Browse > Article
http://dx.doi.org/10.12989/scs.2020.35.1.077

Geometrically nonlinear dynamic analysis of FG graphene platelets-reinforced nanocomposite cylinder: MLPG method based on a modified nonlinear micromechanical model  

Rad, Mohammad Hossein Ghadiri (Civil Engineering Department, Quchan University of Technology)
Shahabian, Farzad (Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad)
Hosseini, Seyed Mahmoud (Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad)
Publication Information
Steel and Composite Structures / v.35, no.1, 2020 , pp. 77-92 More about this Journal
Abstract
The present paper outlined a procedure for geometrically nonlinear dynamic analysis of functionally graded graphene platelets-reinforced (GPLR-FG) nanocomposite cylinder subjected to mechanical shock loading. The governing equation of motion for large deformation problems is derived using meshless local Petrov-Galerkin (MLPG) method based on total lagrangian approach. In the MLPG method, the radial point interpolation technique is employed to construct the shape functions. A micromechanical model based on the Halpin-Tsai model and rule of mixture is used for formulation the nonlinear functionally graded distribution of GPLs in polymer matrix of composites. Energy dissipation in analyses of the structure responding to dynamic loads is considered using the Rayleigh damping. The Newmark-Newton/Raphson method which is an incremental-iterative approach is implemented to solve the nonlinear dynamic equations. The results of the proposed method for homogenous material are compared with the finite element ones. A very good agreement is achieved between the MLPG and FEM with very fine meshing. In addition, the results have demonstrated that the MLPG method is more effective method compared with the FEM for very large deformation problems due to avoiding mesh distortion issues. Finally, the effect of GPLs distribution on strength, stiffness and dynamic characteristics of the cylinder are discussed in details. The obtained results show that the distribution of GPLs changed the mechanical properties, so a classification of different types and volume fraction exponent is established. Indeed by comparing the obtained results, the best compromise of nanocomposite cylinder is determined in terms of mechanical and dynamic properties for different load patterns. All these applications have shown that the present MLPG method is very effective for geometrically nonlinear analyses of GPLR-FG nanocomposite cylinder because of vanishing mesh distortion issue in large deformation problems. In addition, since in proposed method the distributed nodes are used for discretization the problem domain (rather than the meshing), modeling the functionally graded media yields to more accurate results.
Keywords
functionally graded materials; meshless local Petrov-Galerkin method; shock loading; geometrically nonlinear analysis; graphene platelets reinforced nanocomposite;
Citations & Related Records
Times Cited By KSCI : 18  (Citation Analysis)
연도 인용수 순위
1 Arefi, M., Mohammadi, M., Tabatabaeian, A., Dimitri, R. and Tornabene, F. (2018), "Two-dimensional thermo-elastic analysis of FG-CNTRC cylindrical pressure vessels", Steel Compos. Struct., 27(4), 525-536. https://doi.org/10.12989/scs.2018.27.4.525.   DOI
2 Bouguenina, O., Belakhdar, K., Tounsi, A. and Adda Bedia, E.A. (2015), "Numerical analysis of FGM plates with variable thickness subjected to thermal buckling", Steel Compos. Struct., 19(3), 679-695. https://dx.doi.org/10.12989/scs.2015.19.3.679.   DOI
3 Bui, T.Q., Nguyen, N.T., Van Lich, L., Nguyen, M.N. and Truong, T.T. (2018), "Analysis of transient dynamic fracture parameters of cracked functionally graded composites by improved meshfree methods", Theor. Appl. Fract. Mech., 96, 642-657. https://doi.org/10.1016/j.tafmec.2017.10.005.   DOI
