Advances in materials Research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Buckling behavior of smart MEE-FG porous plate with various boundary conditions based on refined theory

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Jafari, Ali (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • Received : 2016.11.26
  • Accepted : 2017.01.31
  • Published : 2016.12.25
⟨ Previous Next ⟩

Abstract

Present disquisition proposes an analytical solution method for exploring the buckling characteristics of porous magneto-electro-elastic functionally graded (MEE-FG) plates with various boundary conditions for the first time. Magneto electro mechanical properties of FGM plate are supposed to change through the thickness direction of plate. The rule of power-law is modified to consider influence of porosity according to two types of distribution namely even and uneven. Pores possibly occur inside FGMs due the result of technical problems that lead to creation of micro-voids in these materials. The variation of pores along the thickness direction influences the mechanical and physical properties. Four-variable tangential-exponential refined theory is employed to derive the governing equations and boundary conditions of porous FGM plate under magneto-electrical field via Hamilton's principle. An analytical solution procedure is exploited to achieve the non-dimensional buckling load of porous FG plate exposed to magneto-electrical field with various boundary condition. A parametric study is led to assess the efficacy of material graduation exponent, coefficient of porosity, porosity distribution, magnetic potential, electric voltage, boundary conditions, aspect ratio and side-to-thickness ratio on the non-dimensional buckling load of the plate made of magneto electro elastic FG materials with porosities. It is concluded that these parameters play remarkable roles on the dynamic behavior of porous MEE-FG plates. The results for simpler states are confirmed with known data in the literature. Presented numerical results can serve as benchmarks for future analyses of MEE-FG plates with porosity phases.

