As we said the scale factor as you use it will generate a deformed imperfect geometry, so it really changes your geometry in system G (it is a deformed geometry) so if you have a half sine as buckling mode for a simple beam, then your geometry will be depending the scale factor like a half sine shape beam - try that and you will see in your static system (G) that the geometry follows the shape of your buckling mode, which is the first one in your screenshot. The higher the scale factor the more deformed the geometry will be. The user as we say needs to define how much we deform and make an imperfect geometry.
I will leave that with you. All the best.
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