User:Eml4500.f08.RAMROD.F/HW1

Chris Fontana's Part
= Notes Summary for Friday, September 5 =

Intro
We discussed the ordered steps to slove a the truss problem from Septmeber 3. We discussed a generalized format to begin with the diagram of a model system and to work our way down to computing reaction forces.

Step 1: Global Picture
The global picture is the overall structural picture of the system. The picture includes the following:
 * 1) Global Forces
 * 2) Global Degrees of Freedom (aka DOF)

The displacement definition are partioned into:
 * 1) Known part, eq., fixed DOF, constraints
 * 2) Unknown part solved by using Finite Elemental Analysis (see the truss example above)

Similarly, the global forces are partioned into:
 * 1) Known part: Applied forces
 * 2) Unknown part: Reactions

Step 2: Element Picture

 * 1) Element definitions
 * 2) Element forces

These can be found in either global coordinate systems or in local coordinate systems

Step 3: Global Force Diagram relationship

 * 1) Element stiffness matrices in global coordinates
 * 2) Element force matrices in global coordinates
 * 3) assembly of element stiffness matrix and element force matrix into global force displacement relation.

K · d = F

(NxN) (Nx1) = (Nx1)

Step 4: Elimination of DOF
Eliminate degrees of known degrees of freedom to reduce the golbal force displacement relationship. (The Stiffness Matrix is non-singular-invertible)
 * 1) M = the number of unkwown DOF
 * 2) N = the number of both known and unknown DOF

K · d = F

(MxN) (Mx1) = (Mx1)                       M>N

Stiffness Matrix K nonsingular => k-1 exists (K is invertible)

K-1 · d = F

Step 5: Compute Element Forces
Compute element forces from known displacements => element stresses

Step 6: Compute Reactions
Compute reaction forces or the unknown forces.