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Un modèle relaxé pour les câbles inextensibles. (Inextensible string: A new model via relaxation). (French) Zbl 0725.73100

Summary: The chain, that is the inextensible string, was one of the earliest problems to be modelled in mechanics. One presents here two new ideas. The first one is to relax the constraint because the usual one is not “closed” in the appropriate topology. It apparently solves the question of the sign of the tension; but one observes that nonnegativity is self- contained in the equations (even the older) by means of the maximum principle. The second idea is to describe the chain as the limit of a stiff elastic string. This gives a criterion of relevance for kinks (namely the conservation of energy). Two examples are investigated. Each one shows a concentration phenomena: either tension in time, or energy in space.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74K05 Strings
35R35 Free boundary problems for PDEs
49M20 Numerical methods of relaxation type
35Q15 Riemann-Hilbert problems in context of PDEs
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References:

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