Page 27 - Finite Element Modeling and Simulations with ANSYS Workbench

12 Finite Element Modeling and Simulation with ANSYS Workbench

d. The FE equation for spring (element) 2 is

 200 − 200       
f i
u i
 − 200    =  

u j
f j
 200       
Here i = 2, j = 3 for element 2. Thus we can calculate the spring force as
u   
2
 2
F = f j = − f i = − [ 200 200  ]  =−[ 200 200 ]   = 200 (N)
3
u 
 3    
Check the results:
Draw the free-body diagram (FBD) of the system and consider the equilib-
rium of the forces.

F = –200 N F = –300 N
4
1
P = 500 N
Equilibrium of the forces is satisfied!

EXAMPLE 1.2

4 k 4 F 1
k 1 1
2
4 1 k 2 F 2 k 3

x 2 3 3 5

Problem
For the spring system with arbitrarily numbered nodes and elements, as shown above,
find the global stiffness matrix.

Solution
First, we construct the following element connectivity table:

Element Node i (1) Node j (2)
1 4 2
2 2 3
3 3 5
4 2 1

This table specifies the global node numbers corresponding to the local node numbers
for each element.