Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-25T05:55:00.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Rotating Moderately Thick Annular Disks via an Extension to Classical Theory

Published online by Cambridge University Press:  08 May 2012

A. M. Zenkour
A. M. Zenkour
Affiliation:
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt
Get access

Abstract

The problem of rotating annular disk subjected to a uniformly distributed load is treated in two ways. Stress is divided into a rotating part because of the angular velocity and a bending part due to force loading. New set of equilibrium equations with small deflections is developed. Solutions for radial displacement, deflection, forces and moment resultants, and the rotating and bending stresses of the first-order theory are presented in terms of corresponding quantities of annular disks based on the classical theory. The boundary conditions at the edges of the annular disk are roller supported, clamped or free. Several examples are presented to illustrate the use and accuracy of these relationships. The effects of several parameters on the radial and vertical displacements and rotating and bending stresses are studied. It is observed that the classical theory is sufficient to study the problem of rotating annular disks. However, the inclusion of the effect of shear deformation is necessary to study precisely the curvature of moderately thick annular disks.

Keywords

Annular disksClassical theoryFirst-order theoryRotatingBending
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 2 , June 2012 , pp. 355 - 360
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Timoshenko, S. P. and Woinowsky-Krieger, S., Theory of Plates and Shells, McGraw Hill, New York (1959).Google Scholar
2. Szilard, R., Theory and Analysis of Plates: Classical and Numerical Methods, Prentice-Hall, Englewood Cliffs, New Jersey (1974).Google Scholar
3. Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, 3rd Ed., McGraw-Hill, New York (1970).Google Scholar
4. Ugural, S. C. and Fenster, S. K., Advanced Strength and Applied Elasticity, Elsevier, New York (1987).Google Scholar
5. Shaffer, B. F., “Orthotropic Annular Disks in Plane Stress.” Journal of Applied Mechanics, ASME, 34, pp. 1027–1029 (1967).CrossRefGoogle Scholar
6. Gamer, U., “Elastic-Plastic Deformation of the Rotating Solid Disk,” Ingenieur-Archiv, 54, pp. 345–354 (1984).CrossRefGoogle Scholar
7. Gamer, U., “Stress Distribution in the Rotating Elastic-Plastic Disk,” ZAMM 65, T136–137 (1985).Google Scholar
8. Horgan, C. O. and Chan, A. M., “The Pressurized Hollow Cylinder or Disk Problem for Functionally Graded Isotropic Linearly Elastic Materials,” Journal of Elasticity, 55, pp. 43–59 (1999).CrossRefGoogle Scholar
9. Horgan, C. O. and Chan, A. M., “The Stress Response of Functionally Graded Isotropic Linearly Elastic Rotating Disks,” Journal of Elasticity, 55, pp. 219–230 (1999).CrossRefGoogle Scholar
10. You, L. H. and Zhang, J. J., “Elastic-Plastic Stresses in a Rotating Solid Disk,” International Journal of Mechanical Sciences, 41, pp. 269–282 (1999).CrossRefGoogle Scholar
11. You, L. H., Tang, Y. Y., Zhang, J. J., and Zheng, C. Y., “Numerical Analysis of Elasticplastic Rotating Disks with Arbitrary Variable Thickness and Density,” International Journal of Solids and Structures, 37, pp. 7809–7820 (2000).CrossRefGoogle Scholar
12. Zenkour, A. M., “Analytical Solutions for Rotating Exponentially-Graded Annular Disks with Various Boundary Conditions,” International Journal of Structural Stability and Dynamics, 5, pp. 557–577 (2005).CrossRefGoogle Scholar
13. Zenkour, A. M., “Thermoelastic Solutions for Annular Disks with Arbitrary Variable Thickness,” Structural Engineering and Mechanics, 24, pp. 515–528 (2006).CrossRefGoogle Scholar
14. Zenkour, A. M., “Steady-State Thermoelastic Analysis of a Functionally Graded Rotating Annular Disk,” International Journal of Structural Stability and Dynamics, 6, pp. 559–574 (2006).CrossRefGoogle Scholar
15. Nie, G. and Zhong, Z., “Axisymmetric Bending of Two-Dimensional Functionally Graded Circular and Annular Plates,” Acta Mechanica Solida Sinica, 20, pp. 289–295 (2007).CrossRefGoogle Scholar
16. Zenkour, A. M., “Stress Distribution in Rotating Composite Structures of Functionally Graded Solid Disks,” Journal of Materials Processing Technology, 209, pp. 3511–3517 (2009).CrossRefGoogle Scholar
17. Reddy, J. N., Wang, C. M., and Kitipornchai, S., “Axisymmetric Bending of Functionally Graded Circular and Annular Plates,” European Journal of Mechanical A/Solids, 18, pp. 185–199 (1999).CrossRefGoogle Scholar
18. Bayat, M., Sahari, B. B., Saleem, M., Ali, A. and Wong, S. V., “Bending Analysis of a Functionally Graded Rotating Disk Based on the First Order Shear Deformation Theory,” Applied Mathematical Modelling, 33, pp. 4215–4230 (2009).CrossRefGoogle Scholar