# Buckling and cracking in structural beams

Beams are important structural components in many constructions. Although every precaution is taken by architects, builders, and engineers there have been a number of disasters caused by the failure of these essential pieces of structure. The occurrence of devastating disasters has generated great interest in the study of engineering and structure; in particular, the understanding of the beam as a structural element and how it behaves under loads and other forces.

The Euler-Bernoulli beam equation is a common classroom example in university engineering classes. This linear model captures very basic movements of a beam under a load. While more general models exist in the literature, Dr. David Yang Gao was the first to observe that many disasters caused buckling of beams within structures, and as a result he proposed that a non-linear term to model buckling and cracking of the beam should be added to the model.

One of the most important steps in developing mathematical equations to model any real world situation is that of parameter estimation. Given some experimental data, how do you work backwards and refine your equations to best describe the data? Typically the first time we see this is when we are asked to find a “line of best fit” in high school. When the equations become more complicated, the act of finding the “best fit” becomes significantly harder.

Dr. Kim Levere works with students and collaborators to develop and implement efficient techniques for solving this inverse problem for situations as described above. This work is ongoing and students interested in learning the computational and mathematical skills necessary to model such phenomena should contact Dr. Herder to see how they can contribute. High school students interested in developing the mathematical and statistical skills to tackle a real world problem such as this should consider our Mathematical Science Major, with an Area of Emphasis in Energy and Mass Transfer.