I am used to interpreting each entry of a stiffness matrix as a 1D (linear or angular) spring joining one DOF (column index) to another (row index). But this interpretation leaves something to be explained:

1. What do diagonal, i.e., DOF-to self entries mean? I mean, a spring connectiong a node to itself makes no physical sense right?
2. What do diagonal SUBMATRICES (relative to a node's DOFs) mean? Those relate each DOF of a node to the other DOFs of the same node, but again, I can't see a physical explanation to that (e.g., why should x-translation of a node influence its z-rotation?)