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Un problème issu de l’étude numérique d’un fil sans raideur soumis au frottement sec. (A problem in the numerical study of a string under friction). (French) Zbl 0778.73028

The problem of a string equilibrium, without internal friction, is studied under the conditions: there exist only inner traction effors in the tangent direction of the medium fiber, and all inner efforts are tractions. To eliminate the difficulties arising from the definition of the normal reaction of the bottom and the nonconvexity of the admissible region, the author considers the infinitesimal displacements. The mathematical expression for the displacement contains the string loading, the geometry of the deformation, and the behaviour law. He proves the existence and the uniqueness of the solution using the minimum of the energy functional, when the external potential effort is convex. Some numerical cases are studied in the final part of the paper.
Reviewer: S.Zanfir (Craiova)

MSC:

74K05 Strings
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
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References:

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