User:Eml4500.f08.ateam.mcnally/Week 2

Friday September 5, 2008
Assigned reading from Fundamental Finite Element Analysis And Appllications: With Mathematica and MATLAB Computations by M. Asghar Bhatti.
 * Chapter 1: Big Picture
 * Section 1.1 Discretization and Element Equations
 * 1.1.1 Plane truss element
 * 1.2 Assembly of Element Equations. See Example 1.4: Five bar truss
 * 1.4 Element Solutions and Model Validity
 * 1.4.1 Plane truss element

This lecture given by Professor Vu-Quoc was a “recipe” for the steps to solve a simple truss system. The steps for solving a simple truss system are as follows:

Step 1: The Global Picture at the Structure Level:
 * Identify the Global Degrees of Freedom (dof). “The displacement dofs”
 * The displacement dofs are divided into a know part which is the fixed dof constraint, and unknown part which is solved for using the Finite Element Method.


 * Identify the Global Forces
 * Similar the Global dofs the Global Forces are also divided into two parts. The know parts are the applied forces, and the unknown are the reaction forces.

Step 2: The Element Picture
 * Break the truss down into individual elements and identify element dofs, and element forces. When identifying the element dofs and forces you may either use the global or a local element coordinate system to make computation easier.

Step 3: The Global Force Displacement Relation
 * Define the element stiffness matrix K in the global coordinate system
 * Define The element force matrix F in the global coordinate system
 * The final step is the assembly of the element stiffness matrix and element force matrix into the global force displacement relation. The global force displacement relation is given by the equation: Kd=F where K is a(nxn) matrix, d is a (nx1) matrix, and F is a (nx1) matrix.It is assumed that the stiffness matrix is non-singular and invertible.

Step 4: Elimination of the known dofs to reduce the global Force Displacement Relation Step 5: Compute the element Forces from the now known ‘’’d’’’ element stresses
 * Because the stiffness matrix K is non-singular and invertible the number of unknown displacement dofs are less than the number of know displacement dofs.
 * The equation above in Step 3 is then solved for d by inverting K and multiplying by F resulting in d=K(inverse)F

Step 6: Compute the unknown reaction Forces from the now known element forces and element stresses

For further explanation please see the example on A team group member Pedro Rivero under the heading weekly notes summary.