Hlaváček, I.; Bock, I.; Lovíšek, J. Optimal control of a variational inequality with applications to structural analysis. I: Optimal design of a beam with unilateral supports. (English) Zbl 0553.73082 Appl. Math. Optimization 11, 111-143 (1984). 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 Cited in 1 ReviewCited in 11 Documents 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 Keywords:state problem; coefficients as control variables; existence theorem; optimal design; elastic or elasto-plastic beam; unilateral support at the end; convergence × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Begis D, Glowinski R (1975) Application de la méthode des élements finis à l’approximation d’un problème de domaine optimal. Appl Math Optim 2: 130–169 · Zbl 0323.90063 · doi:10.1007/BF01447854 [2] Boisserie JM, Glowinski R (1978) Optimization of the thickness law for thin axisymmetric shells. Computers & Structures 8:331–343 · Zbl 0379.73090 · doi:10.1016/0045-7949(78)90176-1 [3] Céa J (1971) Optimization, théorie et algorithmes. Dunod, Paris [4] Hlaváček I, Nečas J (1970) On inequalities of Korn’s type. Arch Rat Mech Anal 36:305–334 · Zbl 0193.39001 · doi:10.1007/BF00249518 [5] Langenbach A (1976) Monotone Potentialoperatoren in Theorie und Anwendung. VEB Deutscher Verlag der Wissenschaften, Berlin · Zbl 0387.47037 [6] Lions JL (1969) Quelques méthodes de resolution des problèmes aux limites non linéaires. Dunod, Paris [7] Mignot F (1976) Contrôle dans les inéquations variationelles elliptiques. J Func Anal 22:130–185 · Zbl 0364.49003 · doi:10.1016/0022-1236(76)90017-3 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.