# isogrids wrapping complex shapes

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## isogrids wrapping complex shapes

 Thin parts can be stengthened by wrapping them in isogrids.   Essentially, I-beams that wrap around the outside that add to their rigidity. For a better explanation, I've cued up this video:         https://www.youtube.com/watch?t=645&v=Qu79vUbcXCUDoes anyone have a suggestion on how to wrap this kind of grid around a cylindrical, conical, or dome-like shape using OpenSCAD? _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
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## Re: isogrids wrapping complex shapes

 On 2021-01-03 10:35, Bryan Lee wrote: > Thin parts can be stengthened by wrapping them in isogrids.   > Essentially, > I-beams that wrap around the outside that add to their rigidity. > > For a better explanation, I've cued up this video: > https://www.youtube.com/watch?t=645&v=Qu79vUbcXCU> > Does anyone have a suggestion on how to wrap this kind of grid around a > cylindrical, conical, or dome-like shape using OpenSCAD? Depending on the shape, I guess it is sometimes possible to do directly in 3d, but if not: Start by mathematically unwrapping the surface to receive the grid into a flat surface area and design the grid in that flat area. Export the flat grid to 3d STL or another format (preferred). Be sure to have good control of the transformation from 3d to flat and back again. Then remesh the still flat model to have uniform small rectangles (you can use AngelCADs polyfix for this purpose). Apply coordinate transformations to deform the dense grid back to the 3d shape as shown for example here https://gist.github.com/arnholm/af72c7d0790bb3d72e6bdf29c7aac1edFinally union the grid with your part. This idea applied for text on a cylinder surface: https://www.thingiverse.com/thing:2054654Carsten Arnholm _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
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## Re: isogrids wrapping complex shapes

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## Re: isogrids wrapping complex shapes

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## Re: isogrids wrapping complex shapes

Also note that the circular hollow features are important in propagating stresses.

I suspect the linear parts are also filleted to the part for the same reason.

From: Discuss [mailto:[hidden email]] On Behalf Of Daniel Shriver
Sent: Mon, 4 Jan 2021 10:07
Subject: Re: [OpenSCAD] isogrids wrapping complex shapes

Could there be some extension to "sweep"/"skin" to "decorate" (either add on or subtract off) the outer surface of something generated via "sweep"/"skin"?

Even if that were easy to do, a complication would be that people would probably want it in various different ways (in 'lines' around the object, as a 'grid' around the object, as a 'helix' around the object...)

On Sun, Jan 3, 2021 at 10:44 AM adrianv <[hidden email]> wrote:

Basically the approach I thought of is to construct continuous paths that
form the desired grid and then use a sweep function to draw the grid.
Here's an example for a cylinder.  It would be I think be not too much
trouble to adapt this approach to other mathematically defined shapes
(sphere, cone, torus).  This code relies on BOSL2, which actually has in
several places examples of a torus with a knot on its surface, demonstrating
basically a grid type structure on the torus.  Now you did say "complex
shape" in your title.  I don't know what you mean, because spheres, cones
and cylinders are all simple shapes.  If the shape doesn't have a simple
mathematical representation this approach is probably going to be difficult.
But the whole idea is probably pretty hard in that case.  You'd need to
triangulate your complex shape and project the grid onto the shape from the
triangulation.  Or downsample a fine triangulation into a coarse one while
keeping the curvature.

r = 10;
h = 30;

pitch = 30;

helix1 = [for(theta=[0:5:360*h/pitch]) [r*cos(theta), r*sin(theta),
theta/360*pitch]];
helix2 = [for(theta=[0:5:360*h/pitch]) [r*cos(-theta), r*sin(-theta),
theta/360*pitch]];

profile = right(.1,p=rect([2,1],anchor=RIGHT));  // Could use a triangle for
3d printability

zrot_copies(n=3){
path_sweep(profile, helix1, method="natural");
path_sweep(profile, helix2, method="natural");
}

zrot_copies(n=6,r=-r)
linear_extrude(height=h) polygon(profile);

cylinder(r=r,h=h,\$fn=128);

leebc wrote
> Thin parts can be stengthened by wrapping them in isogrids.   Essentially,
> I-beams that wrap around the outside that add to their rigidity.
>
> For a better explanation, I've cued up this video:
>
> Does anyone have a suggestion on how to wrap this kind of grid around a
> cylindrical, conical, or dome-like shape using OpenSCAD?
>
> _______________________________________________

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## Re: isogrids wrapping complex shapes

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## Re: isogrids wrapping complex shapes

> I do not understand the role of the holes.  They are not included in the video where

> the guy actually builds his 3d printed model.   In fact, he just uses

> quadrilateral ribs, not triangular, and I don't think any filletting.

