On the optimal design of viscoplastic bars under combined torsion with bending

The governing equation for viscoplastic simultaneous torsion and bending of a prismatic bar is derived. Then a certain particular closed-form solution of this equation is found; it corresponds to an elliptic cross-section with the ratio of semi-axes depending on the bending-to-torsion ratio. This solution proves to be optimal if the optimization constraint is imposed on initiation (nucleation) and growth of material damage and if the material properties conform to the Huber-Mises-Hencky failure hypothesis.