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Towards a space reduction approach for efficient structural shape optimization

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Shape optimization frequently works with geometries involving several dozen design variables. The high dimensionality itself can be an impediment to efficient optimization. Moreover, a possibly high number of explicit/implicit constraints restrict the design space. Traditional CAD geometric parameterization methods present serious difficulties in expressing these constraints leading to a high failure rate of generating admissible shapes. In this paper, we discuss shape interpolation between admissible instances of finite element/CFD meshes. We present an original approach to automatically generate a hyper-surface locally tangent to the manifold of admissible shapes in a properly chosen linearized space. This permits us to reduce the size of the optimization problem while allowing us to morph exclusively between feasible shapes. To this end, we present a two-level a posteriori mesh parameterization approach for the design domain geometry. We use Principal Component Analysis and Diffuse Approximation to replace the geometry-based variables with the smallest set of variables needed to represent an admissible shape for a chosen precision. We demonstrate this approach in two typical shape optimization problems.

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This work has been supported by the French National Research Agency (ANR), through the COSINUS program (project OMD2 no. ANR-08-COSI-007). The authors acknowledge the Projet Pluri-Formations PILCAM2 at the Universite de Technologie de Compiegne (URL: http://pilcam2.wikispaces.com) for providing HPC resources that have contributed to the results reported.

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Correspondence to Piotr Breitkopf.

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Raghavan, B., Breitkopf, P., Tourbier, Y. et al. Towards a space reduction approach for efficient structural shape optimization. Struct Multidisc Optim 48, 987–1000 (2013). https://doi.org/10.1007/s00158-013-0942-5

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  • Model reduction
  • CFD
  • Diffuse approximation
  • Space reduction