Analytical Solution for the Creep Problem of a Rotating Functionally Graded Magneto–Electro–Elastic Hollow Cylinder in Thermal Environment

Abstract

In this paper, an analytical method is presented for the problem of the time-dependent response of a functionally graded magneto–electro–elastic (FGMEE) rotating hollow cylinder in thermal environment. The material properties of FGMEE are supposed to be power-law functions of radius. Applying the equations of equilibrium and electrostatic and magnetostatic equations, a differential equation which includes creep strains is achieved. At first, an exact solution for the primitive stresses, electric and magnetic potentials are achieved by eliminating creep strains in the mentioned differential equation. Then, Prandtl–Reuss equations, as well as Norton’s law, are employed for the FGMEE. Now, creep stress rates can be achieved by considering only creep strains in the mentioned differential equation. As a final step, time-dependent creep stress, electric potential and magnetic potential redistributions at any time can be achieved using an iterative method. Numerical examples are presented to disclose the influence of creep evolution, thermal loading, angular velocity and grading index on the primitive and creep response of the FGMEE hollow cylinder. Results show that the enhancement in tensile hoop stress during the creep evolution must be considered in designing. So, the creep analysis is vital to have more reliable and accurate aerospace smart structures.