14. Summary of results#
% of differences compared to the reference solutions
DKT |
DKQ |
DST |
DSQ |
Q4G |
||
A
|
B
|
E
|
F
|
G
|
H
|
|
50 knots
|
170 knots
|
169 knots
|
170 knots
|
169 knots
|
169 knots
|
|
O |
—1.10 |
—0.09 |
—0.09 |
+0.12 |
—0.11 |
—0.15 |
D |
—1.01 |
—0.1 |
—0.11 |
+0.08 |
—0.13 |
—0.20 |
E |
—1.03 |
—0.09 |
—0.12 |
+0.09 |
—0.13 |
—0.20 |
F |
—1.05 |
—0.09 |
—0.09 |
+0.07 |
—0.15 |
—0.21 |
MEC3QU9H |
MEC3TR7H |
|||||
I |
J |
|||||
96 knots
|
121 knots
|
|||||
O |
1.42 10 —3 |
—0.03 |
||||
D |
|
—0.07 |
||||
E |
|
—0.07 |
||||
F |
||||||
Regarding travel:
Plate and shell elements give good results on fairly coarse meshes.
DKT |
DKQ |
DST |
DSQ |
Q4G |
||||
A Love-Kirchhoff |
B Love-Kirchhoff |
E Love-Kirchhoff |
F Reissner |
G Reissner |
H Reissner |
|||
50 knots 76 TRIA3 |
170 knots 296 TRIA3 |
169 knots 147 QUAD4 |
170 knots 296 TRIA3 |
169 knots 147 QUAD4 |
169 knots 147 QUAD4 |
|||
O Sm/2 |
—1.19 |
+0.02 |
+0.02 |
+0.07 |
+0.07 |
—0.76 |
—0.14 |
|
A Sm/2 |
+5.79 |
—0.06 |
—0.06 |
—0.49 |
—4.40 |
—9.80 |
+17.80 |
|
B Sm/2 |
—13.100 |
—5.100 |
—5.53 |
+1.00 |
—9.10 |
—7.12 |
+19.70 |
|
C Sm/2 |
+5.73 |
—0.06 |
—0.06 |
—0.46 |
—4.41 |
—9.44 |
+17.90 |
|
D Sm/2 |
+0.20 |
+0.35 |
+0.35 |
+0.50 |
+0.43 |
+0.49 |
+0.05 |
|
E Sm/2 |
+0.19 |
+0.19 |
+0.42 |
+0.50 |
+0.50 |
+0.50 |
+0.05 |
|
F Sm/2 |
—0.66 |
+0.25 |
—0.25 |
—0.30 |
+0.15 |
+19.00 |
—0.33 |
|
MEC3QU9H |
MEC3TR7H |
|||||||
I |
J |
|||||||
96 knots 25 QUAD9 |
121 knots 50 TRIA7 |
|||||||
O Sm/2 |
1.05 |
1.14 |
||||||
A Sm/2 |
2.9 |
0.25 |
||||||
B Sm/2 |
||||||||
C Sm/2 |
2.9 |
0.25 |
||||||
D Sm/2 |
0.28 |
—0.28 |
||||||
E Sm/2 |
0.28 |
—0.28 |
||||||
F Sm/2 |
Regarding the efforts:
On the pressed edge, significant errors (up to 20%) are observed compared to analytical solutions. The error is the most pronounced on modeling \(H\) (Q4G).
by refining the mesh of each model, we observe the convergence of efforts, that is to say that the error tends towards 0. However, the order of convergence is lower for modeling \(H\): the Q4G element requires in fact to mesh very finely in the directions stressed during bending (it uses a bilinear approximation of the rotations whereas modeling DST is based on a quadratic approximation).