DOI QR코드

DOI QR Code

Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method

  • Emdadi, Mohsen (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Navi, Borhan Rousta (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • 투고 : 2018.12.15
  • 심사 : 2019.03.30
  • 발행 : 2019.03.25

초록

In this article, the free vibration analysis of annular sandwich plates with various functionally graded (FG) porous cores and carbon nanotubes reinforced composite (CNTRC) facesheets is investigated based on modified couple stress theory (MCST) and first order shear deformation theories (FSDT). The annular sandwich plate is composed of two face layers and a functionally graded porous core layer which contains different porosity distributions. Various approaches such as extended mixture rule (EMR), Eshelby-Mori-Tanaka (E-M-T), and Halpin-Tsai (H-T) are used to determine the effective material properties of microcomposite circular sandwich plate. The governing equations of motion are extracted by using Hamilton's principle and FSDT. A Ritz method has been utilized to calculate the natural frequency of an annular sandwich plate. The effects of material length scale parameters, boundary conditions, aspect and inner-outer radius ratios, FG porous distributions, pore compressibility and volume fractions of CNTs are considered. The results are obtained by Ritz solutions that can be served as benchmark data to validate their numerical and analytical methods in the future work and also in solid-state physics, materials science, and micro-electro-mechanical devices.

키워드

과제정보

연구 과제 주관 기관 : University of Kashan

참고문헌

  1. Abdel Ghafaar, M., Mazen, A.A. and El-Mahallawy, N.A. (2006), "Application of the rule of mixtures and halpin-tsai equations to woven fabric reinforced epoxy composites", J. Eng. Sci. Assiut Univ., 34(1), 227-236.
  2. Ahouel, M., Sid Ahmed, H.M., Bedia, E.A.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., Int. J., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  3. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  4. Arani, A.G., Mohammadimehr, M., Saidi, A.R., Shogaei, S. and Arefmanesh, A. (2011a), "Thermal buckling analysis of doublewalled carbon nanotubes considering the small-scale length effect", Proc. IMechE, Part C, J. Mech. Eng. Sci., 225(1), 248-256. https://doi.org/10.1177/09544062JMES1975
  5. Arani, A.G., Hashemian, M., Loghman, A. and Mohammadimehr, M. (2011b), "Study of dynamic stability of the double-walled carbon nanotubes under axial loading embedded in an elastic medium by the energy method", J. Appl. Mech. Tech. Phys., 52(5), 815-824. https://doi.org/10.1134/S0021894411050178
  6. Arani, A.G., Mobarakeh, M.R., Shams, S. and Mohammadimehr, M. (2012), "The effect of CNT volume fraction on the magnetothermo- electro-mechanical behavior of smart nanocomposite cylinder", J. Mech. Sci. Technol., 26(8), 2565-2572. https://doi.org/10.1007/s12206-012-0639-5
  7. Ashby, M.F., Evans, T., Fleck, N.A., Hutchinson, J., Wadley, H. and Gibson L. (2000), Metal Foams: A Design Guide, Butterworth-Heinemann, Boston, MA, USA.
  8. Belkorissat, I., Sid Ahmed, H.M., Bedia, E.A.A., Tounsi, A. and Hassan, S. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., Int. J., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  9. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Hassan, S. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. M ech., Int. J., 62(6), 695-702.
  10. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2018), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position ", J. Braz. Soc. Mech. Sci. Eng., 38, 265-275 . https://doi.org/10.1007/s40430-015-0354-0
  11. Betts, C. (2012), "Benefits of metal foams and developments in modeling techniques to assess their materials behavior: a review", Mater. Sci. Technol., 28, 129-143. https://doi.org/10.1179/026708311X13135950699290
