Salač, Petr Shape optimization of elastic axisymmetric plate on an elastic foundation. (English) Zbl 0839.73036 Appl. Math., Praha 40, No. 4, 319-338 (1995). This work concerns the two-dimensional optimal design problem for an axisymmetric loaded elastic circular plate of variable thickness fixed on an elastic foundation. Under the condition of constant volume of the plate, the function of thickness is optimized in the class of Lipschitz functions bounded simultaneously from above and below by a positive constant. It is assumed that on the plate act its own weight, a force concentrated at the centre, forces concentrated on the circle, and the so-called rotational symmetrical load. The cost functional is the norm in the weighted Sobolev space consisting of the radial deflection functions. Existence of an optimal solution is proved, an approximate problem is introduced, and convergence of approximate solutions to the exact one is established. Reviewer: L.Prášek (Plzeň) Cited in 2 Documents MSC: 74P99 Optimization problems in solid mechanics 74K20 Plates 74B99 Elastic materials Keywords:existence; optimal design; circular plate; Lipschitz functions; concentrated force; weighted Sobolev space; convergence; approximate solutions × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] D. Begis, R. Glowinski: Application de la méthode des éléments finis à l’approximation d’un problème de domaine optimal. Méthodes de résolution des problèmes approchés. Applied Mathematics. Optimization 2 (1975), 130-169. · Zbl 0323.90063 · doi:10.1007/BF01447854 [2] P.G. Ciarlet: The finite element method for elliptic problems. North-Holland, Amsterdam, 1978. · Zbl 0383.65058 [3] I. Hlaváček: Optimization of the shape of axisymmetric shells. Apl. Mat. 28 (1983), 269-294. [4] J. Nečas, I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies, An Introduction. Elsevier, Amsterdam, 1981. [5] J. Chleboun: Optimal design of an elastic beam on an elastic basis. Apl. Mat. 31 (1986), 118-140. · Zbl 0606.73108 [6] K. Rektorys: Variational methods in mathematics, science and engineering. D. Reidel Publishing Company, Dordrecht-Holland/Boston U.S.A., 1977. · Zbl 0668.49001 [7] A. Kufner: Weighted Sobolev spaces. John Wiley & Sons, New York, 1985. · Zbl 0579.35021 [8] H. Triebel: Interpolation theory, function spaces, differential operators. VEB Deutscher Verlag der Wissenschaften, Berlin, 1975. [9] V. Jarník: Differential calculus II. Academia, Praha, 1976. · Zbl 1160.26301 [10] S. Fučík, J. Milota: Mathematical analysis II, Differential calculus of functions of several variables. UK, Praha, 1975. 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.