Imagine a table with sinuous legs resembling the organic shapes of tree branches rather than straight table legs. Those flowing legs might make the table stronger, better able to handle whatever someone piles on it.

Sandia researchers believe such designs, achieved through a technology called topology optimization, could enable better parts for nuclear weapons, satellites, and other vital uses. Along with advanced additive manufacturing (AM) it opens possibilities for complex shapes that conventional manufacturing methods can’t handle. Partnering the techniques also offers the potential to combine parts to save time and money, reduce the number of joints or other interfaces, and embed sensors or wiring within a structure as it’s formed.

Before the technologies can be widely employed in high-reliability, high-consequence uses, however, researchers must understand how to create the best shapes for parts and guarantee material properties.

“There are aspects of this marriage between additive manufacturing and topology optimization that are going to be critical for us to address if we’re really going to do this well,” says manager Ted Blacker (1543). “If all you do is make the same old parts a new way, it’s taking advantage of only a fraction of what is possible in additive manufacturing. And if you make these new optimal parts but you can’t ensure material quality, they’re of no use.”

Sandia’s expertise in computational mechanics, analysis tools it developed in engineering codes such as Sierra and Alegra, and geometry tools such as Cubit are advantages for working on those critical problems. Sandia also has experts in materials science and computational simulation of materials, experience in handling large amounts of data, and know-how in writing codes for high-performance computers.

Additive manufacturing, typically synonymous with 3-D printing, encompasses techniques to make parts or whole assemblies in plastic, ceramic, or metal.

Additive manufacturing handles complex shapes

New AM technologies, particularly those that produce metal, open possibilities for designs that previously were not realistic because they were too complex for conventional manufacturing. “We need to develop computational tools that will enable us to make the leap to new types of designs; tools that will make modern computer-aided design systems seem as quaint as drafting tables and T-squares,” says manager Andre Claudet (2617).

Sandia is interested in additive manufacturing for nuclear weapons components because the technique can handle complex geometries and is particularly efficient for low-volume production. It’s especially compelling early in product development, when frequent design changes can be quickly evaluated, says Bradley Jared (1832).

Additive manufacturing and topology optimization together could combine several pieces into one, eliminating possible weak points, saving material, and removing the need to model what could happen at those interfaces, Bradley says. “If you can combine interfaces, suddenly you’ve simplified a part for simulation, for testing, and for qualification,” he says.

With topology optimization, engineers start with an allowable space — the area where the part fits — then specify functional requirements, “how heavy they will allow it to be, what material they want to use, the loads, and the constraints,” Ted says. “They allow the optimization calculations to determine where the material is needed, placing material only where it will be used most effectively to meet design demands.”

Thus, a designer no longer focuses on creating a shape, but is free to drive the design by the functions required. For example, a designer might choose tradeoffs between device rigidity and ability to conduct heat. Prioritizing stiffness produces a shell-like structure, with material pushed outward to maximize rigidity. If thermal transfer is more important, the optimization produces a structure with more massive legs, natural paths for heat. If stiffness and heat transfer are equally important, the result is a truss-like structure that adds stiffness but still has material in the legs.

Designers use computer-aided design programs to envision useful shapes for a function. But with topology optimization, that’s reversed. They tell the program, “‘Here are my engineering requirements; you create my geometry for me,’ a major revolution in how we do design,” Ted says.

He displayed a black plastic table and chair, inches in scale, an additive manufacturing example project that demonstrates how topology optimization works. The table top and chair seat are flat, but the organic-looking legs twist in shapes reminiscent of the inverted trunk of a swamp cypress.

Topology optimization program works  from specifications

The project defined an allowable volume for the table and chair, fixed positions on the floor for legs, and stipulated flat surfaces for the tabletop and chair seat, along with uniform loads — the weight they bear — then let the topology optimization program do its thing.

It requires engineering judgment and carefully specifying the entire problem. Parameters such as feature size control whether you get a tree trunk or a more spider web structure holding up the tabletop. If you don’t tell the program to secure the legs so the table doesn’t move, it adds cross members along the floor to increase strength, even though that also prevents a chair from sliding under the table. “With topology optimization, you get what you asked for, whether that’s what you wanted or not,” Ted says.

Thus, topology optimization requires what he calls interactive steering. If engineers watching a shape form on a computer screen realize they didn’t put in enough information, they can stop the program. “Where we stopped we say, ‘Add this additional constraint,’ and let it continue,” Ted says. “Even though the calculations are being done in batch mode on very large machines, we can still have an interactive design environment on those machines. We think it’s a very powerful addition.”

Interactive steering paid off in a test problem to design a bicycle frame. The engineer identified requirements for a seat, handlebars, and pedals, something to hold the tires, and loads to simulate a rider standing on the pedals rather than sitting on the seat. But as the shape evolved on the screen, he realized the specified load on the handlebars was in the wrong direction. He stopped, made adjustments, and finished the design.

Engineering analysis to predict optimal shapes takes full advantage of AM, but poses an extremely difficult computational problem. Static loads, something sitting on top of a table, are easy to include. Dynamic loads, someone jumping on the table, are not.

Optimization requires not only high-performance computing capacity but also expertise in modeling to include as much physics as possible. “If you want a really good optimization, you’ve got to include every possible physical environment that a part will see,” Ted says.

Simulating physics saves time, money

Manager Anthony Geller (1516) says it would be extremely expensive to use only experiments to understand the physics of how something works, and simulations save time and money. “If we need 100 tests, maybe we would do 90 of them through simulation and 10 of them experimentally for validation purposes. Also, the simulation gives us access to certain data points that would be difficult if not impossible to acquire through actual physical experiments,” he says.

A program assumes certain materials properties as it follows specifications for a design. But sometimes engineers overbuild because they’re uncertain about the properties. “The optimization says that if we have that tiny curved strut that’s very thin, that’s all the material you really need to carry the load,” Anthony says. “But if we have to make it thicker because of our uncertainty, we’re losing that benefit.”

Ted says Sandia is working on “robust optimization,” letting calculations derive a shape that will meet requirements with point-by-point uncertainties in material properties or in loading conditions. Such uncertainty quantification determines the likelihood of outcomes when some aspects of a problem aren’t known, and predicts results in a statistical sense.

Senior manager Mark Smith (1830) says that in the near term, additive manufacturing could save time and money in tooling, fixtures, and jigs used in manufacturing components since those items don’t have to be certified like an actual part. “We’re already making very extensive use of additive in those areas,” he says.

He believes Sandia can make significant progress in three to five years but says it could take a decade or more to reach the ultimate goal of design optimization, tying materials assurance and topology optimization together.

Researchers must balance what can be accomplished now with how much work is still needed to qualify parts for the stockpile. “I don’t want to minimize the potential benefit but I also don’t want to minimize that there’s still a lot of work to be done,” Anthony says.