The sensitivity analysis of deep drawing process using flow approach
Tomasz Bednarek1,2
, Piotr Kowalczyk1
1Institute of Fundamental Technological Research of the Polish Academy of Sciences, 02-106 Warsaw, Pawińskiego 5B, Poland.
2Kazimierz Wielki University, 85-064 Bydgoszcz, Chodkiewicza 30, Poland.
DOI:
https://doi.org/10.7494/cmms.2013.1.0406
Abstract:
he objective of the paper is the sensitivity analysis of deep drawing simulations using flow approach with respect to any design parameter. The sensitivity analysis is being implemented into the MFP code developed by IPPT PAN under project Numpress. First, the finite element formulation of flow approach in drawing simulations is presented. The mathematical formulation includes the consistent tangent viscosity matrix. As it is shown in the final sensitivity formulation, the tangent viscosity matrix is necessary in sensitivity calculations. Unfortunately the tangent matrix is asymmetric. The influence of the asymmetric contributions to viscosity matrix in sensitivity analysis is considered. The semi-analytical Direct Differential Method is used. This means that design derivatives of some terms are estimated by finite difference method and next substituted into analytical sensitivity formula. The mathematical formulae and the algorithm to build consistent tangent matrix and to perform sensitivity analysis are presented.
Cite as:
Bednarek, T., & Kowalczyk, P. (2013). The sensitivity analysis of deep drawing process using flow approach. Computer Methods in Materials Science, 13(1), 22 – 29. https://doi.org/10.7494/cmms.2013.1.0406
Article (PDF):
Keywords:
Deep drawing, Flow approach, Sensitivity analysis
References:
Agelet de Saracibar, C., 1990, Finite Element Analysis of Sheet Metal Forming Processes, PhD thesis, Universitat Politecnica de Catalunya, Barcelona (in Spanish).
Agelet de Saracibar, C., Oñate, E., Sosnowski, W., 1992, Some remarks about the flow formulation and the springback computation, Proc. International Conference on Computational Engineering Science, ICES’92, Hong Kong.
Antunez, H. J., Kleiber,M., Sosnowski,W., 1997, Shape and non–shape sensitivity and optimization of metal forming processes, Proc. International Conference COMPLAS V, Computational Plasticity, Barcelona.
Antunez, H.J., 1998, Thermo–mechanical modelling and sensitivity analysis for metal–forming operations, Computer Methods in Applied Mechanics and Engineering, 161, 113–125.
Antunez, H.J., 2001, Bulk metal forming processes from computational modelling via sensitivity analysis to tool shape optimization. Prace IPPT – IFTR Reports no. 1/2001,Warszawa.
Kleiber, M., Sosnowski,W., 1995, Parameter sensitivity analysis in frictional contact problems of sheet metal forming, Computational Mechanics, 16, 297-306.
Kleiber, M., Antunez, H. J., Hien, T. D., Kowalczyk, P., 1997, Parameter Sensitivity in Nonlinear Mechanics. J. Wiley and Sons, New York.
Kowalczyk, P., 2006a, Sensitivity analysis in finite element computations of elasto-plasticity. Prace IPPT – IFTR Reports no. 7/2006, Warszawa.
Kowalczyk, P., 2006b, Design sensitivity analysis in large deformation elasto-plastic and elastoviscoplastic problems, Int. J. Num. Meth. Eng., 66, 1234–1270.
Oñate, E., Agelet de Saracibar, C., 1990, Analysis of sheet metal forming problems using a selective bending–membrane formulations, Int. J. Num. Meth. Eng., 30, 1577-1593.
Oñate, E., Zienkiewicz, O.C., 1983, A viscous shell formulation for the analysis of thin sheet metal forming, Int. J. Mech. Sci., 25, 305–335.
Perzyna, P., 1966, Fundamental problems in viscoplasticity, Advances in Applied Mechanics, 9, 243–377.
Sosnowski, W., 1995, Finite element simulation of industrial sheet metal forming processes. Prace IPPT – IFTR Reports no. 17/1995, Warszawa.
Sosnowski, W., 2003, Symulacja numeryczna, analiza wrażliwości i optymalizacja nieliniowych procesów deformacji konstrukcji (Numerical simulation, sensitivity analysis and optimization of nonlinear deformations of structures), Wydawnictwo Akademii Bydgoskiej, Bydgoszcz (in Polish).