
The purpose of this test is to check laminated plates with
orthotropic materials.
You will use 2D meshes. 

Reference:
Mechanics of Composite Materials, Robert M. Jones, Hemisphere Publishing Corporation, chap 5.5.1, p270.


Specifications
Geometry Specifications
a = 0.1 m
b = 0.1 m
t1 = t3 = 0.0001 m
t2 = 0.0004 m 


Analysis Specifications

Material 1:
 Young Modulus (material):
E_{1 }=
2 x 10^{11} Pa
E_{2
}= 2 x 10^{10} Pa

Poisson's Ratio:
ν_{12}
= 0.3

Shearing coefficient
G_{12} =
G_{23} =
G_{13} = 5.169 x 10^{9} Pa

Density:
= 6000 kg x m^{3}



Material 2:
 Young Modulus (material):
E_{1 }=
7 x 10^{10} Pa
E_{2
}= 7 x 10^{9} Pa

Poisson's Ratio:
ν_{12}
= 0.2

Shearing coefficient
G_{12} =
G_{23} =
G_{13} = 3.203 x 10^{9} Pa

Density:
= 6000 kg x m^{3}

Mesh Specifications:

Restraints (Userdefined):
On
AB, CD, AC and BD: translation along Z = 0 


Results
Analytical Results
For a simply supported plate, we have:
where:
Conditions for a specially orthotropic material are:

D_{11} / D_{22} = 10

D_{12} + 2D_{66} = 1
m: transversal vibration mode
n: longitudinal vibration mode
Computed Results
Modes 
Reference results [Hz] 
Computed results [Hz] 
Normalized results 
Visualization 
m = 1
n = 1 
242.724 
242.16 
0.997676 

m = 1
n = 2 
390.785 
389.992 
0.997971 

m = 1
n = 3 
702.403 
701.991 
0.999413 

m = 2
n = 1 
880.240 
874.553 
0.99354 



To Perform the Test:
The orthotropic_laminates.CATAnalysis document
presents a complete analysis of this case.
To compute the case, proceed as follow:

Open the CATAnalysis document.

Compute the case in the Generative Structural
Analysis workbench.
