
This test lets you check analysis results for a
simplysupported thin square plate, in the context of a transient dynamic
response case. You will use 2D meshes.
This test is used to validate the following attributes:


Reference:
NAFEMSGlasgow, Benchmark newsletter, Report No.
E1261/R002, p.21, February 1989. 

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} 
Restraints:
Tx = Ty = Rz = 0
at all nodes
Tz = 0 along all four edges
Rx = 0 along edges x = 0
and x = 10000 mm
Ry = 0 along edges y = 0
and y = 10000 mm 



Results
You will find here the results for different finite
elements:
Type of values 
Reference solution 
Values 
Linear triangle shell
(TR3)
64 x 64 elements 
Parabolic triangle shell
(TR6)
32 x 32 elements 
Linear quadrangle shell
(QD4)
32 x 32 elements 
Parabolic quadrangle shell
(QD8)
16 x 16 elements 




Values 
Error
[%] 
Values 
Error
[%] 
Values 
Error
[%] 
Values 
Error
[%] 
Peak displacement [mm]
at t=0.210s 
3.523 
3.444 
2.24 
3.445 
2.21 
3.451 
2.04 
3.446 
2.19 
Peak stress [MPa] 
2.484 
2.221 
10.59 
2.217 
10.75 
2.251 
9.38 
2.234 
10.06 
Static displacement [mm] 
1.817 
1.774 
2.37 
1.775 
2.31 
1.776 
2.26 
1.775 
2.31 


To Perform the Test:
The
Transient_forced_vibration_of_a_simply_supported_thin_square_plate.CATAnalysis
document presents a complete analysis of this case, computed with a
mesh formed of linear quadrangle elements (QD4).
To compute the case with parabolic quadrangle (QD8), linear
triangle (TR3) and parabolic triangle (TR6) elements, 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.
