3. Modeling A#
3.1. Characteristics of modeling#
The plate was cut into 200 TRIA3 meshes. Two models for the plate are used: DKT and DST.
For the flexure problem, the boundary conditions are as follows:
in all knots on the edge: \(\mathit{DZ}\mathrm{=}0\)
For the membrane problem, the boundary conditions are:
in all the nodes of the mesh: \(\mathit{DZ}\mathrm{=}0\) \(\mathit{DRX}\mathrm{=}\mathit{DRY}\mathrm{=}\mathit{DRZ}\mathrm{=}0\),
in all the nodes on sides \(\mathit{AB}\) and \(\mathit{BC}\): \(\mathit{DY}\mathrm{=}0\)
At points \(A,B,C,D\), discrete stiffness elements are added (direction \(x\)).
3.2. Characteristics of the mesh#
Number of knots: 121
Number of meshes and types: 200 TRIA3
The characteristic points of the mesh are as follows:
Dot \(A\) = \(\mathit{N1}\) |
Dot \(C\) = \(\mathit{N121}\) |
Dot \(B\) = \(\mathit{N111}\) |
Dot \(D\) = \(\mathit{N11}\) |
3.3. Tested sizes and results#
For flexure modes:
Number of the mode |
Frequencies |
|||
Reference |
Aster **** DKT ** |
% difference |
% tolerance |
|
4 |
35.63 |
35.46 |
—0.477 |
0.5 |
5 |
68.51 |
67.82 |
—1.003 |
1.1 |
6 |
109.62 |
108.67 |
—0.867 |
0.9 |
7 |
123.32 |
121.90 |
—1.150 |
1.2 |
8 |
142.51 |
139.99 |
—1.761 |
1.8 |
9 |
197.32 |
191.70 |
—2.846 |
2.9 |
Aster DST |
% difference |
% tolerance |
35.45 |
—0.492 |
0.5 |
67.80 |
—1.030 |
1.1 |
108.62 |
—0.910 |
|
121.84 |
—1.199 |
1.3 |
139.92 |
—1.815 |
1.9 |
191.57 |
—2.912 |
For the membrane problem:
Reference |
Aster **** DKT ** |
% difference |
% tolerance |
0.14714 |
0.147136 |
—0.002 |
0.1 |
Aster **** DST ** |
% difference |
% tolerance |
|
0.147136 |
—0.001 |
0.1 |
3.4. 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,
rotation mode around the \(z\) axis.