Learning Forum

[Daeho Jang]

I performed a Finite Element Analysis using Proper Orthogonal Decomposition (POD) and obtained results, but I'm not sure what they signify. 

 

Let me first describe the process.

 

1.I analyzed the deformation of 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 is 2400x1, and the K matrix is 2400x2400.

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 encompass 99.999% of the energy (2 basis).

 

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.

 

 

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

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 have completed all work related to POD, but I'm not quite sure what the results signify.

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

Thanks

 

[Ashish Khemka]

Hi,

Proper Orthogonal Decomposition (POD) is a technique used in structural and fluid dynamics analysis to reduce the dimensionality of data while preserving essential features. You may refer to the following paper (external public resource) as well for clarity on the process:

A Tutorial on the Proper Orthogonal Decomposition (tu-berlin.de)

Regards,

Ashish Khemka