## 5. Assembly of system equation (cont'd)

The system boundary conditions now consist of prescribed values for
some of the \(w_i\). One way to handle these
constrained \(w_i\) is to remove them from the vector
of unknowns – with appropriate node numbering,
\(\mathbf w\) can be partitioned into two parts, the
unknown displacements \(\mathbf w _1\) and the
prescribed values \(\mathbf w _2\). Partitioning
\(\mathbf S\) and \(\mathbf f\) correspondingly, we obtain

$\left(\begin{array}{cc}{\text{S}}_{11}& {\text{S}}_{12}\\ {\text{S}}_{21}& {\text{S}}_{22}\end{array}\right)\left(\begin{array}{c}{\text{w}}_{1}\\ {\text{w}}_{2}\end{array}\right)=\left(\begin{array}{c}{\text{f}}_{1}\\ {\text{f}}_{2}\end{array}\right)\phantom{\rule[-0.5ex]{1ex}{0.5ex}}.$
| (Eqn. 13) |

This then gives
${\text{S}}_{11}{\text{w}}_{1}={\text{f}}_{1}-{\text{S}}_{12}{\text{w}}_{2}\text{.}$
| (Eqn. 14) |

The system to be solved is now smaller.

R. Funnell
Last modified: 2018-11-07 12:52:06
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