Australian Mathematical Society Mathematics Department at Macquarie University

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50th Annual Meeting of the Australian Mathematical Society

Plenary Talk in Macquarie Theatre

Wednesday 27 September 2006 at 10:00

Frank de Hoog (Commonwealth Scientific and Industrial Research Organisation)

Industrial Mathematics - a CSIRO Perspective

The application of mathematical modelling has been spectacularly successful in understanding, controlling and improving industrial processes, despite the fact that many industrial processes are quite complex and many models used to describe them are relatively simple. We examine this apparent contradiction by investigating a number of different phenomena that play a role in industry and elsewhere. A unifying feature is that these phenomena are often robust in the sense that they hold under a wide range of operating conditions. The explanation from a mathematical point of view is that the phenomena in question is often only weakly coupled to their environments and that only a few key non-dimensional parameters associated with the underlying mathematical description dominate. Such problems are often amenable to simplifying mathematical analysis and approximation techniques.

In order to explore this further, we investigate a representative example - namely, the analysis of the stresses in coils of strip metal. The analysis of this problem has a long history with roots going back to the winding of gun barrels with wire. Such deliberations underpin the calculation of residual stresses that result from a specified winding policy that is performed routinely in the sheet metal, plastics and paper industries. This is the forward problem. However, as is often the situation in practice, the solution of the forward problem is often performed as an iterative step in solving the backward (inverse) problem; namely, the determination of a tension policy that achieves a predetermined residual stress profile. Normally, an inverse problem is more difficult to analyse than the forward problem. The converse holds for the coil winding problem. This has led to an analysis of stresses in coils that is fundamentally different from that obtained previously.

Finally, we explore the role of computationally intensive simulation for industrial modelling.