Time-Dependent Hygro-Thermal Creep Analysis of Pressurized FGM Rotating Thick Cylindrical Shells Subjected to Uniform Magnetic Field

Time-dependent creep analysis is presented for the calculation of stresses and displacements of axisymmetric thick-walled cylindrical pressure vessels made of functionally graded material (FGM). For the purpose of time-dependent stress analysis in an FGM pressure vessel, material creep behavior and the solutions of the stresses at a time equal to zero (i.e. the initial stress state) are needed. This corresponds to the solution of the problem considering linear elastic behavior of the material. Therefore, using equations of equilibrium, stress–strain and strain–displacement, a differential equation for displacement is obtained and subsequently the initial elastic stresses at a time equal to zero are calculated. Assuming that the Magneto-hygro-thermoelastic creep response of the material is governed by Norton’s law, using the rate form of constitutive differential equation, the displacement rate is obtained and then the stress rates are calculated. Once the stress rates are known, the stresses at any time are calculated iteratively. The analytical solution is obtained for the plane strain condition. The pressure, inner radius and outer radius are considered to be constant and the magnetic field is uniform. Material properties are considered as power law function of the radius of the cylinder and the poisson’s ratio as constant. Following this, profiles are plotted for different values of material exponent for the radial, circumferential and effective stresses as a function of radial direction and time. The in-homogeneity exponent have significant influence on the distributions of the creep stresses.