|
This test lets you check analysis results for a free thin
square plate, in the context of a Free Frequency Case. You will use 2D
meshes.
This test validates the following attributes:
- Rigid body modes (3 modes)
- Repeated eigen values
- Cinematically incomplete suppressions.
|
|
Reference:
NAFEMS-Glasgow, BENCHMARK newsletter, April 1989,
p.17. |
|
Specifications
Geometry Specifications
Length:
L = 10000 mm |
|
Thickness:
th = 50 mm |
Analysis Specifications
Young Modulus (material):
E = 200 GPa |
|
Poisson's Ratio (material):
ν
= 0.3 |
Density:
ρ
= 8000 kg/m3 |
Mesh Specifications:
|
Restraints (User-defined):
The structure is free, hence the boundary conditions
are:
Ty = Tz = Rx = 0 |
|
|
|
The Frequency case must be computed in Lanczos
method with Shift Auto. |
|
|
Results
The computed results present the frequency of the six modes
after the three rigid body modes.
The normalized results are the computed results divided by
the reference solution.
Mode
|
Reference value
[Hz] |
Values |
Linear triangle
(TR3) |
Linear quadrangle
(QD4) |
Parabolic triangle
(TR6) |
Parabolic quadrangle
(QD8) |
|
|
|
|
Computed
results
[Hz] |
Normalized
results |
Computed
results
[Hz] |
Normalized
results |
Computed
results
[Hz] |
Normalized
results |
Computed
results
[Hz] |
Normalized
results |
4 |
1.622 |
1.614 |
0.995 |
1.624 |
1.001 |
1.584 |
0.977 |
1.622 |
1.000 |
5 |
2.360 |
2.379 |
1.008 |
2.389 |
1.012 |
2.376 |
1.007 |
2.367 |
1.003 |
6 |
2.922 |
2.961 |
1.013 |
2.980 |
1.020 |
2.950 |
1.010 |
2.935 |
1.004 |
7 |
4.233 |
4.229 |
0.999 |
4.252 |
1.004 |
4.135 |
0.977 |
4.174 |
0.986 |
8 |
4.233 |
4.231 |
1.000 |
4.252 |
1.004 |
4.149 |
0.980 |
4.174 |
0.986 |
9 |
7.416 |
7.653 |
1.032 |
7.793 |
1.051 |
7.439 |
1.003 |
7.550 |
1.018 |
|
|
To Perform the Test
The
Free_Thin_Square_Plate_QD4.CATAnalysis document presents a complete
analysis of this case, computed with a mesh formed of linear quadrangle
elements (QD4).
To compute the case with other elements (QD8, TR3 and TR6),
proceed as follow:
-
Open the CATAnalysis document.
-
In the Advanced Meshing Tools workbench,
replace the mesh specifications as indicated above.
-
In the Generative Structural Analysis
workbench, compute the case.
|