DOI QR코드

DOI QR Code

Magneto-thermo-elastic response of exponentially graded piezoelectric hollow spheres

  • Allam, M.N.M. (Department of Mathematics, Faculty of Science, Mansoura University) ;
  • Tantawy, R. (Department of Mathematics, Faculty of Science, Damietta University) ;
  • Zenkour, A.M. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • 투고 : 2018.02.09
  • 심사 : 2018.06.12
  • 발행 : 2018.07.25

초록

This article presents a semi-analytical solution for an exponentially graded piezoelectric hollow sphere. The sphere interacts with electric displacement, elastic deformations, electric potentials, magneto-thermo-elasticity, and hygrothermal influences. The hollow sphere may be standing under both mechanical and electric potentials. Electro-magneto-elastic behavior of magnetic field vector can be described in the hollow sphere. All material, thermal and magnetic properties of hollow sphere are supposed to be graded in radial direction. A semi-analytical technique is improved to deduce all fields in which different boundary conditions for radial stress and electric potential are presented. Numerical examples for radial displacement, radial and hoop stresses, and electric potential are investigated. The influence of many parameters is studied. It is seen that the gradation of all material, thermal and magnetic properties has particular effectiveness in many applications of modern technology.

키워드

참고문헌

  1. Akavci, S.S. and Tanrikulu, A.H. (2008), "Buckling and free vibration analyses of laminated composite plates by using two new hyperbolic shear-deformation theories", Mech. Compos. Mater., 44(2), 145-154. https://doi.org/10.1007/s11029-008-9004-2
  2. Akbarzadeh, A.H and Chen, Z.T. (2013), "Hygrothermal stress in one-dimensional functionally graded piezoelectric media in constant magnetic field", Compos. Struct., 97, 317-331. https://doi.org/10.1016/j.compstruct.2012.09.058
  3. Allam, M.N.M. and Tantawy, R. (2011), "Thermomagnetic viscoelastic responses in functionally graded hollow structures", Acta Mech. Sinica, 27(4), 567-577. https://doi.org/10.1007/s10409-011-0467-3
  4. Allam, M.N.M., Tantawy, R. and Zenkour, A.M. (2015), "Semi-empirical and efficient solutions for FGPM hollow spheres in hygrothermal environment", KSCE J. Civil Eng., 20(5), 1-8.
  5. Allam, M.N.M., Tantawy, R., Yousof, A. and Zenkour, A.M. (2017), "Elastic and viscoelastic stresses of nonlinear rotating functionally graded solid and annular disks with gradually varying thickness", Arch. Mech. Eng., 4, 423-440.
  6. Allam, M.N.M., Zenkour, A.M. and Tantawy, R. (2014), "Analysis of functionally graded piezoelectric cylinders in a hygrothermal environment", Adv. Appl. Math. Mech., 6(2), 233-246. https://doi.org/10.4208/aamm.12-m1277
  7. Arani, A.G., Kolahchi, R. and Barzoki, A.M. (2011), "Effect of material in-homogeneity on electro-thermo-mechanical behaviors of functionally graded piezoelectric rotating shaft", Appl. Math. Model., 35, 2771-2789. https://doi.org/10.1016/j.apm.2010.11.076
  8. Arani, A.G., Kolahchi, R., Barzoki, A.M. and Loghman, A. (2012), "Electro-thermo-mechanical behaviors of FGPM spheres using analytical method and ANSYS software", Appl. Math. Model., 36, 139-157. https://doi.org/10.1016/j.apm.2011.05.031
  9. Arani, A.G., Salari, M., Khademizadeh, H. and Arefmanesh, A. (2009), "Magnetothermoelastic transient response of a functionally graded thick hollow sphere subjected to magnetic and thermoelastic fields", Arch. Appl. Mech., 79, 481. https://doi.org/10.1007/s00419-008-0247-0
  10. Arefi, M. and Nahas, I. (2014), "Nonlinear electro thermo elastic analysis of a thick spherical functionally graded piezoelectric shell", Compos. Struct., 118, 510-518. https://doi.org/10.1016/j.compstruct.2014.08.002
  11. Bahrami, A. and Nasier, A. (2007), "Interlaminar hygrothermal stresses in laminated plates", J. Solids Struct., 44, 8119-8142. https://doi.org/10.1016/j.ijsolstr.2007.06.004
