Article
MSC:
49J40,
65N30,
73-08,
73T05,
74A55,
74G30,
74H25,
74M15,
74S05,
74S30,
74S99 | MR 0684711 | Zbl 0513.73089 | DOI: 10.21136/AM.1983.104002
Full entry |
PDF
(1.6 MB)
Feedback
PDF
(1.6 MB)
Feedback
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
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.
References:
[1] J. Cea: Оптиимзация. Теория и алгорифмы. Mir, Moskva 1973. Zbl 0303.93022
[2] G. Duvaut J. L. Lions: Les inéquations en mécanique et en physique. Dunod, Paris 1972. MR 0464857
[3] J. Haslinger I. Hlaváček: Contact between elastic bodies. Part II. Finite element analysis. Apl. Mat. 26 (1981) 324-347.
[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.
[6] I. Ekeland R. Temam: Convex Analysis and Variational Problems. North-Holland, Amsterdam 1976. MR 0463994
[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
[8] J. Haslinger: Mixed formulation of variational inequalities and its approximation. Apl. Mat. 26 (1981) No. 6. MR 0634283
[9] B. N. Pšeničnyj J. M. Danilin: Численные методы в экстремальных задачах. Nauka, Moskva 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.
Search
Partner of
