Physics Practical Magic

A 3D-printed concrete shell can stay standing forever without a single piece of steel reinforcement thanks to an AI that solved a 350-year-old math problem.

April 23, 2026

Original Paper

Physics-informed, Generative Adversarial Design of Funicular Shells

arXiv · 2604.16621

The Takeaway

Large concrete structures usually need internal steel bars to stop them from cracking under tension. This design tool uses a physics-informed AI to find the funicular shape, which carries all the weight through pure compression. This specific geometric challenge has frustrated architects and mathematicians since the late 17th century. By using these optimized shapes, builders can create massive domes and bridges using far less material and zero steel. This technology could drastically reduce the carbon footprint of the global construction industry.

From the abstract

Shell structures are pivotal in the fields of architecture and engineering, due to their aesthetic appeal and structural efficiency. Recently, 3D concrete printing has reignited the interest in these structures. But, as printed concrete cannot be reinforced with steel, structures built in this way must be designed to withstand primarily pure compression: they must be funicular shells. Nevertheless, a fundamental challenge remains unsolved since Robert Hooke's discovered the catenary arch in 1675