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