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How mathematical modeling can help predict crack formation and prevent disaster

On May 23, 2004, four people were killed and several were injured when a terminal collapsed at Paris’ Charles de Gaulle Airport. A section of the roofing fell onto the departure lounge below it. Furthermore, a day after the initial collapse, airport workers reported hearing “fresh cracking” sounds.

French authorities immediately launched a technical inquiry into the building failure. The investigation yielded several potential structural and procedural causes of the collapse, resulting in officials tearing down and rebuilding the terminal from scratch. The terminal is expected to reopen in 2007.

Blaise Bourdin, an assistant professor in LSU’s Department of Mathematics, spends most of his time developing mathematical models to identify ways to avoid catastrophes such as the collapse at the Paris airport. In fact, anything from a water dam to a space shuttle is a potential beneficiary of his research, which is funded by the National Science Foundation.

“If we can understand where and under what conditions cracks start and grow, we can create models that can determine how fast they will propagate along any surface or in any object,” said Bourdin.

Like many mathematicians, Bourdin starts with a series of equations and algorithms – a recipe of ingredients that represent various factors in a certain problem. Once these factors are determined, they are fed into a computer to create a model or simulation. One of Bourdin’s simulations, a hollow cylinder of aluminum filled with rubber, is pre-notched for the beginning of a crack. In the simulation, forces are applied to each side of the cylinder as Bourdin observes where the crack begins propagating and under what conditions it reaches a breaking point.

Bourdin’s area of interest is known as fracture mechanics—a highly active area of mathematical research with vital applications. Just as he observed fractures in the simulated cylinder, he can easily apply the same principles to a countless array of problems. He hopes that a more systematic approach can be developed from his simulations, which could lead to less human error and, among other things, safer travel.

“For instance, the front landing gear of an aircraft is hammered every single time it lands on a runway, thus it’s possible for some sort of fracture to eventually form. We can create a model of the landing gear and get a better idea of its lifespan and the forces acting upon it,” said Bourdin.

According to Bourdin, airlines typically dismantle their planes every few years down to the skeleton of the aircraft. Airline personnel search for cracks by x-raying every piece of the plane that is not welded to the frame. Bourdin’s models could be used to better determine the proper way to change the part outright or reinforce it.

Tools of the Trade

Bourdin has been at LSU four years and says one of the things that attracted him from New York University was LSU’s computational resources.

“With resources like the Center for Computation & Technology and LSU’s supercomputers, I can solve problems in my research that are thousands of times more complicated than I could do before in a fraction of the time,” said Bourdin.

In addition to airline safety, Bourdin hopes his research and LSU’s computational resources will be used to develop aerospace applications that would examine cracks possibly responsible for the Space Shuttle Columbia disaster, as well as ensure the integrity of confinement tanks in the more than 100 nuclear reactors that generate electrical power in the U.S.

LSU Office of Research & Economic Development | LSU Office of Public Affairs
Spring 2007

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