Analytic Solutions For The Stresses Of FGM Cylinders Subjected To Thermal And Mechanical Loads

Thermal stress of functionally graded hollow cylinders is a problem worth studying. In this thesis, a general analysis of one-dimensional thermal stresses in an axisymmetric hollow thick cylinder made of functionally graded materials is developed.The cylinder has finite length and is subjected to axisymmetric thermal and mechanical loads. It is divided into steady state and transient thermoelastic problems depending on the temperature boundary condition. The solutions of temperature, displacements and stresses is classified as the problem of taking appropriate methods to solve heat conduction equation and Navier equation.The following questions have been solved in this thesis:(1)When the material properties (Poisson’s ratio is constant) are assumed to be expressed as power functions of radius, the solutions for the steady temperature and thermo-mechanical stresses making use of Euler equation to solve differential equations.(2)When the material properties (Poisson’s ratio is constant) are assumed to be expressed as the product of power functions and exponential functions, solutions for the steady temperature, displacements and stresses are also obtained.(3) When the material properties (Poisson’s ratio is constant) are assumed to be expressed as power functions of radius.Employing Laplace transform techniques and series solving method for ordinary differential equation, solutions for the transient temperature and thermo-mechanical stresses are obtained.Finally, as an example, the whole field results of a hollow cylinder made of molybdenum and mullite are graphically presented by finite element analysis software, and the results are comparing with theory solutions. Finally the variations of temperature, displacement and stresses are discussed with different indices when the material properties (Poisson’s ratio is constant) are assumed to be expressed as power functions of radius.