Advertisement

Numerical Approximation and Error Estimates for Elastic-Plastic Torsion Problems in Multiply Connected Domains

  • L. D. Marini
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 288)

Summary

A numerical approximation with conforming finite elements is presented for elastic-plastic torsion problems in multiply connected domains. The problem is formulated as a unilateral problem, of the obstacle type, with the obstacle depending on the solution.

Keywords

Error Estimate Variational Inequality Connected Domain Torsion Problem Torsional Rotation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Brézis, H. and M. Sibony, Equivalence de deux inéquations variationnelles et applications, Arch. Rational Mech. Anal., 41, 254, 1971.ADSCrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Falk, R. and B. Mercier, Error estimates for elastoplastic problems, R.A.I.R.O. Anal. numér., 11, 117, 1977.MathSciNetGoogle Scholar
  3. 3.
    Ting, T.W., Elastic-plastic torsion problem over multiply connected domains, Ann. Scuola Norm. Sup. Pisa, 4 (4), 291, 1977.MATHMathSciNetGoogle Scholar
  4. 4.
    Baiocchi, C., Su un problema di frontiera libera connesso a questioni di idraulica, Ann. Mat. Pura Appt., 4 (9), 107, 1972.CrossRefMathSciNetGoogle Scholar
  5. 5.
    Brézis, H. and G. Stampacchia, Sur la régularité de la solution d’inéquations elliptiques, Bull. Soc. Math. France, 96, 153, 1968.MATHMathSciNetGoogle Scholar
  6. 6.
    Caffarelli, L.A. and A. Friedman, The free boundary for elastic-plastic torsion problems, Trans. Amer. Math. Soc., 252, 65, 1979.CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Gerhardt, C., Regularity of solutions of nonlinear variational inequalities with a gradient bound as constraint, Arch. Rational Mech. Anal., 58, 309, 1975.ADSCrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Grisvard, P., Alternative de Fredholm relative au problème de Dirichlet dans un polygone ou un polyèdre, Boll. U.M.I., 5 (4), 132, 1972.MATHMathSciNetGoogle Scholar
  9. 9.
    Caffarelli, L.A. and N.M. Riviere, The smoothness of the elastic-plastic free boundary of a twisted bar, Proc. Amer. Math. Soc., 63, 56, 1977.CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Caffarelli, L.A., Friedman, A. and G.A. Pozzi, Reflection methods in elastic-plastic torsion problems, Indiana Univ. Math. J., 29, 205, 1980.CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Friedman, A. and G.A. Pozzi, The free boundary for elastic-plastic torsion problems, Trans. Amer. Math. Soc., 257, 411, 1980.CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Ciarlet, P.G., The finite element method for elliptic problems, North Holland, Amsterdam, 1978.MATHGoogle Scholar
  13. 13.
    Lions, J.L. and E. Magenes, Non Homogeneous Boundary Value Problems and Applications, 1, Springer, Berlin-Heidelberg-New York, 1972.CrossRefGoogle Scholar
  14. 14.
    Ciarlet, P.G. and P.A. Raviart, General lagrange and hermite interpolation in 7Rn with applications to finite element methods, Arch. Rational Mech. Anal., 46, 177, 1972.ADSCrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Strang, G. and G. Fix, An analysis of the finite element method, Prentice-Hall, Englewood Cliffs (New Jersey ), 1973.MATHGoogle Scholar
  16. 16.
    Brezzi, F., Hager, W.W. and P.A. Raviart, Error estimates for the finite element solution of variational inequalities. Part I, Numer. Math., 28, 431, 1977.CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Cryer, C.W., The solution of a quadratic programming problem using systematic overrelaxation, Siam J. Control, 9, 385, 1971.CrossRefMathSciNetGoogle Scholar
  18. 18.
    Glowinski, R., Lions, J.L. and R. Tremolières, Analyse Numérique des Inequations Variationnelles, 1, Dunod, Paris, 1976.MATHGoogle Scholar
  19. 19.
    Chipot, M., Some results about an elastic-plastic torsion problem, Nonlinear Anal. Theory Methods Appt., 3, 261, 1979.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1985

Authors and Affiliations

  • L. D. Marini
    • 1
  1. 1.Istituto di Analisi Numerica del C.N.R.PaviaItaly

Personalised recommendations