JWST Structural Analysis

The James Webb Space Telescope hardly needs an introduction. It’s size, mission scope, and even its cost/schedule overruns have made it world famous. Let me proudly state that you can count me firmly in the camp of supporters (except for the overruns). I’m very proud to have served as the primary analyst for the design, analysis, and optimization of the Aft Optics Bench (AOB), its mirrors, and its interface.

Despite what its name might imply, the AOB is the black structure nestled in the middle of the gold mirrors in the image below.

This next image points it out in red letters and provides its relationship to the structures around it.

And here’s one more image of it because I’m just so damn proud of the result.

Work Overview

My job was to work with and support Kristin Martinez, the lead mechanical engineer for the structure. I built the finite element models, integrated thermal models, ran analyses, optimized it the nth degree, and did all the miscellaneous work such as sizing shear pins and fasteners. I enjoyed working with Kristin and I think she did a great job juggling the many tasks related to what remains the most scrutinized project I’ve ever worked on. (All of us on the team enjoyed the close supervision of dozens of consultants and NASA engineers.)

The big challenge was that the bench is made of Beryllium. (Specifically, S-200 FH structural grade.) Beryllium has a great stiffness to mass ratio, has a low coefficient of thermal expansion, and is an excellent thermal conductor. It also performs well in cryogenic environments. JWST is a large structure subject to large thermal gradients and, of course, it’s big and heavy. Going with Beryllium was the right choice to address these key concerns. On the other hand, it has a famously low fracture and micro-yield stress, and it’s very expensive and time consuming to make material blanks. (Plus, the health issues with machining it.)

Optimizing the structure to survive bulk yield and ultimate stress values was trivial. Getting it to pass the micro-yield stress level involved all-nighters and pushing our NASTRAN servers to their limits.

The next image shows that one of the hoops I had to jump through was building a model with more than one million nodes. Expert structural analysts are likely to shake their heads at this, expecting this to be a naïve and rookie thing to do. I agree that beam models and simple meshes almost always meet the needs of systems. However, it’s likely I would be forced into the same approach were I to do it again. And, for what it’s worth, we had a customer oversight contractor heavily question and even criticize me for it. Within a couple of months, though, his team ended up having to build an independent model to verify things and they ended up having even more nodes than I did!

There were a few driving motivations for the extreme detail:

1. The low stress limits meant we needed to capture stress at every corner, every edge, and every buckling risk. We used unaveraged corner stresses and if even one corner showed the potential for going over the limit, we were asked to mesh the area in more detail to ensure it wasn’t a modeling artifact.
2. There are compound angles that defy typical meshing approaches. Faces and bodies came together in complex ways and each of these intersections demanded fine detail. If you scrutinize the pictures, things that look like simple ribs in fact have a subtle angle or taper to them. Many subsequent systems I’ve work with would have just left a block of material in place instead of making complicated cuts, but we were driven to shave every gram out of the structure.
3. The customer wanted more detail than thin shell elements provide, especially at joints
4. As the pictures show, it’s a sizable structure as far as typical aerospace structures go

One thing that may be surprising about a model of this density is that there were no tetrahedral elements of any type. Linear tetrahedral elements are awful at estimating stiffness and should never be used for anything, ever. Parabolic tetrahedrals do much better, but they quickly add huge numbers of nodes even for a simple part. Instead, I meticulously hand-meshed most of the bench with rectangles and wedges, using at least three elements through every thickness.

Building complex models is an art. Then you run the variety of static, dynamic, and thermal loads to find that something needs to be changed, and you rework the model. A big part of my job was driving this iteration cycle as tight as possible. This is where hand calculations, experience, and simple models came into play as I could test theories before investing deeply in another complex model.

This effort relied heavily on random vibration stress analysis. It was not sufficient to calculate the RMS of the acceleration, multiply by three to get "Three Sigma Loads", and run a static case as these were too conservative. Our margins were that tight. This meant we had to crush our NASTRAN servers with solving stiffness matrices, applying loads, and pulling von Mises random stresses on a handful of elements. Runs would take hours, which pushed me against deadlines. This ended up being a driving motivation for improving the Matlab code I wrote to run random vibration analyses outside of NASTRAN.

One of the other interesting things about the work is that I couldn’t put in “the best” ribs because numerous optic, machining, handling, and mass constraints prevented their use. I was instead tasked with finding alternate locations and methods to stiffen sections or reroute loads.

Mirror Analysis

The structure houses two mirrors: a fine-steering mirror and a larger flexure optic called the “Tertiary Mirror Assembly”. The optic path is demonstrated in the next image.

I can’t say too much about the mirrors other than they obviously needed their own light-weighting efforts, they have flexures that needed to be optimized for thermal and vibration loads, and I used Zernike analysis tools I wrote to get their surfaces to the correct thickness.

Publication

Kristin Martinez took the lead on writing a paper summarizing our work. I believe she also presented it at the conference. You can find a copy of it here: JWST AOB Paper

Final Thoughts

JWST is way over budget and schedule. However, it remains one of the pinnacles of my career. It’s interesting to me that my career evolved to become an infrared systems expert on the science side. Understanding both the engineering and science aspects of the system really has me excited for its launch.