Question

How to solve the problem of hollow circular cylinder with torsion?

Answer 1

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The problem considered is the torsion of a hollow circular cylinder which is weakened by a symmetric array of radial cracks. It is equivalent to a mixed boundary-value problem for a harmonic function in an annular sector. Separation of variables yields dual- or triple-series equations which are solved exactly. Closed-form expressions are then obtained for the torsional-rigidity and the stress-intensity factors. Some of the results are presented in graphical form.