5. Assembly of system equation (cont'd)

Suppose that a system to be studied consists of two triangular elements interconnected as shown in the Figure. Suppose that substituting the vertex coördinates and material properties into the formulæ obtained from the mechanical analysis gives components \(a_{ij}\) for the element stiffness matrix for the first element, and \(b_{ij}\) for the second element. Then equation 10 yields

$\left(\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right)\left(\begin{array}{c}{w}_1\\ w_2\\ w_3\end{array}\right)=\left(\begin{array}{c}{f}_1\\ f_2\\ f_3\end{array}\right)$ and $\left(\begin{array}{ccc}{b}_{11}& b_{12}& b_{13}\\ b_{21}& b_{22}& b_{23}\\ b_{31}& b_{32}& b_{33}\end{array}\right)\left(\begin{array}{c}{w}_2\\ w_3\\ w_4\end{array}\right)=\left(\begin{array}{c}{g}_2\\ g_3\\ g_4\end{array}\right)\text{.}$

(Eqn. 11)

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