Elastic-Plastic Reduced Order Modelling of Sheet and Profiles Bending-under-Tension

The aircrafts fuselage structure is usually composed of an assembly of stringers and frames made of cold-worked aluminium profiles. In particular, frames need of a forming process that shapes the profile into the frame’s curved shape. To do this, both profile ends are clamped, and then the profile is simultaneously stretched and pressed against the mould so that the material is plastically deformed. Industrial experience shows that most of times the resultant frame does not fulfil neither curvature nor planarity tolerances. These defects are mainly due to spring-back, residual stresses, and some technologic restrictions related to the machinery. The lack of understanding has led industry to reduce the automation level, and thus the forming process is frequently interrupted to perform verifications and adjustments that make the process to be time-consuming and very much dependent on the know-how of the machine operator. Aiming to improve the frame’s industrialisation, this work first analyses the influence of several parameters in the final shape. Then, we propose a computer-aided forming process based on the concept of Computational Vademecum (CV), which is also introduced in this work. It allows reducing the dependence on the operator know-how, while reliability and repeatability of the process can be improved.

[1]  Adrien Leygue,et al.  Proper Generalized Decomposition Based Dynamic Data‐Driven Control of Material Forming Processes , 2011 .

[2]  J. Cohen,et al.  Residual Stress: Measurement by Diffraction and Interpretation , 1987 .

[3]  Gary S. Schajer,et al.  Measurement of Non-Uniform Residual Stresses Using the Hole-Drilling Method. Part II—Practical Application of the Integral Method , 1988 .

[4]  Gustaf Arrhenius,et al.  X-ray diffraction procedures for polycrystalline and amorphous materials , 1955 .

[5]  J Lof,et al.  FEM simulations of the extrusion of complex thin-walled aluminium sections , 2002 .

[6]  S Niroomandi,et al.  Real‐time simulation of surgery by reduced‐order modeling and X‐FEM techniques , 2012, International journal for numerical methods in biomedical engineering.

[7]  Thomas Gerstner,et al.  Numerical integration using sparse grids , 2004, Numerical Algorithms.

[8]  Adrien Leygue,et al.  Proper Generalized Decomposition based dynamic data-driven control of thermal processes ☆ , 2012 .

[9]  A. Nouy Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems , 2010 .

[10]  Filippo Gabrielli,et al.  Artificial neural-network-based control system for springback compensation in press-brake forming , 2001 .

[11]  F. Chinesta,et al.  A Short Review in Model Order Reduction Based on Proper Generalized Decomposition , 2018 .

[12]  Mohammad Bakhshi-Jooybari,et al.  Modeling and optimization of spring-back in bending process using multiple regression analysis and neural computation , 2014 .

[13]  O. C. Zienkiewicz,et al.  Flow of plastic and visco‐plastic solids with special reference to extrusion and forming processes , 1974 .

[14]  Siamak Niroomandi,et al.  Real-time deformable models of non-linear tissues by model reduction techniques , 2008, Comput. Methods Programs Biomed..

[15]  A. Ammar,et al.  PGD-Based Computational Vademecum for Efficient Design, Optimization and Control , 2013, Archives of Computational Methods in Engineering.