2. Benchmark solution#

2.1. Calculation method used for the reference solution#

The critical pressure is given in [bib1] or [bib2] by the following expression:

\({P}_{\mathit{cr}}\mathrm{=}\frac{\mathit{Eh}}{R}\frac{1}{({n}^{2}+\frac{{b}^{2}}{2})}\left[\frac{1}{{(\frac{{n}^{2}}{{b}^{2}}+1)}^{2}}+\frac{{h}^{2}}{12{R}^{2}(1\mathrm{-}{\nu }^{2})}{({n}^{2}+{b}^{2})}^{2}\right]\)

with

\(b\mathrm{=}\frac{\pi R}{L}\)

\(n\) represents the number of circumferential modes

This formula is valid in the case where \(N\mathrm{=}0.5R{p}_{\mathit{cr}}\).

2.2. Benchmark results#

_images/Object_6.svg

2.3. Uncertainties about the solution#

Analytical solution

2.4. Bibliographical references#

  1. S.P. TIMOSHENKO, J.M. GERE: Elastic Stability Theory, page 500, second edition, DUNOD 1966.

  2. BO O. ALMROTH, D.O. BRUSH: Buckling of bars, plates and shells, page 173, Mc Graw-Hill, New York, 1975.