User:Eml4500.f08.ateam.rivero/w2

=Homework Report 2: Pedro Rivero's Contribution=

Meeting 9:

Continuation of Step 3
Figure #: Global Stiffness Matrix

In the image below, figure.....#..... are example calculations when solving for the global stiffness matrix. One can see how both element stiffness matrices come together to form the global stiffness matrix, figure....#.....



Figure #: Example Calculations for Values of Global Stiffness Matrix

Once all the values have been computed as shown above for all the values of the global stiffness matrix, figure....#.... The following matrix below will be the result of combining element stiffness matrix 1 and element stiffness matrix 2.



Figure #: Values of Global Stiffness Matrix

Step 4: Elimination of known degrees of freedom (dofs)
In this step one will apply known degrees of freedom. This will allow us to reduce the global force displacement relation. For example in the problem being described it is known that global node 1 and global node 3 are both fixed. A fixed constraint is the equivalent of stating that displacements 1, 2, 5, 6 are all equal to 0. Knowing this information allows us to reduce the 6x1 global displacement column matrix to a 2x1. Which then allows one to reduce the global stiffness matrix from a 6x6 to a 6x2, as it is shown in figure .....#......

Apply Boundary Conditions:
 * Global Node 1: Fixed
 * Results in:
 * d1=0
 * d2=0
 * Global Node 3: Fixed
 * Results in:
 * d5=0
 * d6=0