Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A dual finite element approach for stresses of elasto-perfectly plastic bodies
HTML articles powered by AMS MathViewer

by P. Neittaanmäki, V. Rivkind and G. Serëgin PDF
Math. Comp. 64 (1995), 1455-1462 Request permission

Abstract:

Primal and dual approaches are introduced for the elasto-perfectly plastic problems. We prove theorems for approximating the stresses of elastic-perfectly plastic bodies.
References
  • G. Anzellotti and M. Giaquinta, On the existence of the fields of stresses and displacements for an elasto-perfectly plastic body in static equilibrium, J. Math. Pures Appl. (9) 61 (1982), no. 3, 219–244 (1983). MR 690394
  • Philippe G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications, Vol. 4, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. MR 0520174
  • G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique, Travaux et Recherches Mathématiques, No. 21, Dunod, Paris, 1972 (French). MR 0464857
  • I. Hlaváček, J. Haslinger, J. Nečas, and J. Lovíšek, Solution of variational inequalities in mechanics, Applied Mathematical Sciences, vol. 66, Springer-Verlag, New York, 1988. Translated from the Slovak by J. Jarník. MR 952855, DOI 10.1007/978-1-4612-1048-1
  • J. Haslinger and P. Neittaanmäki, Finite element approximation for optimal shape design, John Wiley & Sons, Ltd., Chichester, 1988. Theory and applications. MR 982710
  • C. Johnson and B. Mercier, Some equilibrium finite element methods for two-dimensional elasticity problems, Numer. Math. 30 (1978), no. 1, 103–116. MR 483904, DOI 10.1007/BF01403910
  • Robert Kohn and Roger Temam, Dual spaces of stresses and strains, with applications to Hencky plasticity, Appl. Math. Optim. 10 (1983), no. 1, 1–35. MR 701898, DOI 10.1007/BF01448377
    • V. Rivkind, L. Rukhovetz, and L. Oganesjan, Variational-difference schemes, J. Lit. Acad. Sci. Vilnius 1 (1971), 2 (1973). G. Seregin, On the well-posedness of variational problems of mechanics of ideally elastic-plastic media, Soviet Phys. Dokl. 5 (1984), 316-318.
  • G. A. Serëgin, On the differentiability of extremals of variational problems of the mechanics of ideally elastoplastic media, Differentsial′nye Uravneniya 23 (1987), no. 11, 1981–1991, 2022 (Russian). MR 928247
  • G. A. Serëgin, On the regularity of weak solutions of variational problems of plasticity theory, Algebra i Analiz 2 (1990), no. 2, 121–140 (Russian); English transl., Leningrad Math. J. 2 (1991), no. 2, 321–338. MR 1062266
    • —, Variation-difference scheme for problems on the mechanics of ideally elasto-plastic media, USSR Comput. Math. and Math. Phys. 25 (1985), 153-165.
  • Roger Temam and Gilbert Strang, Functions of bounded deformation, Arch. Rational Mech. Anal. 75 (1980/81), no. 1, 7–21. MR 592100, DOI 10.1007/BF00284617
Similar Articles
Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 1455-1462
  • MSC: Primary 73V25; Secondary 65N30, 73E05, 73V05
  • DOI: https://doi.org/10.1090/S0025-5718-1995-1308458-7
  • MathSciNet review: 1308458