I'm simulating bracing alternatives in Autodesk Fusion 360 (its free for 1 year) and will share my results as I get them and edit this post
with more results.
Anchoring the parts:
All tests are with artificially anchored side faces, so the simulation is more or less as if each side face is joined to an infinitely strong material instead of just being an edge of an enclosure. Later on I will simulate full enclosures and half enclosures, so we can get more accurate figures as this one-sheet approach will be very optimistic.
Stress amount and type of application of force:
The stress amount is the amount of air pressure produced by a very beefy 18" driver doing 20mm xmax (from neutral) inside a rather small closed enclosure (about 200-300 liters I don't remember, I'll do a more definite number later on but for now I will use this same number so that all the designs are comparable. The software stores that figure so its very easy to use the same one for all the simulations). The pressure amounts to 0.002 MPa (that's 160db, which is what I assume is the limit that the UM18-22 can do internally in a closed enclosure given its motor strength and cone area). The pressure is applied on the outside face of the enclosure, assuming we brace internally. Just because its very very time intensive to apply pressure to a thousand surfaces on the braced side.
It is mentioned what the material in each simulation is.
Types of simulation:
here we find at what frequencies the bracing and the face that is braced, vibrates. And by how much they vibrate.
-Static stress simulation,
here we find how much displacement the braced face has, in other words how much it moves inwards when pressurized from the outside, and the reverse (later on we will do sims from both sides I bet, since the bracing probably won't be linear from stress from both directions).
The goal is to find out how much to brace before no benefit is to be had. How much benefit there is, is to be decided by us using the total displacement area (Sd sort of) and displacement (xmax, sort of) to then calculate the db output from each surface at modal frequencies. Its not extremely accurate but its a neat yardstick until we have a nine rounder on what yardstick to use.
There's basically two different benefits:
With just tiny differences its possible to remove the need for massive amounts of filler and remove problematic boxiness and internal reflections hitting the inside of the cone of mids and such. The outside enclosure faces themselves can also produce significant output at high frequencies, if the enclosure faces are moving too much as a result of the internal soundwaves.
Bracing has more to do with db output than SQ. Because if the cone loads the internal volume air with 150db with perfect solid faces and then only to 149db with real material, then the output from the vent will be less. The movement of the enclosure faces themselves (as well as the cone) moving at sub-bass frequencies produce basically no db at all compared to the vent output because even a badly braced enclosure face isn't going to move 10mm+. Its not a case of "losing some db from the vent from the faces moving, equals the same output in db because the faces produce as much extra db as the vent would have" as one might first assume.
First simulation (not my first simulation, but the first in this thread):
1100x450x9mm sheet with 70mm tall 1mm thick braces across the 450mm axis. PC/ABS plastic is all of the material. It is assumed the sheets are all fastened to each other with a glue stronger or equal in strength to the PC/ABS plastic, and thus simulated as one solid body with this intricate shape.
Modal analysis shows a lot of vibration from the top of the side-ways-unbraced braces.
One modification, eight 5mm diameter poles through the braces along the 1100mm axis, reduces the vibration but the total displacement in static stress test is unchanged.
But what is the amount of material in this compared to a 22mm sheet without bracing?
Well this bracing has the volume of 2 961 000 mm^3, and then there's 9mm of sheet outside that. If we take 13mm of sheet instead of the bracing, it makes 6 435 000 mm^3, with then a 9mm sheet outside that. So the net volume is increased, while keeping the same outside dimensions.
But how much material is lost if we are to make 94 sheets 70mm wide with 1mm thick material, and lose 2mm width next to the 70mm in each cut? We still use less material overall even accounting for losing 2mm on every cut (assuming we don't have to cut the material into 1mm thin sheets first). That is not counting the volume of the eight 5mm diameter solid poles used. They don't have the volume of 2 500 000 mm^3 I assume so I didn't bother.
That's strike 3 as far as I'm aware: (1) more internal volume with same net external volume, (2) less material used and (3) stronger than less complex designs using far more material.
Here's a 22mm sheet of PC/ABS plastic.
And just to compare, here's 3 times the material, 66mm PC/ABS plastic.
