Solutions of torsion crack problems of a rectangular bar by harmonic function continuation technique

A torsion problem of a rectangular bar with a crack perpendicular to the section contour is discussed (see Figs. 1–3). When solving the Dirichlet problem of the Laplace equation, we divide the original section into several rectangular regions, and using the Duhem theorem [1] (a theorem of continuation of harmonic function), the solution on original section can be found. The calculation of torsional rigidity is in a usual way. Using the compliance method, the K₃ is obtained. All numerical results are shown in Tables 1–6.