Research On Thermal Stresses Around A Circular Hole In Functionally Graded Materials

Thermal stresses usually occur in aerospace, metallurgy, machinery manufacturing, construction industry and many other national defense and civilian industrial strucrures. Especially in high-temperature environment, studies on thermal stresses have received much interest in strength analysis of new materials and structures. Functionally graded materials have many merits such as reducing thermal stress, heat shock resistance, heat fatigue resistance, corrosion resistance, wear resistance and so on. Thus, it is of theoretical and practical importance to study the thermal stresses of functionally graded materials.In the present work, by using complex variable method, we study the stress distribution of a functionally graded material plate with a circular hole under mechanical loads and thermal loads, respectively. Below are the main contents of the work: following the brief introduction given in Chapter 1, key equations to be used in the work are outlined in Chapter 2. In Chapter 3, studied is the stress distribution of a functionally graded material plate with a circular hole under constant loads. Based on the method of piece-wise homogeneous layers, the problem is reduced approximately to the case where the homogeneous plate contains N rings which have different material constants, and thus it can be solved based on Muskhelishvili's theory. In numerical examples we discusse the stress distribution in the plate under different loads, and the effects of the variations of Young's modulus and Poisson's ratio on the stress concentrations. In Chapter 4, we investigate the thermal stresses in a functional graded material plate with a circular hole under uniform heat flux at infinity. By using the similar method to the above, the present problem is reduced to the case where the homogeneous plate contains N rings. However, different from the case under mechanical loads, the temperature field need to be derived here first according to the thermal boundary conditions. Furthermore, numerical examples are also presented to discuss the effects of the variations of Young's modulus, thermal expansion coefficient, thermal conductivity and Poisson's ratio on the thermal stress concentrations. Finally, this work is concluded, and future works on the topic are proposed.