Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Application of shear deformation theory for two dimensional electro-elastic analysis of a FGP cylinder

  • Arefi, M. (Department of Solid Mechanic, Faculty of Mechanical Engineering, University of Kashan) ;
  • Rahimi, G.H. (Department of Mechanical engineering, Tarbiat Modares University)
  • Received : 2012.07.31
  • Accepted : 2013.02.19
  • Published : 2014.01.25
⟨ Previous Next ⟩

Abstract

The present study deals with two dimensional electro-elastic analysis of a functionally graded piezoelectric (FGP) cylinder under internal pressure. Energy method and first order shear deformation theory (FSDT) are employed for this purpose. All mechanical and electrical properties except Poisson ratio are considered as a power function along the radial direction. The cylinder is subjected to uniform internal pressure. By supposing two dimensional displacement and electric potential fields along the radial and axial direction, the governing differential equations can be derived in terms of unknown electrical and mechanical functions. Homogeneous solution can be obtained by imposing the appropriate mechanical and electrical boundary conditions. This proposed solution has capability to solve the cylinder structure with arbitrary boundary conditions. The previous solutions have been proposed for the problem with simple boundary conditions (simply supported cylinder) by using the routine functions such as trigonometric functions. The axial distribution of the axial displacement, radial displacement and electric potential of the cylinder can be presented as the important results of this paper for various non homogeneous indexes. This paper evaluates the effect of a local support on the distribution of mechanical and electrical components. This investigation indicates that a support has important influence on the distribution of mechanical and electrical components rather than a cylinder with ignoring the effect of the supports. Obtained results using present method at regions that are adequate far from two ends of the cylinder can be compared with previous results (plane elasticity and one dimensional first order shear deformation theories).

Keywords

References

  1. Akbarzadeh, A.H., Babaei, M.H. and Chen, Z.T. (2011a), "Thermopiezoelectric analysis of a functionally graded piezoelectric medium", Int. J. Appl. Mech.- T ASME, 3(1), 47- 68. https://doi.org/10.1142/S1758825111000865
  2. Akbarzadeh, A.H., Babaei, M.H. and Chen, Z.T. (2011b), "The thermo-electromagnetoelastic behavior of a rotating functionally graded piezoelectric cylinder", Smart. Mater. Struct., 20(6), 065008. https://doi.org/10.1088/0964-1726/20/6/065008
  3. Alibeigloo, A. (2010), "Thermoelastic solution for static deformations of functionally graded cylindrical shell bonded to thin piezoelectric layers", Compos. Struct., 93(2), 961-972.
  4. Arefi, M. and Rahimi, G.H. (2010), "Thermo elastic analysis of a functionally graded cylinder under internal pressure using first order shear deformation theory", Sci. Res. Essays., 5(12), 1442-1454.
  5. Arefi, M., Rahimi, G.H. and Khoshgoftar, M.J. (2011), "Optimized design of a cylinder under mechanical, magnetic and thermal loads as a sensor or actuator using a functionally graded piezomagnetic material", Int. J. Phys. Sci., 6(27), 6315-6322.
  6. Arefi, M. and Rahimi, G.H. (2011a), "General formulation for the thermoelastic analysis of an arbitrary structure made of functionally graded piezoelectric materials, based on the energy method", Mech. Eng., 62(4), 221-236.
