Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30174
Elastic-Plastic Analysis for Finite Deformation of a Rotating Disk Having Variable Thickness with Inclusion

Authors: Sanjeev Sharma, Manoj Sahni


Transition theory has been used to derive the elasticplastic and transitional stresses. Results obtained have been discussed numerically and depicted graphically. It is observed that the rotating disk made of incompressible material with inclusion require higher angular speed to yield at the internal surface as compared to disk made of compressible material. It is seen that the radial and circumferential stresses are maximum at the internal surface with and without edge load (for flat disk). With the increase in thickness parameter (k = 2, 4), the circumferential stress is maximum at the external surface while the radial stress is maximum at the internal surface. From the figures drawn the disk with exponentially varying thickness (k = 2), high angular speed is required for initial yielding at internal surface as compared to flat disk and exponentially varying thickness for k = 4 onwards. It is concluded that the disk made of isotropic compressible material is on the safer side of the design as compared to disk made of isotropic incompressible material as it requires higher percentage increase in an angular speed to become fully plastic from its initial yielding.

Keywords: Finite deformation, Incompressibility, Transitionalstresses, Elastic-plastic.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1292


[1] S.P. Timoshenko, J.N. Goodier, Theory of Elasticity, 3rd Edi., New York: McGraw-Hill Book Coy., London, 1951.
[2] J. Chakrabarty, Applied Plasticity, Springer Verlag, Berlin, 2000.
[3] W. Han, B.D. Reddy, Plasticity, Mathematical Theory and Numerical Analysis, Springer Verlag, Berlin, 1999.
[4] R.B. Hetnarski, J. Ignaczak, Mathematical Theory of Elasticity, Taylor and Francis, 2003.
[5] I.S. Sokolinikoff, Mathematical Theory of Elasticity, 2nd Edi., New York: McGraw-Hill Book Co., 1950.
[6] J. Heyman, "Plastic design of rotating discs", Proc. Inst. Mech. Engs., 1958, pp. 531-546.
[7] R.P.S. Han, Yeh Kai-Yuan, "Analysis of High-Speed Rotating Disks with Variable Thickness and Inhomogenity", Transactions of the ASME, 61, pp. 186-191, 1994.
[8] A.N. Eraslan, Y.Orcan, "Elastic-plastic Deformation of a rotating solid disk of exponentially varying thickness", Mechanics of Materials, vol. 34, pp. 423-432, 2002.
[9] Xiu-e Wang, Xianjun Yin, "On Large Deformations of Elastic Half Rings", WSEAS Transactions on Applied and Theoretical Mechanics, vol. 2(1), pp. 24, 2007.
[10] B.R. Seth, "Transition Theory of Elastic-Plastic Deformation, Creep and Relaxation", NATURE, vol. 195, No. 4844, pp. 896-897, 1962.
[11] B. R. Seth, "Transition Analysis of Collapse of Thick-walled Cylinder", ZAMM, 50, pp. 617-621, 1970.
[12] B. R. Seth, "Creep Transition", Jr. Math. Phys. Sci., vol. 8, pp. 1-2, 1972.
[13] S. Hulsarkar, "Transition Theory of Creep Shells under Uniform Pressure", ZAMM, Vol. 46, pp. 431-437, 1966.
[14] S.K. Gupta, V.D. Rana, "Thermo Elastic-Plastic and Creep Transition in Rotating Cylinder", J. Math. Phy. Sci., 23(1), pp. 71-90, 1989.
[15] S.K. Gupta, Pankaj, "Thermo Elastic-plastic Transition in a thin rotating Disc with inclusion", Thermal Science Scientific Journal, 11(1), pp.103-118, 2007.
[16] B.N. Borah," Thermo Elastic-plastic transition", Contemporary Mathematics, vol. 379, pp. 93-111, 2005.
[17] S. Sharma, "Elastic-plastic Transition of Non-homogeneous Thick-walled Circular Cylinder under Internal Pressure", Def. Sc. Journal, vol. 54, No. 2, 2004.
[18] S. Sharma, M. Sahni, "Creep Transition of Transversely Isotropic Thick-walled Rotating Cylinder", Adv. Theor. Appl. Mech., vol. 1(7), pp. 315-325, 2008.
[19] Pankaj, Sonia R. Bansal, "Elastic-Plastic Transition in a Thin Rotating Disc with Inclusion", Proceedings of World Academy of Science, Engineering and Technology, Vol. 28, April 2008.
[20] U.Gu&&ven , "Elastic-plastic rotating disk with rigid inclusion", Mech. Struct. and Mach., vol. 27, pp. 117-128, 1999.