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Manuscript ID : JSM-2008-1635 (R2) Visit : 261 Page: 147 - 170

10.22034/jsm.2021.1907364.1635

20.1001.1.20083505.2022.14.2.3.5

Article Type: Original Research

Elasticity Exact Solution for an FGM Cylindrical Shaft with Piezoelectric Layers Under the Saint-Venant Torsion by Using Prandtl’s Formulation

Subject Areas : Mechanics of Solids

M. R Eslami 1 , M Jabbari 2 , A Eskandarzadeh Sabet 3

1 - Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran
2 - Mechanical Engineering Department, Postgraduate School, Islamic Azad University, South Tehran Branch, Iran
3 - Mechanical Engineering Department, Postgraduate School, Islamic Azad University, South Tehran Branch, Iran

Received: 2022-02-09 Accepted : 2022-03-29 Published : 2022-06-01

Keywords: Elasticity, FGM(functionally graded material), Exact solution, Cylindrical shaft, Piezoelectric, Torsion,

Abstract :

Functionally graded materials (FGMs) belong to a noble family of composite material possess material properties varying gradually in a desired direction or orientation. In a past decade, functionally graded materials were remained in an interest of material investigators due to its prominent features, and have extensively used in almost every discipline of engineering which in turn significantly increases the number of research publication of FGM. In this paper the exact elasticity solution for an FGM circular shaft with piezo layers is analysed. piezoelectric layers are homogeneous and the modulus of elasticity for FGM varies continuously with the form of an exponential function. The shear modulus of the non-homogeneous FGM shaft is a given function of the Prandtl’s stress function of considered circular shaft when its material is homogeneous. state equations are derived. The Prandtl’s stress function and electric displacement potential function satisfy all conditions. The shearing stresses, torsional rigidity, torsional function for FGM layer and shearing stresses, electric displacements, torsional rigidity, electrical torsional rigidity ,torsional and electrical potential functions for piezoelectric layers are obtained. Exact analytical solution for hollow circular cross-section presented. At the end some graphs and conclusions are given.

References:


