Structural Engineering and Mechanics

  • 제64권6권
  • /
  • Pages.751-763
  • /
  • 2017
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Buckling characteristics and static studies of multilayered magneto-electro-elastic plate

  • Kiran, M.C. (Department of Mechanical Engineering, National Institute of Technology Karnataka) ;
  • Kattimani, S.C. (Department of Mechanical Engineering, National Institute of Technology Karnataka)
  • 투고 : 2017.03.28
  • 심사 : 2017.09.02
  • 발행 : 2017.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

This article deals with the buckling behaviour of multilayered magneto-electro-elastic (MEE) plate subjected to uniaxial and biaxial compressive (in-plane) loads. The constitutive equations of MEE material are used to derive a finite element (FE) formulation involving the coupling between electric, magnetic and elastic fields. The displacement field corresponding to first order shear deformation theory (FSDT) has been employed. The in-plane stress distribution within the MEE plate existing due to the enacted force is considered to be equivalent to the applied in-plane compressive load in the pre-buckling range. The same stress distribution is used to derive the potential energy functional. The non-dimensional critical buckling load is accomplished from the solution of allied linear eigenvalue problem. Influence of stacking sequence, span to thickness ratio, aspect ratio, load factor and boundary condition on critical buckling load and their corresponding mode shape is investigated. In addition, static deflection of MEE plate under the sinusoidal and the uniformly distributed load has been studied for different stacking sequences and boundary conditions.

키워드

참고문헌

  1. Ansari, R. and Gholami, R. (2016), "Size-dependent buckling and postbuckling analyses of first- order shear deformable magnetoelectro-thermo elastic nanoplates based on the nonlocal elasticity theory", Int. J. Struct. Stab. Dyn., 10, 1750014.
  2. Bhangale, R.K. and Ganesan, N. (2006). "Static analysis of simply supported functionally graded and layered magneto-electroelastic plates", Int. J. Solid. Struct., 43, 3230-3253. https://doi.org/10.1016/j.ijsolstr.2005.05.030
  3. Boomgaard, V. J. and Born, R. (1978), "A sintered magnetoelectric composite material $BaTiO_3$-Ni (Co, Mn)$Fe_2O_4$", J. Mater. Sci., 13(7), 1538-48. https://doi.org/10.1007/BF00553210
  4. Bouazza, M., Lairedj, A., Benseddiq, N. and Khalki, S. (2016), "A refined hyperbolic shear deformation theory for thermal buckling analysis of cross-ply laminated plates", Mech. Res. Commun., 73, 117-126. https://doi.org/10.1016/j.mechrescom.2016.02.015
  5. Buchanan, G.R. (2004), "Layered versus multiphase magnetoelectro-elastic composites", Compos. B Eng., 35(5), 413-420. https://doi.org/10.1016/j.compositesb.2003.12.002
  6. Chen J.Y., Heyliger P.R. and Pan, E. (2014), "Free vibration of three-dimensional multilayered magneto-electro-elastic plates under clamped/free boundary conditions", J. Sound Vib., 333, 4017-4029. https://doi.org/10.1016/j.jsv.2014.03.035
  7. Ebrahimi, F. and Barati, M.R (2016e), "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, 105014. https://doi.org/10.1088/0964-1726/25/10/105014
  8. Ebrahimi, F., Dabbagh, A. and Barati, M.R. (2016), "Wave propagation analysis of a size-dependent magneto-electroelastic heterogeneous nanoplate", Eur. Phys. J Plus, 131(12), 433. https://doi.org/10.1140/epjp/i2016-16433-7
  9. Ebrahimi, F. and Barati, M.R. (2016b), "Nonlocal Thermal Buckling Analysis of Embedded Magneto-Electro-Thermo-Elastic Nonhomogeneous Nanoplates", IJST-T Mech. Eng., 40(4), 243-264.
