I was reading the following article about the direct stiffness method. When it comes to solving the system of equations:
The site states:
[...]There are several different methods available for evaluating a matrix equation including but not limited to Cholesky decomposition and the brute force evaluation of systems of equations[...]
After doing some research, I figured out that the most common way is the Cholesky Decomposition. The problem that I have is that we are not solving for $u$ in the equation $f=Ku$ but for $f$ and $k$. In the Image, it’s clear that for if we do not know the value of $f_i$, we know the value of $u_I$ instead.
I am not sure how to solve this for both, the unknown values in $u$ and $f$ at the same time. I am very happy for any advice