Page 47 - Finite Element Modeling and Simulations with ANSYS Workbench

32 Finite Element Modeling and Simulation with ANSYS Workbench

That is,

 
u i
 
E  
v i
σ =  −  l −m l m    (2.35)

L  
u j
 
v j
 
which is a general formula for 2-D bar elements.

2.5 Examples with Bar Elements
We now look at examples of using the bar element in the analysis of 1-D stress problems
and plane truss problems.

EXAMPLE 2.1
2A, E A, E

1 2
P x
1 2 3
L L

Problem
Find the stresses in the two-bar assembly which is loaded with force P, and constrained
at the two ends, as shown in the above figure.

Solution
Use two 1-D bar elements.
For element 1,

u 1 u 2

2 EA 1 − 1
1 k =  − 
L  1 1 

For element 2,

u 2 u 3

EA 1 − 1
2 k =  − 
L  1 1 

Imagine a frictionless pin at node 2, which connects the two elements. We can assem-
ble the global FE equation as follows: