UDC 621 FUNCTIONALLY GRADED ROTATING DISCS WITH INTERNAL PRESSURE © Manoj Sahni Pandit Deendayal Petroleum University, Gandhinagar, Gujarat, India Ritu Sahni Pandit Deendayal Petroleum University, Gandhinagar, Gujarat, India Abstract. <...> In this paper analytical solution using stress function is developed to determine deformations and stresses (radial and circumferential) made of functionally graded materials subjected to internal pressure. <...> The problem is solved by varying Young’s modulus and density depending on the radial coordinate only, whereas the Poisson’s ratio is taken as constant. <...> The purpose of this research is to find an analytical solution of a thin circular annular rotating disk. <...> The pressure is applied at the internal surface of the disk and the results are compared with those available in literature. <...> Sladeketal [7] presented a meshless local boundary integral equation method for dynamic analysis of an anti-plane crack in functionally graded materials. <...> Zenkour [9] dealt with a solution for a rotating annular disk which is assumed to be graded in the radial direction according to a simple exponential law distribution. <...> All other parameters in equation (2) are geometric parameters. <...> Due to rotational symmetry (independent of ), the Here E0 and 0 strain displacement relations are given as and , where and (3) are strains along radial and circumferential direction. <...> Here u is the displacement in the radial direction. <...> The strain compatibility equation is . (4) The stress – strain relationship is defined as and librium equation of motion (1) as and . (5) Defining the stress function (F) satisfying the equi. (6) Проблемы машиностроения и автоматизации, № 3 – 2014 125 are Young’s modulus and density at MANOJ SAHNI, RITU SAHNI Now using equations (5) and (6) in equation (4), we get (7) Substituting equation (2) in (7), the equation reduces to Cauchy Euler’s differential equation (8) (11) The stress function F is calculated as where A1 and A2 constant given as lated as , (9) are the integration constants, and m is . <...> The stresses – radial and circumferential are calcu(10) the posit ive Fig. 1. <...> Radial stresses for various values of pressure 126 Engineering and automation <...>