Geometric nonlinearity

Hi

I worked on Geometrically Nonlinear (GN) structures for a couple of years and I had the same question in my mind. At the beginning I would think it is only the amount of displacement/rotation which defines whether it is a GN case i.e. if it is small it is a linear case and if it is not, it is a GN case. Howeve, GN cases are not limitted to large displacement/rotations. A cantilever beam with an end force can be assumed liner, if for example the end displacement is up to 1/10 of its length. I mean you can get a good approximation by linear analysis up to that range of displacement. But a shallow simply-supported arch with the same length under vertical downward load at its top point is highly nonlinear even when the displacements are still small, befor going to snap-through and change of its shape. Another example is buckling of shells which happen with small initial displacements but under a very nonlinear behavior. Long story short, I beleive it needs a lot of experiment to be able to judge the case by just looking at it. However if the case is somehow related to buckling and bifurcation analysis, it is most probabely a GN case because bucklings (and snap-throughs) happen in small displacements and deal with membrane or axial loads.

You can look at the structure and guess if the deformation is mostly driven by bending or an axial loads. if it is by axial loads it is mostly a GN case and if it is bending, it is GN when deformations are large. of course the best way is to do GN analysis and compare with linear analysis and if there is a big difference it is GN :)    

GEBT is suitable for both geometry linear and geometrical nonlinear analysis. It implements a geometrically exact theory and versatile enough to handle any slender structures made of arbitrary material with arbitrary cross-sectional geometry. Of course, VABS needs to be used first to reduce the original 3D model into a 1D beam model.