> Adding the holes seems pretty hard to do, and so does filleting the joints

> of the ribs to each other.

>

I'm just talking about the properties of isogrids (not so much OpenSCAD implementability);

"The triangular pattern is very efficient because it retains rigidity while saving material and therefore weight. The term isogrid is used because the structure acts like an isotropic material, with equal properties measured in any direction, and grid, referring to the sheet and stiffeners structure.

A similar variant is the Orthogrid (sometimes called a waffle grid), which uses rectangular rather than triangular openings. This is not isotropic (has different properties from different angles), but matches many use cases well and is easier to manufacture.

Traditionally, the equilateral triangle pattern was used because it was amenable to simplified analysis. Since the equilateral triangle pattern has isotropic strength characteristics (no preferential direction), it was named isogrid."

Interestingly it turns out the holes are related to the milling process

The holes are cut to save weight in the left over node. I presumed it was for stress propagation allowing elasticity.

Also the holes can be used as attachment point.

It does specifically call for fillets at the nodes, ie in XY plane.

Diagrams do show fillets in the stringer, but I didn't see it mentioned in my cursory look.

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[hidden email]
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* on the Forum, click on my MichaelAtOz label, there is a link to email me.

Unless specifically shown otherwise above, my contribution is in the Public Domain;
to the extent possible under law, I have waived all copyright and related or neighbouring rights to this work.
Obviously inclusion of works of previous authors is not included in the above.
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## Re: isogrids wrapping complex shapes

I have a cylindrical_extrude() function in BOSL2 that will take a 2D geometry and extrude it radially out from a cylinder.  It may be doable to alter it to take r1/r2 args to do cones.  With a function literal argument, or list of radii, you can have a varying radius along a profile.  You could do bell shapes for rocket nozzles.  (I think I watched the same YouTube video a few days ago.)

The necessary trapezoidal scaling of the 2D geometry may be too hard to fake cleanly, however, for a conical or bell surface.  If so, I can see a way to do it using BOSL2 Paths and Regions code, but it’s definitely more work.  However, it would let you map almost arbitrary isogrid patterns to the surface of a rotationally extruded shape:

- Create a rectangular Region of isogrid pattern, assembled with region-wise union()/difference()/intersection()/offset().
- Subsample the resultant Region paths, then do radial coordinates transformations around the cone/bell/cylindroid.
- Generate a VNF (Vertices ’N’ Faces partial polyhedron structure) for the bottom of the remapped isogrid pattern.
- Generate a VNF for the top of the remapped isogrid pattern.
- Generate VNFs for the walls of each remapped isogrid Region path using vnf_vertex_array().
- Merge the VNF’s together and instantiate the polyhedron for the curved isogrids with vnf_polyhedron().

The code for linear_sweep() may be alterable to do much of this.  I was thinking of implementing this, myself.

- Revar

On Jan 3, 2021, at 8:29 PM, MichaelAtOz <[hidden email]> wrote:

> I do not understand the role of the holes.  They are not included in the video where
> the guy actually builds his 3d printed model.   In fact, he just uses
> quadrilateral ribs, not triangular, and I don't think any filletting.
> Adding the holes seems pretty hard to do, and so does filleting the joints
> of the ribs to each other.
>

<image002.jpg>

I'm just talking about the properties of isogrids (not so much OpenSCAD implementability);

"The triangular pattern is very efficient because it retains rigidity while saving material and therefore weight. The term isogrid is used because the structure acts like an isotropic material, with equal properties measured in any direction, and grid, referring to the sheet and stiffeners structure.

A similar variant is the Orthogrid (sometimes called a waffle grid), which uses rectangular rather than triangular openings. This is not isotropic (has different properties from different angles), but matches many use cases well and is easier to manufacture.

Traditionally, the equilateral triangle pattern was used because it was amenable to simplified analysis. Since the equilateral triangle pattern has isotropic strength characteristics (no preferential direction), it was named isogrid."

Interestingly it turns out the holes are related to the milling process
<image003.jpg>
The holes are cut to save weight in the left over node. I presumed it was for stress propagation allowing elasticity.
Also the holes can be used as attachment point.
It does specifically call for fillets at the nodes, ie in XY plane.
Diagrams do show fillets in the stringer, but I didn't see it mentioned in my cursory look.

 Virus-free. www.avg.com
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