Determination of the Three-Dimensional Stress-Strain State of a Thick-Walled Two-Layer Cylinder

摘要

As a result of the separation of the angular variable, the investigation of the three-dimensional stress-strain state of a finite two-layer thick-walled cylinder is reduced to the solution of one-dimensional boundary-value problems. The components of the vector of displacements and the stress tensor are represented in the form of series specified by the constructed eigenfunctions. A method for the analytic-numerical solution of the boundary-value problems for two-layer cylinders is developed. The numerical criteria for the convergence of the method are theoretically established for the first time. It is shown that the accuracy with which the boundary conditions are satisfied is determined by a single number, namely, by the minimum of the quadratic form.