变厚度非均匀粘弹性复合圆柱体的旋转应力

A·M·任库尔

doi:10.3879/j.issn.1000-0887.2011.04.010

变厚度非均匀粘弹性复合圆柱体的旋转应力

doi: 10.3879/j.issn.1000-0887.2011.04.010

A·M·任库尔^1,2

1.
阿卜杜勒阿齐兹国王大学理学院数学系,80203邮箱,吉达 21589,沙特阿拉伯;2.卡夫拉-谢赫大学理学院数学系,卡夫拉-谢赫 35516,埃及

详细信息

中图分类号: O343
计量
- 文章访问数: 1453
- HTML全文浏览量: 110
- PDF下载量: 719
- 被引次数: 0
出版历程
- 收稿日期: 2010-05-02
- 修回日期: 2010-11-25
- 刊出日期: 2011-04-15

Stresses in a Rotating Heterogeneous Viscoelastic Composite Cylinder With Variable Thickness

A. M. Zenkour^1,2

1.
Department of Mathematics, Faculty of Science, King AbdulAziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia;

摘要

摘要: 在平面应变的假设下，给出了两个复合弹性圆柱体旋转时的解析解．外柱是由厚度按公式变化的正交各向异性材料所组成，它包裹着一个等厚度纤维增强粘弹性均匀各向同性的实心圆柱体．外圆柱体的厚度和弹性性质按半径方向的幂函数变化．应用边界和连续条件，确定复合圆柱体旋转时的径向位移和应力，应用等效模量和Illyushin逼近法，得到问题的粘弹性解．讨论了各向异性、厚度变化、本构参数以及时间参数，对径向位移和应力的影响．
- 旋转的复合圆柱体 /
- 正交各向异性 /
- 非均匀性 /
- 变厚度 /
- 纤维增强的粘弹性核心体
Abstract: 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.
- rotating composite cylinder /
- orthotropic /
- heterogeneous /
- variable thickness /
- fiber-reinforced viscoelastic core

HTML全文

参考文献(27)

[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.)