3. A simple element analysis (cont'd)
This equation is the one that would have to be solved if the
element were alone. If it is part of a larger system, however, the
equation must be transformed so that it can be combined with similar
equations representing other elements. We do this by expressing it in
terms of the nodal displacements \(w_i\) rather than
the \(c_i\), by using equation 7
(\( \mathbf w = \mathbf X \mathbf c \))
.
The algebraic
equations describing the behaviour of the element now become
\(\mathbf A \mathbf X^{1} \mathbf w = \mathbf B \mathbf g\)

 (Eqn. 9) 
or, changing notation,
\(\mathbf S \mathbf w = \mathbf f\).

 (Eqn. 10) 
R. Funnell
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