  12. Chen, J.Y., Pan, E. and Heyliger, P.R. (2015), "Static deformation of a spherically anisotropic and multilayered magneto-electro-elastic hollow sphere", J. Solids Struct., 60-61, 66-74. https://doi.org/10.1016/j.ijsolstr.2015.02.004
  13. Chiroiu, V. and Munteanu, L. (2007), "On the free vibrations of a piezoceramic hollow sphere", Mech. Res. Commun., 34, 123-129. https://doi.org/10.1016/j.mechrescom.2006.06.011
  14. Dai, H.L. and Fu, Y.M. (2005), "Electromagnetotransient stress and perturbation of magnetic field vector in transversely isotropic piezoelectric solid spheres", Mater. Sci. Eng. B, 129(1-3), 86-92. https://doi.org/10.1016/j.mseb.2005.12.020
  15. Dai, H.L. and Rao, Y.N. (2011), "Investigation on electromagnetothermoelastic interaction of functionally graded piezoelectric hollow spheres", Struct. Eng. Mech., 40(1), 49-64. https://doi.org/10.12989/sem.2011.40.1.049
  16. Dai, H.L. and Wang, X. (2004), "Dynamic responses of piezoelectric hollow cylinders in an axial magnetic field", J. Solid Struct., 41, 5231-5246. https://doi.org/10.1016/j.ijsolstr.2004.04.019
  17. Dai, H.L. and Wang, X. (2005), "Thermo-electro-elastic transient responses in piezoelectric hollow structures", J. Solids Struct., 42, 1151-1171. https://doi.org/10.1016/j.ijsolstr.2004.06.061
  18. Dai, H.L., Fu, Y.M. and Yang, J.H. (2007), "Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere", Acta Mech. Sinica, 23, 55-63. https://doi.org/10.1007/s10409-006-0047-0
  19. Dai, H.L., Fu, Y.M., Yang, J.H. and Dong, Z.M. (2006), "Exact solutions for functionally graded pressure vessels in a uniform magnetic field", J. Solids Struct., 43, 5570-5580. https://doi.org/10.1016/j.ijsolstr.2005.08.019
  20. Dai, H.L., Hong, L., Fu, Y.M. and Xiao, X. (2010), "Analytical solution for electromagneto thermoelastic behaviors of a functionally graded piezoelectric hollow cylinder", Appl. Math. Model., 34, 343-357. https://doi.org/10.1016/j.apm.2009.04.008
  21. Dai, H.L., Jiang, H.J. and Yang, L. (2012), "Time-dependent behaviors of a FGPM hollow sphere under the coupling of multi-fields", Solid State Sci., 14, 587-597. https://doi.org/10.1016/j.solidstatesciences.2012.02.011
  22. Dai, H.L., Xiao, X. and Fu, Y.M. (2010), "Analytical solutions of stresses in functionally graded piezoelectric hollow structures", Solid State Commun., 150, 763-767. https://doi.org/10.1016/j.ssc.2010.01.028
  23. Dai, H.L., Yang, L. and Zheng, H.Y. (2011), "Magnetothermoelastic analysis of functionally graded hollow spherical structures under thermal and mechanical loads", Solid State Sci., 13, 372-378. https://doi.org/10.1016/j.solidstatesciences.2010.11.038
  24. Ding, H.J., Wang, H.M. and Chen, W.Q. (2003), "Dynamic responses of a functionally graded pyroelectric hollow sphere for spherically symmetric problems", J. Mech. Sci., 45, 1029-1051. https://doi.org/10.1016/j.ijmecsci.2003.09.005
  25. Eslami, M.R., Babaei, M.H. and Poultangari, R. (2005), "Thermal and mechanical stresses in a functionally graded thick sphere", J. Press. Vessels Piping, 82, 522-527. https://doi.org/10.1016/j.ijpvp.2005.01.002
  26. Ezzat, M.A. (1997), "Generation of generalized thermomagnetoelastic waves by thermal shock in a perfectly conducting half-space", J. Therm. Stresses, 20, 633-917.
  27. Guo, G., En-Bo, W. and Chen, X. (2009), "Effective elastic properties of piezoelectric composites with radially polarized cylinders", Phys. B, 404, 4001-4006. https://doi.org/10.1016/j.physb.2009.07.149
  28. Heyliger, P. (1997), "A note on the static behavior of simply-supported laminated piezoelectric cylinders", J. Solids Struct., 34, 3781-3794. https://doi.org/10.1016/S0020-7683(97)00009-7
  29. Jabbari, M, Karampour, S. and Eslami, M.R. (2013), "Steady state thermal and mechanical stresses of a poro-pizo-FGM hollow sphere", Mecc., 48, 699-719. https://doi.org/10.1007/s11012-012-9625-3
  30. Kar, A. and Kanoria, M. (2009), "Generalized thermoelastic functionally graded orthotropic hollow sphere under thermal shock with three-phase-lag effect", Europ. J. Mech. A/Solids, 28, 757-767. https://doi.org/10.1016/j.euromechsol.2009.01.003
