| Title:
|
Approximation and numerical solution of contact problems with friction (English) |
| Author:
|
Haslinger, Jaroslav |
| Author:
|
Tvrdý, Miroslav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
1 |
| Year:
|
1983 |
| Pages:
|
55-71 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\Cal L$ 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. (English) |
| Keyword:
|
suitable choice of multipliers |
| Keyword:
|
saddle-point of Lagrangian function |
| Keyword:
|
certain convex set |
| Keyword:
|
approximation |
| Keyword:
|
rate of convergence |
| Keyword:
|
Uzawa’s algorithm |
| Keyword:
|
plane problem |
| Keyword:
|
linear-elastic body |
| Keyword:
|
rigid foundation |
| Keyword:
|
influence of friction |
| Keyword:
|
minimum of non-differentiable functional |
| MSC:
|
49J40 |
| MSC:
|
65N30 |
| MSC:
|
73-08 |
| MSC:
|
73T05 |
| MSC:
|
74A55 |
| MSC:
|
74G30 |
| MSC:
|
74H25 |
| MSC:
|
74M15 |
| MSC:
|
74S05 |
| MSC:
|
74S30 |
| MSC:
|
74S99 |
| idZBL:
|
Zbl 0513.73089 |
| idMR:
|
MR0684711 |
| DOI:
|
10.21136/AM.1983.104002 |
| . |
| Date available:
|
2008-05-20T18:21:03Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104002 |
| . |
| Reference:
|
[1] J. Cea: Оптиимзация. Теория и алгорифмы.Mir, Moskva 1973. Zbl 0303.93022 |
| Reference:
|
[2] G. Duvaut J. L. Lions: Les inéquations en mécanique et en physique.Dunod, Paris 1972. MR 0464857 |
| Reference:
|
[3] J. Haslinger I. Hlaváček: Contact between elastic bodies. Part II. Finite element analysis.Apl. Mat. 26 (1981) 324-347. |
| Reference:
|
[4] M. Tvrdý: The Signorini problem with friction.Thesis, Fac. Math. Phys., Charles Univ., Prague (in Czech). |
| Reference:
|
[5] R. Glowinski J. L. Lions R. Trémolières: Analyse numérique des inéquations variationnelles.Dunod, Paris 1976. |
| Reference:
|
[6] I. Ekeland R. Temam: Convex Analysis and Variational Problems.North-Holland, Amsterdam 1976. MR 0463994 |
| Reference:
|
[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. MR 0649858 |
| Reference:
|
[8] J. Haslinger: Mixed formulation of variational inequalities and its approximation.Apl. Mat. 26 (1981) No. 6. MR 0634283 |
| Reference:
|
[9] B. N. Pšeničnyj J. M. Danilin: Численные методы в экстремальных задачах.Nauka, Moskva 1975. |
| Reference:
|
[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. |
| . |