Keywords

References

  1. Aghelinejad, M., Zare, K., Ebrahimi, F. and Rastgoo, A. (2011), "Nonlinear thermomechanical post-buckling analysis of thin functionally graded annular plates based on von-karman's plate theory", Mech. Adv. Mater. Struct., 18(5), 319-326. https://doi.org/10.1080/15376494.2010.516880
  2. Atmane, H.A., Tounsi, A. and Bernard, F. (2015), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", J. Mech. Mater. Des., 1-14.
  3. Boutahar, L. and Benamar, R. (2016), "A homogenization procedure for geometrically non-linear free vibration analysis of functionally graded annular plates with porosities, resting on elastic foundations", Ain Shams Eng. J., 7(1), 313-333. https://doi.org/10.1016/j.asej.2015.11.016
  4. Chen, W., Lee, K.Y. and Ding, H. (2005), "On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates", J. Sound Vibr., 279(1), 237-251. https://doi.org/10.1016/j.jsv.2003.10.033
  5. Ebrahimi, F., Ghasemi, F. and Salari, E. (2016), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities", Meccan., 51(1), 223-249. https://doi.org/10.1007/s11012-015-0208-y
  6. Ebrahimi, F., Naei, M.H. and Rastgoo, A. (2009), "Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation", J. Mech. Sci. Technol., 23(8), 2107-2124. https://doi.org/10.1007/s12206-009-0358-8
  7. Ebrahimi, F. and Rastgoo, A. (2011), "Nonlinear vibration analysis of piezo-thermo-electrically actuated functionally graded circular plates", Arch. Appl. Mech., 81(3), 361-383. https://doi.org/10.1007/s00419-010-0415-x
  8. Ebrahimi, F. and Rastgoo, A. (2009), "Nonlinear vibration of smart circular functionally graded plates coupled with piezoelectric layers", J. Mech. Mater. Des., 5(2), 157-165. https://doi.org/10.1007/s10999-008-9091-1
  9. Ebrahimi, F. and Barati, M.R. (2016a), "Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory", J. Smart Nano Mater., 7(3), 1-25. https://doi.org/10.1080/19475411.2016.1148077
  10. Ebrahimi, F. and Barati, M.R. (2016b), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vibr. Contr., 1077546316646239.
  11. Ebrahimi, F. and Barati, M.R. (2016c), "Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments", Appl. Phys. A, 122(10), 910. https://doi.org/10.1007/s00339-016-0441-9
  12. Ebrahimi, F. and Barati, M.R. (2016d), "Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory", Smart Mater. Struct., 25(10), 105014. https://doi.org/10.1088/0964-1726/25/10/105014
  13. Ebrahimi, F. and Barati, M.R. (2016e), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intell. Mater. Syst. Struct., 1045389X16672569.
  14. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", J. Eng. Sci., 107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008
  15. Ebrahimi, F. and Dabbagh, A. (2016), "On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory", Compos. Struct., 162, 281-293.
  16. Ebrahimi, F. and Hosseini, S.H.S. (2016a), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Therm. Str., 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684
  17. Ebrahimi, F. and Hosseini, S.H.S. (2016b), "Double nanoplate-based NEMS under hydrostatic and electrostatic actuations", Eur. Phys. J. Plus, 131(5), 1-19. https://doi.org/10.1140/epjp/i2016-16001-3
  18. Ebrahimi, F. and Barati, M.R. (2016f), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arab. J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4
  19. Ebrahimi, F. and Barati, M.R. (2016g), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", Eur. Phys. J. Plus, 131(8), 279. https://doi.org/10.1140/epjp/i2016-16279-y
  20. Ebrahimi, F. and Barati, M.R. (2016h), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18.
  21. Ebrahimi, F. and Barati, M.R. (2016i), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Appl. Phys. A, 122(9), 792. https://doi.org/10.1007/s00339-016-0322-2
  22. Ebrahimi, F. and Barati, M.R. (2016j), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001
  23. Ebrahimi, F. and Barati, M.R. (2016k), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444.
  24. Ebrahimi, F. and Barati, M.R. (2016l), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 1-16.
  25. Ebrahimi, F. and Barati, M.R. (2016m), "Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams", Eur. Phys. J. Plus, 131(7), 1-14. https://doi.org/10.1140/epjp/i2016-16001-3
  26. Ebrahimi, F. and Barati, M.R. (2016n), "Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams", J. Mech., 1-11.
  27. Ebrahimi, F. and Barati, M.R. (2017), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159, 174-182. https://doi.org/10.1016/j.compstruct.2016.09.058
  28. Ebrahimi, F., Ghadiri, M., Salari, E., Hoseini, S.A.H. and Shaghaghi, G.R. (2015a), "Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams", J. Mech. Sci. Technol., 29(3), 1207-1215. https://doi.org/10.1007/s12206-015-0234-7
  29. Ebrahimi, F. and Salari, E. (2015a), "Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments", Compos. Struct., 128, 363-380. https://doi.org/10.1016/j.compstruct.2015.03.023
  30. Ebrahimi, F. and Salari, E. (2015b), "Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method", Compos. Part B: Eng., 79, 156-169. https://doi.org/10.1016/j.compositesb.2015.04.010
  31. Ebrahimi, F. and Salari, E. (2015c), "Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment", Acta Astronaut., 113, 29-50. https://doi.org/10.1016/j.actaastro.2015.03.031
  32. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2015b), "Thermomechanical vibration behavior of FG nanobeams subjected to linear and nonlinear temperature distributions", J. Therm. Stresses, 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  33. Ebrahimi, F. and Barati, M.R. (2016o), "An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams", Adv. Nano Res., 4(2), 65-84. https://doi.org/10.12989/anr.2016.4.2.065
  34. Ebrahimi, F. and Barati, M.R. (2016p), "Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment", J. Smart Nano Mater., 7(2), 69-90. https://doi.org/10.1080/19475411.2016.1191556
  35. Ebrahimi, F. and Barati, M.R. (2016q), "Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., 1-13.
  36. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2016), "In-plane thermal loading effects on vibrational characteristics of functionally graded nanobeams", Meccan., 51(4), 951-977. https://doi.org/10.1007/s11012-015-0248-3
