The sensitivity analysis of deep drawing process using flow approach

Tomasz Bednarek^1,2, 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

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