Nonlinear thermal analysis of a hollow functionally graded cylinder with temperature-variable material properties

A nonlinear thermal analysis of a hollow functionally graded cylinder is performed in the present paper. A power function distribution is used for simulation of non-homogeneity of the material used. A temperature dependence is employed for the thermal conductivity. These simulations reduce the problem to a nonlinear differential equation with a variable coefficient. A semi-analytical method of successive approximations is employed for solving this equation. The convergence of the method is studied for different parameters of the problem by checking two criteria: convergence of the sum of the infinite series and condition of smallness of the residual of the responses. An exponentially function is used for simulation of the nonlinear dependence of cylinder material properties on temperature.