  7. Arefi, M. and Rahimi, G.H. (2011b), "Non linear analysis of a functionally graded square plate with two smart layers as sensor and actuator under normal pressure", Smart. Struct. Syst., 8(5), 433-446. https://doi.org/10.12989/sss.2011.8.5.433
  8. Arefi, M. and Rahimi, G.H. (2012a), "Studying the nonlinear behavior of the functionally graded annular plates with piezoelectric layers as a sensor and actuator under normal pressure", Smart. Struct. Syst., 9(2), 127-143. https://doi.org/10.12989/sss.2012.9.2.127
  9. Arefi, M. and Rahimi, G.H. (2012b), "Three-dimensional multi-field equations of a functionally graded piezoelectric thick shell with variable thickness, curvature and arbitrary nonhomogeneity", Acta. Mech., 223(3), 63-79. https://doi.org/10.1007/s00707-011-0536-5
  10. Arefi, M. and Rahimi, G.H. (2012c), "The effect of nonhomogeneity and end supports on the thermo elastic behavior of a clamped-clamped FG cylinder under mechanical and thermal loads", Int. J. Pres. Ves. Pip., 96-97, 30-37. https://doi.org/10.1016/j.ijpvp.2012.05.009
  11. Arefi, M. and Rahimi, G.H. (2012d), "Comprehensive thermoelastic analysis of a functionally graded cylinder with different boundary conditions under internal pressure using first order shear deformation theory", Mechanika., 18(1), 5-13.
  12. Arefi, M., Rahimi, G.H. and Khoshgoftar, M.J. (2012e), "Electro elastic analysis of a pressurized thick-walled functionally graded piezoelectric cylinder using the first order shear deformation theory and energy method" , Mechanika., 18(3), 292-300.
  13. Arefi, M., Rahimi, G.H. and Khoshgoftar, M.J. (2012f), "Exact solution of a thick walled functionally graded piezoelectric cylinder under mechanical, thermal and electrical loads in the magnetic field", Smart. Struct. Syst., 9(5), 427-439. https://doi.org/10.12989/sss.2012.9.5.427
  14. Babaei, M.H. and Chen, Z.T.(2010a),"Transient thermopiezoelectric response of a one-dimensional functionally graded piezoelectric medium to a moving heat source", Arch. Appl. Mech., 80 (7), 803 - 813. https://doi.org/10.1007/s00419-009-0342-x
  15. Babaei, M.H. and Chen, Z.T. (2010b), "Transient hyperbolic heat conduction in a functionally graded hollow cylinder", J. Thermophys. Heat. Tr., 24(2), 325-330. https://doi.org/10.2514/1.41368
  16. Babaei, M.H. and Chen, Z.T. (2010c), "The transient coupled thermopiezoelectric response of a functionally graded piezoelectric hollow cylinder to dynamic loadings", P. Roy. Soc. A - Math. Phy., 466, 1077-1091. https://doi.org/10.1098/rspa.2009.0543
  17. Babaei, M.H. and Chen, Z.T. (2008a), "Analytical solution for the electromechanical behavior of a rotating functionally graded piezoelectric hollow shaft", Arch. Appl. Mech., 78, 489-500. https://doi.org/10.1007/s00419-007-0172-7
  18. Babaei, M.H. and Chen, Z.T. (2008b), "Exact solutions for radially polarized and magnetized magnetoelectroelastic rotating cylinders", Smart. Mater. Struct., 17, 025035 (11pp). https://doi.org/10.1088/0964-1726/17/2/025035
  19. Chen, W.Q., Lu, Y., Ye, J.R. and Cai, J.B. (2002), "3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loading", Arch. Appl. Mech., 72, 39-51. https://doi.org/10.1007/s004190100184
  20. Dai, H.L., Fu, Y.M. and Yang, J.H. (2007), "Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere", Acta. Mech. Solida. Sin., 23, 55-63. https://doi.org/10.1007/s10409-006-0047-0
  21. H-Hashemi, Sh., Es'haghi, M. and Taher, H.R.D. (2010), "An exact nalytical solution for freely vibrating piezoelectric coupled circular/annular thick plates using Reddy plate theory", Compos. Struct., 92(6), 1333-1351. https://doi.org/10.1016/j.compstruct.2009.11.006
  22. Jabbari, M., Sohrabpour, S. and Eslami, M.R. (2002), "Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads", Int. J. Pres. Ves. Pip., 79, 493-497. https://doi.org/10.1016/S0308-0161(02)00043-1
  23. Jabbari, M., Bahtui, A. and Eslami, M.R. (2009), "Axisymmetric mechanical and thermal stresses in thick short length FGM cylinders", Int. J. Pres. Ves. Pip., 86, 296-306. https://doi.org/10.1016/j.ijpvp.2008.12.002
  24. Khoshgoftar, M.J., Arani, A.G. and Arefi, M. (2009) "Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material", Smart. Mater. Struct., 18, 115007 (8 pp). https://doi.org/10.1088/0964-1726/18/11/115007
  25. Liu, X., Wang, Q. and Quek, S.T. (2002), "Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates", Int. J. Solids. Strutct., 39(8), 2129-2151. https://doi.org/10.1016/S0020-7683(02)00081-1
  26. Lu, P., Lee, H.P. and Lu, C. (2005), "An exact solution for functionally graded piezoelectric laminated in cylindrical bending", Int. J. Mech. Sci., 47(3), 437-458. https://doi.org/10.1016/j.ijmecsci.2005.01.012
  27. Mirsky, I. and Hermann, G. (1958), "Axially motions of thick cylindrical shells", J. Appl. Mech. - T ASME, 25, 97-102.
