2. Benchmark solution#

2.1. Calculation method used for the reference solution#

At a point with the x coordinate:

  1. radial displacement: \({U}_{r}=-\frac{\gamma R\nu x}{E}\)

  2. axial displacement: \({U}_{x}=\frac{\gamma {x}^{2}}{2E}\)

  3. generator rotation: \(\psi =-\frac{\gamma R\nu }{E}\)

  4. axial stress: \({\sigma }_{11}=\gamma x\)

  5. Circumferential stress: \({\sigma }_{22}=0\)

2.2. Benchmark results#

  1. High end axial displacement: \({U}_{x}=2.99\times {10}^{-6}m\)

  2. Radial displacement at low end: \({U}_{r}=–4.49\times {10}^{-7}m\)

  3. \(\psi =–1.12\times {10}^{-7}\mathrm{rad}\)

  4. \({\sigma }_{11}=3.14\times {10}^{5}\mathrm{Pa}\), at the low end

  5. \({\sigma }_{22}=0\) everywhere

2.3. Uncertainty about the solution#

Analytical solution.

2.4. Bibliographical reference#

  • Guide VPCS — 1990 edition (SSLS 09/89)

  • R.J. ROARK and W.C. YOUNG: Formulas for stress and strain, 5th edition, New York, McGraw-Hill, 1975