Signorini’s problem with friction in linear elasticity. (English) Zbl 0627.73098

Kato, Yoshio

Japan J. Appl. Math. 4, 237-268 (1987).

Author treats the following problem: A linear elastic body with pescribed displacements on a part of its surface and given forces at another part is in contact with a rigid support where friction is present. The existence of the solution for the displacement field u had already been studied by J. Nečas, J. Jarušek, J. Haslinger [e.g. Boll. Unione Mat. Ital., V. Ser., B 17, 796-811 (1980; Zbl 0445.49011)]. Their results are modified in this paper where the continuity of the solutions is investigated additionally. The problem is characterized by means of a variational inequality due to G. Duvaut [Actes Congr. internat. Math. 1970, 3, 71-77 (1971; Zbl 0281.73005)]. Author contributes essentially to the mathematical theory of frictional contact.

Reviewer: H.Bufler

MSC:

74A55	Theories of friction (tribology)
74M15	Contact in solid mechanics
74S30	Other numerical methods in solid mechanics (MSC2010)
35B99	Qualitative properties of solutions to partial differential equations
35J50	Variational methods for elliptic systems
49J40	Variational inequalities

Keywords:

Signorini’s problem; continuity of the solutions; frictional contact

Citations:

Zbl 0445.49011; Zbl 0281.73005

References:

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