  28. Naghdi, P.M. and Cooper, R.M. (1956), "Propagation of elastic waves in cylindrical shells including the effects of transverse shear and rotary inertia", J. Acoust Soc. Am., 28, 56-63. https://doi.org/10.1121/1.1908222
  29. Peng-Fei, H. and Andrew, Y.T. (2004) "The transient responses of magneto-electro-elastic hollow cylinders", Smart. Mater. Struct., 13(4), 762-776. https://doi.org/10.1088/0964-1726/13/4/014
  30. Qian, Z.H., Jin, F., Lu, T. and Kishimoto, K, (2008), "Transverse surface waves in functionally graded piezoelectric materials with exponential variation", Smart, Mater, Struct., 17, 065005 (7pp). https://doi.org/10.1088/0964-1726/17/6/065005
  31. Qian, Z.H., Jin, F., Kishimoto, K. and Lu, T.J. (2009), "Propagation behavior of Love waves in a functionally graded half-space with initial stress", Int. J. Solids. Struct., 46,1354-1361. https://doi.org/10.1016/j.ijsolstr.2008.11.003
  32. Qian, Z.H., Jin, F. and Hirose S. (2011a), "Effects of covering layer thickness on Love waves in functionally graded piezoelectric substrates", Arch. Appl. Mech., 81(11), 1743-1755. https://doi.org/10.1007/s00419-011-0515-2
  33. Qian, Z.H., Jin, F. and Hirose, S. (2011b), "Piezoelectric Love waves in an FGPM layered structure", Mech. Adv. Mater. Struct., 18(1), 77-84. https://doi.org/10.1080/15376494.2010.519231
  34. Qian, Z.H., Jin, F., Lu, T.J. and Kishimoto, K. (2009), "Transverse surface waves in a functionally graded piezoelectric substrate coated with a finite-thickness metal waveguide layer", Appl. Phy. Lett., 94(2), 023501. https://doi.org/10.1063/1.3070540
  35. Qian, Z.H., Jin, F., Hirose, S. and Lu, T.J. (2009), "Effects of material gradient on transverse surface waves in piezoelectric coupled solid media", Appl. Phy. Lett., 95(7), 073501. https://doi.org/10.1063/1.3205126
  36. Qian, Z.H., Jin, F., Lu, T.J. and Kishimoto, K. (2009), "Transverse surface waves in a layered structure with a functionally graded piezoelectric substrate and a hard dielectric layer", Ultrasonics, 49(3), 293-297. https://doi.org/10.1016/j.ultras.2008.10.004
  37. Rahimi, G.H., Arefi, M. and Khoshgoftar, M.J. (2011), "Application and analysis of functionally graded piezoelectrical rotating cylinder as mechanical sensor subjected to pressure and thermal loads", Appl. Math. Mech. - Eng., 32(8), 997-1008. https://doi.org/10.1007/s10483-011-1475-6
  38. Shi, Z.F. 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
  39. Shao, Z.S. (2005), "Mechanical and thermal stresses of a functionally graded circular hollow cylinder with finite length", Int. J. Pres. Ves. Pip., 82(3), 155-163. https://doi.org/10.1016/j.ijpvp.2004.09.007
  40. Sheng, G.G. and Wang, X. (2010), "Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells", Appl. Math. Model., 34(9), 2630-2643. https://doi.org/10.1016/j.apm.2009.11.024
  41. Timoshenko, S.P. (1976), Strength of Materials, Part II (Advanced Theory and Problems), 3rd Ed., Van Nostrand Reinhold Co, New York.
