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Optimal control of a variational inequality with applications to structural analysis. I: Optimal design of a beam with unilateral supports. (English) Zbl 0553.73082
This paper considers a class of optimization problems, where the state problem is given in the form of a variational inequality with coefficients as control variables. The existence theorem is proved. The result is then applied to the optimal design of an elastic or elasto- plastic beam with a unilateral support at the end of the beam. Finite element approximations are also proposed and their convergence to a solution of the continuous problem in case of an elastic beam is studied.
Reviewer: Zh.-H.Guo

MSC:
74P99 Optimization problems in solid mechanics
49J40 Variational inequalities
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74S05 Finite element methods applied to problems in solid mechanics
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