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Stamping Process Design Using Shape Optimization Techniques Based on Adjoint Methods
ISSN: 0148-7191, e-ISSN: 2688-3627
Published March 04, 2002 by SAE International in United States
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Many design processes could be made faster and cheaper by use of shape optimization techniques. However, the computational cost of evaluating the necessary derivatives often limits the application of optimization methods to simple engineering problems. Nevertheless, techniques based on the control theory have been shown to decrease dramatically this cost when compared with Finite Difference methods.
In this paper we describe how an optimization algorithm can be used, along with adjoint based methods, in the stamping process design. We first show how the stamping process can be stated in mathematical terms and expressed as a classical optimization problem. In this formulation, the objective and constraint functions are expressed in terms of the strain distribution in the part. This strain distribution is evaluated by a simplified finite element procedure. We then show how the gradients and Hessians can be computed with adjoint based methods. In our approach we use the shape of the entire addendum surface as the design variable. This surface is approximated by the finite element mesh and the discrete design variables are the vertical coordinates of the nodes. Finally, plane strain examples illustrate the model described.
CitationLuet, D. and Martinelli, L., "Stamping Process Design Using Shape Optimization Techniques Based on Adjoint Methods," SAE Technical Paper 2002-01-0788, 2002, https://doi.org/10.4271/2002-01-0788.
- Jameson A. Alonso J.J. Reuther J. Martinelli L. Vassberg J.C. 1998 Aerodynamic Shape Optimization Techniques Based on Control Theory 29th AIAA Fluid Dynamics Conference
- Bernadou M. Finite Element Methods for Thin Shell Problems Wiley New York 1996
- Luet D. Duval J.-L. Di Pasquale E. Rigaud V. Le Roch Y. Quality Function Approach to Design and Optimization of Stamping Process: Application to an Industrial Case SAE International Congress and Exposition Detroit, Michigan February 23-26 1998
- Barlet O. Université de Technologie de Compiègne 1998
- Batoz J.-L. Guo Y.Q. Mercier F. The inverse approach with simple triangular shell elements for large strain predictions of sheet metal forming parts Engineering Computations 15 7 1998 864 892
- Guo Y.Q. Batoz J.-L. Detraux J.-M. Duroux P. Finite Element Procedures for Strain Estimations of Sheet Metal Forming Parts International Journal for Numerical Methods in Engineering 30 1385 1401 1990
- Mercier F. Université de Technologie de Compiègne 1998
- Lemaitre J. Chaboche J.-L. Dunod, Paris 1996
- Vanderbei R.J. Shanno D.F. An interior point method algorithm for nonconvex nonlinear programming Computational Optimization and Applications 13 231 252 1999
- Haug E.J. Choi K.K. Komkov V. Design Sensitivity Analysis of Structural Systems Mathematics in Science and Engineering 177 1986