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:

(2.1)#\[ {P} _ {\ mathrm {CR}}} =\ frac {E} {12. (1- {\nu} ^ {2})}\ mathrm {.} {n} ^ {2}\ mathrm {.} {(\ frac {e} {R})}} ^ {3}\]

with \(n\) the mode number (here \(n=\mathrm{2,4}\mathrm{,6}\))

2.2. Benchmark results#

The critical pressures (in \(\mathrm{Pa}\)) are:

Mode (n)

Reference

2

73260

4

293040

6

659340

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.