Optimal control of a variational inequality with applications to structural analysis. II: Local optimization of the stress in a beam. III: Optimal design of an elastic plate. (English) Zbl 0582.73081

This is a continuation of the authors’ paper, ibid. 11, 111-143 (1984; Zbl 0553.73082). Firstly, using the dual variational formulation of the state problem, the authors analyze the problem of optimal design with respect to the variable thickness of an elastic beam with unilateral supports under the criterion of minimal value of the maximal stress. The proof of the convergence of some approximations is given. Secondly, the analogous problem for an elastic or elasto-plastic plate unilaterally supported on a part of its edge is dealt with. Here only the primal variational formulation of the state problem is used, and some numerical analysis for elastic plates is carried out.
Reviewer: Zh.H.Guo


74P99 Optimization problems in solid mechanics
49J40 Variational inequalities
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K20 Plates


Zbl 0553.73082
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[1] Ciarlet PG (1978) The finite element method for elliptic problems. North-Holland, Amsterdam · Zbl 0383.65058
[2] Demengel F (1983) Problèmes varationels in plasticité des plaques. Num Funct Anal & Optim 6:73–119 · Zbl 0554.73030
[3] Hlaváček I, Bock I and Lovíšek J (1984) Optimal control of a variational inequality with applications to structural analysis. I. Optimal design of a beam with unilateral supports. Appl Math Optim 11:111–143 · Zbl 0553.73082
[4] Langenbach A (1976) Monotone Potentialoperatoren in Theorie und Anwendung. VEB Deutscher Verlag der Wissenschaften, Berlin · Zbl 0387.47037
[5] Nečas J (1967) Les méthodes directes en théorie des équations elliptiques. Academia, Praha
[6] Temam R (1983) Problèmes mathématiques in plasticité. Gauthier-Villars, Paris
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