  10. Ebrahimi, F., Jafari, A. and Barati, M.R. (2016), "Free Vibration Analysis of Smart Porous Plates Subjected to Various Physical Fields Considering Neutral Surface Position", Arab. J. Sci. Eng., 1-17.
  11. Ebrahimi, F. and Barati, M.R. (2016c), "Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams", Eur. Phys. J Plus, 131(9), 346. https://doi.org/10.1140/epjp/i2016-16346-5
  12. Ebrahimi, F. and Barati, M.R. (2017), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magnetoelectrical field in thermal environment", Journal of Vibration and Control, Doi: 10.1177/1077546317708105.
  13. Ebrahimi, F. and Barati, M.R. (2016d), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intell. Mater. Syst. Struct., Doi: 10.1177/1045389X16672569.
  14. Ebrahimi, F. and Barati, M.R. (2016a), "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
  15. Farajpour, A. and Rastgoo, A., (2017), "Size-dependent static stability of magneto-electro-elastic CNT/MT-based composite nanoshells under external electric and magnetic fields", Microsyst. Technol., 23(12), 1-18. https://doi.org/10.1007/s00542-015-2713-2
  16. Farajpour, A., Yazdi, M.H., Rastgoo, A., Loghmani, M. and Mohammadi, M. (2016) "Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates", Compos. Struct., 140, 323-336. https://doi.org/10.1016/j.compstruct.2015.12.039
  17. Grover, N., Maiti, D.K. and Singh, B.N. (2014), "An efficient C0 finite element modeling of an inverse hyperbolic shear deformation theory for the flexural and stability analysis of laminated composite and sandwich plates", Finite Elem. Anal. Des., 80, 11-22. https://doi.org/10.1016/j.finel.2013.11.003
  18. Jadhav, P. and Bajoria, K. (2013), "Stability analysis of piezoelectric FGM plate subjected to electro-mechanical loading using finite element method", Int. J. Appl. Sci. Eng., 11(4), 375-391.
  19. Jamalpoor, A., Ahmadi-Savadkoohi, A. and Hosseini-Hashemi, S. (2016), "Free vibration and biaxial buckling analysis of magneto-electro-elastic microplate resting on visco-Pasternak substrate via modified strain gradient theory", Smart Mater. Struct., 25(10), 105035. https://doi.org/10.1088/0964-1726/25/10/105035
  20. Kattimani, S.C. and Ray, M.C. (2015), "Control of geometrically nonlinear vibrations of functionally graded Magneto-electroelastic plates", Int. J. Mech. Sci., 99, 154-167. https://doi.org/10.1016/j.ijmecsci.2015.05.012
  21. Kattimani, S.C. and Ray, M.C. (2014a), "Smart damping of geometrically nonlinear vibrations of magneto-electro-elastic plates", Compos. Struct., 114, 51-63. https://doi.org/10.1016/j.compstruct.2014.03.050
  22. Kattimani, S.C. and Ray, M.C. (2014b), "Active control of large amplitude vibrations of smart magneto-electro-elastic doubly curved shells", Int. J. Mech. Mater. Des., 10, 351-378. https://doi.org/10.1007/s10999-014-9252-3
  23. Kattimani S.C (2015), "Active control of geometrically nonlinear vibrations of Magneto-Electro-Elastic plates and dhells", Ph.D. Dissertation, IIT Kharagpur, India.
