Architects gain a new superpower for complex curved designs

Architects place high priority on surfaces that can bear their own load. Some visually appealing examples are known as shells, and these have traditionally been made from reinforced concrete. Modern architects, however, are interested in limiting concrete due to its cost, waste, and lack of visual transparency. This has led to growing interest in gridshells, which use intersecting curved elements of metal, glass or timber to span wide areas without interior supports.

Why Gridshells Are Gaining Interest

Gridshells are well suited for covering expansive public spaces without columns. They are found at sites such as train station entrances, restored historic courtyards, and public squares. Notable examples include the British Museum's Great Court, the glass roof at the Dutch Maritime Museum, and New York's Moynihan Train Hall. Although these structures showcase what gridshells can achieve, designers have lacked standard computational tools that can efficiently manage the wide range of shapes they might want to build.

Masaaki Miki of the University of Tokyo and Toby Mitchell from the engineering firm Thornton Tomasetti collaborated to address this gap. Their new algorithm identifies ideal gridshell shapes that support complex geometries while still maintaining structural reliability.

Solving Long-Standing Challenges in Gridshell Design

Even though gridshell projects exist, the many geometric, mechanical, fabrication and construction requirements have made them difficult for most clients to pursue. Miki and Mitchell had already introduced a NURBS-based system capable of addressing many of these issues within one computational framework. However, two major limitations remained: their earlier method struggled with highly irregular shapes, and the computing time required was not practical. The updated method removes these obstacles, creating a more efficient workflow and making advanced gridshell form-finding feasible for a larger group of architects and designers.

"The project began in 2020 with an interest in shell structures, often made of concrete. Traditional designs aim for shapes that carry their own weight entirely through the force of compression, but this limits how expressive or sculptural they can be," said Miki. "We set out to find new ways to design shells that consider forces of compression as well as tension, allowing greater design freedom. We adapted our approach to more modern metal-and-glass gridshells, developing methods to balance mechanical reliability, aesthetics and ease of construction. Recent advances in computational speed have made it possible to solve such complex conditions using rigorous methods."

Using NURBS to Improve Precision and Speed

A major strength of the new method is that it works directly with NURBS surfaces. Unlike mesh-based approaches that use thousands of triangular pieces, NURBS provide smooth, continuous and mathematically accurate representations of curved surfaces. Because NURBS are already widely used in architectural design, integrating this method into existing workflows is straightforward. The research team created a plug-in for Rhinoceros, a popular NURBS-focused CAD program, allowing architects to use the approach within familiar software.

The method represents stress distribution on a NURBS surface and uses newly developed algorithms that increase processing speed by 98%. This improvement removes the need for high-end GPUs and provides a more accessible way to generate shapes that meet both geometric and structural requirements. The resulting gridshells remain stable under gravity and support metal-and-glass construction that is practical to assemble.

"Because we are addressing a real-world problem, we have been rigorously validating our solutions by several test methods we also developed," said Miki. "When the tests revealed failures in the method, it was stressful. However, we are now totally happy because all solutions pass the tests."

Future Directions

While the current research focuses on metal-and-glass gridshells, the team plans to expand the technique to include composite timber gridshells in the future.

This research was partially supported by the Nomura Foundation, the JSPS Grants-in-Aid for Scientific Research (KAKENHI; grant number 23K17784), and JST ASPIRE (grant number JPMJAP2401).