4 Celigoj, C.C. (2001), "An improved 'assumed enhanced displacement gradient'ring-element for finite deformation axisymmetric and torsional problems", Int. J. Numer. Method. Eng., 50(4), 899-918. https://doi.org/10.1002/1097-0207(20010210)50:4<899::AID-NME58>3.0.CO;2-Y.   DOI
5 Chen, D., Yang, J. and Kitipornchai, S. (2017), "Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams", Compos. Sci. Technol., 142, 235-245. https://doi.org/10.1016/j.compscitech.2017.02.008.   DOI
6 Chen, J.S., Pan, C. and Wu, C.T. (1997), "Large deformation analysis of rubber based on a reproducing kernel particle method", Comput. Mech., 19(3), 211-227. https://doi.org/10.1007/s004660050170.   DOI
7 Chu, F., He, J., Wang, L. and Zhong, Z. (2016), "Buckling analysis of functionally graded thin plate with in-plane material inhomogeneity", Eng. Anal. with Bound. Elem., 65, 112-125. https://doi.org/10.1016/j.enganabound.2016.01.007.   DOI
8 Feng, C., Kitipornchai, S. and Yang, J. (2017). "Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs)", Eng. Struct., 140, 110-119. https://doi.org/10.1016/j.engstruct.2017.02.052.   DOI
9 Ferezghi, Y.S., Sohrabi, M.R. and MosaviNezhad, S.M. (2018), "Dynamic analysis of non-symmetric FG cylindrical shell under shock loading by using MLPG method", Struct. Eng. Mech., 67(6), 659-669. https://doi.org/10.12989/sem.2018.67.6.659.   DOI
10 Ghayoumizadeh, H., Shahabian, F. and Hosseini, S.M. (2013), "Elastic wave propagation in a functionally graded nanocomposite reinforced by carbon nanotubes employing meshless local integral equations (LIEs)", Eng. Anal. Bound. Elem., 37(11), 1524-1531. https://doi.org/10.1016/j.enganabound.2013.08.011.   DOI
11 Gu, Y., Wang, Q.X. and Lam, K.Y. (2007), "A meshless local Kriging method for large deformation analyses", Comput. Method. Appl. M., 196(9-12), 1673-1684. https://doi.org/10.1016/j.cma.2006.09.017.   DOI
12 Gupta, N. (2007), "A functionally graded syntactic foam material for high energy absorption under compression", Mater. Lett., 61(4-5), 979-982. https://doi.org/10.1016/j.matlet.2006.06.033.   DOI
13 Hajnayeb, A. and Khadem, S.E. (2015), "An analytical study on the nonlinear vibration of a double-walled carbon nanotube", Struct. Eng. Mech., 54(5), 987-998. https://dx.doi.org/10.12989/sem.2015.54.5.987.   DOI
14 Hasselman, D.P.H. and Youngblood, G.E. (1978), "Enhanced thermal stress resistance of structural ceramics with thermal conductivity gradient", J. Am. Ceramic Soc., 61(1-2), 49-52. https://doi.org/10.1111/j.1151-2916.1978.tb09228.x.   DOI
15 Hosseini, S.M. and Zhang, C. (2018), "Elastodynamic and wave propagation analysis in a FG graphene platelets-reinforced nanocomposite cylinder using a modified nonlinear micromechanical model", Steel Compos. Struct., 27(3), 255-271. https://doi.org/10.12989/scs.2018.27.3.255.   DOI
16 Hosseini, S. M., Sladek, J. and Sladek, V. (2015). "Two dimensional analysis of coupled non-Fick diffusion-elastodynamics problems in functionally graded materials using meshless local Petrov-Galerkin (MLPG) method", Appl. Math. Comput., 268, 937-946. https://doi.org/10.1016/j.amc.2015.07.009.   DOI
17 Yang, J., Wu, H. and Kitipornchai, S. (2017), "Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams", Compos. Struct., 161, 111-118. https://doi.org/10.1016/j.compstruct.2016.11.048.   DOI
18 Zhang, N., Khan, T., Guo, H., Shi, S., Zhong, W. and Zhang, W. (2019), "Functionally graded materials: An overview of stability, buckling, and free vibration analysis", Adv. Mater. Sci. Eng., 2019. https://doi.org/10.1155/2019/1354150.
19 Zhu, P. and Liew, K.M. (2011), "Free vibration analysis of moderately thick functionally graded plates by local Kriging meshless method", Compos. Struct., 93(11), 2925-2944. https://doi.org/10.1016/j.compstruct.2011.05.011.   DOI
20 Zienkiewicz, O.C. and Taylor, R.L. (2005), The Finite Element Method for Solid and Structural Mechanics, Elsevier, United Kingdom.
