A thermoelastic boundary value problem of a hollow circular disc made of functionally graded materials with arbitrary gradient is analysed. The steady-state temperature distribution is assumed to be the function of the radial coordinate with prescribed temperature at the inner and outer cylindrical boundary surfaces. The material properties are assumed to be arbitrary smooth functions of the radial coordinate. A coupled system of ordinary differential equations containing the radial displacement and stress function is derived and used to get the distribution of thermal stresses and radial displacements caused by axisymmetric mechanical and thermal loads. General analytical solutions of functionally graded disc with thermal loads are not available. The results obtained by the presented numerical method are verified by an analytical solution. The considered analytical solution is valid if the material properties, except the Poisson ratio, are expressed as power functions of the radial coordinate.
Thermal buckling behavior of a functionally graded material (FGM) Timoshenko beam is studied based on the transformed-section method. The material and thermal properties of the FGM beam are assumed to vary across the beam thickness according to a power-law function, a sigmoid function and an exponential function. The results of buckling temperature for the FGM beams with respective temperature-dependent and temperature-independent properties under uniform and non-linear temperature rises are presented. Some results are compared with those in the published literature to verify the accuracy of the present work. The effects of the material distributions, temperature fields, temperature-dependent properties and slenderness ratios on the thermal buckling behaviors of FGM beams are discussed. It is believed that the present model provides engineers with a simple and effective method to study the effects of various parameters of the FGM beam on its thermal buckling behavior.