Steady Thermal Stresses in a Thin Rotating Disc of Finitesimal Deformation with Mechanical Load

Journal of Solid Mechanics

مقاله 15، دوره 8، شماره 1، خرداد 2016، صفحه 204-211   

نوع مقاله: Research Paper

نویسندگان

J Kaur¹؛ P Thakur^{* 2}؛ S.B Singh¹

¹Department of Mathematics, Punjabi University Patiala, Punjab 147002, India

²Department of Mathematics, IEC University Baddi, Solan, Himachal Pradesh 174103, India

چکیده

Seth’s transition theory is applied to the problems of thickness variation parameter in a thin rotating disc by finite deformation. Neither the yield criterion nor the associated flow rule is assumed here. The results obtained here are applicable to compressible materials. If the additional condition of incompressibility is imposed, then the expression for stresses corresponds to those arising from Tresca yield condition. It has observed that for rotating disc made of compressible material required higher angular speed to yield at the internal surface as compare to disc made of incompressible material and a much higher angular speed is required to yield with the increase in radii ratio. With the introduction of thermal effects, lesser angular speed is required to yield at the internal surface. Thermal effect in the disc increase the value of circumferential stress at the internal surface and radial stresses at the external surface for compressible as compare to incompressible material.

کلیدواژه‌ها

Plastic؛ Transitional؛ Finitesimal؛ Stresses؛ Disc؛ Load؛ temperature

مراجع

[1] Timoshenko S.P., Goodier J.N., 1951, Theory of Elasticity , 3rd Edition, New York, McGraw-Hill Book Coy, London.
[2] Chakrabarty J., 1987, Theory of Plasticity, New York, McGraw-Hill Book Coy.
[3] Heyman J., 1958, Plastic design of rotating discs, Proceedings of the Institution of Mechanical Engineers 172(1): 531-546.
[4] Parmaksigoglu C., Guven U., 1998, Plastic stress distribution in a rotating disc with rigid inclusion under a radial tem perature gradient, Mechanics of Structures and Machines 26 : 9-20.
[5] Seth B.R., 1962, Transition theory of elastic-plastic deformation, creep and relaxation, Nature 195:896-897.
[6] Seth B.R., 1966, Measure concept in mechanics, International Journal of Non-Linear Mechanics 1(1): 35-40.
[7] Parkus H., 1976, Thermo-Elasticity, Springer-Verlag, Wien, New York, USA.
[8] Gupta S. K., Thakur P. , 2008, Creep transition in an isotropic disc having variable thickness subjected to internal pressure, Proceedings of the National Academy of Sciences Section A 78(1): 57-66.
[9] Gupta S.K., Thakur P. ,2007, Thermo elastic - plastic transition in a thin rotating disc with inclusion, Thermal Science 11(1): 103-118.
[10] Gupta S.K., Thakur P.,2007, Creep transition in a thin rotating disc with rigid inclusion, Defence Science Journal 57(2) : 185-195.
[11] Thakur P. ,2009, Elastic - plastic transition in a thin rotating disc having variable density with Inclusion, Structural Integrity and Life 9(3):71-179.
[12] Thakur P., 2010 , Elastic-plastic transition stresses in a thin rotating disc with rigid inclusion by infinitesimal deformation under steady state Temperature, Thermal Science International Scientific Journal 14(1): 209-219.
[13] Thakur P., 2010, Creep transition stresses in a thin rotating disc with shaft by finite deformation under steady state temperature, Thermal Science International Scientific Journal 14(2) : 425-436.
[14] Thakur P., 2011, Effect of transition stresses in a disc having variable thickness and Poisson’s ratio subjected to internal pressure, Wseas Transactions on Applied and Theoretical Mechanics 6(4): 147-159.
[15] Thakur P., 2012, Deformation in a thin rotating disc having variable thickness and edge load with inclusion at the elastic-plastic transitional stress, Integritet i Vek Konstrukcija 12(1): 65-70.
[16] Thakur P., 2013 , Stresses in a thin rotating disc of variable thickness with rigid shaft, International Journal for Technology of Plasticity 37(1): 1-14.
[17] Thakur P., Singh S. B., Kaur J., 2013, Steady thermal stresses in a rotating disk with shaft having density variation parameter subjected to thermal load , Structural Integrity and Life 13(2): 109-116.
[18] Thakur P., 2013, Analysis of stresses in a thin rotating disc with inclusion and edge loading, Scientific Technical Review 63(3): 9-16.
[19] Thakur P., Singh S. B., Kaur J., 2013, Thickness variation parameter in thin rotating disc, FME Transaction 41(2) : 96-102.
[20] Thakur P., Singh S. B., Kaur J., 2014, Elastic-plastic transitional stress in a thin rotating disc with shaft having variable thickness under steady state temperature, Kragujevac Journal of Science 36: 5-17.
[21] Levitsky M., Shaffer B. W., 1975, Residual thermal stresses in a solid sphere form a thermosetting material, Journal of Applied Mechanics 42 (3): 651-655.