Torsion of a Saint-Venant Cylinder with a Non-Simply Connected Cross-Section

The Finite Element Method solution to the torsion problem of a linearly elastic, homogeneous, isotropic cylinder with a non-simply connected cross-section of variable wall thickness is presented. The computed displacement, warping, stress, strain and Mises invariant are shown for several shapes of the cross-section: a rectangle, a rectangle with a crossbar, and rings with sinusoidal boundaries of various amplitudes and periods. The computed results enable us to analyze the shape sensitivity to warping under torsion in thick-walled cylinders with complicated cross-sectional shapes.