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Some of the projects our mathematical modellers have
been involved in:
Thin materials such as magnetic tape, paper, cellophane, plastics,
fabric and metals are often wound into rolls or coils to store for
future use. Flat strip needs to be wound without folding or cutting and
typically, strip is wound and unwound a number of times before its end
use. Winding stresses play an essential role in the structure of wound
coils via the frictional forces between wraps.
For a coil with inadequate inter-wrap pressure, the wraps may slip or
telescope (causing surface scuffing) or the coil may slump and collapse.
On the other hand, large internal stresses can cause increased creep
and stress relaxation phenomena, collapse at the bore, stress wrinkling
and rupture of the material in the coil, etc.
We calculate winding stresses for wound coils and have developed a
winding policy that achieves a target inter-wrap pressure. We also
examined the internal stresses for wound coils stacked in a store room
where the bottom ones experience a very high load. On calculating the
shear stress inside the coils we can determine slip zones of material in
the coils.
This work helps to protect wound coils during storage and transport,
which can improve profitability by waste reduction, and maintenance of
product quality.
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Curved, thin-walled structures called `shells' find increasing
application in modern industry due to a combination of their light
weight and mechanical strength. Motor vehicle bodies, engine liners,
roofs on buildings, skin panels on flight structures and submarines are
just some examples. Knowledge of the vibration behaviour of shells is
important, for example, to be able to prevent resonance from adjacent
oscillating parts of a machine, or to predict sound radiation from
structures.
We are collaborating with CTIP in an investigation of the poorly
studied phenomenon of mode transformation. This transformation is
characterised by dramatic changes in natural frequencies and mode shapes
which can accompany relatively small changes in shell curvature.
To date, the focus has been on a relatively simple, but important and
widely-used type of shell geometry -- an open cylindrical shell of
arbitrarily varying curvature and thickness. For this type of shell, we
are developing an analysis, based on asymptotic methods and scaling
which is providing a relatively simple method for predicting the shell's
vibration behaviour.
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 The
Australian Defence Forces (ADF) and the DSTO are engaged in a research
program to develop effective means of landmine detection. As most
landmines now contain only a small amount of metal, traditional
detection technologies which are based on metal detection are not
particularly effective. One of the new methods being investigated by
DSTO involves using thermal infra-red imagery to detect disturbances in
ground surface temperature which may occur above buried objects. This
method has the advantage of using the sun's energy and enables some
degree of remote detection.
Heat conduction models of both periodic and transient heating of the
soil have been developed. The periodic model relates to the natural
daily heating and cooling of the soil; while the transient model applies
to transient heat inputs arising from relatively short term events such
as the passage of clouds, local shading, or rain. These models allow
predictions to be made of the effect on the surface temperature
disturbance of parameters such as the kind of soil and buried object,
the depth of the buried object, and the surface heat input.
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Coke is produced from crushed coal by heating it in a coke oven. A
coke oven is a refractory lined box that is heated by flues on the
vertical walls. During the heating process, the crushed coal first gives
off moisture, then softens and releases volatile gases. At higher
temperatures, it resolidifies to form coke.
Coke is required for use in the blast furnace process, which produces
molten iron. Australia is a significant producer of both thermal and
coking coal. There are large reserves of high quality coking coal in the
Bowen Basin of Central Queensland, from which about 60-70 million tonnes
are produced annually.
We are providing modelling of the performance of particular coals in
coke ovens, because different coals perform differently.
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 We have worked for a number of years with Sola, a major multinational
spectacle lens manufacturer, through their Research Centre in Adelaide.
The main area of work has been in the design, analysis, and
manufacture of progressive multifocal lenses. Progressive lenses are an
alternative to bifocals for the correction of presbyopia, the gradual
loss with age of the ability to focus at near distances. Like bifocals,
progressive lenses have different zones for correcting near and distance
vision, but the transition between these zones is continuous. This
eliminates many of the optical and cosmetic problems associated with
bifocals.
Mathematical modelling has provided a greater understanding of the
optical characteristics of progressive lenses. This understanding has
been incorporated into design software which allows lens performance to
be optimised and thereby helps spectacle-wearers see more clearly.
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