  12. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  13. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409- 423. https://doi.org/10.12989/scs.2015.18.2.409
  14. Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052
  15. Chen, D., Kitipornchai, S. and Yang, J. (2016), "Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core", Thin-Wall. Struct., 107, 39-48. https://doi.org/10.1016/j.tws.2016.05.025
  16. Dukhan, N. (2013), Metal Foams: Fundamentals and Applications, DEStech Publications, Inc Lancaster USA.
  17. Ghorbanpour Arani, A., Rousta Navi, B. and Mohammadimehr, M. (2016), "Surface stress and agglomeration effects on nonlocal biaxial buckling polymeric nanocomposite plate reinforced by CNT using various approaches", Adv. Compos. Mater., 25(5), 423-441. https://doi.org/10.1080/09243046.2015.1052189
  18. Guo, J., Shi, D., Wang, Q., Pang, F. and Liang, Q. (2018), "A domain decomposition approach for static and dynamic analysis of composite laminated curved beam with general elastic restrains", Mech. Adv. Mater. Struct., 1-13. DOI: 10.1080/15376494.2018.1432810
  19. Halpin, J.C. and Kardos, J.L. (1976), "The Halpin -Tsaiequation: a review", Polym. Eng. Sci., 16, 344-352. https://doi.org/10.1002/pen.760160512
  20. Jalaei, M.H., Ghorbanpour, Arani, A. and Tourang, H. (2018), "On the dynamic stability of viscoelastic graphene sheets", Int. J.of En. Sci., 132, 16-29. https://doi.org/10.1016/j.ijengsci.2018.07.002
  21. Jasion, P. and Magnucki, K. (2013), "Global buckling of a sandwich column with metal foam core", J. Sandw. Struct. Mater., 1099636213499339.
  22. Jia, J., Zhao, J., Xu, G., Di, J., Yong, Z., Tao, Y., Fang, C., Zhang, Z., Zhang, X., Zheng, L. and Li, Q. (2011), "A comparison of the mechanical properties of fibers spun from different carbon nanotubes", Carbon, 49, 1333-1339. https://doi.org/10.1016/j.carbon.2010.11.054
  23. Karami, B., Janghorban, M. and Tounsi, A. (2018), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025
  24. Ke, L.L. and Wang, Y.S. (2013), "Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory", Int. J. Eng. Sci., 64, 37-53. https://doi.org/10.1016/j.ijengsci.2012.12.002
  25. Kong, S., Zhou, S., Nie, Z. and Wang, K. (2009), "Static and dynamic analysis of micro beams based on strain gradient elasticity theory", Int. J. Eng. Sci., 47(4), 487-498. https://doi.org/10.1016/j.ijengsci.2008.08.008
  26. Lam, D.C.C., Yang, F. and Chong, A.C.M. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51, 1477-1508 . https://doi.org/10.1016/S0022-5096(03)00053-X
  27. Lei, Z.X., Zhang, L.W., Liew, K.M. and Yu, J.L. (2014 ), "Dynamic stability analysis of carbon nanotube-reinforced functionally graded cylindrical panels using the element-free kp-Ritz method", Compos. Struct., 113, 328-338. https://doi.org/10.1016/j.compstruct.2014.03.035
  28. Lei, Z.X., Zhang, L.W. and Liew, K.M. (2015 ), "Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method", Compos. Struct., 127, 245-259. https://doi.org/10.1016/j.compstruct.2015.03.019
  29. Lei, Z.X., Zhang, L.W. and Liew, K.M. (2016a ), "Analysis of laminated CNT reinforced functionally graded plates using the element-free kp-Ritz method", Compos. part B, 84, 211-221. https://doi.org/10.1016/j.compositesb.2015.08.081
  30. Lei, Z.X., Zhang, L.W. and Liew, K.M. (2016b), "Analysis of laminated CNT reinforced functionally graded plates using the element-free kp-Ritz method", Compos. part B, 85, 140-149. https://doi.org/10.1016/j.compositesb.2015.09.044
  31. Magnucka-Blandzi, E. (2009), "Dynamic stability of a metal foam circular plate", J. Theor. Appl. Mech., 47(2), 421-433.
  32. Magnucka-Blandzi, E. (2011), "Mathematical modeling of a rectangular sandwich plate with metal foam core", J. Theor. Appl. Mech., 49(2), 439-455.