21 Li, C. and Weng, G.J. (2002), "Antiplane crack problem in functionally graded piezoelectric materials", J. Appl. Mech., 69(4), 481-488. https://doi.org/10.1115/1.1467091.   DOI
22 Li, K., Wu, D., Chen, X., Cheng, J., Liu, Z., Gao, W. and Liu, M. (2018). "Isogeometric Analysis of functionally graded porous plates reinforced by graphene platelets", Compos. Struct., 204, 114-130. https://doi.org/10.1016/j.compstruct.2018.07.059.   DOI
23 Liew, K.M., Lei, Z.X. and Zhang, L.W. (2015), "Mechanical analysis of functionally graded carbon nanotube reinforced composites: a review", Compos. Struct., 120, 90-97. https://doi.org/10.1016/j.compstruct.2014.09.041.   DOI
24 Lin, J., Li, J., Guan, Y., Zhao, G., Naceur, H. and Coutellier, D. (2018), "Geometrically nonlinear bending analysis of functionally graded beam with variable thickness by a meshless method", Compos. Struct., 189, 239-246. https://doi.org/10.1016/j.compstruct.2018.01.063.   DOI
25 Liu, D., Kitipornchai, S., Chen, W. and Yang, J. (2018), "Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell", Compos. Struct., 189, 560-569. https://doi.org/10.1016/j.compstruct.2018.01.106.   DOI
26 Liu, Z.S., Swaddiwudhipong, S. and Koh, C.G. (2002), "Stress wave propagation in 1-D and 2-D media using smooth particle hydrodynamics method", Struct. Eng. Mech., 14(4), 455-472. https://doi.org/10.12989/sem.2002.14.4.455.   DOI
27 Mirzaei, M. and Kiani, Y. (2017). "Isogeometric thermal buckling analysis of temperature dependent FG graphene reinforced laminated plates using NURBS formulation", Compos. Struct., 180, 606-616. https://doi.org/10.1016/j.compstruct.2017.08.057.   DOI
28 Mohammadimehr, M., Arshid, E., Alhosseini, S.M.A.R., Amir, S. and Arani, M.R.G. (2019), "Free vibration analysis of thick cylindrical MEE composite shells reinforced CNTs with temperature-dependent properties resting on viscoelastic foundation", Struct. Eng. Mech., 70(6), 683-702. https://doi.org/10.12989/sem.2019.70.6.683.   DOI
29 Thai, C.H., Ferreira, A.J.M. and Phung-Van, P. (2019b), "Size dependent free vibration analysis of multilayer functionally graded GPLRC microplates based on modified strain gradient theory". Compos. Part B: Eng., 169, 174-188. https://doi.org/10.1016/j.compositesb.2019.02.048.   DOI
30 Thai, C.H., Ferreira, A.J.M., Rabczuk, T. and Nguyen-Xuan, H. (2018b), "A naturally stabilized nodal integration meshfree formulation for carbon nanotube-reinforced composite plate analysis". Eng. Anal. Bound. Elem., 92, 136-155. https://doi.org/10.1016/j.enganabound.2017.10.018.   DOI
31 Thai, C.H., Ferreira, A.J.M., Tran, T.D. and Phung-Van, P. (2019a), "Free vibration, buckling and bending analyses of multilayer functionally graded graphene nanoplatelets reinforced composite plates using the NURBS formulation". Compos. Struct., 220, 749-759. https://doi.org/10.1016/j.compstruct.2019.03.100.   DOI
32 Thai, C.H., Ferreira, A.J.M., Tran, T.D. and Phung-Van, P. (2019c), "A size-dependent quasi-3D isogeometric model for functionally graded graphene platelet-reinforced composite microplates based on the modified couple stress theory". Compos. Struct., 111695. https://doi.org/10.1016/j.compstruct.2019.111695.
