Page 48 - Finite Element Modeling and Simulations with ANSYS Workbench

Bars and Trusses 33

 2 − 2 0  u 1   F 1 

EA  − 2 3 − 1  u 2 =  

 
F 2
L   − 1       
 0 1  u 3   F 3 
Load and boundary conditions (BCs) are
u 1 = u 3 = 0, F 2 = P

FE equation becomes

 2 − 2 0  0   F 1 
EA  − 2 3 −    
P

L   1  u 2 =  

 

 0 − 1 1   0   F 3 
“Deleting” the first row and column, and the third row and column, we obtain
EA 3 []{} P
u 2 = {}
L
Thus,

PL
u 2 =
3 EA

and

 u 1   0
  PL  
 u 2 =  1 
  3 EA  
0
 u 3   
Stress in element 1 is

 1 u 
σ= E ε= EBu = E  −  1 L 1 L   
/
/

1
1
11
 2 u  
2 u − u 1 E  PL  P
= E =  − 0 =

 
L L  3EA 3 A
Similarly, stress in element 2 is
 2 u 
σ= ε= EBu 2 = E  −  1 L 1 L   
E
/
/

2
2
2
 3 u  
3 u − u 2 E  PL  P
= E =  0 −  =−
L L  3EA  3 A
which indicates that bar 2 is in compression.