  33. Magnucki, K. and Stasiewicz, P. (2004), "Elastic buckling of a porous beam", J. Theor. Appl. Mech., 42(4), 859-868.
  34. Mahi, A., Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded sandwich and laminated composite plates", Appl. Math. Model., 39, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  35. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., Int. J., 25(2), 157-175.
  36. Meziane, A.A., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  37. Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., Int. J., 59(3), 431-454. https://doi.org/10.12989/sem.2016.59.3.431
  38. Mohammadimehr, M. and Alimirzaei, S. (2017), "Buckling and free vibration analysis of tapered FG- CNTRC micro Reddy beam under longitudinal magnetic field using FEM", Smart Struct. Syst., Int. J., 19(3), 309-322. https://doi.org/10.12989/sss.2017.19.3.309
  39. Mohammadimehr, M. and Mehrabi, M. (2017), "Stability and free vibration analyses of double-bonded micro composite sandwich cylindrical shells conveying fluid flow", Appl. Math. Model., 47, 685-709. https://doi.org/10.1016/j.apm.2017.03.054
  40. Mohammadimehr, M. and Mehrabi, M. (2018), "Electro-thermomechanical vibration and stability analyses of double-bonded micro composite sandwich piezoelectric tubes conveying fluid flow", Appl. Math. Model., 60, 255-272. https://doi.org/10.1016/j.apm.2018.03.008
  41. Mohammadimehr, M. and Rahmati, A.H. (2013), "Small scale effect on electro-thermo-mechanical vibration analysis of single-walled boron nitride nanorods under electric excitation", Turkish J. Eng. Environ. Sci., 37(1), 1-15.
  42. Mohammadimehr, M. and Salemi, M. (2014), "Bending and buckling analysis of functionally graded Mindlin nano-plate model based on strain gradient elasticity theory", Indian J. Sci. Res., 2(2), 587-598.
  43. Mohammadimehr, M. and Shahedi, S. (2017) "High-order buckling and free vibration analysis of two types sandwich beam including AL or PVC-foam flexible core and CNTs reinforced nanocomposite face sheets using GDQM", Compos. Part B: Eng., 108, 91-107. https://doi.org/10.1016/j.compositesb.2016.09.040
  44. Mohammadimehr, M., Saidi, A.R., Arani, A.G., Arefmanesh, A. and Han, Q. (2010), "Torsional Buckling of a DWCNT Embedded on Winkler and Pasternak Foundations Using Nonlocal Theory", J. Mech. Sci. Tech., 24(6), 1289-1299. https://doi.org/10.1007/s12206-010-0331-6
  45. Mohammadimehr, M., Rousta-Navi, B. and Ghorbanpour-Arani, A. (2014), "Biaxial buckling and bending of smart nanocomposite plate reinforced by CNTs using extended mixture rule approach", Mech. Adv. Compos. Struct., 1, 17-26.
  46. Mohammadimehr, M., Shahedi, S. and Rousta Navi, B. (2016a), "Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using generalized differential quadrature method", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(20), 3866-3885. https://doi.org/10.1177/0954406216653622
  47. Mohammadimehr, M., Navi, B.R. and Arani, A.G. (2016b), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of doublecoupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Part B, 87, 132-148. https://doi.org/10.1016/j.compositesb.2015.10.007
  48. Mohammadimehr, M., Rostami, R. and Arefi, M. (2016c), "Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT", Steel Compos. Struct., Int. J., 20(3), 513-544. https://doi.org/10.12989/scs.2016.20.3.513
  49. Mohammadimehr, M., Mohammadimehr, M.A. and Dashti, P. (2016d), "Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic microplate based on surface stress and modified couple stress theories using differential quadrature method (DQM)", Appl. Math. Mech. (English Edition), 37(4), 529-554. https://doi.org/10.1007/s10483-016-2045-9
