Contact between elastic perfectly plastic bodies

Jaroslav Haslinger; Ivan Hlaváček

Aplikace matematiky (1982)

  • Volume: 27, Issue: 1, page 27-45
  • ISSN: 0862-7940

Abstract

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If the material of the bodies is elastic perfectly plastic, obeying the Hencky's law, the formulation in terms of stresses is more suitable than that in displacements. The Haar-Kármán principle is first extended to the case of a unilateral contact between two bodies without friction. Approximations are proposed by means of piecewise constant triangular finite elements. Convergence of the method is proved for any regular family of triangulations.

How to cite

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Haslinger, Jaroslav, and Hlaváček, Ivan. "Contact between elastic perfectly plastic bodies." Aplikace matematiky 27.1 (1982): 27-45. <http://eudml.org/doc/15222>.

@article{Haslinger1982,
abstract = {If the material of the bodies is elastic perfectly plastic, obeying the Hencky's law, the formulation in terms of stresses is more suitable than that in displacements. The Haar-Kármán principle is first extended to the case of a unilateral contact between two bodies without friction. Approximations are proposed by means of piecewise constant triangular finite elements. Convergence of the method is proved for any regular family of triangulations.},
author = {Haslinger, Jaroslav, Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {elastic perfectly plastic; Hencky’s law; extension of Haar-Kármán principle; case of unilateral contact on boundary; piecewise constant triangular elements; convergence; any regular family of triangulations; simplification; approximate problem with bounded contact zone; nonlinear; elastic perfectly plastic; Hencky's law; extension of Haar-Kármán principle; case of unilateral contact on boundary; piecewise constant triangular elements; convergence; any regular family of triangulations; simplification; approximate problem with bounded contact zone; nonlinear programming},
language = {eng},
number = {1},
pages = {27-45},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Contact between elastic perfectly plastic bodies},
url = {http://eudml.org/doc/15222},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Haslinger, Jaroslav
AU - Hlaváček, Ivan
TI - Contact between elastic perfectly plastic bodies
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 1
SP - 27
EP - 45
AB - If the material of the bodies is elastic perfectly plastic, obeying the Hencky's law, the formulation in terms of stresses is more suitable than that in displacements. The Haar-Kármán principle is first extended to the case of a unilateral contact between two bodies without friction. Approximations are proposed by means of piecewise constant triangular finite elements. Convergence of the method is proved for any regular family of triangulations.
LA - eng
KW - elastic perfectly plastic; Hencky’s law; extension of Haar-Kármán principle; case of unilateral contact on boundary; piecewise constant triangular elements; convergence; any regular family of triangulations; simplification; approximate problem with bounded contact zone; nonlinear; elastic perfectly plastic; Hencky's law; extension of Haar-Kármán principle; case of unilateral contact on boundary; piecewise constant triangular elements; convergence; any regular family of triangulations; simplification; approximate problem with bounded contact zone; nonlinear programming
UR - http://eudml.org/doc/15222
ER -

References

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  1. J. Haslinger I. Hlaváček, Contact between elastic bodies. I. Continuous problems, Apl. mat. 25 (1980), 324-347. (1980) Zbl0449.73117MR0590487
  2. J. Haslinger I. Hlaváček, Contact between elastic bodies. II. Finite element analysis, Apl. mat. 26 (1981), 263-290. (1981) Zbl0465.73144MR0623506
  3. J. Haslinger I. Hlaváček, Contact between elastic bodies. III. Dual finite element analysis, Apl. mat. 26 (1981), 321-344. (1981) Zbl0513.73088MR0631752
  4. G. Duvaut J. L. Lions, Les inéquations en mécanique et en physique, Paris, Dunod 1972. (1972) Zbl0298.73001MR0464857
  5. B. Mercier, Sur la théorie et l'analyse numérique de problèmes de plasticité, Thésis, Université Paris VI, 1977. (1977) MR0502686
  6. I. Hlaváček J. Nečas, Mathematical theory of elastic and elasto-plastic solids, Elsevier, Amsterdam 1981. (1981) Zbl0448.73009
  7. P.-M. Suquet, Existence and regularity of solutions for plasticity problems, Proc. IUTAM Congress in Evanston - 1978. (1978) 
  8. J. Céa, Optimisation, théorie et algorithmes, Dunod, Paris 1971. (1971) Zbl0211.17402MR0298892

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