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This paper provides two parallel solutions on the mixed boundary valueproblem of a unit annulus subjected to a partially fixed outer periphery and anarbitrary traction acting along the inner periphery using the complex variablemethod. The analytic continuation is applied to turn the mixed boundary valueproblem into a Riemann-Hilbert problem across the free segment along the outerperiphery. Two parallel interpreting methods of the unused traction anddisplacement boundary condition along the outer periphery together with thetraction boundary condition along the inner periphery respectively form twoparallel complex linear constraint sets, which are then iteratively solved viaa successive approximation method to reach the same stable stress anddisplacement solutions with the Lanczos filtering technique. Finally, fourtypical numerical cases coded by \texttt{FORTRAN} are carried out and comparedto the same cases performed on \texttt{ABAQUS}. The results indicate that thesetwo parallel solutions are both accurate, stable, robust, and fast, andvalidate that these two parallel solutions are numerically equivalent.

Parallel generalized solutions of mixed boundary value problem on partially fixed unit annulus subjected to arbitrary traction