rmation?" I know that this can already be accomplished using the brilliant Kangaroo plugin, but I wanted a simpler and faster (yet still accurate) single component that could replicate this unique curve using a variety of inputs: the length of the rod/wire, the width/distance between the endpoints, the height of the bend, and the tangent angle at the start. I also wanted make the unknowns (such as height if only length and width are known) easily accessible for plugging into additional components.
The resulting script, being an all-in-one solution, is somewhat unwieldy, but it could easily be broken down into smaller components (custom .gha's which I don't have the ability to code). If someone wants to tackle this, please do! I'm not an expert coder by any means, and as this was only my second time diving into Grasshopper scripting, if the script seems somewhat strange, that's probably why. I did try to comment the code pretty well though. Here's the full description:
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DESCRIPTION: This beast creates the so-called 'elastica curve', the shape a long, thin rod or wire makes when it is bent elastically (i.e. not permanently). In this case, force is assumed to only be applied horizontally (which would be in line with the rod at rest) and both ends are assumed to be pinned or hinged meaning they are free to rotate (as opposed to clamped, when the end tangent angle is fixed, usually horizontally). An interesting finding is that it doesn't matter what the material or cross-sectional area is, as long as they're uniform along the entire length. Everything makes the same shape when bent as long as it doesn't cross the threshold from elastic to plastic (permanent) deformation (I don't bother to find that limit here, but can be found if the yield stress for a material is known).
Key to the formulas used in this script are elliptic integrals, specifically K(m), the complete elliptic integral of the first kind, and E(m), the complete elliptic integral of the second kind. There was a lot of confusion over the 'm' and 'k' parameters for these functions, as some people use them interchangeably, but they are not the same. m = k^2 (thus k = Sqrt(m)). I try to use the 'm' parameter exclusively to avoid this confusion. Note that there is a unique 'm' parameter for every configuration/shape of the elastica curve.
This script tries to find that unique 'm' parameter based on the inputs. The algorithm starts with a test version of m, evaluates an expression, say 2*E(m)/K(m)-1, then compares the result to what it should be (in this case, a known width/length ratio). Iterate until the correct m is found. Once we have m, we can then calculate all of the other unknowns, then find points that lie on that curve, then interpolate those points for the actual curve. You can also use Wolfram|Alpha as I did to find the m parameter based on the equations in this script (example here: http://tiny.cc/t4tpbx for when say width=45.2 and length=67.1).
Other notes:
* This script works with negative values for width, which will creat a self-intersecting curve (as it should). The curvature of the elastica starts to break down around m=0.95 (~154°), but this script will continue to work until M_MAX, m=0.993 (~169°). If you wish to ignore self-intersecting curves, set ignoreSelfIntersecting to True
* When the only known values are length and height, it is actually possible for certain ratios of height to length to have two valid m values (thus 2 possible widths and angles). This script will return them both.
* Only the first two valid parameters (of the required ones) will be used, meaning if all four are connected (length, width or a PtB, height, and angle), this script will only use length and width (or a PtB).
* Depending on the magnitude of your inputs (say if they're really small, like if length < 10), you might have to increase the constant ROUNDTO at the bottom
REFERENCES: {1} "The elastic rod" by M.E. Pacheco Q. & E. Pina, http://www.scielo.org.mx/pdf/rmfe/v53n2/v53n2a8.pdf {2} "An experiment in nonlinear beam theory" by A. Valiente, http://www.deepdyve.com/lp/doc/I3lwnxdfGz {3} "Snap buckling, writhing and Loop formation In twisted rods" by V.G.A. GOSS, http://myweb.lsbu.ac.uk/~gossga/thesisFinal.pdf {4} "Theory of Elastic Stability" by Stephen Timoshenko, http://www.scribd.com/doc/50402462/Timoshenko-Theory-of-Elastic-Stability (start on p. 76)
INPUT: PtA - First anchor point (required) PtB - Second anchor point (optional, though 2 out of the 4--length, width, height, angle--need to be specified) [note that PtB can be the same as PtA (meaning width would be zero)] [also note that if a different width is additionally specified that's not equal to the distance between PtA and PtB, then the end point will not equal PtB anymore] Pln - Plane of the bent rod/wire, which bends up in the +y direction. The line between PtA and PtB (if specified) must be parallel to the x-axis of this plane
