User:Eml4500.f08.delta 6.lopez/HW4

=Justification of assembly of elemental stiffness matrix into global stiffness matrix= Consider the example of the 2-bar truss system discussed earlier. If we recall the elemental Force-Discplacement relationship:

$$ k^{(e)}d^{(e)} = f^{(e)} $$

The equilibrium of node 2 can be found using three methods we have discussed earlier this semester. 1. The Euler Cut Principle 2. The Free Body Diagrams of each element 3. The Identity of Global D.O.F.'s to Element D.O.F.'s

At node 2, the elquilibrium can be found by simple summing the forces in each direction.



$$ \sum{F_{x}} = 0 = -f_{3}^{(1)} - f_{1}^{(2)} = 0 $$ $$ \sum{F_{y}} = 0 = P -f_{4}^{(1)} - f_{2}^{(2)} = 0 $$

=Homework: Plot the eigenvectors corresponding to the zero eigenvalues, and interpret the results=

Using MATLAB, the output of the Global Stiffness Matrix is:

The V and D matrices below correspond to the eigenvectors and eignevalues, respectively.

As can be seen by the D matrix, the first four columns of the V matrix correspond to the eigenvectors of the zero eigenvalues.

Columns 1 & 2

Columns 3 & 4