User:Eml4500.f08.qwiki.bishop/Lecture 5

 Read:  Chapter 4 Chapter 1: Big Picture
 * 1.1 Discritization (1.1.1 Plane truss elem)
 * 1.2 Assembly of elem. eqs. Ex. 1.4: Five-bar truss
 * 1.4 Elem Soln and model validity (1.4.1 Plane truss elem)

Steps to solve simple truss system described on 9/3

1. Global:  The displacement dofs are partitioned into: 1)a known part,e.g.(fixed dofs, constraints) 2)an unknown part: solve using FEA

The same for global forces: 1) known part 2) unknown part

2. Element picture: 
 * Element dofs
 * Element forces

3. Global FD relation: 
 * Element stiffness matrices in global coordinates
 * Element force matrices in global coordinates
 * Assembly of element stiffness matrix and element force matrix into global FD relation k nxn d nx1= F nx1

4. Elimination:  The elimination of known dofs to reduce the global FD rel. (stiffness matrix non-singular => invertible)

m = number of unknown displacement dofs

n = number of all displacement dofs
 * m < n

d = k-1 F

5. Compute Element Forces 

6. Compute Reactions 

 Example (HW2): 


 * L(1)=4    L(2)=2 (Length)
 * E(1)=3 E(2)=5 (Young's Modulus)
 * A(1)=1 A(2)=2 (Area)

1. Global Picture

 $$F$$ = $$Kd$$