  50. Mohammadimehr, M., Zarei, H.B., Parakandeh, A. and Arani, A.G. (2017), "Vibration analysis of double-bonded sandwich microplates with nanocomposite facesheets reinforced by symmetric and un-symmetric distributions of nanotubes under multi physical fields", Struct. Eng. Mech., Int. J., 64(3), 361-379.
  51. Mohammadimehr, M., Emdadi, M., Afshari, H. and Rousta Navi, B. (2018a), "Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo- magneto-mechanical loadings using DQM", Int. J. Smart Nano Mater., 9(4), 223-260.
  52. Mohammadimehr, M., Emdadi, M. and Rousta Navi, B. (2018b), "Dynamic stability analysis of microcomposite annular sandwich plate with CNT reinforced composite facesheets based on MSGT", J. Sandw. Struct. Mater., DOI: org/10.1177/1099636218782770
  53. Mojahedin, A., Jabbari, M., Khorshidvand, A.R. and Eslami, M.R. (2016), "Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory", Thin-Wall. Struct., 99, 83-90. https://doi.org/10.1016/j.tws.2015.11.008
  54. Nguyen, H.X., Nguyen, T.N., Abdel-Wahab, M., Bordas, S.P.A., Nguyen-Xuan, H. and Vo, T.P. (2017), "A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory", Comput. Methods Appl. Mech. Eng., 313, 904-940. https://doi.org/10.1016/j.cma.2016.10.002
  55. Shi, D., Feng, X.Q. and Huang, Y.Y. (2004), "The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composite", J. Eng. Mater. Technol., 126, 250-257. https://doi.org/10.1115/1.1751182
  56. Simseka, M. and Reddy, J.N. (2014), "Bending and free vibration of functionally graded piezoelectric beam based on modified strain gradient theory", Compos. Struct., 115, 41-50. https://doi.org/10.1016/j.compstruct.2014.04.005
  57. Smith, B.H., Szyniszewski, S., Hajjar, J.F., Schafer, B.W. and Arwade, S.R. (2012), "Steel foam for structures: a review of applications, manufacturing and material properties", J. Constr. Steel Res., 117, 1-10. https://doi.org/10.1016/j.jcsr.2015.10.001
  58. Sun, C.H., Li, F., Cheng, H.M. and Lu, G.Q. (2005), "Axial Young's modulus prediction of single walled carbon nanotube arrays with diameters from nanometer to meter scales", Appl. Phys. Lett., 87, 193-201.
  59. Ugale, V., Singh, K. and Mishra, N. (2015), "Comparative study of carbon fabric reinforced and glass fabric reinforced thin sandwich panels under impact and static loading", J. Compos. Mater., 49, 99-112. https://doi.org/10.1177/0021998313514874
  60. Wang, Z.X. and Shen, H.S. (2012), "Nonlinear vibration and bending of sandwich plates with nanotube reinforced composite", Compos. Part B, 43, 411-421. https://doi.org/10.1016/j.compositesb.2011.04.040
  61. Wang, B., Zhou, S., Zhao, J. and Chen, X. (2011), "A sizedependent Kirchhoff micro-plate model based on strain gradient elasticity theory", Eur. J. Mech. A-Solid, 30, 517-524. https://doi.org/10.1016/j.euromechsol.2011.04.001
  62. Wang, Q., Shi, D., Liang, Q. and Shi, X. (2016), "A unified solution for vibration analysis of functionally graded circular, annular and sector plates with general boundary conditions", Compos. Part B-Eng., 88, 264-294. https://doi.org/10.1016/j.compositesb.2015.10.043
  63. Wen, P.H. (2012), "The analytical solutions of incompressible saturated poroelastic circular Mindlin's plate", J. Appl. Mech., 79(5), 203-210.
  64. Whitney, J. (1972), "Stress analysis of thick laminated composite and sandwich plates", J. Compos. Mater., 6, 426-440. https://doi.org/10.1177/002199837200600401
  65. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories ", Struct. Eng. Mech., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  66. Yin, L., Qian, Q., Wang, L. and Xia, W. (2010), "Vibration analysis of micro scale plates based on modified couple stress theory", Acta Mech. Solid Sin., 23, 386-393. https://doi.org/10.1016/S0894-9166(10)60040-7
  67. Zeighampour, H. and Beni, Y.T. (2014), "Cylindrical thin-shell model based on modified strain gradient theory", Int. J. Eng. Sci., 78, 27-47. https://doi.org/10.1016/j.ijengsci.2014.01.004
