IVR Incremental Volumetric Remapping Method NUMISHEET 2005

352 views
255 views

Published on

Published in: Technology, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
352
On SlideShare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
3
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

IVR Incremental Volumetric Remapping Method NUMISHEET 2005

  1. 1. Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes A.J. Baptista*, J.L. Alves**, M.C. Oliveira*, D.M. Rodrigues*, L.F. Menezes* * Department of Mechanical Engineering, University of Coimbra, Polo II, 3030 Coimbra, PORTUGAL ** Department of Mechanical Engineering, University of Minho, Campus de Azurém,4080-058,Guimarães, PORTUGAL CENTRO DE ENGENHARIA MECÂNICA DA UNIVERSIDADE DE COIMBRA THE 6th INTERNATIONAL CONFERENCE AND WORKSHOP ON NUMERICAL SIMULATION OF 3D SHEET FORMING PROCESSES August 15-19, 2005, Detroit, Michigan, USA
  2. 2. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC  OUTLOOK I. Introduction II. Remapping algorithms III. Numerical example IV. Results V. Conclusions
  3. 3. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” I. Introduction II. Remapping algorithms III. Numerical example IV. Results V. Conclusions  OUTLOOK CEMUC
  4. 4. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes”  INTRODUCTION  The Remapping operation CEMUC Donor mesh Target mesh  Generic definition of a remapping procedure (2D example)  Remapping in the Nodes  Nodal Variables: Force, displacement, etc.  Remapping in the Gauss Points  State Variables: Stress, density, etc.
  5. 5. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes”  INTRODUCTION  Remapping characterization CEMUC APPLICATION FIELDS • Solid Mechanics • Fluid Dynamics • Combustion • Multidisciplinary subjects • Adaptive mesh operations • Multigrid methods • Texture mapping • Trimming operations REMAPPING NECESSITY • Keep the equilibrium state • Minimize the transfer error • Overall accuracy of the simulations OPERATION REQUIREMENTS
  6. 6. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes”  INTRODUCTION  Remapping methodologies and features CEMUC  Remapping methodologies (X. Jiao and M.T. Heath 2004)  Pointwise interpolation and extrapolation  Area / Volume averaging (Rezoning techniques)  Mortar elements (Project the data interface of subdomains)  Common refinement (Intersection of two overlay meshes)  Specialized methods  Methods desirable features (M. M. Rashid 2002)  Self-consistency (Identity operator for the degenerate case)  Locality (Avoid wrong domain/interfaces contributions)  Freedom from excessive smoothing  Freedom from spurious local extremes  Potential to incorporate constrains (Equilibrium, yield criteria, etc.)
  7. 7. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC I. Introduction II. Remapping algorithms III. Numerical example IV. Results V. Conclusions  OUTLOOK
  8. 8. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes”  REMAPPING ALGORITHMS CEMUC  Standard method  Standard extrapolation-interpolation remapping Donor mesh Target mesh Original meshes Extrapolation Interpolation I Interpolation II INCREMENTAL VOLUMETRIC REMAPPING – IVR Using the finite element shape functions: i i i     Volume averaging method  Incremental / discrete intersecting volumes calculation DD3TRIM
  9. 9. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC  Remapping basis Donor mesh Target mesh (State variable ) (Unload) Transfer Operator  REMAPPING ALGORITHMS  Incremental Volumetric Remapping
  10. 10. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC  Step 1 – Divide all donor elements in 8 Gauss Volumes Gauss Volume Gauss Point  REMAPPING ALGORITHMS  Incremental Volumetric Remapping  2D case view: Quadrilateral meshes overlay Homogeneous properties Step 1
  11. 11. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” (Step 1) CEMUC  Step 2 – For each target element to treat: division in 8 Gauss Volumes to remap  REMAPPING ALGORITHMS  Incremental Volumetric Remapping  2D case view: Quadrilateral meshes overlay Step 2
  12. 12. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC  Step 3 – Intersect each target Gauss volume with the donor Gauss volumes  REMAPPING ALGORITHMS  Incremental Volumetric Remapping  2D case view: Quadrilateral meshes overlay Step 3(Step 2)
  13. 13. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC  Step 4 – For each target Gauss volume: Gauss volume division  REMAPPING ALGORITHMS  Incremental Volumetric Remapping  2D case view: Quadrilateral meshes Step 4 NL Gauss volume part (Step 3)
  14. 14. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC  Step 5 – For each target Gauss Volume part centroid: Find the donor Gauss volume that encloses it  REMAPPING ALGORITHMS  Incremental Volumetric Remapping 3 1 1 NL i jNG j ii i tot V V        Remap state variable calculus Weighted average as function of the intersection Gauss volumes
  15. 15. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC I. Introduction II. Remapping algorithms III. Numerical example IV. Results V. Conclusions  OUTLOOK
  16. 16. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC  NUMISHEET Benchmark#3: Channel Draw/Cylindrical Cup 2-Stage Test (DP600)  NUMISHEET Benchmark#3 Stage 1: Channel Draw  NUMERICAL EXAMPLE  Cyclic bending and unbending  Three layers in thickness direction  More elements in the longitudinal direction Good in thickness gradients prediction Deep-Drawing simulations: DD3IMP (Static Implicit)
  17. 17. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC  NUMISHEET Benchmark#3: Channel Draw/Cylindrical Cup 2-Stage Test (DP600)  NUMISHEET Benchmark#3 Stage 2: Cylindrical Cup  NUMERICAL EXAMPLE Intermediate State: Trimming Specimen A  Plane-strain conditions Homogenize the number of elements in the two principal directions + Remeshing 359 45 4 64
  18. 18. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC  Remapping operation: Comparison of methods  Remapping operation tests  NUMERICAL EXAMPLE  Standard extrapolation-interpolation method  Incremental Volumetric Remapping  State variable analysed: sxx stress Original Mesh Remeshed Mesh Remap Remap 2 Test methodology Stage 2 1
  19. 19. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC I. Introduction II. Remapping algorithms III. Numerical example IV. Results V. Conclusions  OUTLOOK
  20. 20. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC  Remapping operation: Error comparison of the methods (IVR - NL5)  Remapping operation tests  Results Initial state Extrapolation-Interpolation IVR ( NL = 5 ) 0 500 1000 1500 2000 2500 3000 3500 4000 5 25 45 65 85 105 125 145 165 Error [MPa] Numberofnodes 0 500 1000 1500 2000 2500 3000 3500 4000 5 25 45 65 85 105 125 145 165 Error [MPa] Numberofnodes X = 54.7 X = 29.8 – 45%
  21. 21. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” 0 500 1000 1500 2000 2500 3000 3500 4000 5 25 45 65 85 105 125 145 165 Error [MPa] Numberofnodes CEMUC  Remapping operation: Error comparison of the methods (IVR – NL10)  Remapping operation tests  Results Initial state Extrapolation-Interpolation IVR ( NL = 10 ) X = 17.5 0 500 1000 1500 2000 2500 3000 3500 4000 5 25 45 65 85 105 125 145 165 Error [MPa] Numberofnodes X = 54.7 – 68%
  22. 22. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” 0 500 1000 1500 2000 2500 3000 3500 4000 5 25 45 65 85 105 125 145 165 Error [MPa] Numberofnodes 0 500 1000 1500 2000 2500 3000 3500 4000 5 25 45 65 85 105 125 145 165 Error [MPa] Numberofnodes CEMUC  Remapping operation: Error comparison of the methods (IVR – NL15)  Remapping operation tests  Results Initial state Extrapolation-Interpolation IVR ( NL = 15 ) X = 54.7 X = 12.4 – 77%
  23. 23. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC I. Introduction II. Remapping algorithms III. Numerical example IV. Results V. Conclusions  OUTLOOK
  24. 24. THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes” CEMUC  Remarks and main conclusions  The developed IVR method of DD3TRIM prove to be a very effective and straightforward way to remap a given mesh.  The method is both self-consistent and makes use of constrains such as yield criteria conservation.  The mean error, the smoothing effects and gradients distortion, can be greatly reduced when compared with the extrapolation- interpolation base methods.  The discrete approximation used for calculating the intersecting volumes is a reliable option face the complex geometrical methods.  An adjustable parameter (NL) allows the accuracy control of the remapping operation and also, the flexibility face the meshes dimensions and asymmetries.  Conclusions
  25. 25. Application of the Incremental Volumetric Remapping Method in the Simulation of Multi-Step Deep Drawing Processes A.J. Baptista*, J.L. Alves**, M.C. Oliveira*, D.M. Rodrigues*, L.F. Menezes* * Department of Mechanical Engineering, University of Coimbra, Polo II, 3030 Coimbra, PORTUGAL ** Department of Mechanical Engineering, University of Minho, Campus de Azurém,4080-058,Guimarães, PORTUGAL CENTRO DE ENGENHARIA MECÂNICA DA UNIVERSIDADE DE COIMBRA THE 6th INTERNATIONAL CONFERENCE AND WORKSHOP ON NUMERICAL SIMULATION OF 3D SHEET FORMING PROCESSES August 15-19, 2005, Detroit, Michigan, USA

×