33 Thai, C.H., Ferreira, A.J.M., Wahab, M.A. and Nguyen-Xuan, H. (2018a), "A moving Kriging meshfree method with naturally stabilized nodal integration for analysis of functionally graded material sandwich plates". Acta Mechanica, 229(7), 2997-3023. https://doi.org/10.1007/s00707-018-2156-9.   DOI
34 Tutuncu, N. and Ozturk, M. (2001), "Exact solutions for stresses in functionally graded pressure vessels", Compos. Part B: Eng., 32(8), 683-686. https://doi.org/10.1016/S1359-8368(01)00041-5.   DOI
35 Vaghefi, R., Hematiyan, M.R. and Nayebi, A. (2016), "Three-dimensional thermo-elastoplastic analysis of thick functionally graded plates using the meshless local Petrov-Galerkin method", Eng. Anal. with Bound. Elem., 71, 34-49. https://doi.org/10.1016/j.enganabound.2016.07.001.   DOI
36 Nguyen, T.N., Thai, C.H., Luu, A.T., Nguyen-Xuan, H. and Lee, J. (2019), "NURBS-based postbuckling analysis of functionally graded carbon nanotube-reinforced composite shells", Comput. Method. Appl. M., 347, 983-1003. https://doi.org/10.1016/j.cma.2019.01.011.   DOI
37 Nguyen, T.N., Thai, C.H., Nguyen-Xuan, H. and Lee, J. (2018), "Geometrically nonlinear analysis of functionally graded material plates using an improved moving Kriging meshfree method based on a refined plate theory", Compos. Struct., 193, 268-280. https://doi.org/10.1016/j.compstruct.2018.03.036.   DOI
38 Ocylok, S., Weisheit, A. and Kelbassa, I. (2010), "Functionally graded multi-layers by laser cladding for increased wear and corrosion protection", Phys. Procedia, 5, 359-367. https://doi.org/10.1016/j.phpro.2010.08.157.   DOI
39 Rad, M.H.G., Shahabian, F. and Hosseini, S.M. (2015a), "A meshless local Petrov-Galerkin method for nonlinear dynamic analyses of hyper-elastic FG thick hollow cylinder with Rayleigh damping", Acta Mechanica, 226(5), 1497-1513. https://doi.org/10.1007/s00707-014-1266-2.   DOI
40 Rad, M.H.G., Shahabian, F. and Hosseini, S. M. (2015b), "Large deformation hyper-Elastic modeling for nonlinear dynamic analysis of two dimensional functionally graded domains using the meshless local Petrov-Galerkin (MLPG) method", CMES: Comput. Model. Eng. Sci., 108(3), 135-157. https://doi.org/10.3970/cmes.2015.108.135.
41 Rad, M.H.G., Shahabian, F. and Hosseini, S.M. (2015c), "Geometrically nonlinear elastodynamic analysis of hyper-elastic neo-Hooken FG cylinder subjected to shock loading using MLPG method", Eng. Anal. with Bound. Eelem., 50, 83-96. https://doi.org/10.1016/j.enganabound.2014.08.002.   DOI
42 Rad, M.H.G., Shahabian, F. and Hosseini, S.M. (2019), "Nonlocal geometrically nonlinear dynamic analysis of nanobeam using a meshless method", Steel Compos. Struct., 32(3), 293-304. https://doi.org/10.12989/scs.2019.32.3.293.   DOI
43 Verma, D., Gope, P.C., Shandilya, A. and Gupta, A. (2014), "Mechanical-thermal-electrical and morphological properties of graphene reinforced polymer composites: A review", Transact. Indian Inst. Metals, 67(6), 803-816. https://doi.org/10.1007/s12666-014-0408-5.   DOI
44 Wang, H. and Qin, Q.H. (2008), "Meshless approach for thermo-mechanical analysis of functionally graded materials", Eng. Anal. with Bound. Elem., 32(9), 704-712. https://doi.org/10.1016/j.enganabound.2007.11.001.   DOI
45 Wu, C. P. and Liu, Y. C. (2016). "A state space meshless method for the 3D analysis of FGM axisymmetric circular plates", Steel Compos. Struct., 22(1), 161-182. https://doi.org/10.12989/scs.2016.22.1.161.   DOI
46 Xu, Y., Li, Z. and Guo, K. (2018), "Active vibration robust control for FGM beams with piezoelectric layers", Struct. Eng. Mech., 67(1), 33-43. https://doi.org/10.12989/sem.2018.67.1.033.   DOI
