User:Eml4500.f08.team.foskey.ckf/HW1c

 Example Problem 

Using the methods explained earlier, we will now look at an example problem, and solve it using the finite element method.

Data

Element Lengths

L(1) = 4

L(2) = 2

Young’s Moduli

E(1) = 3

E(2) = 5

Cross Sectional Areas

A(1) = 1

A(2) = 2

Inclination Angles

θ(1) = 30°

θ(2) = 45°

Solving The Problem

Using the previously explained methodology, we create a free body diagram for the Global Picture. The internal forces and displacements are labeled using the established conventions.

The variables are then placed into the force displacement relation equation. The global system has six degrees of freedom (displacements) and six internal forces. Thus the equation contains a (6x1) global force matrix, a (6x6) global stiffness matrix, and a (6x1) global displacement matrix.

Global Force-Displacement relationship