If a member is very slender then its length will be large compared to its cross-sectional area. I've heard and read that slender members can potentially cause the stiffness matrix of a beam/frame element to become ill-conditioned in FEM.
Question: How/why can a slender member cause the stiffness matrix to become ill-conditioned?
Here are my own thoughts regarding this question, which may or may not be correct - I'd like some confirmation. A long slender member will have larger axial stiffness than flexural stiffness. In the stiffness matrix, the axial stiffness term has the length of the member ($L$) in the denominator. However, the flexural stiffness terms typically have $L^2$ and $L^3$ in their denominators. Therefore, given constant cross-sectional properties ($A$ and $I$), as $L$ grows the flexural stiffness terms approach zero much quicker than axial stiffness. Is this the reason for the potential for ill-conditioning? Or is there something I'm missing?