Keywords: optimisation, self-designing structures, finite element method, topological optimisation.

The research program entitled 'Self-Designing Structures' has developed a suite of computer programs capable of both two and three-dimensional topological optimisation. The Self-Designing Structures optimisation research models the natural behaviour of bone where, when stressed, the bone adds material and when not stressed, the bone discards material. The Self-Designing Structures program uses a similar methodology, but based on the iterative use of finite elements. The structure is reshaped and remeshed at each design iteration. The paper presents an outline of some of the algorithms developed and presents the results of a number of practical industrial engineering problems.

In continuous structures, the configuration of the structure is defined by general shape parameters. Shape design variables, describing the boundary of the structure, are usually optimised by numerical methods. A change in the shape of a continuum structure can cause particular difficulties in the solution process and requires a finite-element model that changes during the optimisation. To ensure the accuracy of the finite element throughout the design process, mesh refinement must be included in the iterative cycle as an optimum topology is approached so that the shape becomes very clear. This mesh refinement is a major part of the Self- Designing Structures approach.

The Self-Designing Structures research has developed a suite of computer programs capable of two-dimensional and three-dimensional topological optimisation. The algorithms developed for use in the EMERGE program include: a) Interactive Design Refinement, b) Approximate Contour Evolution, c) Orthogonal and Laminate Design, d) Plate Depth Refinement, e) Element Removal and Accretion, f) Reverse Adaptivity and g) Evolutionary Material Translation.

The SDS research developed finite element mesh based algorithms for determining the optimal structural solutions to engineering redesign problems. The research produced a means of automatically developing from an initial structure, subject to given boundary conditions, loading and maximum and minimum stress requirements of a final structure where the material used in the structure is minimised. The methodology is based on the iterative use of finite elements, with the structure reshaped and remeshed at each design iteration. EMERGE produces optimal designs for two-dimensional and three-dimensional plate structures and three-dimensional solid structures while the structures themselves may be made of more than one material type. EMERGE can obtain any geometric shape required by the solution. EMERGE requires a finite element solver and has been interfaced with several commercial packages to ensure a high quality graphical user interface is used at all stages of the evolutionary process.

The motivation for the SDS research relates to the natural behaviour of bones. When bone is under sustained loading, large stresses give rise to a denser and stronger bone structure while low stresses cause a more porous and weaker bone structure. The SDS project adopts this technique by augmenting material in zones of high stress and removing material in zones of low stress.

The SDS research was very successful from the academic point of view. It trained six researchers in leading edge optimisation concepts and led to the publication of a substantial number of papers, mostly in excellent, high impact journals. The results were also placed before the engineering industry at various conferences.

The project was also very successful as a collaboration between industry and academia, with genuine advice and guidance from the industrial partners and with attempts made by the academics to solve genuine industrial problems, leading in at least one case to a significant commercial pay off. It also involved a transfer of technology in that the latest developments in optimisation algorithms were transmitted from the project to the industrial sponsors.

The only slightly disappointing feature of the project was the lack of transfer of the algorithms developed, into a commercial finite element program, which could have been used by the industrial partners and which would have given them in-house advantages, in evolving better designs. It had originally been intended to do this, but this area is still being pursued. It is hoped to continue the SDS research work in a further project, but the interaction with commercial software will be made an over- riding priority, in order to give the industrial partners a more tangible and quantifiable benefit.

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