Computer Aided Geometric and Functional Design

Prof M.I.G. Bloor
Dr J.M. Brown
Mr D.R. Clother
Dr M.J. Wilson

The PRIDE Project

A novel method for the design of surfaces for computer-aided design (CAD) has been developed. The approach regards surfaces as solutions to partial differential equations (PDEs), in particular elliptic PDEs, and creates a surface as a solution to an appropriately chosen boundary-value problem. The method defines a surface in terms of data distributed around its edges, i.e. along its boundary curves.

The major difficulty in the analysis inherent in the design of engineering surfaces is being able to represent them by a method which involves few design parameters and which allows easy manipulation in a predictable way. It has been demonstrated how the PDE Method can describe the surfaces of complicated objects, such as cylinder heads for internal combustion engines, ship hulls, and marine propellers. NASA has funded research to investigate the way in which the PDE method can be used to efficiently parametrise aircraft geometries, in particular the double-delta geometry characteristic of a high-speed civil transport.

Much of our research has been concerned with bridging the gap between design and analysis, with an emphasis on the efficient parametrisation of shape. Owing to its boundary-value approach, the method can define complicated surfaces in terms of a small parameter set, which makes optimisation of these surfaces computationally feasible. One of the most important aspects of the work is its use for automatic design for function. The aim of this part of the research is to develop a methodology whereby an initial design, parametrised by the PDE method, can automatically be optimised against suitable functional criteria, subject to constraints specified by the designer in order to ensure a sensible final design. Problems so far considered have included objects designed for their heat transfer, strength, hydrodynamic, or aerodynamic performance.