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Section: New Results
Shape and topology optimization
Deterministic approximation methods in shape optimization under random uncertainties
G. Allaire and C. Dapogny
This work is concerned with the treatment of uncertainties in shape optimization. We consider uncertainties in the loadings, the material properties, the geometry and the vibration frequency, both in the parametric and geometric optimization setting. We minimize objective functions which are mean values, variances or failure probabilities of standard cost functions under random uncertainties. By assuming that the uncertainties are small and generated by a finite number of random variables, and using first- or second-order Taylor expansions, we propose a deterministic approach to optimize approximate objective functions. The computational cost is similar to that of a multiple load problems where the number of loads is . We demonstrate the effectiveness of our approach on various parametric and geometric optimization problems in two space dimensions.
Molding direction constraints in structural optimization via a level-set method
G. Allaire, F. Jouve and G. Michailidis
In the framework of structural optimization via a level-set method, we develop an approach to handle the directional molding constraint for cast parts. A novel molding condition is formulated and a penalization method is used to enforce the constraint. A first advantage of our new approach is that it does not require to start from a feasible initialization, but it guarantees the convergence to a castable shape. A second advantage is that our approach can incorporate thickness constraints too. We do not adress the optimization of the casting system, which is considered a priori defined. We show several 3d examples of compliance minimization in linearized elasticity under molding and minimal or maximal thickness constraints. We also compare our results with formulations already existing in the literature.
Identification of magnetic deposits in 2-D axisymmetric eddy current models via shape optimization
Zixian Jiang, Houssem Haddar, Armin Lechleiter and Mabrouka El-Guedri
The non-destructive control of steam generators is an essential task for the safe and failure-free operation of nuclear power plants. Due to magnetite particles in the cooling water of the plants, a frequent source for failures are magnetic deposits in the cooling loop of steam generators. From eddy current signals measured inside a U-tube in the steam generator, we propose and analyze a regularized shape optimization algorithm to identify magnetic deposits outside the U-tube with either known or unknown physical properties. Motivated by the cylindrical geometry of the U-tubes we assume an axisymmetric problem setting, reducing Maxwell's equations to a 2-D elliptic eddy current problem. The feasibility of the proposed algorithms is illustrated via numerical examples demonstrating in particular the stability of the method with respect to noise.