The dragonfly wing pattern reinforces vaults and domes better than ancient Roman and technology-generated methods.

Skoltech researchers and their colleagues at the University of Granada, Spain, have determined the most effective ways to strengthen vaults and domes in architecture. The team compared how well various traditional and unconventional designs of stiffening ribs enable a structure to resist both uniformly distributed and asymmetrical loads.

Published in Thin-walled structuresThe study relied on numerical analysis and physical experiments and led its authors to propose an unprecedented rib pattern inspired by dragonfly wings, which surprisingly outperformed all other arrangements examined in the paper.

Reinforcing ribs have been used in vaults and domes since Roman times to allow thinner structures for technical and aesthetic reasons. This solution conserves materials and allows for more complex designs, larger column-free floor spans, and larger windows, such as those in Gothic cathedrals.

The use of ribs to distribute the weight of the ceiling is also not foreign to civil engineering. Certain metro stations and industrial facilities offer a striking example of this.

However, when it comes to selecting the geometric pattern for rib placement, it usually comes down to old favorites, such as barrel vaults with coffered ceilings – a long arch with a square rib reinforcement lattice at the interior – and the cross vaults, familiar from early Roman architecture and the Renaissance churches which are inspired by it. No complex analysis is usually attempted to identify the potential for improvement.

“We decided to analyze several rib designs to see which of them could better resist vertical and asymmetric loads,” said Anastasiia Moskaleva, lead author of the study and a Ph.D. at Skoltech. student in the Mathematics and Mechanics program.

“We conducted numerical simulations and experiments on the curved surface polymer composite shells designed in last year’s study, equipping them with reinforcing ribs positioned in five different ways, limiting the amount of material spent on the ribs in each case to half the material used in the shell itself.

Pictured above, the original hull was developed via an optimization technique called shape finding, in which the final shape is obtained through a logical process inspired by natural processes.

This goes back to experiments like those carried out by Antoni Gaudí, who used to achieve very effective shapes by suspending models in the air to let them sag under their own weight. He then took the form they had taken and reversed it. In fact, he let gravity do the work, which is why this approach is often called “form follows force.”

The five stiffening rib designs initially studied by the researchers included two traditional designs: the coffered ceiling and the cross vault, as well as two layouts obtained via topology optimization. The upper pattern of the central column was achieved by optimizing the thickness of the shell at each point, effectively redistributing material where it is most needed.

The bottom pattern was achieved by starting with two shells on top of each other and optimizing only the bottom one as the seed structure for the ribs. Finally, the fifth biomimetic pattern appears in turtle shells, dragonfly wings and elsewhere, but not in its mathematically pure form known as the Voronoi diagram.

Physical experiment and numerical simulation showed that topologically optimized designs were superior to conventional and biomimetic rib arrangements in resisting central loading. But the situation was reversed when an asymmetrical load was applied, which roughly corresponds to snow accumulating on one side of the roof or many people moving in groups from one place to another.

In this situation, cross-vault was king, followed by bulk topology optimization. It is important to note that the coffered ceiling and the Voronoi pattern stood out as the two options whose performance suffered the least when changing from symmetrical to asymmetrical loading.

“This prompted us to combine Voronoi’s model with the best-optimized layout from the vertical loading experiment in the hope of getting the best of both worlds,” Moskaleva commented.

“We carefully examined the structure of the dragonfly wing, which does not exactly follow the Voronoi model, and found that the reinforcing ribs it contains can be considered to form two distinct groups. There is the type the stiffer one which prevents twisting And then there are thinner ribs, which ensure the overall structural integrity of the wing and we thought we could replicate that in the arches.

To obtain the sixth hybrid pattern, the team first repeated the topology optimization, but with a tighter constraint on material expenditure, allocating 70% of the rib material to these primary ribs. This was followed by an additional step in which a parametric algorithm used the remaining material, filling the finer secondary ribs according to the Voronoi pattern.

The idea worked so well that the new combined model outperformed each of the five initial configurations in both scenarios: for central and asymmetric loads.

“This demonstrates that topology optimization could really do a lot for structural design. And yet it’s almost never used in civil engineering, only in mechanical engineering for things like automobile and aircraft parts,” Moskaleva said.

“Of course, optimized shapes are quite complex and therefore difficult to manufacture. But once parts of a standard building, such as a parking lot, have been optimized and can be reproduced on demand, it will pay off in the long run in because of the material preserved And then there is greater creative freedom for the architect.