On numerical equivalence of parallel generalized solutions of mixed boundary value problem of annulus

Abstract

This paper provides two parallel generalized solutions on a fundamental mixed boundary value problem that a unit annulus is subjected to a partially fixed outer periphery and an arbitrary traction acting along the inner periphery by using the complex variable method. The mixed problem is transformed into two parallel Riemann-Hilbert problems with respective sets of different mathematically rigorous boundary conditions, which are solved by successive approximation method with the Lanczos filtering technique to obtain numerically equivalent stress and displacement results. Four typical numerical cases coded by FORTRAN are carried out and compared to the same cases performed on ABAQUS to validate these two parallel solutions. Based on the case results, the detailed reasons of numerically equivalence between these two parallel solutions are analytically elaborated and several insights of the application of the complex variable method are revealed.