  42. Tutuncu, N. and Ozturk, M. (2001), "Exact solution for stresses in functionally graded pressure vessels", Compos. Part B - Eng., 32(8), 683-686.
  43. Wu, L., Zhiqing, J. and Jun, L. (2005), "Thermoelastic stability of functionally graded cylindrical shells". Compos. Struct., 70(1), 60-68. https://doi.org/10.1016/j.compstruct.2004.08.012
  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. Yamanouchi, M, Koizumi, M. and Shiota, I. (1990), Proceedings of the 1st International Symposium on Functionally Gradient Materials, Sendai, Japan.

Cited by

  1. Coupled electro-elastic analysis of functionally graded piezoelectric material plates vol.16, pp.5, 2015, https://doi.org/10.12989/sss.2015.16.5.781
  2. Nonlinear responses of an arbitrary FGP circular plate resting on the Winkler-Pasternak foundation vol.16, pp.1, 2015, https://doi.org/10.12989/sss.2015.16.1.081
  3. The effect of axially variable thermal and mechanical loads on the 2D thermoelastic response of FG cylindrical shell vol.39, pp.12, 2016, https://doi.org/10.1080/01495739.2016.1217178
  4. Free vibration, wave propagation and tension analyses of a sandwich micro/nano rod subjected to electric potential using strain gradient theory vol.3, pp.11, 2016, https://doi.org/10.1088/2053-1591/3/11/115704
  5. Two-dimensional thermoelastic analysis of FG cylindrical shell resting on the Pasternak foundation subjected to mechanical and thermal loads based on FSDT formulation vol.39, pp.5, 2016, https://doi.org/10.1080/01495739.2016.1158607
  6. Analysis of wave in a functionally graded magneto-electro-elastic nano-rod using nonlocal elasticity model subjected to electric and magnetic potentials vol.227, pp.9, 2016, https://doi.org/10.1007/s00707-016-1584-7
  7. Effect of thermo-magneto-electro-mechanical fields on the bending behaviors of a three-layered nanoplate based on sinusoidal shear-deformation plate theory 2017, https://doi.org/10.1177/1099636217697497
  8. Size-dependent thermoelastic analysis of a functionally graded nanoshell vol.32, pp.03, 2018, https://doi.org/10.1142/S0217984918500331
  9. Size-dependent electro-magneto-elastic bending analyses of the shear-deformable axisymmetric functionally graded circular nanoplates vol.132, pp.10, 2017, https://doi.org/10.1140/epjp/i2017-11666-6
  10. Nonlinear electromechanical analysis of a functionally graded square plate integrated with smart layers resting on Winkler-Pasternak foundation vol.16, pp.1, 2015, https://doi.org/10.12989/sss.2015.16.1.195
  11. Transient sinusoidal shear deformation formulation of a size-dependent three-layer piezo-magnetic curved nanobeam vol.228, pp.10, 2017, https://doi.org/10.1007/s00707-017-1892-6
  12. Nonsymmetric thermomechanical analysis of a functionally graded cylinder subjected to mechanical, thermal, and magnetic loads vol.40, pp.6, 2017, https://doi.org/10.1080/01495739.2017.1280380
  13. Employing the coupled stress components and surface elasticity for nonlocal solution of wave propagation of a functionally graded piezoelectric Love nanorod model vol.28, pp.17, 2017, https://doi.org/10.1177/1045389X17689930
  14. A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment vol.18, pp.5, 2016, https://doi.org/10.1177/1099636216652581
  15. Thermal stress and deformation analysis of a size-dependent curved nanobeam based on sinusoidal shear deformation theory 2017, https://doi.org/10.1016/j.aej.2017.07.003
  16. Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory 2017, https://doi.org/10.1177/1099636217723186