** 2 of the following 4 need to be specified ** Len - Length of the rod/wire, which needs to be > 0 Wid - Width between the endpoints of the curve [note: if PtB is specified in addition, and distance between PtA and PtB <> width, the end point will be relocated Ht - Height of the bent rod/wire (when negative, curve will bend downward, relative to the input plane, instead) Ang - Inner departure angle or tangent angle (in radians) at the ends of the bent rod/wire. Set up so as width approaches length (thus height approaches zero), angle approaches zero
* Following variables only needed for optional calculating of bending force, not for shape of curve. E - Young's modulus (modulus of elasticity) in GPa (=N/m^2) (material-specific. for example, 7075 aluminum is roughly 71.7 GPa) I - Second moment of area (or area moment of inertia) in m^4 (cross-section-specific. for example, a hollow rod would have I = pi * (outer_diameter^4 - inner_diameter^4) / 32 Note: E*I is also known as flexural rigidity or bending stiffness
OUTPUT: out - only for debugging messages Pts - the list of points that approximate the shape of the elastica Crv - the 3rd-degree curve interpolated from those points (with accurate start & end tangents) L - the length of the rod/wire W - the distance (width) between the endpoints of the rod/wire H - the height of the bent rod/wire A - the tangent angle at the (start) end of the rod/wire F - the force needed to hold the rod/wire in a specific shape (based on the material properties & cross-section) **be sure your units for 'I' match your units for the rest of your inputs (length, width, etc.). Also note that the critical buckling load (force) that makes the rod/wire start to bend can be found at height=0
THANKS TO: Mårten Nettelbladt (thegeometryofbending.blogspot.com) Daniel Piker (Kangaroo plugin) David Rutten (Grasshopper guru) Euler & Bernoulli (the O.G.'s)
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Edit: More on the math behind this here.
Cheers,
Will
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Added by Will McElwain at 4:08pm on February 26, 2014
as one element.
Thank you
Comment by karamba on October 7, 2014 at 11:27pm
Hello Patricio, divide the beams in such a way that each boundary vertex of the shell becomes an endpoint of a beam segment.
Best, Clemens
Comment by Llordella Patricio on October 8, 2014 at 8:30amDelete Comment
Hi Clemens,
I did what you suggested but now assemble element doesn´t work properly. Could you please tell me how to fix it? Thanks in advance, Patricio
8-10-14losa%20cadena.gh
Comment by karamba on October 8, 2014 at 11:59am
Hi Patricio, if you flatten the 'Elem'-input at the 'Assemble'-component the definition works. The triangular shell elements have linear displacement interpolations whereas the beam deflections are exact. In order to get correct results you should refine the shell mesh.
Best, Clemens
Comment by Llordella Patricio on October 9, 2014 at 8:35amDelete Comment
Hello, succeeds in creating the mesh to the slab, and built the beam segment, but when I see the deformations are not expected because the beam is deformed as the slab.
Thanks for the help
PS: maybe I'm using the program for a type of structure that is not the most appropriate, as I saw in the examples of other structures. But this type of structure is that students taught
best regards
Patricio
9-10-14%20Example%201.gh
Comment by karamba on October 9, 2014 at 10:46am
You could use the 'Mesh Edges'-component to retrieve the naked edges and turn them into beams - see attached file:91014Example1_cp.gh
Best regards,
Clemens
Comment by Llordella Patricio on October 15, 2014 at 3:41pmDelete Comment
Dear clemens
I was doing a rough estimate of the deformation, and I can not achieve the same result with Karamba. When I make a rough estimate of the result with Karamba beams and mine are very similar, I think the problem is when I connect the shell, because there are no similar results.
I sent the GH file, and an image of the calculation
The structure is concrete The result I get is 0.58cm
thank youPatricio
15-10-14%20Example.gh
Comment by karamba yesterday
Dear Patricio,
try to increase the number of shell elements. As mentioned in the manual they are linear elements. A mesh that is too coarse leads to a response which is stiffer than the real structure.
Best,
Clemens
…
y (movement, protection, temperature regulation) but also the evolution of cultural expression precisely by exceeding the purely indexical performative relations. Designing not only for the needs but for the desires.
Computational couture looks at the creation of exclusive custom-fitted clothing (typical of haute couture) through the lens of a systemic approach, extending the sartorial techniques with 3D modeling and computation-based approaches developed in Rhinoceros and the visual programming environment Grasshopper.
