Summary of results
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The analytical solution gives us 3 buckling modes whose critical loads are roots of a 3rd degree equation.

Are there other critical loads interspersed between the 3 values found?

*Aster* finds the right critical loads, but in the middle of many others... for example for case 3, the 3 critical loads sought correspond to NUME_MODE: 1, 10 and 19.

This is true for both models.