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[Daeho Jang]

Im trying to do  Finite Element Analysis using Proper Orthogonal Decomposition (POD), but i cant get force matrix and dont know what result mean. 

 

Let me first describe the process.

 

1.I analyzed a cantilever beam under a sinusoidal load using the transient structural analysis in ANSYS. 

 

2. I exported the nodal force and nodal displacement for each node.

-The mesh had 828 nodes, but excluding the 28 nodes with fixed support, I extracted the forces in the xyz direction for 800 nodes(2400 total).

-The F matrix should be 2400x1. But exported txt file only contain force of 28 nodes which are fixed.  

-K matrix is 2400x2400( I used APDL code to export it)

3. I stored the deformation every 0.05 seconds for 1 second into a snapshot matrix (2400x20).

I subtracted the mean from the data and performed 1/N*(C*C').

 

4. I proceeded with singular value decomposition on the obtained snapshot matrix and extracted 2 modes that contain 99.999% of the energy (2 basis).

-I manually extracted results at 0.05-second intervals, obtaining 20 data points. Is there a method to acquire the results for all time steps at once?

 

5. Using the Galerkin method, ∅^T F= ∅^T Kc∅(c is coefficient), I projected the governing equation F=KU onto the obtained basis ∅, resulting in reduced dimension of  F and K matrices. ( if F matirx is 2400x1)

 

 

6. Consequently, in the equation F = KU, all values are constants except c, and U has been reduced from 2400 variables to just 2.

 

Theres two main question. 

 

First, are there any method that i can export nodal force of every nodes(800)?

obtained nodal forces are useless since they are force of Fixed nodes.

 

Second, while the original U matrix represented the deformation at each node, the reduced u_approx consists of only 2 values. What do these 2 values mean? I know those values represent the most important feature of original system but what are they?

 

If there were any mistakes in the process, please let me know.

 

Thanks

[Ashish Khemka]

Hi,

I have provided a response to your query here: Purpose of using POD in the finite element method, and how should i use it? (ansys.com)

Regards,

Ashish Khemka