Symmetric thermoelastic stress in cylinders by the Lanczos-Chebyshev method

The Lanczos-Chebyshev method is used to reduce the linear heat conduction equation to a set of ordinary differential equations. The eigenvalues and eigenvectors defining the axial decay of temperature components in a solid cylinder are obtained. The thermal stresses are found by applying the same reduction technique to the linear displacement equations, considering thermal and self-equilibrating stress fields separately. Numerical examples are used to illustrate the speed and accuracy of the method in comparison with semi-analytical Bessel function type solutions and to show the end effects in cylinders. (orig.)