Skip to main content
SpringerLink
Log in

Extremum Principles for a Rigid-Perfectly Plastic Material

  • Chapter
Engineering Plasticity

  • 102 Accesses

Abstract

In the theory of plasticity a number of general theorems have an important role and the most important of these are the theorems on the extremum properties of a solution or extremum principles and the so-called uniqueness theorems. These theorems permit the possibility of the direct construction of solutions which do not demand the integration of the differential equations of equilibrium. This possibility is very important because in plasticity the problems are usually nonlinear.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gvozdev, A. A., Calculation of load bearing capacity of structures by the method of limiting equilibrium (in Russian), Stroyisdat, U.S.S.R. (1949)

    Google Scholar 

  2. Gvozdev, A. A. (translated by R. M. Haythornthwaite), The determination of the value of the collapse load for statically indeterminate systems undergoing plastic deformation, Int. J. mech. Sci., 1, 322 (1960)

    Article  Google Scholar 

  3. Hill, R., The Mathematical Theory of Plasticity, ch. III, Oxford University Press, London (1950)

    Google Scholar 

  4. Koiter, W. T., General theorems for elastic-plastic solids, in Progress in Solid Mechanics (ed. by Sneddon and Hill), vol. 1, North-Holland, Amsterdam (1960)

    Google Scholar 

  5. Drucker, D. C., Greenberg, W. and Prager, W., The safety factor of an elastic-plastic body in plane strain, Trans. Am Soc. mech. Engrs, 73, J. appl. Mech., 371 (1957)

    Google Scholar 

  6. Koiter, W. T., Stress—strain relations, uniqueness and variational theorems for elastic—plastic materials with a singular yield surface, Q. appl. Math., 11, 350 (1953)

    Google Scholar 

  7. Johnson, W., Estimation of upper bound loads for extrusion and coining operations, Proc. Instn mech. Engrs, 173, 61 (1959)

    Article  Google Scholar 

  8. Slater, R. A. C., Velocity and thermal discontinuities encountered during the forging of steels, Proc. Manchester Association of Engineers, No. 5 (1965–66)

    Google Scholar 

  9. Green, A. P., The compression of a ductile material between smooth dies, Phil. Mag., 42, 900 (1951)

    Article  Google Scholar 

  10. Johnson, W., de Malherbe, M. C. and Venter, R., Upper bounds to the loads for the plane strain working of anisotropic metals, J. Mech. Engng Sci., 14, 280 (1972)

    Article  Google Scholar 

  11. Massey, H. F., The flow of metal during forging, Proc. Manchester Association of Engineers (November 1921)

    Google Scholar 

  12. Johnson, W., Baraya, G. L. and Slater, R. A. C., On heat lines or lines of thermal discontinuity, Int. J. mech. Sci., 6, 409 (1964)

    Article  Google Scholar 

  13. Tanner, R. I. and Johnson, W., Temperature distributions in some fast metal-working operations, Int. J. mech. Sci., 1, 28 (1960)

    Article  Google Scholar 

  14. Bishop, J. F. W., An approximate method for determining the temperatures reached in steady motion problems of plane plastic strain, Q. Jl Mech. appl. Math., 9, 236 (1956)

    Google Scholar 

  15. Green, A. P., The plastic yielding of notched bars due to bending, Q. JI Mech. appl. Math., 6, 223 (1953)

    Article  Google Scholar 

  16. Kudo, H., An upper bound approach to plane strain forging and extrusion—I, Int. J. mech. Sci., 1, 57 (1960)

    Article  Google Scholar 

  17. Kudo, H., Some analytical and experimental studies of axisymmetric cold forging and extrusion—I, Int. J. mech. Sci., 2, 102 (1960)

    Article  Google Scholar 

  18. Kobayashi, S., Upper bound solutions of axisymmetric forming problems—I, Trans. Am. Soc. mech. Engrs, J. Engng Ind., 122 (May 1964)

    Google Scholar 

  19. Kobayashi, S., Upper bound solutions of axisymmetric forming problems—II, Trans. Am Soc. mech. Engrs, J. Engng Ind, 326 (November 1964)

    Google Scholar 

  20. McDermott, R. P. and Bramley, A. N., An elemental upper bound technique for general use in forging analysis, Proc. 15th Intern. Mach. Tool Des. and Res. Conf., p. 437, University of Birmingham, 18–20 September, 1974, Macmillan Press, London (1975)

    Google Scholar 

  21. Johnson, W., Upper bounds to the load for the transverse bending of flat, rigid—perfectly plastic plates, Int. J. mech. Sci., 11, 913 (1969)

    Article  Google Scholar 

  22. Collins, I. F., On the analogy between plane strain and plate bending solutions in rigid perfect plasticity theory, Int. J. Solids Struct., 7, 1037 (1971)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, The City University, London, UK

    R. A. C. Slater

Authors
  1. R. A. C. Slater
    View author publications

    You can also search for this author in PubMed Google Scholar

Copyright information

© 1977 R. A. C. Slater

About this chapter

Cite this chapter

Slater, R.A.C. (1977). Extremum Principles for a Rigid-Perfectly Plastic Material. In: Engineering Plasticity. Palgrave, London. https://doi.org/10.1007/978-1-349-02160-4_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-349-02160-4_10

  • Publisher Name: Palgrave, London

  • Print ISBN: 978-1-349-02162-8

  • Online ISBN: 978-1-349-02160-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation