Skip to main content
Log in

Nonlinear programming in process modeling and design

  • Overview
  • Process Modeling
  • Published:
JOM Aims and scope Submit manuscript

Abstract

In today’s competitive market, it is no longer practical to design by trial and error. Yet, this remains the normal practice, whether through the testing of numerous prototype designs or the simulations of these designs. Of course, the latter is preferred because it is cheaper, but there remains the issue of finding the best possible design. A trial-and-error approach simply does not address this task. In this paper, the authors describe their work combining computational process modeling and nonlinear programming to optimally design manufacturing processes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J.V. Beck, B. Blackwell, and C.R. St. Claire, Jr., Inverse Heat Conduction (New York: Wiley-Interscience, 1981).

    Google Scholar 

  2. D.A. Murio, The Mollification Method and the Numerical Solution of Ill-Posed Problems (New York: Wiley, 1993).

    Google Scholar 

  3. D.E. Smith and D.A. Tortorelli, “Manufacturing Process Optimization,” Encyclopedia of Materials Science and Engineering, ed. K.H.J. Buschom et al. (New York: Elsevier Sciences, 2001), pages 5733–5743.

    Google Scholar 

  4. P.E. Gill, W. Murray, and M.H. Wright, Practical Optimization (New York: Academic Press, 1981).

    Google Scholar 

  5. D.G. Luenberger, Linear and Nonlinear Programming, 2nd edition (Reading, MA: Addison-Wesley Publishing Company, 1984).

    Google Scholar 

  6. R.H. amd D.C. Montgomery Myers. Response Surface Methodology: Process and Product Optimization Using Designed Experiments (New York: John Wiley & Sons, Inc., 1995).

    Google Scholar 

  7. P. Michaleris, D.A. Tortorelli, and C.A. Vidal, “Tangent Operators and Design Sensitivity Formulations for Transient Nonlinear Coupled Problems with Applications to Elasto-Plasticity,” International Journal for Numerical Methods in Engineering, 37 (1994), pp. 2471–2499.

    Article  Google Scholar 

  8. D.A. Tortorelli, R.B. Haber, and S.C.Y. Lu, “Design Sensitivity Analysis for Nonlinear Thermal Systems,” Computer Methods in Applied Mechanics and Engineering, 77 (1989), pp. 61–77.

    Article  Google Scholar 

  9. D.A. Tortorelli et al., “Optimal Design of Advanced Parabolic Systems—Part II: Variable Spatial Domain with Applications to Casting Optimization,” Computer Methods in Applied Mechanics and Engineering, 113 (1–2) (1994), pp. 157–172.

    Article  Google Scholar 

  10. N. Olhoff and J. Rasmoussen, “Study of Inaccuracy in Semi-Analytical Sensitivity Analysis—A Model Problem,” Structural Optimization, 3 (1991), pp. 203–213.

    Article  Google Scholar 

  11. G.A. Dorai and D.A. Tortorelli, “Transient Inverse Heat Conduction Problem Solutions Via Newton’s Method,” International Journal of Heat and Mass Transfer, 40 (17) (1997), pp. 4115–4127.

    Article  CAS  Google Scholar 

  12. J.E. Scheuing and D.A. Tortorelli, “Inverse Heat Conduction Problem Solutions via Second-Order Design Sensitivities and Newton’s Method,” Inverse Problems in Engineering, 2 (1) (1996), pp. 227–262.

    Google Scholar 

  13. DOT User’s Manual, Version 3.00 (Goleta, CA: Vanderplaats, Miura and Associates, Inc., 1992).

  14. Ya.I. Burak et al., “Controlling the Longitudinal Plastic Shrinkage of Metal During Welding,” Avt. Svarka, 3 (1997), pp. 27–29.

    Google Scholar 

  15. Ya.I. Burak et al. “Selection of the Optimum Fields for Preheating Plates Before Welding,” Avt. Svarka, 5 (1979), pp. 5–9.

    Google Scholar 

  16. M.V. Deo and P. Michaleris, “Mitigation of Welding Induced Buckling Distortion Using Transient Thermal Tensioning,” Science and Technology in Welding, (2002).

  17. K. Masubuchi, Analysis of Welded Structures (Oxford, U.K.: Pergamon Press, 1980).

    Google Scholar 

  18. R. Gunnert, Residual Welding Stresses (Stockholm, Norway: Almqvist & Wiksell, 1955).

    Google Scholar 

  19. K. Terai, Study on Prevention of Welding Deformation in Thin-Skin Plate Structures, Technical Report 61 (Kawasaki, 1978).

  20. Y. Shim et al., “Determination of Residual Stress in Thick-Section Weldments,” Welding Journal, 71 (1992), pp. 305s-312s.

    Google Scholar 

  21. L.P. Connor, editor, Welding Handbook, eighth edition (Miami, FL: American Welding Society, 1987).

    Google Scholar 

  22. J.C. Simo and R.L. Taylor, “Consistent Tangent Operators for Rate-Independent Elasto-Plasticity,” Computer Methods in Applied Mechanics and Engineering, 48 (1985), pp. 101–118.

    Google Scholar 

  23. H. Hibbitt and P.V. Marcal, “A Numerical, Thermo-Mechanical Model for the Welding and Subsequent Loading of a Fabricated Structure,” Computers & Structures, 3 (1973), pp. 1145–1174.

    Article  Google Scholar 

  24. H.J. Braudel, M. Abouaf, and J.L. Chenot, “An Implicit and Incremental Formulation for the Solution of Elastoplastic Problems by the Finite Element Method.” Computers and Structures, 22 (5) (1986), pp. 801–814.

    Article  Google Scholar 

  25. P. Michaleris, D.A. Tortorelli, and C.A. Vidal, “Analysis and Optimization of Weakly Coupled Thermo-Elasto-Plastic Systems with Applications to Weldment Design,” International Journal for Numerical Methods in Engineering, 38 (8) (1995), pp. 2471–2500.

    Article  Google Scholar 

  26. J. Goldak, A. Chakravarti, and M. Bibby, “A New Finite Element Model for Welding Heat Sources,” Metallurgical Transactions B, 15B (1984), pp. 299–305.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

For more information, contact D.A. Tortorelli, University of Illinois at Urbana-Champaign, 1206 W. Green St., Urbana, Illinois 61801; (217) 333-5991; Fax (217) 244-6534.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tortorelli, D.A., Michaleris, P. Nonlinear programming in process modeling and design. JOM 55, 46–54 (2003). https://doi.org/10.1007/s11837-003-0160-5

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11837-003-0160-5

Keywords

Navigation