  1.  Rooney J.F., Ferrari M.,1995, Torsion and flexure of inhomogeneous elements, Composites Engineering 5: 901-911.
    2.
  2.  Alibeigloo A., Chen W.Q., 2010, Elasticity solution for an FGM cylindrical panel integrated with piezoelectric layers, Europen Journal of Mechanics A/Solids 29: 714-723.
    3.
  3.  Arghavan S., Hematiyan M.R., 2009, Torsion of functionally graded hollow tubes, European Journal Mechanics A/Solids 28(3): 551-559.
    4.
  4.  Talebanpour A., Hematiyan M.R., 2014, Torsional analysis of piezoelectric hollow bars, International Journal  of  Applied Mechanics 6(2): 1450019.
    5.
  5.  Gurel M.A., PekgökgözK., Kisa M., 2008, Approximate torsion analysis of closed moderately thick-walled, thick-walled, and solid cross-sections, Turkish Journal of Engineering and Environmental Sciences 32(5): 277-287.
    6.
  6.  Tarn J.Q., Chang H.H., 2007, Torsion of cylindrically orthotropic elastic circular bars with radial inhomogeneity: some exact solutions and end effects, International Journal of Solids and Structures 45: 303-319.
    7.
  7.  Ecsedi I., Baksa A., 2010, Prandtl’s formulation for the saint-venant’s of homogeneous piezoelectric beams, International Journal of Solids and Structures 47:3076-3083.
    8.
  8.  Higgins T.J., 1942, A comprehensive review of Saint-Venant torsion problem, American Journal of Physics 10: 248-259.
    9.
  9.  Timoshenko S.P., Goodier J.N., 1970, Theory of Elasticity, McGraw-Hill, New York.
    10.
  10.  Sokolnikoff I.S., 1956, Mathematical Theory of Elasticity, McGraw-Hill, New York.
    11.
  11.  Chen T., 2011, A novel class of graded cylinders neutral to host shafts of arbitrary cross-sections under torsion, Mechanics Research Communications 38: 68-71.
    12.
  12.  Baron F.M., 1942, Torsion of multi-connected thin-walled cylinders, Journal of AppliedMechanics 9: 72-74.
    13.
  13.  Li Z., Ko J.M., Ni Y.Q., 2000, Torsional rigidity of reinforced concrete bars with arbitrary sectional shape, Finite Elements in Analysis and Design 35: 349-361.
    14.
  14.  Mejak G., 2000, Optimization of cross-section of h ollow prismatic bars in torsion, Communications in Numerical Methods in Engineering 16: 687-695.
    15.
  15.  Sezawa K., Kubo K., 1931, The Buckling of a Cylindrical Shell Inder Torsion, Aerospace Research Institute, Tokyo Imperial University.
    16.
  16.  Lundquist E., 1932, Strength Tests on Thin-Walled Duralumin Cylinders in Torsion, NACA Technical Notes 427: 1-24.
    17.
  17.  Doostfatemeh A., Hematiyan M.R., Arghavan S., 2009, Closed-form approximate formulations for torsional analyses of hollow tube with straight and circular edges, Journal of Mechanics 25: 401-409.
    18.
  18.  Muskhelishvilli N.I., 1953, Some Basic Problems of the Mathematical Theory of Elasticity, Groningen Holland.
    19.
  19.  Booker J.R., Kitipornchai S., 1971, Torsion of multilayered rectangular section, Journal of the Engineering Mechanics Division 97(EM5): 1451-1468.
    20.
  20.  Kuo Y.M., Conway H.D., 1973, The torsion of composite tubes and cylinders, International Journal of Solids and Structures 9(12): 1553-1565.
    21.
  21.  Kuo Y.M., Conway H.D., 1974, Torsion of cylinders with multiple reinforcement, Journal of the Engineering Mechanics Division 100(EM2): 221-234.
    22.
  22.  Kuo Y.M., Conway H.D., 1974, Torsion of composite rhombus cylinder, Journal of AppliedMechanics 31(2): 302-303.
    23.
  23.  Kuo Y.M., Conway H.D., 1980, Torsion of reinforced square cylinder, Journal of the Engineering Mechanics Division 106(EM6): 1341-1347.
    24.
  24.  Packham B.A., Shail R., 1978, Saint- Venant torsion of composite cylinders, Journal of Elasticity 8(4): 393-407.
    25.
  25.  Ripton R., 1998, Optimal fiber configurations for maximum torsional rigidity, Archive for Rational Mechanics and Analysis 144(1):79-106.
    26.
  26.  Herrmann L.R., 1965, Elastic torsional analysis of irregular shapes, Journal of the Engineering Mechanics Division 91(EM6): 11-19.
    27.
  27.  Tarn J.Q., Chang H.H., 2008, Torsion of cylindrically orthotropic elastic circular bars with radial inhomogeneity: some exact solutions and end effects, International Journal of Solids and Structures 45: 303-319.
    28.
  28.  Lekhnitskii S.G., 1971, Torsion of Anisotropic and Non-Homogeneous Beams, Fizmatlit, Moscow.
    29.
  29.  Lekhnitskii S.G., 1981, Theory of Elasticity of an Anisotropic Body, Mir, Moscow.
    30.
  30.  Bisegna P., 1998, The Saint–Venant problem in the linear theory of piezoelectricity, Atti dei Convegni Lincei, Accademia dei Lincei 140: 151-165.
    31.
  31.  Bisegna P., 1999, The Saint–Venant problem for monoclinic piezoelectric cylinders, ZAMM 78(3): 147-165.
    32.
  32.  Horgan C.O., 2007, On the torsion of functionally graded anisotropic linearly elastic bars, IMA Journal of Applied Mathematics 72(5): 556-562.
    33.
  33.  Rovenski V., Harash E., Abramovich H., 2006, Saint-Venant’s problem for homogeneous piezoelectric beams, Technical Notes 967: 1-100.
    34.
  34.  Rovenski V., Harash E., Abramovich H., 2007, Saint-Venant’s problem for homogeneous piezoelectric beams, Journal of AppliedMechanics 47(6): 1095-1103.
    35.
  35.  Yang Y.S., 2005, Introduction to the Theory of Piezoelectricity, Springer Verlag, New York.
    36.
  36. Tawaka T., Fudaka T., Takada T., 1987, Flexural-torsion coupling vibration control of fiber composite cantilever beam by using piezoelectric actuators, Smart Materials  and  Structures 6: 477-484.
    37.
  37.  Zehetner C., 2009, Compensation of torsional vibrations in rods by piezoelectric actuation, Acta Mechanica 207(1-2): 121-133.
    38.
  38.  Maleki M., Naei M.H., Hoseinian E., Babahaji A., 2010, Exact three  dimensional  analysis  for static torsion of piezoelectric rods, International Journal of Solids and Structures 28: 217-226.
    39.
  39.  Sadd Martin H., 2009, Elasticity,Theory,Applications,and Numerics , Elsevier, USA.
    40.
  40.  Prandtl L., 1903, Zur torsion von prismatischen Stäben, Physics 4: 758-770.
    41.
  41.  Lurje A., 1970, Theory of Elasticity, Fizmatlit, Moscow.
    42.
  42.  Ely J.F., Zienkiewicz O.C., 1960, Torsion of compound bars a relaxation solution, International Journal of Mechanical Sciences 1: 356-365.
    43.
  43.  Ecsedi I., 2009, Some analytical solutions for saint-venant torsion of non-homogeneous cylindrical bars, Europen Journal of Mechanics A/Solids 28: 985-990.
    44.
  44.  Yang J., 2005, An Introduction to the Theory of Piezoelectric, Springer, USA.
    45.
  45.  Horgan C.O., Chan A.M., 1999, Torsion of functionally graded isotropic linearly elastic bars, Journal of Elasticity 52(2): 181-189.
    46.

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