Page 49 - Finite Element Modeling and Simulations with ANSYS Workbench

34 Finite Element Modeling and Simulation with ANSYS Workbench

Check the results: Draw the FBD as follows and check the equilibrium of the
structures.

–2P/3 P –P/3

Notes:
• In this case, the calculated stresses in elements 1 and 2 are exact. It will not
help if we further divide element 1 or 2 into smaller elements.
• For tapered bars, averaged values of the cross-sectional areas should be used
for the elements.
• We need to find the displacements first in order to find the stresses, and this
approach is called the displacement-based FEM.

EXAMPLE 2.2

A, E
1 2
1 2 P 3 x

L L

Problem
Determine the support reaction forces at the two ends of the bar shown above, given
the following:

4
4
.
.
P = 60 × 10 N , E = 20 × 10 N/mm 2 ,
A = 250 mm 2 , L = 150 mm, ∆ = 1.2 mm

Solution
We first check to see if contact of the bar with the wall on the right will occur or not. To
do this, we imagine the wall on the right is removed and calculate the displacement at
the right end

4
60 ×
PL (. 10 )( 150)
∆ 0 = = 4 = 18 . mm > ∆ = . mm
12
20 ×
EA (. 10 )( 250)
Thus, contact occurs and the wall on the right should be accounted for in the analysis.
The global FE equation is found to be
 1 − 1 0  u 1   F 1 
 


EA  − 1 2 − 1  u 2 =  
F 2
L        
 0 − 1 1   u 3   F 3 