Сравнительный анализ приближенного аналитического и конечно-элементного решений для несоосной трубы

Abstract

The boundary value problem of steady-state creep for thick-walled misaligned tube under internal pressure was considered. The approximate analytical solution of this problem by method of small parameter including the second approach is under construction. The solution for the state of plane deformation is constructed. The hypothesis of incompressibility of material for creep strain is used. As a small parameter the misalignment of the centers of the inner and outer radii of the tube is used. The main attention to the convergence of the resulting analytical solution considering the second approximation and assessment of its error is paid. It is noted that the convergence problem is solved only for boundary value problems in the theory of elasticity. Therefore the error assessment in the problem is solved on the basis of a comparison of the approximate analytical solution with the numerical solution constructed on the finite element method, for some special cases. Considering the symmetry of the problem, the finite element model was built for the half tube. The number of finite elements is about 18,000. Considering the symmetry of the problem the second half of the tube is replaced by boundary conditions. Analysis of analytical and numerical solutions is executed depending on the steady-state creep nonlinearity parameter and misaligned parameter that is ratio of the misalignment of the centers of the outer and inner diameter to the outer radius. It is shown that the error of deviation of the approximate analytical solution in the second approximation from numerical solution until the misalignment value of the centers of the inner and outer diameters of 0.1 for the tubes with small exponent of the steady-state creep (3 to 8) is not more than 9 %, and error to 8 % for the tubes with a large exponent of the steady-state creep nonlinearity is observed in the misaligned parameter to 0.06. Results of computations are presented in tabular form and in the form of graphs. Recommendations for the use of the constructed approximate analytical solution in applied problems are given.