User:Eml4500.f08.delta 6.castrillon/HW 4

= Connectivity & Location Matrix Master Arrays =

Consider the two-bar truss below:



and its respective bar element:



We can notice that there is a common global node, and its corresponding dofs, when comparing both bar element diagrams. Since the FEA method can be applied to a large system with multiple common nodes an elements, then it is important to organize these element notations so as to visualize which elements share which nodes and bounded by which dofs.

The Connectivity Array, "conn"
This array is set up as follows:


 * $$\begin{matrix}

1 & 2 \end{matrix}$$   <-- Local node numbers


 * conn = $$\left.\ \begin{vmatrix}

1 & 2\\ 2 & 3 \end{vmatrix} \right\}$$ <-- Global node numbers, each row for each element

In short-hand notation, we say that conn = (e,j): global node number of local node j of element e.

The Location Matrix Master Array, "lmm"
This array is set up as follows:


 * $$\begin{matrix}

1 & 2 & 3 & 4 \end{matrix}$$   <-- Local dofs numbers


 * lmm = $$\left.\ \begin{vmatrix}

1 & 2 & 3 & 4\\ 3 & 4 & 5 & 6 \end{vmatrix} \right\}$$ <-- Global dofs numbers, each row for each element

In short-hand notation, we say that lmm = (i,j): equation number (global dof number) for the element stiffness coefficient corresponding to the jth local dof number.