  17. Surface effect and non-local elasticity in wave propagation of functionally graded piezoelectric nano-rod excited to applied voltage vol.37, pp.3, 2016, https://doi.org/10.1007/s10483-016-2039-6
  18. Size-dependent analysis of a sandwich curved nanobeam integrated with piezomagnetic face-sheets vol.7, 2017, https://doi.org/10.1016/j.rinp.2017.06.032
  19. Effects of electrodes and electrical connections of piezoelectric layers on dynamic characteristics of radially polarized multilayer piezoelectric cylindrical transducers pp.1530-8138, 2019, https://doi.org/10.1177/1045389X18803454
  20. Nonlocal strain gradient theory for the magneto-electro-elastic vibration response of a porous FG-core sandwich nanoplate with piezomagnetic face sheets resting on an elastic foundation pp.1530-7972, 2018, https://doi.org/10.1177/1099636218795378
  21. Magneto-electro-mechanical bending analysis of three-layered exponentially graded microplate with piezomagnetic face-sheets resting on Pasternak's foundation via MCST pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1473538
  22. Electro-elastic displacement and stress analysis of the piezoelectric doubly curved shells resting on Winkler's foundation subjected to applied voltage pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1455937
  23. Free vibration analysis of a sandwich nano-plate including FG core and piezoelectric face-sheets by considering neutral surface pp.1537-6532, 2019, https://doi.org/10.1080/15376494.2018.1455939
  24. Higher-Order Thermo-Elastic Analysis of FG-CNTRC Cylindrical Vessels Surrounded by a Pasternak Foundation vol.9, pp.1, 2019, https://doi.org/10.3390/nano9010079
  25. Nonlinear and linear thermo-elastic analyses of a functionally graded spherical shell using the Lagrange strain tensor vol.19, pp.1, 2014, https://doi.org/10.12989/sss.2017.19.1.033
  26. Electro-magneto-elastic analysis of a three-layer curved beam vol.19, pp.6, 2014, https://doi.org/10.12989/sss.2017.19.6.695
  27. Nonlocal free vibration analysis of a doubly curved piezoelectric nano shell vol.27, pp.4, 2018, https://doi.org/10.12989/scs.2018.27.4.479
  28. Two-dimensional thermo-elastic analysis of FG-CNTRC cylindrical pressure vessels vol.27, pp.4, 2014, https://doi.org/10.12989/scs.2018.27.4.525
  29. Size-dependent free vibration and dynamic analyses of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory vol.22, pp.1, 2014, https://doi.org/10.12989/sss.2018.22.1.027
  30. Creep analysis of the FG cylinders: Time-dependent non-axisymmetric behavior vol.28, pp.3, 2014, https://doi.org/10.12989/scs.2018.28.3.331
  31. Investigation of the Thermo-elastic Response of Adhesively Bonded Two-Dimensional Functionally Graded Circular Plates Based on Theory of Elasticity vol.42, pp.4, 2014, https://doi.org/10.1007/s40997-018-0261-y
  32. Size-Dependent Free Vibrations of FG Polymer Composite Curved Nanobeams Reinforced with Graphene Nanoplatelets Resting on Pasternak Foundations vol.9, pp.8, 2014, https://doi.org/10.3390/app9081580
  33. Two-Dimensional Electro-Elastic Analysis of FG-CNTRC Cylindrical Laminated Pressure Vessels With Piezoelectric Layers Based on Third-Order Shear Deformation Theory vol.142, pp.2, 2014, https://doi.org/10.1115/1.4043842
  34. Static and free vibration analysis of graphene platelets reinforced composite truncated conical shell, cylindrical shell, and annular plate using theory of elasticity and DQM vol.48, pp.4, 2020, https://doi.org/10.1080/15397734.2019.1646137
  35. Radial vibration analysis for functionally graded ring piezoelectric transducers based on electromechanical equivalent circuit method vol.120, pp.None, 2022, https://doi.org/10.1016/j.ultras.2021.106640