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Topological derivative for multi-scale linear elasticity models applied to the synthesis of microstructures

The research reported in this paper was developed in collaboration with colleagues at the National Laboratory for Scientific Computing (LNCC) in Brazil and the University of Avignon (France). The collaboration with LNCC was funded by a Royal Society International Joint Project (RS Grant no. JP080066). The paper follows up from fundamental theoretical results obtained by the UK and Brazil researchers (within the context of the same RS-funded international collaboration project) and proposes a new algorithm for the optimisation of elastic microstrutures. The techniques proposed here led to further collaboration with LNCC and University of Avignon, funded by the Brazilian Government, in the development of new algorithms for structural optimisation under point-wise stress constraints.