  24. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory", Acta Mech. Sinica, 30(4), 516-525. https://doi.org/10.1007/s10409-014-0072-3
  25. Kulkarni, K., Singh, B.N. and Maiti, D.K. (2015), "Analytical solution for bending and buckling analysis of functionally graded plates using inverse trigonometric shear deformation theory", Compos. Struct., 134, 147-157. https://doi.org/10.1016/j.compstruct.2015.08.060
  26. Kumaravel, A., Ganesan, N. and Sethuraman, R. (2007), "Buckling and vibration analysis of layered and multiphase magneto-electro-elastic beam under thermal environment", Multidisc. Model. Mater. Struct., 3(4), 461-476. https://doi.org/10.1163/157361107782106401
  27. Lage, R.G., Soares, C.M.M., Soares, C.A.M. and Reddy, J.N. (2004), "Layerwise partial mixed finite element analysis of magneto-electro-elastic plates", Comput. Struct., 82, 1293-301. https://doi.org/10.1016/j.compstruc.2004.03.026
  28. Lang, Z. and Xuewu, L. (2013), "Buckling and vibration analysis of functionally graded magneto-electro-thermo-elastic circular cylindrical shells", Appl. Math. Model., 37(4), 2279-2292. https://doi.org/10.1016/j.apm.2012.05.023
  29. Li, Y.S., Cai, Z.Y. and Shi, S.Y. (2014), "Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory", Compos. Struct., 111(1), 522-529. https://doi.org/10.1016/j.compstruct.2014.01.033
  30. Li, Y.S. (2014), "Buckling analysis of magnetoelectroelastic plate resting on Pasternak elastic foundation", Mech. Res. Commun., 56, 104-114. https://doi.org/10.1016/j.mechrescom.2013.12.007
  31. Li, Y.S., Ma, P. and Wang, W. (2016), "Bending, buckling, and free vibration of magnetoelectroelastic nanobeam based on nonlocal theory", J. Intell. Mater. Syst. Struct., 27(9), 1139-1149. https://doi.org/10.1177/1045389X15585899
  32. Liu, J., Zhang, P., Lin, G., Wang, W. and Lu, S. (2016a), "Solutions for the magneto-electro-elastic plate using the scaled boundary finite element method", Eng. Anal. Bound. Elem., 68, 103-114. https://doi.org/10.1016/j.enganabound.2016.04.005
  33. Liu, J., Zhang, P., Lin, G., Wang, W. and Lu, S. (2016b), "High order solutions for the magneto-electro-elastic plate with nonuniform materials", Int. J. Mech. Sci., 115, 532-551.
  34. Liu, M.F and Chang, T.P (2010), "Closed form expression for the vibration problem of transversely isotropic magneto-electroelastic plate", ASME J. Appl. Mech., 77, 24502-10. https://doi.org/10.1115/1.3176996
  35. Luccioni, L.X. and Dong, S.B. (1998), "Levy-type finite element analyses of vibration and stability of thin and thick laminated composite rectangular plates", Compos. B Eng., 29B, 459-475.
  36. Milazzo, A. (2016), "Unified formulation for a family of advanced finite elements for smart multilayered plates", Mech. Adv. Mater. Struct., 23(9), 971-980. https://doi.org/10.1080/15376494.2015.1121523
  37. Moita, J., Soares, C.M.M. and Soares, C.A.M. (1996), "Buckling behaviour of laminated composite structures using a discrete higher-order displacement model", Compos. Struct., 35(1), 75-92. https://doi.org/10.1016/0263-8223(96)00025-6
  38. Pan, E. (2001), "Exact solution for simply supported and multilayered magneto-electroelastic plates", J. Appl. Mech.-T., 68, 608-618. https://doi.org/10.1115/1.1380385
  39. Pan, E. and Heyliger, P.R. (2002), "Free vibration of simply supported and multilayered magnetoelectro-elastic plates", J. Sound Vib., 252(3), 429-442. https://doi.org/10.1006/jsvi.2001.3693
  40. Pan, E. and Heyliger, P.R. (2003), "Exact solutions for magnetoelectro-elastic laminates in cylindrical bending", Int. J. Solid. Struct., 40(24), 6859-6876. https://doi.org/10.1016/j.ijsolstr.2003.08.003
  41. Pan, E. and Han F. (2005), "Exact solutions for functionally graded and layered magneto-electro-elastic plates", Int. J. Eng. Sci., 43, 321-339. https://doi.org/10.1016/j.ijengsci.2004.09.006
  42. Ramirez, F., Heyliger, P.R. and Pan, E. (2006), "Free vibration response of two-dimensional magneto-electro-elastic plates", J. Sound Vib., 292, 626-644. https://doi.org/10.1016/j.jsv.2005.08.004
  43. Ray, M.C., Bhattacharya, R. and Samanta, B. (1994), "Static analysis of an intelligent structure by the finite element method", Comput. Struct., 52, 617-631. https://doi.org/10.1016/0045-7949(94)90344-1
  44. Razavi, S. (2017), "On the buckling the behavior of a multiphase smart plate based on a higher-order theory", Mech. Adv. Compos. Struct. , 4(1), 47-58.
