1. Linear strain triangular Tieme Willems
Finite element method
Linear strain triangular
Tieme Willems

2. introduction Plane stress situation
Normal stress and shear stress directed perpendicular to the plane (assumed to be 0)
Loads act only in x-y plane
In this presentation:
Investigate amount of elements/ nodes
Investigate aspect ration

3. Chapter 1, Aspect ratio
Changing the aspect ratio, by increasing the amount of elements.
4 elements
8 elements
10 elements
20 elements

4. 1.2 conclusion Exact = PL = 10000*20 EA 10*(30*10^6) Case Aspect ratio
# nodes
# elements
FEM
e-004
Exact
% error 1 6 4
674.68
670
0.69 2 10 8
670.41
0.06 3
2.5 12
668.44
0.23 5 22 20
663.45
0.98
Exact = PL = 10000* EA 10*(30*10^6)

5. Chapter 2, elements
Increase the amount of elements, but maintain the aspect ratio
Aspect ratio 1
4 elements
16 elements
64 elements
Aspect ratio 2
2 elements
8elements

6. Chapter 2, number of elements
Increase the amount of elements, but maintain the aspect ratio
More elements gives in this case at first a more accurate solution, but with 64 nodes a less accurate solution due to the distribution of force on the nodes
Case
Aspect ratio
# nodes
# elements
FEM
e-004
Exact
% error 1 6 4
674.68
670
0.69 2 15 16
671.93
0.29 3 45 64
722.48
7.27
Case
Aspect ratio
# nodes
# elements
FEM
e-004
Exact
% error 1 2 4
663.70
670
0.95 10 8
670.41
0.06

7. Chapter 2, conclusion
Increasing the amount of elements results into a more exact solution;
If can distribute the forces appropriate over more notes, the result becomes more accurate;
If can keep the aspect ratio close to 1 the result comes closest to the exact result;
Amount of elements is situation related (meaning we should run the program with different aspect ratio to see which result comes closest to the exact)