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A global existence result for the quasistatic frictional contact problem with normal compliance. (English) Zbl 0761.73104
Unilateral problems in structural analysis IV, Proc. 4th Meet., Capri/Italy 1989, ISNM 101, 85-111 (1991).
Summary: [For the entire collection see Zbl 0745.00040.]
We consider the quasistatic problem of the contact of an elastic body with a rigid foundation in the presence of friction. The contact condition is taken as a power law normal compliance. We prove, for forces and initial data that are not too large, the existence of a solution \({\mathbf u}\) such that \({\mathbf u}\in C([0,T];{\mathbf H}^ 1(\Omega))\) and \(d{\mathbf u}/dt\in L^ 2([0,T];{\mathbf H}^ 2(\Omega))\). The main tools are from the theory of differential inclusions.

74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
49J40 Variational inequalities