A non-invasive node-based form finding approach with discretization-independent target configuration
Tóm tắt
Form finding is used to optimize the shape of a semi-finished product, i.e. the material configuration in a forming process. The geometry of the semi-finished product is adapted so that the computed spatial configuration corresponds to a prescribed target spatial configuration. Differences between these two configurations are iteratively minimized. The algorithm works non-invasively, thus there is a strict separation between the form update and the finite element (FE) forming simulation. This separation allows the use of arbitrary commercial FE-solvers. In particular, there is no need for a modification of the FE forming simulation, only the material configuration is iteratively updated. A new method is introduced to calculate the difference between the target and the computed spatial configuration. Thereby the target mesh is separated from the mesh for the FE forming simulation, which enables a more accurate and independent representation of the target configuration. In addition, the possibility of taking into account manufacturing constraints in the optimization process is presented. The procedure is illustrated for the example of the first stage of a novel two-stage sheet-bulk metal forming process.
Tài liệu tham khảo
Merklein M, Allwood JM, Behrens B-A, Brosius A, Hagenah H, Kuzman K, Mori K, Tekkaya AE, Weckenmann A. Bulk forming of sheet metal. CIRP Ann Manuf Technol. 2012;61(2):725–45. https://doi.org/10.1016/j.cirp.2012.05.007.
Schulte R, Hildenbrand P, Vogel M, Lechner M, Merklein M. Analysis of fundamental dependencies between manufacturing and processing tailored blanks in sheet-bulk metal forming processes. Procedia Engineering 207(Supplement C), 2017;207:305–10. https://doi.org/10.1016/j.proeng.2017.10.779. In: International conference on the technology of plasticity, ICTP 2017, 17–22 September 2017, Cambridge, United Kingdom.
Chenot J-L, Massoni E, Fourment J. Inverse problems in finite element simulation of metal forming processes. Eng Comput. 1996;13(2/3/4):190–225. https://doi.org/10.1108/02644409610114530.
Landkammer P, Steinmann P. A non-invasive heuristic approach to shape optimization in forming. Comput Mech. 2016;57(2):169–91. https://doi.org/10.1007/s00466-015-1226-2.
Landkammer P, Caspari M, Steinmann P. Improvements on a non-invasive, parameter-free approach to inverse form finding. Computational mechanics. Heidelberg: Springer; 2017. https://doi.org/10.1007/s00466-017-1468-2.
Caspar, M, Landkammer P, Steinmann P. Inverse from finding with h-adaptivity and an application to a notch stamping process. In: Computational plasticity XIV on fundamentals and applications. 2017.
Steinmann P. Geometrical foundations of continuum mechanics. Heidelberg: Springer; 2015. https://doi.org/10.1007/978-3-662-46460-1.
Altenbach H. Kontinuumsmechanik: einführung in die materialunabhängigen und materialabhängigen gleichungen. Heidelberg: Springer; 2015. https://doi.org/10.1007/978-3-662-47070-1.
Wriggers P. Nonlinear finite element methods. Heidelberg: Springer; 2008. https://doi.org/10.1007/978-3-540-71001-1.
Schmitt O, Friederich J, Riehl S, Steinmann P. On the formulation and implementation of geometric and manufacturing constraints in node-based shape optimization. Struct Multidiscip Optim. 2016;53(4):881–92. https://doi.org/10.1007/s00158-015-1359-0.
Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates. Part 1—the recovery technique. Int J Numer Methods Eng. 1992;33(7):1331–64.
Sieczkarek P, Wernicke S, Gies S, Martins PAF, Tekkaya AE. Incipient and repeatable plastic flow in incremental sheet-bulk forming of gears. Int J Adv Manuf Technol. 2016;86(9—-12):3091–100. https://doi.org/10.1007/s00170-016-8442-6.
Schmaltz S, Willner K. Comparison of different biaxial tests for the inverse identification of sheet steel material parameters. Strain. 2014;50(5):389–403. https://doi.org/10.1111/str.12080.STRAIN-0903.R1.