Reduced order modeling for design optimization-with applications to metal forming and inverse problems
Résumé
The challenge of Reduced Order Modelling techniques is to provide approximate full-field simulations within delays compatible with the design process requirements. The POD and PGD approaches are particularly interesting when repetitive simulations are required, in optimization and reliability analysis.In this contribution, we present recent advances in reduced order approaches applied both to physical analysis and to geometry representation.The overall idea is to reduce one hand the physical field (displacements, stresses, temperatures…) in a non-intrusive manner and to define the reduced space of admissible shapes on another hand. This latter approach consists in representing the structure by means of projection of its level-set surface representation on a set of carefully chosen basis vectors. This allows us to identify the intrinsic dimensionality of the problem, independently of the original design parameters. Also, an optimal parameterization may be obtained automatically for arbitrary shapes, where the parameters are a priori unknown. This allows us to build a family of predictor-corrector optimization “manifold walking” algorithms in a reduced shape-space that guarantee the admissibility of the solution with no additional constraints.Several applications will be presented such as shape optimization of car engine intake duct, minimizing springback effect in 3D stamping process and identification of material parameters by instrumented indentation.1. Guenhael Le Quilliec, Balaji Raghavan, P. Breitkopf, A manifold learning-based reduced order model for springback shape characterization and optimization in sheet metal forming, Computer Methods in Applied Mechanics and Engineering, DOI:10.1016/j.cma.2014.11.029, 20152. Balaji Raghavan, Guenhael Le Quilliec, Piotr Breitkopf-, Alain Rassineux, Jean-Marc Roelandt, Pierre Villon, Numerical assessment of springback for the deep drawing process by level set interpolation using shape manifolds, International Journal of Material Forming, DOI:10.1007/s12289-013-1145-8, 20143. Mohamed Hamdaoui, Guénhaël Le Quilliec, Piotr Breitkopf, Pierre Villon, POD surrogates for real-time multi-parametric sheet metal forming problems, International Journal of Material Forming, doi :10.1007/s12289-013-1132-0, 20144. Balaji Raghavan ; Liang Xia, Piotr Breitkopf ; Alain Rassineux ; Pierre Villon,Towards simultaneous reduction of both input and output spaces for interactive simulation-based structural design, Computer Methods in Applied Mechanics and Engineering, DOI:10.1016/j.cma.2013.06.010, 20135. Balaji Raghavan, Piotr Breitkopf, Yves Tourbier, Pierre Villon, Towards a space reduction approach, for efficient structural shape optimization, Structural and Multidisciplinary Optimization, DOI : 10.1007/s00158-013-0942-5, 2013