Optimization of a subframe - multiple stiffness targets 1

[GregLocock]

This week our team needs to throw together a good concept for a non-isolated subframe. We have various loadcases, and the allowable package, and the hardpoints identified. So far we've been running topology optimization using these load cases.

However, I would like to develop an optimum topology based on the /stiffness/ targets we have also set for many of the hardpoints. I've read various SAE papers, they mostly seem to be happy to optimise by increasing modal frequencies, or by improving the stress distribution. I haven't seen any references to people trying to optimise several stiffnesses.

I am rather confused, in that I am not sure whether to optimise the structure for each stiffness requirement uniquely, or whether I need (or can) use the entire set of stiffnesses as one loadcase. I don't think I can combine them, but if I treat each one as a separate case then I'll end up with a whole bunch of separate structures.

Secondly, I have some choice in the positions available to bolt the subframe to the chassis rail. I can use any 2 of four available on each rail. Obviously I'd like to concentrate my work on the most likely subset of mounting points, is there a way to eliminate the bad ones early in the analysis?

Thirdly I have always been puzzled by one aspect of stiffness optimization. If you consider the tip deflection of a simple cantilever then the sensitivity of the deflection to material along the length of the cantilever is biased towards the root of the cantilever, since the contribution of the bending stiffness of each dx slice is proportional to its distance from the tip times its local deformation. This means you should end up with a different optimum shape for stiffness than you would for stress (which is a parabola, I think, for a rectangular cross section beam). What is the name for this sort of contribution?

As you can probably tell, it is many years since I've done any serious structural analysis, and I'm a complete novice when it comes to optimization.

Cheers

Greg Locock

 

[mloew]

Greg,


Great set of questions. My understanding is that you can indeed optimize for several load cases (BC are the same) simultaneously. I am just getting started at developing a procedure for topological optimization, so I am not an expert (yet). Pretty sure that the multiple load cases show up in the problem statement as additional design constraints (displacement of element x1 NTE y1 mm for load case 1; displacement of element x2 NTE y2 mm for load case 2; etc.). Check out the Altair OptiStruct Product Brochure. I think it is explained pretty well there.

You are correct in that optimizations for stress and stiffness will indeed be different; your example is a good one. They way I approach this is that structures should not be stiffness limited; stiffness comes from design (load paths). Strength is obtained from suitable selection of semi-materials (material and process). I did find this reference from the Altair support pages How to account for stresses in topology optimization.

I hope this helps. I will try to look through my collection of technical papers to see if I can find anything else.


Best regards,

Matthew Ian Loew
"Organizations cannot make a genius out of an incompetent. On the other hand, disorganization can scarcely fail to result in efficiency." -- Dwight D. Eisenhower

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[GregLocock]

Thanks for that.

I'm limited to 300 nodes at home, so I used a spaceframe in the end, the CAD guys can use it as a thought starter to build a production feasible design.

I ran each point mobility as a separate loadcase, and then each loadcase (ie loads at multiple points and directions) as a separate loadcase, checking for max deflection and max stress respectively.

I used a standard bar diameter throughout, and just added more bars as each failure required, and, for our targets at least, the design that was stiff enough was also strong enough, using mild steel.

Result was a non feasible (in our context), but sensible, spaceframe design at 12 kg, the best we've seen designed by vendors is 22kg, so I am pretty confident that a great deal of meat has been left on the bone. This discussion is not over by a long chalk, I'll have a read and a think.

Cheers

Greg Locock

 

[mloew]

Greg,

I am sure you have looked though the SAE Technical Papers on Topology Optimization. If you are looking for papers on optimization of load paths starting from “full ground structures” (every node connected initially to every other node) take a look at the following papers:



2004-01-1661 First Order Analysis for Automotive Body Structure Design - Part 4: Noise and Vibration Analysis Applied to a Subframe
2004-01-1658 First-Order Analysis for Automotive Body Structure Design - Part 1: Overview and Applications
2004-01-1660 First-Order Analysis for Automotive Body Structure Design - Part 3: Crashworthiness Analysis Using Beam Elements
2001-01-0768 First Order Analysis - New CAE Tools for Automotive Body Designers

You may also want to search for anything by Noboru Kikuchi from the University of Michigan. He has done a lot of work on this area.

Hope this helps.

Best regards,

Matthew Ian Loew
"Organizations cannot make a genius out of an incompetent. On the other hand, disorganization can scarcely fail to result in efficiency." -- Dwight D. Eisenhower

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[GregLocock]

Thanks, that'll give me something to ponder. I'll even give you a star!

Last night I did this:

It turns out that three (out of 11) of the stiffness targets are the critical ones, and the loading one (ie forces).

So, having come up with the concept in the previous post, it was too stiff, by about 20%. This seemed like a good chance to get a further weight saving. I reduced the size of all the members by 20%. I also added a shear panel in an obvious place. In other words my topology was incorrect, really. This gave a structure that was stiff enough, but much too weak. I then made a group of all the weak members, and increased their CSA by the ratio of the max stress in any of them to my desired stress.

This was strong enough, and too stiff, again, so I reduced the CSA of the smaller rods by the factor by which it was too stiff.

This turned out to be strong enough, and stiff enough.

Result: 8.5 kg from a starting weight of 12 kg, and a clear load path that the CAD guys can use to design the structure around, and a detail identified that will need to be included.

Very successful! Now the real work begins.

Incidentally I have long waged a war against people who optimise structures by using the resonant frequencies as a guide. This can be useful, but often leads people astray. In my opinion structures are there to support loads first and foremeost, so stiffness and stresses are the fundamental targets, frequencies are an additional requirement. Otherwise root (k/m) tells you to keep chopping material out, with no end in sight.


Cheers

Greg Locock

 

[mloew]

Greg,

Thanks. I think I like your process. Some of the interesting work I have found on the subject of topological optimization actually came from the design of compliant structures. That is where I first found some information on the "full ground structure".

Anyway, my experience has been that if you are serious about structural design, you can always get a stiff enough (or too stiff) structure through topology. Once the design is not stiffness limited, the structure can then be optimized for strength through the use of shape optimization and choice of semi-materials. It is both easy and appropriate to develop the load-path concepts with a space-frame topology. Very good technique! I also agree with you on the frequency item. I only use modal analysis on structures as a check, not an objective variable.

Best regards,

Matthew Ian Loew
"Organizations cannot make a genius out of an incompetent. On the other hand, disorganization can scarcely fail to result in efficiency." -- Dwight D. Eisenhower

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.