An emerging industrial design technique gets a speed boost

What is Topology Optimization? Redefining Industrial Design

With the rise of 3D printing and other cutting-edge advanced manufacturing methods, engineers are no longer limited by traditional fabrication constraints. This has paved the way for design strategies like topology optimization—a sophisticated, computer-driven technique that systematically determines the most effective distribution of material within a given design space. The result? Optimized structures that achieve maximum performance with minimal material usage, leading to breakthroughs in fields from aerospace to medical devices.

As Boyan Lazarov, a research scientist at Lawrence Livermore National Lab, aptly puts it, “In the past, when we wanted to design something, we’d use simple geometric forms and then connect them together in some way. But with topology optimization, we start with a blank canvas and we use a computer to place material on it such that we eventually get a structure that performs optimally with respect to certain criteria.” It’s akin to “painting in 3D,” where the algorithm intelligently places material to sculpt the ideal form.

The Challenge: Computationally Intensive Design

While the benefits of topology optimization are clear, the underlying process is inherently iterative and computationally demanding. The optimizer continuously refines its material pattern, adding or removing material in tiny increments, then rigorously testing the design’s physical properties with each iteration. This cycle repeats until the algorithm converges on a final design that maximizes structural integrity while minimizing material. For complex designs or high-resolution models, this can mean algorithms running for days, or even weeks, even on powerful high-performance computing clusters. This significant time and resource investment has been a major barrier to wider adoption and rapid prototyping in industrial settings.

Introducing SiMPL: A Game-Changer in Algorithm Optimization

A collaborative research team, including mathematicians from Brown University, Lawrence Livermore National Laboratory, and Simula Research Laboratory in Norway, has unveiled a revolutionary solution: the SiMPL (Sigmoidal Mirror descent with a Projected Latent variable) method. This innovative approach dramatically improves the speed and stability of topology optimization algorithms, as detailed in their recent papers in the SIAM Journal on Optimization and Structural and Multidisciplinary Optimization.

Brendan Keith, an assistant professor of applied mathematics at Brown, highlights the breakthrough: “Our method beats some existing methods by four or five times in terms of efficiency. That’s a huge computational savings that could enable people to make designs more quickly and inexpensively, or to develop more complex designs with higher resolution.”

The SiMPL method tackles a common inefficiency in traditional optimizers: the generation of “impossible” material values (less than zero or more than one) in discrete design pixels. These invalid assignments force algorithms to waste iterations on corrections. SiMPL cleverly streamlines this by transforming the design space into a “latent” realm, allowing material values to approach infinities without reaching them. These transformed values are then mapped back to the valid 0-1 range for each iteration, effectively eliminating invalid solutions from the outset.

Impact and Future Implications for Digital Fabrication

Benchmark tests reveal that SiMPL requires up to 80% fewer iterations compared to conventional algorithms to achieve an optimal design. This translates into drastically reduced computing time—often shrinking a design process from days to mere hours. Such efficiency gains make sophisticated topology optimization more accessible across a broader spectrum of industries, from automotive to consumer electronics, and enable the exploration of designs at much finer resolutions than previously feasible.

In a move to accelerate innovation, the team has made a version of the SiMPL algorithm freely available. Dohyun Kim, a postdoctoral researcher at Brown and lead author, notes, “While the mathematical theory behind this algorithm is quite complicated, it’s actually quite simple to incorporate into standard topology optimization methods with just a few lines of code. We think this could be quite impactful in the engineering community.” This accessibility positions SiMPL as a pivotal development in the realm of algorithm optimization for digital fabrication, promising to unlock new possibilities in product design and engineering.