Grasshopper

generative modeling for Rhino

# Principal Stress grid

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Comment by Odysseas Georgiou on August 31, 2010 at 2:21am
Hello Matt,

The principal stress data was derived from Robot Structural and the streamlines were plotted in GH using custom scripts. I'm not aware of the matlab functions but I'm sure there's some way you can do it by obtaining stress data from GSA as well. You can link GH and GSA using their API. You can find some examples here : http://geometrygym.blogspot.com/.

The above work is part of my masters thesis which is not completely finished yet. I would gladly share the process with you when it is done though. I will keep you posted on this!
Comment by Matt Schmid on August 23, 2010 at 9:03pm
Hi Odysseas,

Very interesting stuff, I'm currently looking into doing something similar and was just wondering how you managed to derive your streamlines for this project. Did you create a custom script? Do you know of any FEA software out there that is capable of doing it? I looked into the CGAL algorithm listed below but it's a bit beyond my basic scripting abilities. I recently discovered that matlab has a few functions for deriving streamlines of 2d and 3d vector fields. Do you think that would be the best way to go about it? I was thinking I could use Oasys GSA to do the analysis and export the vector field in a text file and then bring it into Matlab to derive the streamlines. Sorry for all the questions!

All the best,

Matt
Comment by Daniel Hambleton on July 29, 2010 at 7:40pm
Wouldn't you then get two sets of integral curves (although very nicely spaced - that paper is great!) from one 2d vector field (say the max curvature directions)? As opposed to the composition of the integral curves of two 2d vectors fields (both the max and min directions)?

Incidentally, the only equation I could find with both the stress tensor and the curvature tensor (Riemann) was Einstein's field equations.
Comment by Daniel Piker on July 29, 2010 at 4:34pm
Hi Odysseas, John and Daniel,

Very interesting discussion. This is something I've also been fascinated by for some time.

For generating evenly spaced streamlines of certain 2D fields I found a way that I could split the vector field into a pair of scalar fields and contour them to get nice conformal grids:

While this presents some of its own challenges related to multi-valued functions, it sidesteps many of the usual issues with vector field integration and streamline placement.

I've been wondering if one could find a way to apply a similar technique to plotting principal curvatures and stresses on curved surfaces.
However, the way this technique works is dependent on the particular characteristics of the field I was looking at (potential flow). Splitting and contouring general vector fields in this way does not produce the same results.

What I'm wondering is what would happen if you were to use Helmholtz-Hodge decomposition to separate the field into curl-free and divergence free parts.
I think one could then take the curl-free part and apply the same contouring technique as I used with my rheotomic surfaces. I'm not sure yet exactly how the resulting conformal grid would relate to the principal stress field, but it might be interesting to try.

Incidentally, on a related note - I remember seeing several years ago a book of Nervi's writings translated into English which had few pages at the end where he talked briefly about mutually perpendicular systems of curved lines and why they are interesting, along with some of his hand sketches of a few such systems. I've not been able to track the book down since. Can anyone give me a title ?
Comment by Odysseas Georgiou on July 29, 2010 at 5:35am
Hello John,

I'm fine, how are you?

it seems like the principal stresss problem is of great interest lately!

I think you are looking into surface reparametrization (N. Ray- Periodic Global Parametrization) , Michalatos' and P. Winslows' work on principal stress plotting in mailnly based on that .

Mine is based only on self weight . Indeed, you get funny results even if you use the outer layer stresses(which include bending) from the self weight case to plot the trajectories. I'm generating some images for my thesis, i'll send you some that illustrate this case when i'm done.

When is the exhibition? I'm currently in Cyprus writing my thesis. I'll be back by the end of august . We should arrange for the beer when i'm back !
Comment by John Harding on July 28, 2010 at 8:02am
Thank you Daniel, I will try it out!

I wonder if there's a way to influence 2d parameter space so that each coordinate is representative of R3 embedding space in terms of point spacing (a kind of morphed grid). This way the 'Farthest point seeding strategy' could avoid streamline bunching when translating from parameter space to R3.

Does that make any sense!?
Comment by Daniel Hambleton on July 28, 2010 at 7:42am
Have you checked out CGAL's streamline placement? It's a 2d algorithm, but if you work in UV coordinates and use local tangent planes, it should work...
Comment by John Harding on July 28, 2010 at 5:00am
Hey Odysseas, how's it going?

Spoke to Paul a couple of weeks ago about finding some code that will do streamlines automatically with equal density, and he told me you were doing similar things at the moment - turns out quite similar in fact! We are doing an exhibition in the office foyer of some slab designs much like Nervi's, if you're in London soon let me know and come and have a look.

As with the sawapan stuff, if the self-weight of the material is quite considerable compared to the imposed loads the result can be quite misleading - especially for prinicpal 'bending' stress directions as opposed to in-plane ones. How are your loads defined? Is it just self-weight?

Anyway, hope you're well - we should meet up again soon for a beer.

John
Comment by Daniel Hambleton on July 26, 2010 at 2:54pm
The thing I always get hung up on is that stress lines are determined by the loads, supports, and geometry, whereas curvature lines depend on geometry only. So by changing loading conditions, you can get a different set of stress lines for a given surface. Which kind of means that given a surface, and some arbitrary load/support conditions, the stress lines and curvature lines should almost never coincide....unless there's some special relationship. Which I don't understand.
Comment by Odysseas Georgiou on July 26, 2010 at 2:23pm
Hello Daniel,
Well, in some cases they seem to coincide. You can notice this if you compare the two last images.(one is principal curvutures ans the othe principal stresses). It is an interesting issue though, i'll superimpose the two in different surfaces and see what is coming out.

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