  68. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., Int. J., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693
  69. Zenkour, A. (2005), "A comprehensive analysis of functionally graded sandwich plates, Part 1 - deflection and stresses", Int. J. Solids Str., 42, 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015
  70. Zhao, C. (2012), "Review on thermal transport in high porosity cellular metal foams with open cells", Int. J. Heat Mass Transf., 55, 3618-3632. https://doi.org/10.1016/j.ijheatmasstransfer.2012.03.017
  71. Zhang, L.W. (2017a), "Geometrically nonlinear large deformation of CNT-reinforced composite plates with internal column supports", J. Model. Mech. Mater., 1, 20160154. DOI: https://doi.org/10.1515/nano.0070.00001
  72. Zhang, L.W. (2017b), "On the study of the effect of in-plane forces on the frequency parameters of CNT-reinforced composite skew plates", Compos. Struct., 160, 824-837. https://doi.org/10.1016/j.compstruct.2016.10.116
  73. Zhang, L.W. and Liew, K.M. (2016a ), "Postbuckling analysis of axially compressed CNT reinforced functionally graded composite plates resting on Pasternak foundations using an element-free approach", Compos. Struct., 138, 40-51. https://doi.org/10.1016/j.compstruct.2015.11.031
  74. Zhang, L.W. and Liew, K.M. (2016b ), "Element-free geometrically nonlinear analysis of quadrilateral functionally graded material plates with internal column supports", Compos. Struct., 147, 99-110. https://doi.org/10.1016/j.compstruct.2016.03.034
  75. Zhang, L.W. and Selim, B.A. (2017), "Vibration analysis of CNTreinforced thirck laminated composite plates based on Reddy's higher-order shear deformation theory", Compos. Struct., 160, 689-705. https://doi.org/10.1016/j.compstruct.2016.10.102
  76. Zhang, L.W. and Xiao, L.N. (2017) , "Mechanical behavior of laminated CNT-reinforced composite skew plates subjected to dynamic loading", Compos. part B, 122, 219-230. https://doi.org/10.1016/j.compositesb.2017.03.041
  77. Zhang, L.W. and Liew, K.M. (2015 ), "Large deflection analysis of FG-CNT reinforced composite skew plates resting on Pasternak foundations using an element-free approach", Compos. Struct., 132, 974-993. https://doi.org/10.1016/j.compstruct.2015.07.017
  78. Zhang, L.W., Zhub, P. and Liew, K.M. (2014 ), "Thermal buckling of functionally graded plates using a local Kriging meshless method", Compos. Struct., 108, 472-492. https://doi.org/10.1016/j.compstruct.2013.09.043
  79. Zhang, L.W., Huang, D. and Liew, K.M. (2015a ), "An elementfree IMLS-Ritz method for numerical solution of threedimensional wave equations", Comput. Meth. Appl. Mech. Eng., 297, 116-139. https://doi.org/10.1016/j.cma.2015.08.018
  80. Zhang, L.W., Song, Z.G. and Liew, K.M. (2015b ), "State-space Levy method for vibration analysis of FG-CNT composite plates subjected to in-plane loads based on higher-order shear deformation theory", Compos. Struct., 134, 989-1003. https://doi.org/10.1016/j.compstruct.2015.08.138
  81. Zhang, L.W., Song, Z.G. and Liew, K.M. (2015c ), " Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLSRitz method", Compos. Struct., 128, 165-175. https://doi.org/10.1016/j.compstruct.2015.03.011
  82. Zhang, L.W., Lei, Z.X. and Liew, K.M. (2015d), "Buckling analysis of FG-CNT reinforced composite thick skew plates using an element-free approach", Compos. part B, 75, 36-46. https://doi.org/10.1016/j.compositesb.2015.01.033
  83. Zhang, L.W., Liew, K.M. and Jiang, Z. (2016a ), "An element-free analysis of CNT-reinforced composite plates with column supports and elastically restrained edges under large deformation", Compos. part B, 95, 18-28. https://doi.org/10.1016/j.compositesb.2016.03.078
