Mathematics onboard

EU PLATO-N project on software-supported structural optimisation

Holes don’t weigh anything – that’s hardly surprising. But, if your aim is weight reduction, it becomes apparent how useful empty spaces can be. However, they don’t contribute to stability. That is why constructions that must be both resilient and as light as possible require the right balance of holes and load-bearing parts. This is particularly important in the field of aviation, where weight reduction can significantly reduce energy consumption and safety is paramount. An EU project for software-based design optimisation of aircraft involving mathematicians from Erlangen-Nuremberg University is now drawing to a close. It is already clear that the project has been a success.

“The EU support created the essential conditions for this unusual and successful development,” stressed Prof. Dr. Günter Leugering, Professor for Applied Mathematics II, who worked on this project with Prof. Dr. Michael Stingl, Junior Professor for Mathematic Optimisation. Additional research teams from Bayreuth (Germany), Haifa (Israel), Birmingham (UK) and Lyngby (Denmark) and industry actors EADS, Airbus UK, Altair, RISK and Eurocopter are involved in the PLATO-N project, which has been running for three years. The project, whose name stands for “Platform for Topology Optimisation”, has been supported since 2006 as a “Special Targeted Research Project” (STREP) within the European Union’s 6th Framework Programme.

PLATO-N builds on a previous project from the 1990s. When the Airbus 380, the world’s largest aircraft, was being planned one thing became clear: its weight was going to have to be kept very low if the giant was to run any chance of ever taking off. That meant radical reductions in the materials used in the project’s design. Integrating hollow spaces into the design appeared to offer a solution. But how could functionality and safety be ensured at the same time?

“The art of structure is where to put the holes,” acknowledged prize-winning French architect, Robert Le Ricolais, who, in the mid-1930s, wanted to introduce the principle of lighter, load-bearing outer shell constructions in the construction industry. However, this wonderful and simple line of thought contains no “technical teaching”, as demanded by patent lawyers. Mathematical abstraction offers a remedy. Mathematical “drilling”, without using any tools or materials, is the best way to ascertain where holes can be placed in aircraft construction without posing any risk, even when this only becomes clear on closer inspection. Nowadays, design is created onscreen in a virtual reality world where real materials are not cut or drilled. “Hole or no hole?”, “A lot of material or just a little?” has been transformed into a question for mathematics.

Sensational weight savings
These ideas inspired researchers from EADS Munich. Working with mathematicians from Bayreuth University and Erlangen-Nuremberg, they developed codes that enabled form and topology optimisation for the Airbus 380, and more specifically, for its forward fin, a key part of the wing. These codes made it possible to reduce the weight of the real structure by 33%. Presented to the public after a lengthy implementation process, the Airbus 380 has now been taking to the skies since 2006 – and mathematics is very much onboard.

After this sensational success, the aim was to consolidate and expand ideas behind software-based structural optimisation for use in other technologies. The way to the EU’s PLATO-N project was open: a simulation platform was sought to solve topology optimisation problems in aerodynamic practice. In the last three years, the five research teams have developed a comprehensive software package based on mathematical theories. It is now to be presented to the public. This will open up new dimensions in industrial design and lightweight construction. As spin-offs from the technologies developed in the EU project, material foams and other complex materials may see their structures optimised. This new approach is now being researched in the “Centre for Multiscale Modelling and Simulation” at the “Engineering of Advanced Materials” excellence cluster. Prof. Leugering is convinced: “Mathematics as a catalyst has always been relevant in interdisciplinary practical applications – and this relevance is only set to increase!”

Further information for the media:

Prof. Dr. Günter Leugering
Tel.: 09131/85-27509