And here's 22mm Steel ASTM A36:
But now is the question, how much worse is it if we half the height from 70mm to 35mm and use the 35mm extra material instead to brace in the other axis. PC/ABS plastic again. Technically slightly more internal volume if you used this instead of the one-axis 70mm bracing because this is equally much material minus the 8 cylindrical braces. But much worse strength.
Strangely, this 44mm material not filled in, is apparently stronger than the 66mm sheet itself. But I'm guessing that's down to the finer mesh used in the braced simulations. So I'm going to have to be better at making sure results aren't because of changed mesh settings. As we wait I'm doing even higher polygon-count simulations on smaller sections to see if the fidelity of the mesh may make more or less optimistic results on complex bracing simulation.
The goal is to get most strength from least material and least assembly complexity. 1mm plastic is well within realms of practicality, even if there are many of them, as long as there's not too much CNC cutout lines (they get paid by each meter of cutting, pretty much). 22mm titanium however.. Well you get the idea.
If the bracing has a lot of volume loss from the enclosure, resulting in a bigger enclosure net external volume, its not ideal, but sometimes it can be a worthwhile design choice if the strength and practicality of the bracing scheme is good enough.
Feel free to install Fusion 360 yourself and get cracking making better bracing schemes. If you're familiar with google sketchup you should get to grips with Fusion 360 after a few furious hours fusing the keyboard to your forehead while watching youtube tutorials.
EDIT/Update1: I have completed a very high resolution simulation of a 200mm by 450mm portion of the 70mm tall braces with 8 cylindrical braces. But I anchored it wrong (on the 450mm sides in addition to 200mm sides), so the results are not comparable to the 1100x450mm simulation with lower resolution. Another hour+ long simulation it is then.
EDIT/Update2: Here's a new simulation between braced 9mm sheet and 79mm solid sheet. Since we had that funny one above where the braced thing with less overall material was stronger than the entire untreated sheet.
Now it seems they are correct, they have the same dimensions, only one lacks tons of material and the other is solid. Now the correct one is strongest by a huge margin. No idea what happened in the comparison between the square pattern 35mm tall bracing scheme.
EDIT/Update3: Lets test how anchoring affects the outcome:
braced edgewise by anchor:
Not braced on the immediate edge but another edge, so the corner is free-standing, with one pressure face so it can be compared to the last:
Then also the comparison between internal pressure and external pressure.
Two faces under pressure inwards:
Two faces under pressure outwards:
Note how the displacement changes. Especially between force applied into the middle or out from the middle, since there's more surface area on the outside than the inside and the force applied is in pascal (newtons per square meter).
EDIT/Update4: Lets use Pythagorean theorem to cut the use of bracing material while keeping the same enclosure strength. Question: What is the most effective brace on the bottom side of this profile of an enclosure? The answer is the nearby faces to the sides. We use the Pythagorean theorem to calculate what distance from the wall this is true. As long as sqrt(4x^2) with x being the distance to the nearest wall, is shorter than the distance to the opposite wall, this is more efficient.
The amount of material used in bracing: 37 000 mm^3
The amount of material used in bracing: 13 143 mm^3.
Both sims are anchored on the left wall face.
That's a 74.5% reduction in material used. This extra saved material can easily be used to brace the span between the corner braces enough to get more strength than the alternative braces. But now if you do the math and compare the bracing locations in the span in the middle, you get the figures that you are better off bracing against the braces instead of running material all the way across the enclosure.
How many here are going to consider using bracing like the first simulation now?
Then I tried to find (or rather just confirm) the optimal placement of the corner to corner braces.
The below one has the center-line of the brace 65mm from the corner, and the total length from corner to corner is 190mm internally and 200mm externally. So we can see that bracing with 2 braces is best by splitting up the span into three equal pieces (obvious really). So when you make your braces you should measure 1/3 out on the face if you are using 2 braces like this.
The volume of bracing used in the best placement is 18 799 mm^3, compare that to the 37 000 volume of bracing to the opposite face (the picture below in update 6). So bracing corner to corner requires half as much material as the alternative below in update 6, and translates to less external enclosure size if you want the same performance tune.
EDIT/Update6: Here's the optimal 1/3 placement of braces across to the opposite face as well, just to compare to the optimal placed corner braces:
These are quite small models, btw, hence the low displacement figures. Not like the entire sheets I simulated first.