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Multi-fidelity optimization of metal sheets concerning manufacturability in deep-drawing processes
(2023)
Multi-fidelity optimization, which complements an expensive high-fidelity function with cheaper low-fidelity functions, has been successfully applied in many fields of structural optimization. In the present work, an exemplary cross-die deep-drawing optimization problem is investigated to compare different objective functions and to assess the performance of a multi-fidelity efficient global optimization technique. To that end, hierarchical kriging is combined with an infill criterion called variable-fidelity expected improvement. Findings depend significantly on the choice of objective function, highlighting the importance of careful consideration when defining an objective function. We show that one function based on the share of bad elements in a forming limit diagram is not well suited to optimize the example problem. In contrast, two other definitions of objective functions, the average sheet thickness reduction and an averaged limit violation in the forming limit diagram, confirm the potential of a multi-fidelity approach. They significantly reduce computational cost at comparable result quality or even improve result quality compared to a single-fidelity optimization.
finite element simulation of sheet metal forming, shell elements are widely used. The limits of applicability of the shell elements are sometimes disregarded, which leads to an error in predictions of important values such as springback geometry. The underlying kinematic assumptions of the shell elements do not hold where the thickness of In the metal sheet approaches the value of the radius of curvature. Complex three-dimensional material behavior effects cannot be represented precisely as the result of the simplified kinematics. Here we present a model adaptivity scheme based on a model error indicator. The model-adaptive technique presented in this paper aides to resolve only the critical areas of the structure with a three-dimensional discretization while keeping reasonable computational cost by utilizing shell elements for the rest of the structure. The model error indicator serves as a guide for subsequent automatic adaptive re-meshing of the work-piece followed by a model-adaptive finite element analysis. The accuracy of the approximation obtained by the model-adaptive technique coincides well with that of a more expensive solution obtained with solid elements only.