The Polyhedral Structures Laboratory, a research group based out of PennDesign, is showcasing an exhibit at the Pennovation Center that teases their work on designs with wide-reaching implications for construction.
A model of an ultra-transparent bridge made of glass sheets, with a structure of polyhedral cells as hollow glass blocks. Use of materials and resources is minimized in the design, which was developed with the use of 3-D graphic statics.
A culmination of work in mathematics, structural engineering, and architecture is the Polyhedral Structures Lab (PSL), a cohort of undergraduate, graduate, and postdoctoral student researchers led by Masoud Akbarzadeh, an assistant professor of architecture in structures and advanced technologies at the School of Design. The lab’s mission? Nothing short of rethinking and reshaping today’s construction design and practice through these disciplines’ common language of geometry.
“It’s an intersection between computer science, material science, structural engineering, architectural design…We have quite a bit of everyone,” Akbarzadeh says. “We’re trying to make a base foundation for this research to grow further because if this method works—and it shows it works—it can be applied not only to architecture and structures, but also to the design of cars and airplanes.”
In essence, Akbarzadeh and his team extend the hand-drawn graphic statics method—once used to diagram the structural forces of buildings like the Eiffel Tower, for example—to design their way around the need for heavy construction materials in three dimensions. The technique, which is called 3D graphic statics, draws from the principles originally proposed by William John Macquorn Rankine and James Clerk Maxwell, whom Akbarzadeh studied and analyzed in depth while working toward his Ph.D.
Conceptually, the idea of PSL goes back to 2012, when Akbarzadeh began work toward his doctorate in structural design at the ETH Zurich, after completing his master’s degree in architecture at MIT.
A discrete structure, designed by Ali Tabatabaei Ghomi and Ayodh Kamath.
“By the time I graduated, I felt, ‘OK, there should be a way I can connect this idea of design and structural engineering,’ because there is a big chasm between the two,” Akbarzadeh says. “Usually, structural engineers talk back to architects and say, ‘You do not consider physics,’ and architects say, ‘You’re not creative enough.’ So, there’s always this conflict between architects and structural engineers, and as a person having been trained as both architect and structural engineer, I thought I might be able to reconcile these two. And I can do something about it because I have the education in both sides.”
After joining Penn in December of 2016, Akbarzadeh launched PSL in January of 2017 as a way to bring together disciplines and build upon the graphic statics principles of Maxwell and Rankine. The primary goal of the lab, he says, is to design efficient spatial structures using software he’s created based on the 3D graphic static techniques that he developed in his Ph.D. work.
A historic structural example of the efficient structures, he says, is Spain’s elaborate Sagrada Familia church that was designed using a “hanging chain” method, which is an intuitive form-finding method developed by Robert Hooke in 1675.
“If you have the right form,” Akbarzadeh explains, “you can reduce the material and work with efficient and elegant forms.” The difference, in product, is that they can create designs that carry a surprising amount of weight while not requiring as many materials. One object they’ve created, he says, weighs in at 24 pounds but can carry a load of 50,000 pounds—the equivalent of four elephants on top of one another.
An ultra-thin concrete prototype being load-tested. The object was found to be able to withstand the weight of four elephants.
“Because we are using the right geometry to develop that form, we are able to get a really good performance out of that material,” he says. “This is what we do in my lab.”
Unconventional structural forms then become possible when working with conventional materials through a new lens, he adds. With plenty of interesting creative possibilities for architects, to boot—a boon to the design process, because architects often are more comfortable with geometry than mathematics.
“There’s a lot of art happening here,” Akbarzadeh adds.
Also notable is that the root of the polyhedral patterns applied in these designs are also found in nature.
“If you take a section of a body, a femur, look at the spatial structure inside the bone and you see the stress patterns that follow the direction of forces” Akbarzadeh explains. “They’re all polyhedral systems. The method we’re using is applicable to the really small scale—the scale of a bone—to the scale of a bridge.”
And he means “a bridge” quite literally: His lab is currently working on developing an “ultra-transparent” bridge made entirely of thin layers of glass that, he says confidently, would be designed so efficiently that it could go toe-to-toe with the harder, more conventional materials.
A model of that bridge is included in the “Spatial Efficiency” exhibit, on display this week at the Pennovation Center, supported by PennPraxis, and as part of Design Philadelphia, through Friday, Oct. 12, from 9 a.m. to 5 p.m.
Julie Donofrio, managing director of PennPraxis, explains that the seven-object exhibit, broken down by categories like “spatial tensile structures” and “design infrastructure,” was a perfect fit for the Pennovation Center. They learned from a historical analysis that the site has a long-running history as, Donofrio says, “a seat of innovation” in the city—particularly with transportation and infrastructure, considering the innovative-for-its-time Gray’s Ferry bridge.
Spatial, discrete structures. They're designed using geometric principles of equilibrium in 3-D.
“When we saw the work, we knew it would be an amazing exhibit because it’s 3-D and visually intriguing, and a representation of the innovative work coming out of PennDesign,” she says. “It’s exactly what we wanted to showcase [at the Center].”
She hopes the local design community—and out-of-towners in the city for DesignPhiladelphia—will turn out to get a look at what the lab is working on.
Akbarzadeh plans to work with PennPraxis to bring the exhibit on the road and travel to other venues, whether in Philadelphia or elsewhere.
The Polyhedral Structures Laboratory is housed at the Pennovation Center and brings together designers, engineers, and computer scientists to reimagine the built world. Using graphic statics, a method where forces are mapped as lines, they design forms that balance compression and tension. These result in structures that use far fewer materials while remaining strong and efficient.
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