47 Kawasaki, A. and Watanabe, R. (2002). "Thermal fracture behavior of metal/ceramic functionally graded materials", Eng. Fract. Mech., 69(14-16), 1713-1728. https://doi.org/10.1016/S0013-7944(02)00054-1.   DOI
48 Khayat, M., Poorveis, D. and Moradi, S. (2017), "Buckling analysis of functionally graded truncated conical shells under external displacement-dependent pressure", Steel Compos. Struct., 23(1), 1-16. https://doi.org/10.12989/scs.2017.23.1.001.   DOI
49 Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Design, 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061.   DOI
50 Kou, K.P. and Yang, Y. (2019), "A meshfree boundary-domain integral equation method for free vibration analysis of the functionally graded beams with open edged cracks", Compos. Part B: Eng., 156, 303-309. https://doi.org/10.1016/j.compositesb.2018.08.089.   DOI
51 Krahulec, S., Sladek, J., Sladek, V. and Hon, Y.C. (2016), "Meshless analyses for time-fractional heat diffusion in functionally graded materials", Eng. Anal. with Bound. Elem., 62, 57-64. https://doi.org/10.1016/j.enganabound.2015.09.008.   DOI
52 Lee, W.Y., Stinton, D.P., Berndt, C.C., Erdogan, F., Lee, Y.D. and Mutasim, Z. (1996), "Concept of functionally graded materials for advanced thermal barrier coating applications", J. Am. Ceramic Soc., 79(12), 3003-3012. https://doi.org/10.1111/j.1151-2916.1996.tb08070.x   DOI
53 Lei, Z.X., Zhang, L.W. and Liew, K.M. (2016), "Buckling analysis of CNT reinforced functionally graded laminated composite plates", Compos. Struct., 152, 62-73. https://doi.org/10.1016/j.compstruct.2016.05.047.   DOI
54 Lei, Z.X., Zhang, L.W. and Liew, K.M. (2017), "Meshless modeling of geometrically nonlinear behavior of CNT-reinforced functionally graded composite laminated plates", Appl. Math. Comput., 295, 24-46. https://doi.org/10.1016/j.amc.2016.09.017.   DOI
55 Reddy, J.N. (2014), An Introduction to Nonlinear Finite Element Analysis: With Applications to Heat Transfer, Fluid Mechanics, and Solid Mechanics. OUP Oxford, Texas, USA.
56 Sahmani, S., Aghdam, M.M. and Rabczuk, T. (2018), "Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory", Compos. Struct., 186, 68-78. https://doi.org/10.1016/j.compstruct.2017.11.082   DOI
57 Schulz, U., Peters, M., Bach, F.W. and Tegeder, G. (2003), "Graded coatings for thermal, wear and corrosion barriers", Mater. Sci. Eng.: A, 362(1-2), 61-80. https://doi.org/10.1016/S0921-5093(03)00579-3.   DOI
58 Shi, Z.A. and Chen, Y. (2004), "Functionally graded piezoelectric cantilever beam under load", Arch. Appl. Mech., 74(3-4), 237-247. https://doi.org/10.1007/s00419-004-0346-5.   DOI
59 Sladek, J., Sladek, V., Stanak, P., Zhang, C. and Wunsche, M. (2013), "Analysis of the bending of circular piezoelectric plates with functionally graded material properties by a MLPG method", Eng. Struct., 47, 81-89. https://doi.org/10.1016/j.engstruct.2012.02.034.   DOI
60 Sladek, V., Sladek, J., Tanaka, M. and Zhang, C. (2005). "Transient heat conduction in anisotropic and functionally graded media by local integral equations", Eng. Anal. with Bound. Elem., 29(11), 1047-1065. https://doi.org/10.1016/j.enganabound.2005.05.011.   DOI
61 Soltanimaleki, A., Foroutan, M. and Alihemmati, J. (2016), "Free vibration analysis of functionally graded fiber reinforced cylindrical panels by a three dimensional mesh-free model", J. Vib. Control, 22(19), 4087-4098. https://doi.org/10.1177/1077546315570717.   DOI
62 Thai, C.H., Do, V.N. and Nguyen-Xuan, H. (2016), "An improved Moving Kriging-based meshfree method for static, dynamic and buckling analyses of functionally graded isotropic and sandwich plates", Eng. Anal. with Bound. Elem., 64, 122-136. https://doi.org/10.1016/j.enganabound.2015.12.003.   DOI