×

Contact problem with friction. (English) Zbl 0615.73120

Trends in applications of pure mathematics to mechanics IV, Pap. 4th Symp., Bratislava/Czech. 1981, Monogr. Stud. Math. 20, 74-100 (1983).
[For the entire collection see Zbl 0612.00020.]
The paper presented is based on two communications given by each of the authors during the IVth Symposium ’Trends in applications of pure mathematics to mechanics’. The paper deals with a simple contact problem of plane linear elasticity with Coulomb friction boundary conditions.
In Section 1 the variational formulations of contact problems with friction are given. For the sake of simplicity restriction is made to the plane case, when an elastic body is unilaterally supported by a rigid foundation. The extension of results to the case of two elastic bodies in contact is straightforward. The same holds for boundary conditions. Also other conditions than those described here may be considered. Section 2 discusses approximation by finite elements and the Uzawa method. Finally in section 3 the catastrophic behaviour of a finite element model of Coulomb friction is considered.

MSC:

74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
65K10 Numerical optimization and variational techniques
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
49M29 Numerical methods involving duality
49J40 Variational inequalities

Citations:

Zbl 0612.00020