Thermal stresses around a circular hole in a functionally graded plate

An exact thermal stress solution if provided for a functionally graded plate that has a circular hole, with the material properties and applied temperature varying arbitrarily in the radial direction. Building on an existing solution for homogeneous materials, an exact formulation for the functionally graded plate is established by generalizing the material constants and the two integration constants as variables and unknown functions of r, the radial coordinate. By solving a pair of first-order ordinary differential equations, the exact series expressions for the two unknown functions are presented. Numerical results are furnished to demonstrate the numerical effectiveness and application potential of the formulation and the solution. Further extension is established to present an exact thermal stress solution for a composite, piecewise functionally graded plate with a circular hole.