Thermal stresses in a cylinder: Application to optical waveguide blanks

An analysis is presented for the calculation of thermal stresses in a hollow cylinder with free ends, in which the elastic and thermal properties are all functions of radius, r. When Young's modulus and Poisson's ratio vary with r, the solution is obtained by the method of successive approximations, but the first approximation is sufficiently accurate for most purposes. For the particular case of optical waveguide blanks, it is shown that the variation in set point with radius can have a significant effect on the calculated stresses. When variations in all properties are considered, the calculated axial stress is in good agreement with a measured value.