4. B modeling#
4.1. Characteristics of modeling#
We cut the plate into 100 QUAD4 meshes.
Three models for the plate are used: Q4G, DKT (DKQ), DST (DSQ).
Compared to modeling A, the plate was rotated in plane \((o,x,y)\) by an angle of \(60°\)
For the flexure problem, the boundary conditions are as follows:
in all knots on the edge: \(\mathrm{DZ}=0\)
For the membrane problem, the boundary conditions are:
in all the nodes of the mesh: \(\mathrm{DZ}=0\) \(\mathrm{DRX}=\mathrm{DRY}=\mathrm{DRZ}=0\),
at node \(A\), we block the movement \(\mathrm{DY}\) in the coordinate system \((A,x\text{'},y\text{'})\),
At points \(A,B,C,D\), discrete stiffness elements are added (direction \(x\text{'}\)).
4.2. Characteristics of the mesh#
Number of knots: 121 |
Number of stitches and types: 100 QUAD4 |
The characteristic points of the mesh are as follows:
Point \(A\) = \(\mathrm{N1}\) |
Point \(B\) = \(\mathrm{N111}\) |
Point \(C\) = \(\mathrm{N121}\) |
Point \(D\) = \(\mathrm{N11}\) |
4.3. Tested sizes and results#
For flexure modes:
Number of the mode |
Frequencies |
||||
Reference |
Aster **** DKQ ** |
% difference |
% tolerance |
||
4 |
35.63 |
35.359 |
—0.760 |
0.8 |
|
5 |
68.51 |
67.491 |
—1.427 |
1.5 |
|
6 |
109.62 |
108.563 |
—0.964 |
||
7 |
123.32 |
121.144 |
—1.765 |
1.8 |
|
8 |
142.51 |
138.402 |
—2.882 |
2.9 |
|
9 |
197.32 |
188.500 |
—4.470 |
4.5 |
|
Aster **** DSQ ** |
|||||
4 |
35.63 |
35.351 |
—0.782 |
0.8 |
|
5 |
68.51 |
67.464 |
—1.527 |
1.6 |
|
6 |
109.62 |
108.494 |
—1.027 |
1.1 |
|
7 |
123.32 |
121.060 |
—1.832 |
1.9 |
|
8 |
142.51 |
138.291 |
—2.961 |
||
9 |
197.32 |
188.298 |
—4.572 |
4.6 |
|
Aster Q4G |
|||||
4 |
35.63 |
36.011 |
36.011 |
1.068 |
1.1 |
5 |
68.51 |
70.795 |
70.795 |
3.5 |
|
6 |
109.62 |
114.593 |
4.536 |
4.6 |
|
7 |
123.32 |
134.899 |
9.39 |
9.4 |
|
8 |
142.51 |
142.941 |
4.513 |
4.6 |
|
9 |
197.32 |
212.045 |
7.463 |
7.5 |
For the membrane problem:
Reference |
Aster |
% difference |
% tolerance |
|
DKQ |
0.14714 |
0.14713 |
—0.003 |
0.1 |
DSQ |
0.14714 |
0.14714 |
—0.002 |
0.1 |
Q4G |
0.14714 |
0.14714 |
0.1 |
4.4. notes#
For the flexure problem, the modal position of the first mode found in band \((5.,200.)\) is the fourth, because there are three solid body modes at the zero frequency:
translation modes \(u\) and \(v\) in the plane,
mode of rotation around the \(z\) axis.