Alternative method to FEA for Structural Analysis?

[pl15]

I have started to develop a structural analysis tool (linear elastic response) using an alternative method to FEA, and I am wondering if the tool would be useful. The method uses a regular grid rather than a mesh. So it is less accurate for sharp shapes but seems to be very fast. Since I am not a structural engineer, I wanted to get thoughts on this to see if this kind of tool (coming from microstructure studies) could be helpful for the design process? For example, at a very early stage of a design, drawings could be done in a few seconds. Here is the tool I am working on: fsa.plvaldenaire.com

 

[FEA way]

Very interesting. It reminds me of Simulia SimKraft application (it uses regular FEM though). I think that your code would fit mobile devices too. Can you say more about the theoretical basics of this method ? Is it based on some research paper ?

 

[pl15]

This is based on this original method (

https://www.sciencedirect.com/science/article/pii/S0045782597002181)

that I improved during my PhD.

It involves the same equations as the ones used by FEA (mechanical equilibrium and linear elasticity from continuous mechanics). The difference is from the numerical integration. Here, it uses Finite Difference rather than Finite Element/Volume so the fields (stress and strain tensors) are discretised on a regular grid. That leads to one drawback: shapes are 'aliased' but also one advantage: very fast and less memory usage. The quality of the result depends directly on the resolution of the grid. At high resolution it should give the same exact solution as FEA.

I usually use this method to predict microstructure stress concentration because microstructure models are often on grid (like from microscopy images).

 

[rb1957]

how does a "grid" differ from a "mesh" ?

Finite Difference models have been around for a long time. I reviewed one on a recent project … wasn't that impressed with a 25 grid "FEM" but maybe I missed the point ?

One way to get good results without a superfine mesh is using the P method (where you increase the element order, instead of reducing it's size).

another day in paradise, or is paradise one day closer ?

 

[pl15]

Discrete derivatives with FDM lead to a grid with nodes periodically spaced (see picture). A grid may not be as good at describing shapes as a mesh, but a grid has some advantages. For example, using Fourier Transform to solve equations in Fourier space, which is very fast (you don’t inverse a huge matrix, but simply multiply matrices).

The comparison of computation time between FDM and FEM is hard as most recent softwares (Solidworks, Catia) propose highly parallelized computation using GPU. FDM are not widely used so are less optimised. For instance, I just use one core. I did a comparison with a one core FEM simulation, and it seems to take the same order of time and less memory.

I was thinking that FDM is not supposed to replace FEM for Structural Analysis since it works really well. But FDM could have advantages for specific uses like from quick drawings and images that are on a grid.

 

[rb1957]

if you're limited to square (rectangular?) spaces … then you're very limited ('cept buildings).

an "interesting" application of this may be is investigating a 1:1 mapping to a non-square space ?

but these days FEM computation time/cost is pretty negligible … probably more time/cost in preparing the model and interpreting the results.

another day in paradise, or is paradise one day closer ?

 

[IRstuff]

oooh... Schwarz-Christoffel transform!! I learned that in junior year math; the last time I tried to do something like that was about 1983 , but I wussed out and brute-force numerically cranked the solution.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

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[pl15]

You can draw any shape. It is only limited by the resolution. I have attached a screenshot showing shapes with curves.

 

[fred palmieri]

An interesting discussion on a subject that I have been interested in for a long time. I have made several presentations at seminars about this very subject and have attached one in response to your post.

freddiep

 

[pl15]

Interesting analysis. I am thinking that the way FEA is currently used changed a lot over the past years (now used a lot for 'real-time' simulation, generative design, etc). So it would not be surprising if there are new alternative methods in the future for some applications. Thank you for your comment!