  45. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, LLC.
  46. Rogowski, B. (2015), "The transient analysis of a conducting crack in magneto-electro-elastic half-space under anti-plane mechanical and in-plane electric and magnetic impacts", Arch. Appl. Mech., 85(1), 29-50. https://doi.org/10.1007/s00419-014-0898-y
  47. Simoes Moita, J.M., Mota Soares, C.M. and Mota Soares, C.A. (2009), "Analyses of Magneto-electro-elastic plates using a higher order finite element model", Compos. Struct., 91, 421-426. https://doi.org/10.1016/j.compstruct.2009.04.007
  48. Sladek, J., Sladek, V., Kharulec, S. and Pan, E. (2013), "Analyses of functionally graded plates with magnetoelectroelasic layer", Smart Mater. Struct., 22, 035003. https://doi.org/10.1088/0964-1726/22/3/035003
  49. Sreehari, V.M., George, L.J. and Maiti, D.K. (2016), "Bending and buckling analysis of smart composite plates with and without internal flaw using an inverse hyperbolic shear deformation theory", Compos. Struct., 138, 64-74. https://doi.org/10.1016/j.compstruct.2015.11.045
  50. Thai, H.T and Vo, T.P. (2013), "A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates", Appl. Math. Model., 37(5), 3269-81. https://doi.org/10.1016/j.apm.2012.08.008
  51. van Suchtelen, J. (1972), "Product properties: a new application of composite materials", Philips Res. Rep., 27, 28-37.
  52. Vinyas, M. and Kattimani, S.C. (2017a), "Static studies of stepped functionally graded magneto-electro-elastic beam subjected to different thermal loads", Compos. Struct., 163, 216-237. https://doi.org/10.1016/j.compstruct.2016.12.040
  53. Vinyas, M. and Kattimani, S.C. (2017b), "Finite element based assessment of static behaviour of multiphase magneto-electroelastic beam under different thermal loading", Struct. Eng. Mech., 62(5), 519-535. https://doi.org/10.12989/sem.2017.62.5.519
  54. Viun, O., Loboda, V. and Lapusta, Y. (2016), "Electrically and magnetically induced Maxwell stresses in a magneto-electroelastic medium with periodic limited permeable cracks", Arch. Appl. Mech., 86(12), 2009-2020. https://doi.org/10.1007/s00419-016-1166-0
  55. Vuksanovic, D. (2000), "Linear analysis of laminated composite plates using single layer higher-order discrete models", Compos. Struct., 48, 205-211. https://doi.org/10.1016/S0263-8223(99)00096-3
  56. Wu, C.P., Chen, S.J. and Chiu, K.H. (2010), "Three-dimensional static behavior of functionally graded magneto-electro-elastic plates using the modified Pagano method", Mech. Res. Commun., 37(1), 54-60. https://doi.org/10.1016/j.mechrescom.2009.10.003
  57. Xin, L. and Hu, Z. (2015), "Free vibration of simply supported and multilayered magneto-electro-elastic plates", Compos. Struct., 121, 344-350. https://doi.org/10.1016/j.compstruct.2014.11.030
  58. Zhou, K., Li, Y.D. and Liu, S.L. (2016), "Effects of the volume fraction of piezoelectric particles in the magneto-electro-elastic interfacial region on the fracture behavior of a laminate multiferroic plate", Acta Mech., 228(4), 1229-1248.