STRESS-ANALYSIS FOR END EFFECTS IN CYLINDRICAL RODS BY THE LANCZOS-CHEBYSHEV METHOD

The Lanczos-Chebyshev method is used to reduce the two-dimensional displacement equilibrium equations in cylindrical co-ordinates, to a set of coupled ordinary differential equations. The eigenvalues and eigenvectors defining the axial decay of self-equilibrating stress systems in a solid cylinder are obtained, and used to solve a particular problem of specified self-equilibrating end stresses applied to a semi-infinite cylinder, for which an accurate reference solution is known. The method is compared with a Galerkin and a finite element method of achieving the same result, and is shown to have definite advantages in simplicity, speed and accuracy, over the two approximation methods. © 1979.