  37. Harshe, G., Dougherty, J. and Newnham, R. (1993), "Theoretical modelling of multilayer magnetoelectric composites", J. Appl. Electrom. Mater., 4(2), 145-145.
  38. Huang, D., Ding, H. and Chen, W. (2007), "Analytical solution for functionally graded magneto-electro-elastic plane beams", J. Eng. Sci., 45(2), 467-485. https://doi.org/10.1016/j.ijengsci.2007.03.005
  39. Jiang, A. and Ding, H. (2004), "Analytical solutions to magneto-electro-elastic beams", Struct. Eng. Mech., 18(2), 195-209. https://doi.org/10.12989/sem.2004.18.2.195
  40. Kattimani, S. and Ray, M. (2015), "Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates", J. Mech. Sci., 99, 154-167. https://doi.org/10.1016/j.ijmecsci.2015.05.012
  41. Ke, L.L. and Wang, Y.S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory", Phys. E: Low-dimens. Syst. Nanostruct., 63, 52-61. https://doi.org/10.1016/j.physe.2014.05.002
  42. Ke, L.L., Yang, J., Kitipornchai, S. and Bradford, M.A. (2012), "Bending, buckling and vibration of size-dependent functionally graded annular microplates", Compos. Struct., 94(11), 3250-3257. https://doi.org/10.1016/j.compstruct.2012.04.037
  43. Larbi, L.O., Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Based Des. Struct. Mach., 41(4), 421-433. https://doi.org/10.1080/15397734.2013.763713
  44. Liu, M.F. and Chang, T.P. (2010), "Closed form expression for the vibration problem of a transversely isotropic magneto-electro-elastic plate", J. Appl. Mech., 77(2), 024502. https://doi.org/10.1115/1.3176996
  45. Mantari, J., Bonilla, E. and Soares, C.G. (2014), "A new tangential-exponential higher order shear deformation theory for advanced composite plates", Compos. Part B: Eng., 60, 319-328. https://doi.org/10.1016/j.compositesb.2013.12.001
  46. Mechab, I., Mechab, B., Benaissa, S., Serier, B. and Bouiadjra, B.B. (2016), "Free vibration analysis of FGM nanoplate with porosities resting on winkler pasternak elastic foundations based on two-variable refined plate theories", J. Brazil. Soc. Mech. Sci. Eng., 38(8), 1-19. https://doi.org/10.1007/s40430-015-0330-8
  47. Mohammadi, M., Saidi, A.R. and Jomehzadeh, E. (2010), "Levy solution for buckling analysis of functionally graded rectangular plates", Appl. Compos. Mater., 17(2), 81-93. https://doi.org/10.1007/s10443-009-9100-z
  48. Nguyen, T.K., Nguyen, T.T.P., Vo, T.P. and Thai, H.T. (2015), "Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory", Compos. Part B: Eng., 76, 273-285. https://doi.org/10.1016/j.compositesb.2015.02.032
  49. Pan, E. and Han, F. (2005), "Exact solution for functionally graded and layered magneto-electro-elastic plates", J. Eng. Sci., 43(3), 321-339. https://doi.org/10.1016/j.ijengsci.2004.09.006
  50. Ramirez, F., Heyliger, P.R. and Pan, E. (2006), "Free vibration response of two-dimensional magneto-electro-elastic laminated plates", J. Sound Vibr., 292(3), 626-644. https://doi.org/10.1016/j.jsv.2005.08.004
  51. Rezaei, A. and Saidi, A. (2016), "Application of carrera unified formulation to study the effect of porosity on natural frequencies of thick porous-cellular plates", Compos. Part B: Eng., 91, 361-370. https://doi.org/10.1016/j.compositesb.2015.12.050
  52. Simsek, M. and Yurtcu, H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038
  53. Sladek, J., Sladek, V., Krahulec, S., Chen, C. and Young, D. (2015), "Analyses of circular magnetoelectroelastic plates with functionally graded material properties", Mech. Adv. Mater. Struct., 22(6), 479-489. https://doi.org/10.1080/15376494.2013.807448
  54. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018
  55. Thai, H.T. and Choi, D.H. (2012), "An efficient and simple refined theory for buckling analysis of functionally graded plates", Appl. Math. Model., 36(3), 1008-1022. https://doi.org/10.1016/j.apm.2011.07.062
  56. Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015), "A quasi-3D theory for vibration and buckling of functionally graded sandwich beams", Compos. Struct., 119, 1-12. https://doi.org/10.1016/j.compstruct.2014.08.006
  57. Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Flexural vibration of imperfect functionally graded beams based on timoshenko beam theory: Chebyshev collocation method", Meccan., 50(5), 1-12. https://doi.org/10.1007/s11012-014-0082-z
  58. Wattanasakulpong, N., Prusty, B.G., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190. https://doi.org/10.1016/j.matdes.2011.10.049
  59. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aeros. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  60. Xin, L. and Hu, Z. (2015), "Free vibration of layered magneto-electro-elastic beams by SS-DSC approach", Compos. Struct., 125, 96-103. https://doi.org/10.1016/j.compstruct.2015.01.048
  61. 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., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  62. Zeng, X., Yue, Z., Zhao, B. and Wen, S. (2014), "Analysis of a three-dimensional FEM model of a thin piezoelectric actuator embedded in an infinite host structure", Adv. Mater. Res., 3(1), 237-257. https://doi.org/10.12989/amr.2014.3.1.237
  63. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of ZrO 2-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68(1), 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2

Cited by

  1. Vibration Analysis of Non-Uniform Imperfect Functionally Graded Beams with Porosities in Thermal Environment vol.33, pp.6, 2017, https://doi.org/10.1017/jmech.2017.81
  2. Nonlocal strain gradient-based vibration analysis of embedded curved porous piezoelectric nano-beams in thermal environment vol.20, pp.6, 2016, https://doi.org/10.12989/sss.2017.20.6.709
  3. Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments vol.65, pp.6, 2018, https://doi.org/10.12989/sem.2018.65.6.645
  4. An electromechanical model for functionally graded porous plates attached to piezoelectric layer based on hyperbolic shear and normal deformation theory vol.274, pp.None, 2016, https://doi.org/10.1016/j.compstruct.2021.114352
  5. Three-Dimensional Buckling Analysis of Functionally Graded Saturated Porous Rectangular Plates under Combined Loading Conditions vol.11, pp.21, 2021, https://doi.org/10.3390/app112110434