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.
