Curved geometry provides architects with both impressive design and material savings

Researchers from Skoltech and Granada University have found ways to speed up the architectural design of vaults and domes with wavy patterns while preserving construction materials. By extending the applicability of a technique known as force density method to this new class of curved objects called corrugated surfaces, the team offers architects a way to unleash creativity and check budgets with the same token. This study was published in the Journal Engineering Structure.

“In architecture, saving resources and maximizing aesthetics is often seen as two mutually exclusive possibilities. This view expresses creativity by choosing a more primitive shape and choosing more structurally involved and expensive solutions that are not necessarily justified in terms of overall structural integrity.

“It shows that visual attraction and economy need not be at odds. The structure stated that Anastasiia Moskaleva’s research lead author, who holds a doctoral degree in Skoltech Mastileva’s mathematics and mechanisms.

When four walls or columns are topped with curved surfaces, i.e. vaults or domes, the shape itself makes the structure stronger than a flat rectangular slab of concrete. Its surface can be further strengthened by thickening it or attaching it to a hardening rib bone. This is an additional bar of material that thickens the surface at a strategic point. Previously, the Granada team’s Skoltech-University optimized the rib configuration to enhance curved shells designed via force density methods.

In their new research, researchers adapt the same method to designing wavy, wavy or corrugated surfaces.

“In this paper, we study how a geometric template called Q-Patterns can enhance the shell that acts as an architecture vault and dome,” says Moskaleva. “We propose a new approach to making the shell more stable: the shell is formed with a preset load distribution pattern that fuses ribs, waves, or folds into the structure.

The researchers calculated the stability of a dome with five different folding geometry. Each was calculated for a set of four columns, each serving as a contour of the four walls or as a foundational support. Previous studies have identified the loss of stability as the single most common failure mode of such structures.

The calculations performed by the team highlighted the corrugated dome shape, the most stable cover of the four walls and four columns, optimizing different geometry depending on the type of support used. One of the five patterns examined proved to be inferior in terms of stability regardless of underlying support.

“Our findings can expand the applicability of folded surfaces in architecture. It gives architects and spare computational resources and construction materials more freedom compared to adding materials to the entire surface,” Moscaleva said.

“In addition, simplification applies not only to structural design, but also to manufacturing. For miniature structures, it is easier and cheaper to create an essentially curved surface from metal, concrete or plastic. Cost and speed up construction.”

This study relied on a modified version of the force density method tailored to the design of the corrugated surface using Q-patterns that reflected the force distribution within the structure. The approach used is particularly suitable for structures made of isotropic materials. Its properties remain the same when tested in different orientations. One such material, steel, was estimated through numerical modeling and final element analysis performed by the team in this latest study.

However, this method is not limited to steel. Works with concrete, plastic, and other isotropic materials. Plastic shells are an option for miniature architecture. Gazebos, canopies, pavilions. Curved steel surfaces are useful for industrial structures, such as fuel storage and other liquids.

Researchers believe the method can even be adapted to composite materials containing fiber-reinforced plastics, but they believe that a more detailed numerical model will be required to explain the anisotropy of these materials.