Method of homogeneous solutions in the mixed problem for a finite circular cylinder: PMM vol. 43, no. 6, 1979, pp. 1073–1081

Abstract

The mixed axisymmetric problem of elasticity theory on the torsion of a finite circular cylinder by a stamp is considered. The stamp is fixed rigidly to one plane face of the cylinder, the other plane face is fixed, and conditions for no displacements or stresses are given on the cylinder surface. The problem is investigated by the method of homogeneous solutions [1], which permits obtaining its approximate solution for practically any values of the parameters. Such efficiency of the method is determined by the fact that the solution of the problem reduces to investigating an infinite algebraic system of the Poincaré — Koch normal systems type. When the ratio of the cylinder height to the radius of the stamp is sufficiently large, the system coefficients, the contact stresses, and the other characteristics of the problem are evaluated to any degree of accuracy, and effective asymptotic expressions are obtained for small values of this ratio. Results of numerical computations are presented. A solution of the problem for the case of a large value of the ratio ( R − a) / h and small values of the ratio λ = h / a is obtained in [2].