The exact moment for the plastic torsion of a cylindrical bar of elliptical cross section
An exact expression for the limiting moment of the torsion of an isotropic, perfectly plastic elliptical bar has not been previously derived. In this note, the solution of this classical problem is reduced in form to a single quadrature. It is shown by comparison that an approximation due to \textit{V. V. Sokolovsky} [Theory of plasticity (German) (1955; Zbl 0067.174)] is inaccurate for large aspect ratios of semiaxes. Through a transformation of coordinates, the exact solution is also applicable to the plastic torsion of an orthotropic circular cylinder with generators perpendicular to a principal axis. It follows that for highly orthotropic materials an approximate solution derived by \textit{R. Hill} [J. Mech. Phys. Solids 2, 87-91 (1954)] may also prove inaccurate.
isotropic, perfectly plastic elliptical bar
scientific article; zbMATH DE number 3945463