The goal of this project is to provide affordable numerical methods for the optimisation of composite structures with randomly distributed heterogeneities. We assume that the elastic constants of inclusions can be chosen within a range of admissible values. Depending on the load in the structure, an optimal set of these parameters can be found. We investigate the reduction of numerical costs associated to the calculation of the gradient of the objective function with respect to the material characteristics. A classical homogenisation technique is used, and associated with certified reduced order modelling.
The reduction of the RVE problem relies on the Galerkin-POD. An upper and a lower bound for the reduced order modelling error are developed. They upper bounding technique makes use of the concept of the Constitutive Relation Error (see below).
Kerfriden, P., Ródenas, J. J. and Bordas, S. P.-A. (2014), Certification of projection-based reduced order modelling in computational homogenisation by the constitutive relation error. Int. J. Numer. Meth. Engng, 97: 395–422. doi:10.1002/nme.4588
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