Structural optimization of multiscale problems based on numerical homogenization using FE2 method

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The following goals of the project are based on existing FE2 realisations in own simulation tools.The computational methods of the FE2-strategy for the treatment of multi-scale problems will be enhanced by an analytical sensitivity analysis. Additionally, a structural optimization approach for problems consisting of objectives, constraints and design variables on different scales will be developed.The methodology will be applied to non-linear elastic materials and their optimal material design. The methodology is especially suited for problems which cannot be solved sequentially by separated optimisation problems on the micro- and macro-scale. Overall, the shape and the material parameters on both scales should be modified.The project focuses on two-dimensional simulation models for static problems using OpenMP parallelism on multi-core architectures.