I just started studying FEM in a more structured basis compared to what I used to do during my undergraduate courses. I am doing this because, despite the fact that I can use the "FEM" in commercial (and other non-commercial) software, I would like to really understand the underground techniques that support the method. That's why I am coming here with such, at least for the experienced user of the technique, basic question.
Now I'm reading a quite popular (I think) and "engineer-friendly" book called "Finite element method- The basics" from Zienkwicz. I've been reading this book from the first page but I yet can't understand the concept of shape function in the way Zienkwicz explains it.
What I know about from the things that I'd read is that a "Stiffness" matrix, the one that relates the unknowns with the result ($A$ in: $Ak=b$), has its components from the "relationships between the nodes", and if that "relationship" changes, (i.e. if we change it to a Higher order interpolant), that stiffness matrix changes, because the relationship between the nodes does.
But in this book, the definition is quite fuzzy for me, because in some point it says that you can arbitrarily chose the function as, i.e., the identity matrix:
The only explanation I found is in this blog , but it is still not so clear for me. So, somebody can give me a simple plain explanation of what is a Shape functon and how it is done to "put it" in the stifness matrix?