Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Thermoelastic solutions for annular disks with arbitrary variable thickness

  • Zenkour, Ashraf M. (Department of Mathematics, Faculty of Science, King AbdulAziz University)
  • Received : 2006.02.02
  • Accepted : 2006.06.27
  • Published : 2006.11.30
⟨ Previous Next ⟩

Abstract

This article presents a unified analytical solution for the analysis of thermal deformations and stresses in elastic annular disks with arbitrary cross-sections of continuously variable thickness. The annular disk is assumed to be under steady heat flow conditions, in which the inner surface of the annular disk is at an initial temperature and the outer surface at zero temperature. The governing second-order differential equation is derived from the basic equations of the thermal annular disks and solved with the aid of some hypergeometric functions. Numerical results for thermal stresses and displacement are given for various annular disks. These disks include annular disks of thickness profiles in the form of general parabolic and exponential functions. Additional annular disks with nonlinearly variable thickness and uniform thickness are also included.

Keywords

References

  1. Callioglu, H., Topcu, M. and Altan, G (2005), 'Stress analysis of curvilinearly orthotropic rotating discs under mechanical and thermal Loading', J Reinf. Plast. Compos' 24, 831-838 https://doi.org/10.1177/0731684405047770
  2. Eraslan, AN. (2002), 'Von Mises yield criterion and nonlinearly hardening variable thickness rotating annular disks with rigid inclusion', Mech Res. Commun., 29, 339-350 https://doi.org/10.1016/S0093-6413(02)00282-3
  3. Gamer, U. (1983), 'Tresca's yield condition and the rotating disk', J Appl. Mech, ASME, 50, 676-678 https://doi.org/10.1115/1.3167110
  4. Guven, U. (1998), 'Elastic-plastic stress distribution in a rotating hyperbolic disk with rigid inclusion', Int. J Mech Sci., 40, 97-109 https://doi.org/10.1016/S0020-7403(97)00036-2
  5. Horgan, C.O. and Chan, AM. (1999a), 'The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials', J Elasticity, 55, 43-59 https://doi.org/10.1023/A:1007625401963
  6. Horgan, C.O. and Chan, AM. (1999b), 'The stress response of functionally graded isotropic linearly elastic rotating disks', J Elasticity, 55, 219-230 https://doi.org/10.1023/A:1007644331856
  7. Kennedy, W. and Gorman, D. (1977), 'Vibration analysis of variable thickness discs subjected to centrifugal and thermal stresses', J Sound Vib., 53, 83-101 https://doi.org/10.1016/0022-460X(77)90096-7
  8. Parida, J. and Das, AK. (1972), 'Thermal stress in a thin circular disc of orthotropic material due to an instantaneous point heat source', Acta Mech, 13, 205-214 https://doi.org/10.1007/BF01586793
  9. Sayman, O. (2006), 'Stress analysis of a thermoplastic composite disc under uniform temperature distribution', J Thermoplas. Compos. Mater., 19,61-77 https://doi.org/10.1177/0892705706055445
  10. Shaffer, B.F. (1967), 'Orthotropic annular disks in plane stress', J Appl. Mech, ASME, 34, 1027-1029 https://doi.org/10.1115/1.3607811
  11. Sugano, Y, Chiba, R., Hirose, K. and Takahashi, K. (2004), 'Material design for reduction of thermal stress in a functionally graded material rotating disk', JSME Int. J, Series A: Solid Mech Mater. Eng., 47, 189-197 https://doi.org/10.1299/jsmea.47.189
  12. Timoshenko, S.P. and Goodier, J.N. (1970), Theory of Elasticity, McGraw-Hill, New York
  13. Zenkour, AM. (2005), 'Analytical solution for rotating exponentially-graded annular disks with various boundary conditions', Int. J Struct. Stab. Dynam., 5, 557-577 https://doi.org/10.1142/S0219455405001726
  14. Zenkour, AM. (2006), 'Rotating variable-thickness orthotropic cylinder containing a solid core of uniformthickness', Arch Appl. Mech, 76, 89-102 https://doi.org/10.1007/s00419-006-0007-y
  15. Zenkour, A.M. and Allam, M.N.M. (2006), 'On the rotating fiber-reinforced viscoelastic composite solid and annular disks of variable thickness', Int. J Comput. Meth Eng. Sci. Mech, 7, 21-31 https://doi.org/10.1080/155022891009639

Cited by

  1. STEADY-STATE THERMOELASTIC ANALYSIS OF A FUNCTIONALLY GRADED ROTATING ANNULAR DISK vol.06, pp.04, 2006, https://doi.org/10.1142/S0219455406002064
  2. Stress Function of a Rotating Variable-Thickness Annular Disk Using Exact and Numerical Methods vol.03, pp.04, 2011, https://doi.org/10.4236/eng.2011.34048
  3. Rotating Moderately Thick Annular Disks via an Extension to Classical Theory vol.28, pp.02, 2012, https://doi.org/10.1017/jmech.2012.39
  4. Analytical and Numerical Solutions for a Rotating Annular Disk of Variable Thickness vol.01, pp.05, 2010, https://doi.org/10.4236/am.2010.15057
  5. Elastic and Viscoelastic Stresses of Nonlinear Rotating Functionally Graded Solid and Annular Disks with Gradually Varying Thickness vol.64, pp.4, 2017, https://doi.org/10.1515/meceng-2017-0025
  6. Thermo-elastic analysis of rotating functionally graded micro-discs incorporating surface and nonlocal effects vol.5, pp.3, 2006, https://doi.org/10.12989/aas.2018.5.3.295