Optimal design of metal forming die surfaces with evolution strategies

Abstract A common characteristics in the simulation of automotive sheet metal forming processes is that nearly all die surfaces are manually created within conventional computer-aided design systems (CAD). The solutions produced using these CAD systems are undoubtedly valuable from the point of view of applicability in sheet metal forming practice. However, this approach is time consuming and most of the design time is spent within these CAD systems. This paper presents the development of a computer-based approach for the evolutionary automatic design (EAD) of geometry and process parameters for industrial metal forming processes. The main characteristics of the solution methodology are the use of evolution strategies within the optimizer, the use of sheet metal formability as objective functions and a parameterization of die surfaces. The results of a comparative study of our EAD die surface generation against conventional CAD die surface generation for a representative structural design problem show the efficiency of the former. It is observed that EAD often finds the region of the search space containing the global optimum, thus supporting engineers in practice with automatic generated sheet metal forming tools.

[1]  Anshul Gupta,et al.  Recent advances in direct methods for solving unsymmetric sparse systems of linear equations , 2002, TOMS.

[2]  Tamara G. Kolda,et al.  Asynchronous Parallel Pattern Search for Nonlinear Optimization , 2001, SIAM J. Sci. Comput..

[3]  James Demmel,et al.  A Scalable Sparse Direct Solver Using Static Pivoting , 1999, PPSC.

[4]  Anshul Gupta,et al.  Improved Symbolic and Numerical Factorization Algorithms for Unsymmetric Sparse Matrices , 2002, SIAM J. Matrix Anal. Appl..

[5]  Wolfgang Fichtner,et al.  Efficient Sparse LU Factorization with Left-Right Looking Strategy on Shared Memory Multiprocessors , 2000 .

[6]  K. Heiduschke An elastic isotropic, plastic orthotropic constitutive model based on deviator transformations , 1997 .

[7]  K. Bathe Finite Element Procedures , 1995 .

[8]  Waldemar Kubli Prozessoptimierte implizite FEM-Formulierung für die Umformsimulation grossflächiger Blechbauteile , 1995 .

[9]  Iain S. Duff,et al.  The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices , 1999, SIAM J. Matrix Anal. Appl..

[10]  Josef Reissner,et al.  Optimization of sheet-metal forming processes using the special-purpose program AUTOFORM , 1995 .

[11]  Thomas Bäck,et al.  Evolutionary computation: comments on the history and current state , 1997, IEEE Trans. Evol. Comput..

[12]  Patrick Amestoy,et al.  A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling , 2001, SIAM J. Matrix Anal. Appl..

[13]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

[14]  Olaf Schenk,et al.  Solving unsymmetric sparse systems of linear equations with PARDISO , 2004, Future Gener. Comput. Syst..