
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:
NAFEMSGlasgow, 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/m^{3} 
Mesh Specifications:

Restraints (Userdefined):
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.
