Skip to main content
Log in

The material derivative method for shape optimization problem in electro-chemical machining

  • Published:
Japan Journal of Industrial and Applied Mathematics Aims and scope Submit manuscript

Abstract

The main idea of this paper is the application of the material derivative (or speed) method (Zolesio [8]) for a shape optimization problem in the electrochemical machining. We develop the material derivative method for the optimal shape design for systems described by a variational inequality. We introduce a penalty method for the problem and discuss a numerical method using the finite element method.

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. R. Butt, Optimal shape design for differential inequalities. Ph.D. Thesis, Leed University, England, 1988.

    Google Scholar 

  2. A. Dervieux, A perturbation study of a jet-like annular free boundary problem. Comm. Partial Differntial Equations,6(2), (1981).

  3. C.M. Elliott, On a variational inequality formulation of an electrochemical machining moving boundary problem and its approximation by the finite element method. J. Inst. Math. Appl.,25 (1980), 121–131.

    Article  MATH  MathSciNet  Google Scholar 

  4. J.L. Lions, Some topic on variational inequalities and applications. New Developments in Differential Equations (ed. W. Eckaus), North-Holland Publishing Company, 1976.

  5. J.A. McGeough, Principles of Electrochemical Machining. Chapman and Hall, London, 1974.

    Google Scholar 

  6. O. Pironneau, Optimal Shape Design for Elliptic System. Springer-Verlag, New York, 1984.

    Google Scholar 

  7. C. Sagues, Controle d’un système gouverne par une inéquation variationnelle parabolique; observation du domain de contact. C. R. Acad. Sci. Paris,287 (1978), 957–959.

    Google Scholar 

  8. J.P. Zolesio, The material derivative method for shape optimization. Optimization of Distributed Parameter Structures, Sijthoff and Noordhoff, Alphen aan den rihn, Netherlands, 1980, 1089–1151.

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Butt, R. The material derivative method for shape optimization problem in electro-chemical machining. Japan J. Indust. Appl. Math. 14, 279–293 (1997). https://doi.org/10.1007/BF03167268

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03167268

Key words

Navigation