Approximation and numerical solution of contact problems with friction

Jaroslav Haslinger; Miroslav Tvrdý

Aplikace matematiky (1983)

  • Volume: 28, Issue: 1, page 55-71
  • ISSN: 0862-7940

Abstract

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The present paper deals with numerical solution of the contact problem with given friction. By a suitable choice of multipliers the whole problem is transformed to that of finding a saddle-point of the Lagrangian function on a certain convex set K × Λ . The approximation of this saddle-point is defined, the convergence is proved and the rate of convergence established. For the numerical realization Uzawa’s algorithm is used. Some examples are given in the conclusion.

How to cite

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Haslinger, Jaroslav, and Tvrdý, Miroslav. "Approximation and numerical solution of contact problems with friction." Aplikace matematiky 28.1 (1983): 55-71. <http://eudml.org/doc/15274>.

@article{Haslinger1983,
abstract = {The present paper deals with numerical solution of the contact problem with given friction. By a suitable choice of multipliers the whole problem is transformed to that of finding a saddle-point of the Lagrangian function $\mathcal \{L\}$ on a certain convex set $K\times \Lambda $. The approximation of this saddle-point is defined, the convergence is proved and the rate of convergence established. For the numerical realization Uzawa’s algorithm is used. Some examples are given in the conclusion.},
author = {Haslinger, Jaroslav, Tvrdý, Miroslav},
journal = {Aplikace matematiky},
keywords = {suitable choice of multipliers; saddle-point of Lagrangian function; certain convex set; approximation; rate of convergence; Uzawa’s algorithm; plane problem; linear-elastic body; rigid foundation; influence of friction; minimum of non-differentiable functional; suitable choice of multipliers; saddle-point of Lagrangian function; certain convex set; approximation; rate of convergence; Uzawa's algorithm; plane problem; linear-elastic body; rigid foundation; influence of friction; minimum of non-differentiable functional},
language = {eng},
number = {1},
pages = {55-71},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Approximation and numerical solution of contact problems with friction},
url = {http://eudml.org/doc/15274},
volume = {28},
year = {1983},
}

TY - JOUR
AU - Haslinger, Jaroslav
AU - Tvrdý, Miroslav
TI - Approximation and numerical solution of contact problems with friction
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 1
SP - 55
EP - 71
AB - The present paper deals with numerical solution of the contact problem with given friction. By a suitable choice of multipliers the whole problem is transformed to that of finding a saddle-point of the Lagrangian function $\mathcal {L}$ on a certain convex set $K\times \Lambda $. The approximation of this saddle-point is defined, the convergence is proved and the rate of convergence established. For the numerical realization Uzawa’s algorithm is used. Some examples are given in the conclusion.
LA - eng
KW - suitable choice of multipliers; saddle-point of Lagrangian function; certain convex set; approximation; rate of convergence; Uzawa’s algorithm; plane problem; linear-elastic body; rigid foundation; influence of friction; minimum of non-differentiable functional; suitable choice of multipliers; saddle-point of Lagrangian function; certain convex set; approximation; rate of convergence; Uzawa's algorithm; plane problem; linear-elastic body; rigid foundation; influence of friction; minimum of non-differentiable functional
UR - http://eudml.org/doc/15274
ER -

References

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  1. J. Cea, Оптиимзация. Теория и алгорифмы, Mir, Moskva 1973. (1973) Zbl0303.93022
  2. G. Duvaut J. L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris 1972. (1972) Zbl0298.73001MR0464857
  3. J. Haslinger I. Hlaváček, Contact between elastic bodies. Part II. Finite element analysis, Apl. Mat. 26 (1981) 324-347. (1981) Zbl0465.73144
  4. M. Tvrdý, The Signorini problem with friction, Thesis, Fac. Math. Phys., Charles Univ., Prague (in Czech). 
  5. R. Glowinski J. L. Lions R. Trémolières, Analyse numérique des inéquations variationnelles, Dunod, Paris 1976. (1976) Zbl0358.65091
  6. I. Ekeland R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam 1976. (1976) Zbl0322.90046MR0463994
  7. J. Haslinger I. Hlaváček, Approximation of the Signorini problem with friction by a mixed finite element method, JMAA, Vol. 86, No. 1, 99-122. Zbl0486.73099MR0649858
  8. J. Haslinger, Mixed formulation of variational inequalities and its approximation, Apl. Mat. 26 (1981) No. 6. (1981) Zbl0483.49003MR0634283
  9. B. N. Pšeničnyj J. M. Danilin, Численные методы в экстремальных задачах, Nauka, Moskva 1975. (1975) 
  10. N. Kikuchi J. T. Oden, Contact problems in elasticity, TICOM Report 79 - 8, July 1979, Texas Inst. for computational mechanics, The University of Texas at Austin. (1979) Zbl0685.73002

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