Aim of the workshop is to exert, infuse and expand the sartorial sensibilities to body proportions and dress making into an algorithmic approach that loops through design and fabrication by means of laser cutting and 3d printing for the design and production of a garment. Participants will be divided in teams focusing on specific aspects of the garment related to the production technique (laser cutting or 3D printing).
////////////////////////////////////
WORKSHOP | calendar
Day 1
Introduction to algorithms and computational design for creative disciplines Basics of 3D modeling in Rhinoceros Basics of Grasshopper Introduction to basic sartorial techniques
Day 2 Testing design options for the dress in Grasshopper (tutored work)
Day 3 Fabrication session . file preparation . parts testing and pre-assembly
Day 4 dress fabrication and assembly
Day 05 finalization of dress final presentation
////////////////////////////////////
WORKSHOP | registration
FEE FOR PARTICIPANTS
Early bird (until 4/5): 250 € Full fee (from 5/5 until 15/5): 350 €
The fee includes materials and fabrication. Plane tickets and accommodation are not included in the fee.
////////////////////////////////////
REGISTRATION (until 15/5/2015)
For registration please write at :
beyond@iaac.net
for more info visit:
http://beyond.iaac.net/?page_id=1620
…
make-this-form-...
Other than that:
1. Tensegrity is a "static" thingy in the sense that you use some module (let's call it "mode") and repeat. Creating some code that does INVENT new modes for T trusses (Pulitzer/EMMY/Nobel on sight, he he) ... I would strongly suggest to forget that THIS VERY MOMENT.
2. Applying some T "mode" on something (see my examples in the above thread where I use surfaces for the T nodes) is another animal. If you intend to use Kangaroo to "relax" that something (NOT the T itself) well ... you can do it but has nothing to do with T.
3. The Kangaroo def provided is a "way" to test the "rigidity" of the T in use. It's a "post-processing" thing NOT a T solving thing.
4. I have a terrible feeling: are you saying that (a) without knowing a thing (or two) from C#, (b) without knowing K1/K2, (c) with a limited GH experience ... your goal is to write down from scratch a FEA ("Femap") thingy that ALSO does node "relaxation" ? If so ... well ... what about sky diving (without parachute) or that classic Russian roulette "game"?
PS: shown double tetra (classic) and XFrames (classic) T trusses applied in open and closed surfaces.
But of course these are abstract stupid "arrangements" utterly out of question in real-life: read CAREFULLY the discussion in the thread provided above AND also study the 3dPDF attached (with a system out of many available) in order to get the gist about what real-life means (Note: EVEN if no real-parts are used ... the node calculation is different from the abstract "star" connections pictured above - by "star" I mean that cables meet at a single point in space without any "offset" etc etc).
Moral: Seppuku
Plan Z: Skype ASAP
…
a machine that is light and very sturdy. I have taken my Macbook Pro all around the world, carry it with me every day, even dropped it a few times and its still totally fine. Its thin and light.
2) You get some actual support for your hardware even a few years down the line. My Macbook Pro is from 2012 and I can still walk in to any Apple Store and get help with it, which I have done many, many times in different places around the world - I never had to show a receipt or was charged any money for help. There is no PC/Laptop manufacturer in the world with anything close to that, because companies like Asus, Dell, etc. bring out dozens of new versions of laptops every year, so its much harder to service them after a few years.
3) This is the most important one, which usually people forget when they say that Macbooks are overpriced: Resale Value. If you have ever tried to sell an old PC/Laptop (I have a few times), you will know how little value they have even after just 2-3 years. Macbooks retain their value very well and even after 4 years you can still get 50% of your original price.
4) Of course you can install Windows on it and it runs perfectly. I have MacOS and Windows on it and both run absolutely fine. On the Windows side I have Rhino+GH, Maya and a few others. Having Windows is good, because some software still only runs on Windows (looking at you, 3DSMax!). Most other software also runs on MacOS. In the interest of sanity it is great to have an alternative to Windows for all the day to day stuff, like Mail, Calender, Photos, Presentations, etc. that just always works.
