Torsion of cylindrically orthotropic elastic circular bars with radial inhomogeneity: some exact solutions and end effects. (English) Zbl 1167.74476
Summary: Torsion of elastic circular bars of radially inhomogeneous, cylindrically orthotropic materials is studied with emphasis on the end effects. To examine the conjecture of Saint-Venant’s torsion, we consider torsion of circular bars with one end fixed and the other end free on which tractions that results in a pure torque are prescribed arbitrarily over the free end surface. Exact solutions that satisfy the prescribed boundary conditions point by point over the entire boundary surfaces are derived in a unified manner for cylindrically orthotropic bars with or without radial inhomogeneity and for their counterparts of Saint-Venant’s torsion. Stress diffusion due to the end effect is examined in the light of the exact solutions.
MSC:
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74E05 | Inhomogeneity in solid mechanics |
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