Keywords: self-designing structures, optimisation, EMERGE, reverse adaptivity.

The research program entitled 'Self-Designing Structures' developed two and three- dimensional topological optimisation computer programs based on the iterative use of finite elements. Where the stresses were high, material was added. Where the stresses were low, material was taken away. The paper presents an outline of the EMERGE program, the Element Removal and Accretion algorithm and the Evolutionary Material Translation algorithm. Three problems were solved using the Self-Designing Structures optimisation method.

The Self-Designing Structures research developed a number of algorithms as follows: 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.

From all the developments of Self-Designing Structures, Evolutionary Material Translation and Element Removal and Accretion, the extended version of the Hard Kill method is described in this paper. Evolutionary Material Translation radically improves mesh handling and appropriateness, producing inherently well defined structures after each refinement and provides a means of addition and removal of material in an evolutionary way.

The main advantage of the Evolutionary Material Translation over traditional shape optimisation methods is that it possesses the generality of all evolutionary methods and has simplicity and generalisation in its material addition and removal algorithms. Another advantage of Evolutionary Material Translation is that the algorithms can reduce the maximum stress in a structure whilst keeping constant, or even decreasing the amount of material used. This is not the case with a removal- only algorithm such as Hard Kill, yet this is a very real objective of structural optimisation. Although Hard Kill or Reverse Adaptivity could use a large mesh to enclose any parts of the design that would be created by addition in Evolutionary Material Translation, it would present a large increase in computational resources. Evolutionary Material Translation improves structural resolution as the evolution proceeds. If Hard Kill wanted to imitate such fine resolution, it would require a large number of switched-off elements. In this approach, it is possible that high stresses might occur near to any boundary. Evolutionary Material Translation can be restricted to add or remove material within certain specified design domains. Another advantage is that it can be readily extended to three-dimensional design problems.

The Element Removal and Accretion method is a version of the Hard Kill method. Starting with an initial, uniform finite element model, Hard Kill then iteratively carries out modifications to the mesh based upon new analyses of the model after each modification. The modifications made in Hark Kill typically involve setting the Young's modulus of low stressed elements to almost zero. This reduces their load-bearing capability, and hence effectively removes such elements from the model. The model is then re-analysed, and the process repeated until a satisfactory structure is obtained.

Element Removal and Accretion was initially developed to provide a means of comparison with the results obtained from other refinement methods. Nonetheless, additional capabilities have been added namely; redesign in terms of strain energy as well as stress, multiple load cases, non-design regions, element addition outside of the original domain, evolution for shape as well as topology and an ability to handle pressure and gravity loads as well as point loads. A main advantage is its straightforward implementation and its ability to handle an extensive range of problems.

The paper shows how the research program entitled 'Self-Designing Structures' has developed two-dimensional topological optimisation computer programs, based on the iterative use of finite elements. Where the structure's stresses are high, the boundary has been redrawn with the effect that material is added. Where the stresses are less than a specified cut off stress, the boundary is redrawn and material taken away. Smoothing of the redrawn boundaries takes place. An outline of the EMERGE program and two of the algorithms developed are given. These two algorithms are used to solve three problems. The first problem is a loaded concrete block overlaying soil for which there is no analytic solution. A solution is presented. The second and third problems represent a loaded cantilever. There is no analytic solution for the first cantilever with which to compare the Self-Designing Structures solution, but the Self-Designing Structures solution for the second cantilever agrees with the analytic solution.

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