On-the-fly model reduction for large-scale structural topology optimization using principal components analysis

Manyu Xiao (1) , Dongcheng Lu (1) , Piotr Breitkopf (2) , Balaji Raghavan (3) , Subhrajit Dutta (4) , Weihong Zhang (1)

1 NPU - Northwestern Polytechnical University [Xi'an]
2 Roberval - Roberval
3 LGCGM - Laboratoire de Génie Civil et Génie Mécanique
4 National Institute of Technology [Silchar]

Despite a solid theoretical foundation and straightforward application to structural design problems, 3D topology optimization still suffers from a prohibitively high computational effort that hinders its widespread use in industrial design. One major contributor to this problem is the cost of solving the finite element equations during each iteration of the optimization loop. To alleviate this cost in large-scale topology optimization, the authors propose a projection-based reduced-order modeling approach using proper orthogonal decomposition for the construction of a reduced basis for the FE solution during the optimization, using a small number of previously obtained and stored solutions. This basis is then adaptively enriched and updated on-the-fly according to an error residual, until convergence of the main optimization loop. The method of moving asymptotes is used for the optimization. The techniques are validated using established 3D benchmark problems. The numerical results demonstrate the advantages and the improved performance of our proposed approach.

Mots clés: Meta-modeling; Design; High-performance computing; Additive manufacturing; 3D printing; POD

Domaines: Génie mécanique [physics.class-ph]

Manyu Xiao, Dongcheng Lu, Piotr Breitkopf, Balaji Raghavan, Subhrajit Dutta, et al.. On-the-fly model reduction for large-scale structural topology optimization using principal components analysis. Structural and Multidisciplinary Optimization, 2020, 62 (1), pp.209-230. ⟨10.1007/s00158-019-02485-3⟩. ⟨hal-02531425⟩