2. Benchmark solution#

2.1. Calculation method used for the reference solution#

Analytical solution:

In short trips:

in elastic regime (for \(F<{\sigma }_{Y}\)) the theoretical critical value corresponds to the Euler load. In the context of beam kinematics, the critical load is equal to:

, so the critical pressure:

with

and

either

under elastoplastic conditions, as uniform compression without elastic discharge is considered and due to the law of behavior, the critical buckling load is equal to:

or a critical pressure of:

Critical load values for both load cases.

In elastic mode, for \(F<4\mathrm{MPa}\), which is \(t<0.61538462\), we have to get: \({P}_{\mathrm{cr}}=12.95\mathrm{MPa}\).

Under plastic conditions the critical buckling pressure value is: \(\mathrm{4,32}\mathrm{MPa}\).

The critical coefficients as a function of loading are: