A continuum Lagrangian sensitivity analysis for metal forming processes with applications to die design problems

International Journal for Numerical Methods in Engineering

Volumn 48, Issue 5, 2000, Pages 679-720

  Zabaras, Nicholas ^a   Bao, Yangang ^a   Srikanth, Akkaram ^a   Frazier, William Garth ^b  

^a Cornell University   (United States)

^b AIR FORCE RESEARCH LABORATORY   (United States)

Author keywords

Die design; Lagrangian analysis; Large deformation; Metal forming processes; Optimization; Plasticity; Sensitivity analysis

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTER SIMULATION; CONTINUUM MECHANICS; DIES; DIFFERENTIAL EQUATIONS; FINITE DIFFERENCE METHOD; LAGRANGE MULTIPLIERS; METAL FORMING; PROBLEM SOLVING; TRACTION (FRICTION);

BEZIER REPRESENTATION; CONTINUUM LAGRANGIAN SENSITIVITY ANALYSIS; OPEN FORGING DIE;

SENSITIVITY ANALYSIS;

EID: 0034204554     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(20000620)48:5<679::AID-NME895>3.0.CO;2-U     Document Type: Article

References (34)

1. Kobayashi S, Oh S, Altan T. Metal Forming and the Finite-Element Method. Oxford University Press: New York, 1989.
2. Tsay J, Arora JS. Non-linear structural design sensitivity analysis for path-dependent problems, Parts I and II: General theory and analytical example problems. Computer Methods in Applied Mechanics and Engineering 1990; 81: 183-228.
3. Tortorelli D. Sensitivity analysis for non-linear constrained elastostatic systems. International Journal for Numerical Methods in Engineering 1992; 33:1643-1660.
4. Vidal CA, Haber RB. Design sensitivity analysis for rate-independent elastoplasticity. Computer Methods in Applied Mechanics and Engineering 1993; 107:393-431.
5. Lee TH, Arora JS. Shape design sensitivity analysis of viscoplastic structures. Computer Methods in Applied Mechanics and Engineering 1993; 108:237-259.
6. Kleiber M, Antúnez H, Hien TD, Kowalczyk P. Parameter Sensitivity in Nonlinear Mechanics: Theory and Finite Element Computations. Wiley: New York, 1997.
7. Noor AK, Needleman A, Peters JM. Sensitivity analysis for failure and damage in dynamically loaded tensile bars. Computer Methods in Applied Mechanics and Engineering 1998; 151:461-478.
8. Antúnez HJ, Kleiber M. Sensitivity analysis of metal forming processes involving frictional contact in steady state. Journal of Materials Processing Technology 1996; 60:485-491.
9. Antúnez HJ, Kleiber M. Sensitivity of forming processes to shape parameters. Computer Methods in Applied Mechanics and Engineering 1996; 137:189-206.
10. Antúnez HJ. Thermo-mechanical modelling and sensitivity analysis for metal forming operations. Computer Methods in Applied Mechanics and Engineering 1998; 161:113-125.
11. Mahnken R, Stein E. Parameter identification for finite deformation elasto-plasticity in principal directions. Computer Methods in Applied Mechanics and Engineering 1997; 147:17-39.
12. Karaoglan L, Noor AK. Sensitivity analysis of frictional contact response of axisymmetric composite structures. Computers and Structures 1995; 55(6):937-954.
13. Ghouali MA, Duvaut G, Ortola S, Oster A. Local analytical design sensitivity analysis of the forging problem using FEM. Computer Methods in Applied Mechanics and Engineering 1998; 163:55-70.
14. Fourment L, Chenot JL. Optimal design for non-steady state metal forming processes - I. Shape optimization method. International Journal for Numerical Methods in Engineering 1996; 39:33-50.
15. Fourment L, Balan T, Chenot JL. Optimal design for non-steady state metal forming processes - II. Application of shape optimization in forging. International Journal for Numerical Methods in Engineering 1996; 39:51-65.
16. Zhao G, Wright E, Grandhi RV. Preform Die shape design in metal forming using an optimization method. International Journal for Numerical Methods in Engineering 1997; 40:1213-1230.
17. Joun MS, Hwang SM. Die shape optimal design in three dimensional shape metal extrusion by the finite element method. International Journal for Numerical Methods in Engineering 1998; 41:311-335.
18. Chung SH, Hwang SM. Optimal process design in non-isothermal non-steady metal forming by the finite element method. International Journal for Numerical Methods in Engineering 1998; 42:1343-1390.
19. Coons SA. Surfaces for computer-aided design of space figures, ESL 9442-M-139, MIT, 1969.
20. Bézier PE. Numerical Control - Mathematics and Applications. Wiley: London, 1972.
21. Schumaker LL. Spline Functions: Basic Theory. Wiley: New York, 1981.
22. Gunasekera JS. CAD/CAM of Dies. Halsted Press: New York, 1989.
23. Fletcher R. Practical Methods of Optimization. Wiley: New York, 1987.
24. Badrinarayanan S, Zabaras N. A sensitivity analysis for the optimal design of metal forming processes. Computer Methods in Applied Mechanics and Engineering 1996; 129:319-348.
25. Badrinarayanan S, Constantinescou A, Zabaras N. Preform design in metal forming. In Numiform'95: Simulation of Materials Processing: Theory, Methods and Applications, Shen S-F, Dawson P (eds). Balkema: Rotterdam, 1995; 533-538.
26. Weber G, Anand L. Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids. Computer Methods in Applied Mechanics and Engineering 1990; 79:173-202.
27. Brown SB, Kim KH, Anand L. An internal variable constitutive model for hot working of metals. International Journal of Plasticity 1989; 5:95-130.
28. Zabaras N, Srikanth A. An object oriented programming approach to the Lagrangian FEM analysis of large inelastic deformations and metal forming processes, International Journal for Numerical Methods in Engineering 1999; 45(4):399-445.
29. Laursen TA, Simo JC. On the formulation and numerical treatment of finite deformation frictional contact problems. In: Nonlinear Computational Mechanics - State of the Art, Wriggers P, Wager W (eds). Springer: Berlin, 1991; 716 -736.
30. Simo JC, Laursen TA. An augmented Lagrangian treatment of contact problems involving friction. Computers and Structures 1992; 42(1):97-116.
31. Simo JC, Hughes, TJR. Computational Inelasticity. Springer: New York, 1998.
32. Zabaras N, Srikanth A Using objects to model finite deformation plasticity. Engineering with Computers 1999; 15:37-60.
33. Srikanth A, Zabaras N. Preform design and shape optimization in metal forming processes. Computer Methods in Applied Mechanics and Engineering, 2000, in press.
34. Srikanth A, Zabaras N. A gradient based optimization framework for the design of single and multi-stage metal forming processes. In Symposium on Advances in Metal Forming, Cao J, Liu WK, Xia CZ (eds). ASME, 2000, in press.