University of Florida/Eml4500/f08.qwiki/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 knxndnx1=Fnx1

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-1F

5. Compute Element Forces

6. Compute Reactions

Example:

Truss notation 6 problem.JPG

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