User:Eml4500.f08.team.foskey.ckf/HW4a

The Connectivity Array
In solving a finite element analysis problem, it is beneficial to have a connectivity array, "conn", to create a correlation between the local and global nodes. If the two bar truss system is considered, the connectivity array is:

$$ conn =  \begin{bmatrix}

1 & 2 \\ 2 & 3\\ \end{bmatrix} $$

Where the columns 1 and 2 represent the local node numbers (1 and 2 respectively), the first row represents element 1, the second row represents element 2, and the contents of the matrix are the global node numbers.

The elements of the connectivity array can be given in the following format:

conn(e, j) = global node number of the local node j of element e

The Location Matrix Master Array
A location matrix master array, "lmm", is used to make a relationship between the local degrees of freedom in the elements and the global degrees of freedoms. For the two bar truss example, this array is given as :

$$ lmm = \begin{bmatrix}

1 & 2& 3 & 4 \\ 3 & 4& 5 & 6 \\

\end{bmatrix} $$

Where the columns 1 to 4 are the local degrees of freedom 1 to 4 respectively, the first row corresponds to element 1, and the second row corresponds to element 2. Each component of the array corresponds to a global degree of freedom (or equation number) in K.

The elements of the location matrix master array can be given in the format:

lmm(i, j) = equation number of j (global degree of freedom) for the element stiffness coefficient corresponding to the ith local degree of freedom.

Transforming the System
Referring back to method 2 of deriving k(e)4x4, the goal of using the connectivity and location matrix master arrays would be to transform a system with four degrees of freedom into a system that also has four degrees of freedom (instead of only two) so that the transformation matrix is now a 4x4 matrix that is hopefully invertible.