Study on the effect of different rotational speed functions in elastic-plastic analysis of annular thin disk of functionally graded material

In the present paper, the effect of different rotational speed functions in the elastic-plastic deformation and stress analysis of a rotating annular disc of functionally graded materials (FGM) in Reddy model is studied using the analytical and FEM methods. In this regard, differential equations governing dynamic equilibrium for displacements and stresses in the elastic region of the FGM rotating disk have been derived using theory of elasticity in plane stress condition and have been solved by shooting method. Then, the equations governing the distribution of plastic radial and circumferential stresses on the disc have been extracted using the Prandtl -Ross theory of plasticity and based on Ludwig hardening law in conjecture with the von-Mises yield criterion. Also, by modeling the annular disc in the environment of finite element software ANSYS, the results obtained from elastic analytical solution and finite element numerical solution have been compared to each other and to the results reported in the literature for specific cases and validated accordingly. The effect of variation of the disk geometric parameters, functionally graded material power index as well as type of the time-dependent rotational speed function such as the constant speed, exponential, and accelerated/decelerated linear, quadratic, and square root functions on the elastic behavior of the disk and distribution of radial displacement, and also distribution of radial, circumferential, and shear stresses in the disk have been studied. Moreover, the results of plastic analysis have been presented for distribution of radial and circumferential stresses in the disk.