Reporter 453, 5 June 2000
Mathematics at the University is helping manufacturers save millions on testing the performance of different designs of products - from supersonic aircraft to artificial limbs.
A system of partial differential equations, developed by Professors Malcolm Bloor and Mike Wilson, helps computer-aided design (CAD) software to generate models of the objectís surface that will respond to changing conditions in order to improve the performance of the object.
Down to earth: mathematician Mike Wilson demonstrates the drag factor in aircraft design
While conventional CAD systems represent the surface shape of an object in simple terms, the geometry created by using partial differential equations (PDEs) takes this a step further by allowing the designer to Ďfactor iní processes like heat transfer or air or water resistance.
In designing an aircraft wing, a programme using PDEs can calculate how a change in surface shape will increase or decrease the drag effect. By mapping the parameters of the objectís shape against those of the drag, it can enable the designer to look at a given part of it and work out how drag could be minimised in that area.
"Using mathematical analysis for design optimisation in something as big as a ship or an aircraft is dramatically less expensive than the alternative of building, modifying and testing a series of prototypes," said Professor Bloor. "Some of our results have been counter-intuitive: on an aircraft wing, it produced structures at the tip that maintained the distribution of lift along the wing - features that a designer might not have considered."
Current research is exploring the potential of PDEs in the medical area, including the geometry of the heart. Work is also being done to use the method to represent the shapes adopted by biological membranes. The Leeds mathematicians are collaborating with colleagues at St Jamesís University Hospital and the University of Strathclyde to find how the new approach can help optimise the design of prosthetic limbs.
"This all began more than 10 years ago, as a piece of speculative research," said Professor Wilson. "Since that time, it has been successfully applied in a wide range of down-to-earth areas."
Further information on Professor Bloor and Professor Wilson's research is available on the following pages:
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