  31. Kraus, J.D. (1984), Electromagnetic, McGraw Hill, Inc., U.S.A.
  32. Lo, S.H., Zhen, W.U., Cheung, Y.K. and Wanji, C. (2010), "Hygrothermal effects on multilayered composite plates using a refined higher order theory", Compos. Struct., 92, 633-646. https://doi.org/10.1016/j.compstruct.2009.09.034
  33. Loghman, A., Ghorbanpour Arani, A. and Aleayoub, S.M.A. (2011), "Time-dependent creep stress redistribution analysis of thick-walled functionally graded spheres", Mech. Time-Dependent Mater., 15(4), 353-365. https://doi.org/10.1007/s11043-011-9147-8
  34. Ootao, Y. and Ishihara, M. (2012), "Exact solution of transient thermal stress problem of a multilayered magneto-electro-thermoelastic hollow sphere", Appl. Math. Model., 36(4), 1431-1443. https://doi.org/10.1016/j.apm.2011.08.043
  35. Ootao, Y. and Tanigawa, Y. (2007), "Transient piezothermoelastic analysis for a functionally graded thermopiezoelectric hollow sphere", Compos. Struct., 81(4), 540-549. https://doi.org/10.1016/j.compstruct.2006.10.002
  36. Patel, B.P., GanaPathi, M. and Makhecha, D.P. (2002), "Hygrothermal effect on the structural behavior of thick composite laminates using higher-order theory", Compos. Struct., 56(1), 25-34. https://doi.org/10.1016/S0263-8223(01)00182-9
  37. Poultangari, R., Jabbari, M. and Eslami, M.R. (2008), "Functionally graded hollow spheres under non-axisymmetric thermo-mechanical loads", J. Press. Vessels Piping, 85(5), 295-305. https://doi.org/10.1016/j.ijpvp.2008.01.002
  38. Raja, S., Sinha, P.K., Prathap, G. and Dwarakanathan, D. (2004), "Influence of active stiffening on dynamic behavior of piezo-hygro-thermo elastic composite plates and shell", J. Sound Vib., 278, 257-283. https://doi.org/10.1016/j.jsv.2003.10.002
  39. Reddy, J.N. (2000), "Analysis of functionally graded plates", J. Numer. Meth. Eng., 47, 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  40. Reddy, J.N. and Cheng, Z.Q. (2001), "Three-dimensional thermomechanical deformations of functionally graded rectangular plates", Europ. J. Mech. A/Solids, 20(5), 841-855. https://doi.org/10.1016/S0997-7538(01)01174-3
  41. Reddy, J.N. and Chin, C.D. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stresses, 21(6), 593-626. https://doi.org/10.1080/01495739808956165
  42. Sinha, D.K. (1962), "Note on the radial deformation of a piezoelectric polarized spherical shell with symmetrical temperature distribution", J. Acoust. Soc. Amer., 34(8), 1073-1075. https://doi.org/10.1121/1.1918247
  43. Wang, H.M. and Ding, H.J. (2006), "Transient responses of a magneto-electro-elastic hollow sphere for fully coupled spherically symmetric problem", Europ. J. Mech. A/Solids, 25, 965-980. https://doi.org/10.1016/j.euromechsol.2005.10.008
  44. Wang, H.M. and Xu, Z.X. (2010), "Effect of material inhomogeneity on electromechanical behaviors of functionally graded piezoelectric spherical structures", Comput. Mater. Sci., 48(2), 440-445. https://doi.org/10.1016/j.commatsci.2010.02.004
  45. Whiteny, J.M. and Ashton, J.E. (1971), "Effect of environment on the elastic response of layered composite plates", AIAA J., 9(9), 1708-1713. https://doi.org/10.2514/3.49976
  46. Zenkour, A.M. (2005a) "A comprehensive analysis of functionally graded sandwich plates: Part 1 Deflection and stresses", Int. J. Solids Struct., 42(18-19), 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015
  47. Zenkour, A.M. (2005b), "A comprehensive analysis of functionally graded sandwich plates: Part 2 Buckling and free vibration", Int. J. Solids Struct., 42(18-19), 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016
  48. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009
  49. Zenkour, A.M. (2007), "Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate", Arch. Appl. Mech., 77(4), 197-214. https://doi.org/10.1007/s00419-006-0084-y
  50. Zenkour, A.M., Elsibai, K.A. and Mashat, D.S. (2008), "Elastic and viscoelastic solutions to rotating functionally graded hollow and solid cylinders", Appl. Math. Mech., 29(12), 1601-1616. https://doi.org/10.1007/s10483-008-1208-x