A. M. Zenkour. Stresses in a Rotating Heterogeneous Viscoelastic Composite Cylinder With Variable Thickness[J]. Applied Mathematics and Mechanics, 2011, 32(4): 483-496. doi: 10.3879/j.issn.1000-0887.2011.04.010
Citation: A. M. Zenkour. Stresses in a Rotating Heterogeneous Viscoelastic Composite Cylinder With Variable Thickness[J]. Applied Mathematics and Mechanics, 2011, 32(4): 483-496. doi: 10.3879/j.issn.1000-0887.2011.04.010

Stresses in a Rotating Heterogeneous Viscoelastic Composite Cylinder With Variable Thickness

doi: 10.3879/j.issn.1000-0887.2011.04.010
  • Received Date: 2010-05-02
  • Rev Recd Date: 2010-11-25
  • Publish Date: 2011-04-15
  • An analytical solution for the rotation problem of a two-layer composite elastic cylinder under plane strain assumption was presented.The external cylinder had variable-thickness formulation and made of a heterogeneous orthotropic material.It was contained by a fiber-reinforced viscoelastic homogeneous isotropic solid core of uniform-thickness.The thickness and elastic properties of the external cylinder were taken as power functions of the radial direction.On application of the boundary and continuity conditions,the radial displacement and stresses for the rotating composite cylinder were determined.The effective moduli and Illyushin's approximation methods were used to obtain the viscoelastic solution of this problem.The effects of heterogeneity,thickness variation,constitutive and time parameters on the radial displacement and stresses were investigated.
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  • [1]
    Landau L D, Lifshitz E M. Theory of Elasticity[M]. Oxford: Pergamon Press, 1986.
    [2]
    Senitskii Y E. Stress state of a rotating inhomogeneous anisotropic cylinder of variable density[J]. Prik Mekhan, 1992, 28(5): 28-35.
    [3]
    Vasilenko A T, Sudavtsova G K. Elastic equilibrium of circumferentially inhomogeneous orthotropic cylindrical shells of arbitrary thickness[J]. Int Appl Mech, 2001, 37(8): 1046-1054. doi: 10.1023/A:1013022620746
    [4]
    Liew K M, Kitipornchai S, Zhang X Z, Lim C W. Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders[J]. Int J Solids Struct, 2003, 40(10): 2355-2380. doi: 10.1016/S0020-7683(03)00061-1
    [5]
    Oral A, Anlas G. Effects of radially varying moduli on stress distribution of nonhomogeneous anisotropic cylindrical bodies[J]. Int J Solids Struct, 2005, 42(20): 5568-5588. doi: 10.1016/j.ijsolstr.2005.02.044
    [6]
    Tutuncu N. Stresses in thick-walled FGM cylinder with exponentially-varying properties[J]. Eng Struct, 2007, 29(9): 2032-2035. doi: 10.1016/j.engstruct.2006.12.003
    [7]
    Chandrashekhara K, Gopalakrishnan P. Analysis of an orthotropic cylindricall shell having a transversely isotropic core subjected to axisymmetric load[J]. Thin-Walled Struct, 1986, 4(3): 223-237. doi: 10.1016/0263-8231(86)90004-2
    [8]
    Zenkour A M. Rotating variable-thickness orthotropic cylinder containing a solid core of uniform-thickness[J]. Arch Apl Mech, 2006, 76(1/2): 89-102. doi: 10.1007/s00419-006-0007-y
    [9]
    Zenkour A M. Stresses in cross-ply laminated circular cylinders of axially variable thickness[J]. Acta Mech, 2006, 187(1): 85-102. doi: 10.1007/s00707-006-0356-1
    [10]
    Allam M N M, Zenkour A M, Elazab E R. On the rotating inhomogeneous elastic cylinders of variable-thickness and density[J]. J Appl Math Infor Sci, 2008: 2(3): 237-257.
