Vol.20, No.2, 2020, pp. 113–121 
MODELLING OF ELASTOPLASTIC DEFORMATION OF TRANSVERSELY ISOTROPIC ROTATING DISC OF VARIABLE DENSITY WITH SHAFT UNDER A RADIAL TEMPERATURE GRADIENT A.G. Temesgen^{1}, S.B. Singh^{1}, Pankaj Thakur^{2} ^{1)} Depart. of Mathematics, Punjabi University, Patiala, India ^{ 2)} Department of Mathematics, ICFAI University, Himachal Pradesh, India email: pankaj_thakur15@yahoo.co.in

Abstract This study deals with the elastoplastic deformation of transversely isotropic rotating disc of variable density with shaft subjected to temperature gradient by using transition theory of Seth and generalized strain measure theory. Solving the problems in classical plasticity theory needs the empirical assumption such as the yield criterion. This results from the use of direct strain measures that ignore the nonlinear transition region where the yield occurs and the fact that plastic strains are never straight. The transition theory of Seth requires no adhoc assumptions such as yield condition, incompressibility condition, infinitesimal strains and creep strain laws. Therefore, generalized strain measure and transition theory are the general methods of solving a problem from which the classical theory assumptions can be obtained. The combined impacts of density, temperature, and angular speed have been displayed numerically and graphically. It is seen that the disc made of transversely isotropic material yields at the external surface of the disc, however, the disc of isotropic material yields at the internal surface of the disc as the density of the rotating disc increases from outer to inner surface with the increase of temperature and angular speed. The displacement of the isotropic rotating disc is higher than that of the transversely isotropic rotating disc. Keywords: elastoplastic, rotating disc, transversely isotropic, stresses, strains, displacement, temperature gradient 
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