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The reciprocal variational approach to the Signorini problem with friction. Approximation results. (English) Zbl 0547.73096

The authors study the plane and linear-elastic contact problem with given friction on a straight-line contact segment. They derive a ”primitive variational formulation” (in terms of the displacements), a ”mixed variational formulation” (in terms of the displacements and contact stresses) and a ”reciprocal variational formulation” (in terms of the contact stresses alone) and prove the existence and uniqueness of the solution. Then they discuss the resulting finite element approximations and certain convergence results. Further the more realistic case of friction obeying Coulomb’s law is treated using the contact problem with given friction as an auxiliary problem. At last numerical results are presented for the cases ”without friction”, ”with Coulomb’s friction” and with ”given friction”.
Reviewer: H.Bufler

MSC:

74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74S99 Numerical and other methods in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
49J40 Variational inequalities
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References:

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