Matrix representation

Element system matrix

The element system matrix collects individual system matrices as a multi-dimensional array of shape \(\left[ n_\text{elements} \times n_\text{nodes-per-element} n_\text{dim} \times n_\text{nodes-per-element} n_\text{dim} \right]\). An element system matrix

Ke = K[e,:,:]

obeys the following convention:

\[\underline{f} = \underline{\underline{K}} \underline{u}\]

where

\[f_{(n + i d)} \equiv f_i^{(n)}\]

with \(n\) the node number, \(i\) the dimension, and \(d\) the number of dimensions. For example for a two-dimensional quadrilateral element

\[\underline{f} = \big[ f_x^{(0)}, f_y^{(0)}, f_x^{(1)}, f_y^{(1)}, f_x^{(2)}, f_y^{(2)}, f_x^{(3)}, f_y^{(3)} \big]^T\]