Okay this was even quite difficult to formulate but let's start with some statement's in my FEM book:
- Elastic continuum has a functional which is equal to it's total potential energy
- Elastic system is in balance when the stationary value of it's functional equals the minimum of potential energy
I understand nothing about it but I will try to form some more exact questions:
a) Is there any physical interpretation of a functional? All I can find is that a functional it's an integral of a function and the arguments of that function are also functions. But that doesn't tell me how it is derived and what is it's meaning
b) Connected with a), why is this functional equal to total potential energy in elastic systems?
c) Why is the elastic system in balance when the stationary value of the functional is equal to the minimum of potential energy? Why not maximum or any other state?