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Reliable solution of a Signorini contact problem with friction, considering uncertain data. (English) Zbl 1016.74051
If uncertain input data entering a state problem are considered, then one gets a set of possible solutions of that problem. Since, rather than the solution itself, certain derived quantities (as local stress components, to give an example) are of primal interest, it is natural to introduce cost functionals to evaluate them. To be on a safe side, i.e. to follow the common engineering principle, one has to determine the highest cost value due to uncertainty. Thus, in this paper, reliable solution means the worst scenario among all scenarios induced by uncertain input data.
A Signorini contact problem with an approximate model of friction is analysed, when Lamé coefficients, body forces and friction coefficients are uncertain, but limited to a given set of admissible functions. Three kinds of criteria characterizing the stress intensity are chosen to define three maximization problems. These are approximated on the basis of finite elements, and the solvability of both the original and the approximated maximization problems is proved. Theoretical convergence analysis is presented.

MSC:
74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
49J40 Variational inequalities
65K10 Numerical optimization and variational techniques
74S30 Other numerical methods in solid mechanics (MSC2010)
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