5) As for performance: Yes, Macbook Pros dont necessarily have the latest and greatest in graphics cards (the rest is on par with PC laptops), but unless you want to play games you will not need it. VRay RT can do GPU rendering, but you wont get great performance from a Notebook GPU anyways and it doesnt make sense to do rendering on a laptop (especially since you have a workstation). You could get one of the older Macbook Pro Retina Late 2013 or Mid 2014 models with the GTX750M by Nvidia, which will be usable to render using VRay RT, but of course not huge performance. Better to invest in a good used graphics card for your workstation like an Nvdia GTX980ti, which is the best value for money for GPU rendering right now (lots of used ones available).
So at least consider also getting a Macbook Pro. You can buy refurbished models (depending where you are) and they are like new, but a lot cheaper or even get an older one thats used. It will be a worthwile investment.
Take it from someone who has used dozens of PCs and Macs in my lifetime and have to do the IT support here at work (where we also use both).
I still have my Macbook Pro Retina from 2012 and its still running perfectly, super fast, and I can use Rhino and GH for huge files, do GPU Rendering with Octane Render and all sorts of other heavy computing stuff.
Hope that helps.…
Added by Armin Seltz at 11:12am on September 19, 2016
phere with the maximum number of triangles but not much than a defined threshold.
I scaled that mesh just to fit Rhino grid, but it is not mandatory. What is useful, is to scale not uniformly the mesh (Scale NU). It could be done after cellular modifier applied or before or before and after. The 3 options are possible in the script. If you don’t need them just put 1 in scale sliders.
Ellipsoid mesh is the populated with points, I put 2 independents populations to randomize a bit further. For each vertices of the mesh the closest distance from the populated points is calculated.
Here is an illustration in color of this distance.
This distance is then used to calculate a bump. If domain for bump is beginning with negatives values to 0, it carves the mesh. Instead it bumps/inflates it.
Some images to illustrate the difference with populating 100 points with one or two populations.
Here some images to illustrate the application of scale before carving or after.
Next phase apply noise. At the moment I don't find it good.…
rce=activity
Basically, I want to create a workflow to automatically subdivide a building mass envelope geometry into different floors which will be further subdivided as perimeter zones and core zones.
But I encountered an error for a particular building mass geometry (a quite regular form) which doesn't work with the split building mass component (see item 4&5 below):
The workflow is:
1. import building mass geometry:
2. divide the building mass into floors (one zone per floor) using one of the two different methods depending on whether the floor surface has holes or not:
3. use the split building mass component to further divide the zone for each floor into perimeter zones and core zone:
4. I tested several building forms which work for this workflow as shown below, except for one form C05 which is a courtyard block with small tower blocks on top of it:
5. in the last step, there is an error from the split building mass component saying that "solution exception: index out of range: 0" ...
So, I wonder if this is error is related to the split building mass component or related to the way the building mass geometry is created.
Appreciate your kind advice!
Thank you!…
d simulate the bending process of a flat stell sheet in order to get the same shape. This can be really interesting so we can evaluate the material beheaviour, the deformation on the cross section a
nd explore big deformations in mecanics analysis of materials.
I am not a mecanical engineer nor a civil engineer, I´m an Architect and my interest is the construcction method and extracting the necesary information to consider fabricating the project.
I´m having conceptual challengings on the methodology for this simulation, so I will post a small overview of what I`ve done.
1.- Understanding the Geometry.
This is a sclupture by the Venezuelan/Hungarian/German artist Zoltan Kunckel (KuZo).
The shape is achieved bending a pre water cut square sheet of stainless steel. After bended manually, the different lashes are pulled on the opposite direction. New curvatures are produced after all is deployed.
2.- Reproducing the Shape digitally.
Using Karamba I built a definition to reproduce the produced by physical stress. This model served to find deformations that occur when a set of loads are applied to a mesh. Following this process will allow us to find a coherent and more natural cross section so then we could re-shape simulating the bending process of a piece of ductile material.
3.- Discretizing curve
Reducing the model to its simplest element is a key aspect of finite nonlinear analysis. Once our shape is already defined we can divide its principal characteristic of its principal given curve.
At this point I have already found the desired curve.
I Think the better strategy to simulate bending the steel sheet into this shape, is rationalize the curve and divide it finding the tangents one of the curve that compose this sort of parabola. bur i don`t know how to parametrize that in GH.
Please. If someone have a better Idea about this process I`ll glad to read sugestions.
Tomás Mena
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