Successive approximation method for time-dependent creep modeling of functionally graded piezoelectric cylinder

Abstract

Time-dependent creep behavior of hollow rotating cylinders made from functionally graded piezoelectric material has been investigated using Mendelson's method of successive approximation. All the mechanical, thermal, and piezoelectric properties are modeled as the power-law distribution of volume fraction. Based on equilibrium, strain displacement, stress-strain, and electric displacement relations, a differential equation containing creep strains for displacement is derived. Creep strains are time-, temperature-, and stress-dependent, and the closed-form solution cannot be found for this constitutive differential equation. A semianalytical method in conjunction with the method of successive approximation has therefore been proposed for this analysis. Similar to the radial stress histories, electric potentials increase with time, because the latter is induced by the former during creep deformation of the cylinder, justifying industrial application of such a material as efficient actuators and sensors.