User:EML4500.F08.RAMROD.B/Homework 4

=Connectivity Array "conn"=

The following array is the array that should be used in Matlab to represent the global node numbers corresponding to each element of the truss system. The rows of this array represent the element number and the columns represent the local node number.

$$\displaystyle conn = \begin{bmatrix} 1 & 2\\ 2 & 3 \end{bmatrix}$$

Row one of this array corresponds to element one while row two corresponds to element two. Column one represents local node one and column two represents local node two. So to interpret this array we will do an example. Lets say we want to find the global node number for local node one of element one. Since the columns represent the local node number we go to column one and since the rows represent the element number we go to row one. In spot $$\displaystyle (1,1)$$ of the conn array it can be determined that the global node number of element one, local node one is simply one. In general;

$$\displaystyle conn(e,j) = $$ global node number of local node j of element

=Location Matrix Master Array "Lmm"=

The following array is similar to that of the array above with a minor difference. It is used to determine the global degrees of freedom when the local degrees of freedom and element number are known. The rows represent the element number and instead of representing the local node number, the columns represent the local degrees of freedom. Since the problem being analyzed is a two truss problem, each element has four degrees of freedom so the array has four columns and two rows representing each element.

$$\displaystyle Lmm = \begin{bmatrix} 1 & 2 &3 &4 \\  3& 4 & 5 & 6 \end{bmatrix}$$

To interpret this array we will do an example. Lets say we want to find the global degree of freedom of element two at local degree of freedom three. With this information we go to row two (element two) and column three (local degree of freedom). At this location we find the global degree of freedom corresponding to element two, local degree of freedom three. In general;

$$\displaystyle Lmm(e,j)=$$ the global degree of freedom number for element $$\displaystyle e$$ corresponding to the $$\displaystyle j^{th}$$ local degree of freedom