods Appl. Mech. Engrg., 273, 1-18 (2014) · Zbl 1296.76116
[29] Zhang, L. W.; Liu, W. H.; Liew, K. M., Geometrically nonlinear large deformation analysis of triangular CNT-reinforced composite plates, Int. J. Non-linear Mech., 86, 122-132 (2016)
[30] 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, Compos. Struct., 132, 974-983 (2015)
[31] Zhang, L. W.; Liew, K. M., Geometrically nonlinear large deformation analysis of functionally graded carbon nanotube reinforced composite straight-sided quadrilateral plates, Comput. Methods Appl. Mech. Engrg., 295, 219-239 (2015) · Zbl 1423.74523
[32] Reinoso, J.; Blazquez, A., Geometrically nonlinear analysis of functionally graded power-based and carbon nanotubes reinforced composites using a fully integrated solid shell element, Compos. Struct., 152, 277-294 (2016)
[33] Reinoso, J.; Blazquez, A., Application and finite element implementation of 7-parameter shell element for geometrically nonlinear analysis of layered CFRP composites, Compos. Struct., 139, 263-276 (2016)
[34] Bischoff, M.; Ramm, E., Shear deformable shell elements for large strains and rotations, Internat. J. Numer. Methods Engrg., 40, 4427-4449 (1997) · Zbl 0892.73054
[35] Fidelus, J. D.; Wiesel, E.; Gojny, F. H.; Schulte, K.; Wagner, H. D., Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites, Composites A, 36, 1555-1561 (2005)
[36] Shen, H. S., Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells, Compos. Struct., 93, 2096-2108 (2011)
[37] Shen, H. S.; Xiang, Y., Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments, Comput. Methods Appl. Mech. Engrg., 213-216, 196-205 (2012) · Zbl 1243.74059
[38] Han, Y.; Elliot, J., Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites, Comput. Mater. Sci., 39, 315-323 (2007)
[39] Zhang, C. L.; Shen, H. S., Temperature-dependent elastic properties of single-walled carbon nanotubes: Prediction from molecular dynamics simulation, Appl. Phys. Lett. (2006)
[40] Dammak, F.; Abid, S.; Gakwaya, A.; Dhatt, G., A formulation of the non linear discrete Kirchhoff quadrilateral shell element with finite rotations and enhanced strains, Rev. Eur. Des. Elem. Finis, 14, 7-31 (2005) · Zbl 1186.74104
[41] Zghal, S.; Frikha, A.; Dammak, F., Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures, Appl. Math. Model. (2017) · Zbl 1480.74137
[42] Wali, M.; Hajlaoui, A.; Dammak, F., Discrete double directors shell element for the functionally graded material shell structures analysis, Comput. Methods Appl. Mech. Engrg., 278, 388-403 (2014) · Zbl 1423.74585
[43] Wali, M.; Hentati, T.; Jarraya, A.; Dammak, F., Free vibration analysis of FGM shell structures with a discrete double directors shell element, Compos. Struct., 125, 295-303 (2015)
[44] Frikha, A.; Wali, M.; Hajlaoui, A.; Dammak, F., Dynamic response of functionally graded material shells with a discrete double directors shell element, Compos. Struct., 154, 385-395 (2016)
[45] Frikha, A.; Dammak, F., Geometrically non-linear static analysis of functionally graded material shells with a discrete double directors shell element, Comput. Methods Appl. Mech. Engrg., 315, 1-24 (2017) · Zbl 1439.74174
[46] Zghal, S.; Frikha, A.; Dammak, F., Static analysis of functionally graded carbon nanotube-reinforced plate and shell structures, Compos. Struct., 176, 1107-1123 (2017)
[47] G. Dhatt, G. Touzot, Une presentation de la methode des elements finis, Maloine S.A. Paris et Les Presses de l’Universit de Laval Qubec, 1st edition, 1981.; G. Dhatt, G. Touzot, Une presentation de la methode des elements finis, Maloine S.A. Paris et Les Presses de l’Universit de Laval Qubec, 1st edition, 1981. · Zbl 0534.65067
[48] J.L. Batoz, G. Dhatt, Modelisation des structures par elements finis, Herms-Lavoisier, 1st,2nd,3th edition, 1990.; J.L. Batoz, G. Dhatt, Modelisation des structures par elements finis, Herms-Lavoisier, 1st,2nd,3th edition, 1990. · Zbl 0831.73001
[49] Simo, J. C., On a stress resultants geometrically exact shell model. Part:VII: Shell intersection with 5/6 DOF finite element formulations, Comput. Methods Appl. Mech. Engrg., 108, 319-339 (1993) · Zbl 0855.73074
[50] Gorji, M., On Large deflection of symmetric composite plates under static loading, J. Mech. Eng. Sci., 200, 13-19 (1986)
[51] Shen, H. S., Nonlinear bending of shear deformable laminated plates under transverse and in-plane loads and resting on elastic foundations, Compos. Struct., 50, 131-142 (2000)
[52] Basar, Y.; Ding, Y.; Schultz, R., Refined shear-deformation models for composite laminates with finite rotations., Int. J. Solids Struct., 30, 2611-2638 (1993) · Zbl 0794.73036
[53] Brank, B.; Peric, D.; Damjanic, F. B., On implementation of a nonlinear four node shell finite element for thin multilayered elastic shells, Comput. Mech., 16, 341-359 (1995) · Zbl 0848.73060
[54] Sze, K. Y.; Liu, X. H.; Lo, S. H., Popular benchmark problems for geometric nonlinear analysis of shells, Finite Elem. Anal. Des., 40, 1551-1569 (2004)
[55] Simo, J. C.; Rifai, M. S.; Fox, D. D., On a stress resultants geometrically exact shell model. Part:IV: Variable thickness shells with through the thickness stretching, Comput. Methods Appl. Mech. Engrg., 81, 91-126 (1990) · Zbl 0746.73016
[56] Fox, D. D.; Simo, J. C., A drill rotation formulation for geometrically exact shells, Comput. Methods Appl. Mech. Engrg., 98, 329-343 (1992) · Zbl 0764.73050
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