## 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