  84. Zhang, L.W., Liew, K.M. and Reddy, J.N. (2016b ), "Postbuckling of carbon nanotube reinforced functionally graded plates with edges elastically restrained against translation and rotation under axial compression", Comput. Meth. Appl. Mech. Eng., 298, 1-28. https://doi.org/10.1016/j.cma.2015.09.016
  85. Zhang, L.W., Xiao, L.N., Zou, G.L. and Liew , K.M. (2016c), "Elastodynamic analysis of quadrilateral CNT-reinforced functionally graded composite plates using FSDT element-free method", Compos. Struct., 148, 144-154. https://doi.org/10.1016/j.compstruct.2016.04.006
  86. Zhang, L.W., Zhang, Y., Zou, G.L. and Liew, K.M. (2016d), "Free vibration analysis of triangular CNT-reinforced composite plates subjected to in-plane stresses using FSDT element-free method", Compos. Struct., 149, 247-260. https://doi.org/10.1016/j.compstruct.2016.04.019
  87. Zhang, L.W., Liew, K.M. and Reddy, J.N. (2016e), "Postbuckling analysis of bi-axially compressed laminated nanocomposite plates using the first-order shear deformation theory", Compos. Struct., 152, 418-431. https://doi.org/10.1016/j.compstruct.2016.05.040
  88. Zhang, L.W., Song, Z.G. and Liew, K.M. (2016f ), "Optimal shape control of CNT reinforced functionally graded composite plates using piezoelectric patches", Compos. part B, 85, 140-149. https://doi.org/10.1016/j.compositesb.2015.09.044
  89. Zhang, L.W., Song, Z.G. and Liew, K.M. (2016g), "Computation of aerothermoelastic properties and active flutter control of CNT reinforced functionally graded composite panels in supersonic airflow", Comput. Meth. Appl. Mech. Eng., 300, 427-441. https://doi.org/10.1016/j.cma.2015.11.029
  90. Zhang, L.W., Liu, W.H. and Liew, K.M. (2016h ), "Geometrically nonlinear large deformation analysis of triangular CNTreinforced composite plates", Int. J. Non-Linear Mech., 86, 122-132. https://doi.org/10.1016/j.ijnonlinmec.2016.08.004
  91. Zhong, R., Wang, Q., Tang, J., Shuai, C. and Qin, B. (2018), "Vibration analysis of functionally graded carbon nanotube reinforced composites (FG-CNTRC) circular, annular and sector plates", Compos. Struct., 194(15), 49-67. https://doi.org/10.1016/j.compstruct.2018.03.104
  92. Zhou, D., Au, F.T.K., Cheung, Y.K. and Lo, S.H. (2003), "Threedimensional vibration analysis of circular and annular plates via the Chebyshev-Ritz method", Int. J. Solids Struct., 40, 3089-3105. https://doi.org/10.1016/S0020-7683(03)00114-8
  93. Zhu, P., Zhang, L.W. and Liew, K.M. (2014 ), "Geometrically nonlinear thermo mechanical analysis of moderately thick functionally graded plates using a local Petrov-Galerkin approach with moving Kriging interpolation", Compos. Struct., 107, 298-314. https://doi.org/10.1016/j.compstruct.2013.08.001

피인용 문헌

  1. Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations vol.25, pp.4, 2019, https://doi.org/10.12989/cac.2020.25.4.311
  2. Frequency and thermal buckling information of laminated composite doubly curved open nanoshell vol.10, pp.1, 2019, https://doi.org/10.12989/anr.2021.10.1.001
  3. Computer modeling to forecast accurate of efficiency parameters of different size of graphene platelet, carbon, and boron nitride nanotubes: A molecular dynamics simulation vol.27, pp.2, 2019, https://doi.org/10.12989/cac.2021.27.2.111
  4. Vibration characteristics of microplates with GNPs-reinforced epoxy core bonded to piezoelectric-reinforced CNTs patches vol.11, pp.2, 2019, https://doi.org/10.12989/anr.2021.11.2.115
  5. Free vibration analysis of carbon nanotube RC nanobeams with variational approaches vol.11, pp.2, 2021, https://doi.org/10.12989/anr.2021.11.2.157
  6. Computer modeling for frequency performance of viscoelastic magneto-electro-elastic annular micro/nanosystem via adaptive tuned deep learning neural network optimization vol.11, pp.2, 2019, https://doi.org/10.12989/anr.2021.11.2.203