I need some simple and clear explanation of what is called linear buckling analysis and why it is also called eigenvalue buckling analysis?
In other words how natural vibration frequency or eigenfrequency refers to the static stability of mechanical system?
To be more specific I need some basic understanding of this subject because I'm currently studying a problem of topology (or structural) optimization of some mechanical construction using finite element analysis software. And as I know only linear buckling criteria can be used for topology optimization today. Correct me if I'm wrong.
Below is the most understandable illustration of this item I've found on the internet.
Here is the link. Though it explains the sense and purpose of described items, but actually gives no full and clear explanation of what is actually going on. So here I hope to get at least a good link.