Elastic-Plastic Analysis for Finite Deformation of a Rotating Disk Having Variable Thickness with Inclusion
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50784", author = "Sanjeev Sharma and Manoj Sahni", title = "Elastic-Plastic Analysis for Finite Deformation of a Rotating Disk Having Variable Thickness with Inclusion", abstract = "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.", volume = "5", number = "3", pages = "249-10", }