    [11]
    Shinozuka M, Spillers W R. Axisymmetric reinforced viscoelastic cylindricall shell[J]. Int J Mech Sci, 1966, 8(1): 1-12. doi: 10.1016/0020-7403(66)90059-2
    [12]
    Ting E C, Tuan J L. Effect of cyclic internal pressure on the temperature distribution in a viscoelastic cylinder[J]. Int J Mech Sci, 1973, 15(11): 861-871. doi: 10.1016/0020-7403(73)90017-9
    [13]
    Feng W W, Hung T, Chang G. Extension and torsion of hyperviscoelastic cylinders[J]. Int J Non-Linear Mech, 1992, 27(3): 329-335. doi: 10.1016/0020-7462(92)90001-N
    [14]
    Karnaukhov V G, Senchenkov I K. Thermomechanical behavior of a viscoelastic finite circular cylinder under harmonic deformations[J]. J Eng Math, 2003, 46(3/4): 299-312. doi: 10.1023/A:1025027807089
    [15]
    Bland D. The Linear Theory of Viscoelasticity[M]. New York: Pergamon Press, 1960.
    [16]
    Illyushin A A, Pobedria B E. Foundations of Mathematical Theory of Thermo Viscoelasticity[M]. Moscow: Nauka, 1970.
    [17]
    Allam M N M, Appleby P G. On the plane deformation of fiber-reinforced viscoelastic plates[J]. Appl Math Modell, 1985, 9(5): 341-346. doi: 10.1016/0307-904X(85)90021-6
    [18]
    Allam M N M, Appleby P G. On the stress concentrations around a circular hole in a fiber-reinforced viscoelastic plate[J]. Res Mech, 1986, 19(2): 113-126.
    [19]
    Allam M N M, Zenkour A M. Bending response of a fiber-reinforced viscoelastic arched bridge model[J]. Appl Math Modell, 2003, 27(3): 233-248. doi: 10.1016/S0307-904X(02)00123-3
    [20]
    Zenkour A M, Allam M N M. Stresses around filled and unfilled circular holes in a fiber-reinforced viscoelastic plate under bending[J]. Mech Adv Mater, 2005, 12(6): 379-389. doi: 10.1080/155022891009477
    [21]
    Zenkour A M, Allam M N M. On the rotating fiber-reinforced viscoelastic composite solid and annular disks of variable thickness[J]. Int J Comput Methods Eng Sci Mech, 2006, 7(1): 21-31. doi: 10.1080/155022891009639
    [22]
    Abramowitz M, Stegun A I. Handbook of Mathematical Functions[M]. 5th Printing. Washington DC, USA: US Government Printing Office, 1966.
    [23]
    Bogdanovich A E, Pastore C M. Mechanics of Textile and Laminated Composites With Applications to Structural Analysis[M]. New York: Chapman and Hall, 1996.
    [24]
    Pobedria B E. Structural anisotropy in viscoelasticity[J]. Polym Mech, 1976, 12(4): 557-561.
    [25]
    Zenkour A M. Thermal effects on the bending response of fiber-reinforced viscoelastic composite plates using a sinusoidal shear deformation theory[J]. Acta Mech, 2004, 171(3/4): 171-187. doi: 10.1007/s00707-004-0145-7
    [26]
    Zenkour A M. Buckling of fiber-reinforced viscoelastic composite plates using various plate theories[J]. J Eng Math, 2004, 50(1): 75-93. doi: 10.1023/B:ENGI.0000042123.94111.35
    [27]
    任库尔 A M, 伊莉莎白 K A, 玛沙特 D S. 功能梯度空心及实心圆柱体旋转时的弹性及粘弹性解[J]. 应用数学和力学,2008, 29(12): 1457-1471. (Zenkour A M, Elsibai K A, Mashat D S. Elastic and viscoelastic solutions to rotating functionally graded hollow and solid cylinders[J]. Applied Mathematics and Mechanics(English Edition), 2008, 29(12): 1601-1616.)
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