Page 25 - Finite Element Modeling and Simulations with ANSYS Workbench

10 Finite Element Modeling and Simulation with ANSYS Workbench

1.2.4 Solution Verification
It is very important in FEA to verify the results you obtained through either hand calcula-
tions or analytical solutions in the literature. The following is a list of items to check based
on common sense or intuition, or analytical solutions if they are available.

• Deformed shape of the structure
• Equilibrium of the external forces (Reaction forces should balance with the applied
loads.)
• Order of magnitudes of the obtained values

Notes about the Spring Elements:

• Spring elements are only suitable for stiffness analysis.
• They are not suitable for stress analysis of the spring itself.
• There are spring elements with stiffness in the lateral direction, spring elements
for torsion, and so on.

1.2.5 Example Problems
EXAMPLE 1.1

k 1 k 2 P k 3
x
1 2 3 4

Given: For the spring system shown above,

k 1 = 100 N/mm, k 2 = 200 N/mm, k 3 = 100 N/mm
u =
P = 500 N, 1 u 4 = 0
Find:
a. The global stiffness matrix
b. Displacements of nodes 2 and 3
c. The reaction forces at nodes 1 and 4
d. The force in the spring 2
Solution
a. The element stiffness matrices are (make sure to put proper unit after each
number)
 100 − 100
k 1 =  −  (N/mm )
 100 100 

 200 − 200
k 2 =   (N/mm )
 − 200 200 