Article
MSC:
49H05,
73K15,
73k40,
74K15,
74P99,
74S05,
90C48,
90C90 | MR 0710176 | Zbl 0529.73078 | DOI: 10.21136/AM.1983.104037
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Keywords:
computer aided design; existence of optimal control; axisymmetric thin elastic shells; constant thickness; meridian curves of middle surfaces taken for designe variable; given volume; own weight loading; hydrostatic pressure of liquid; external or internal pressure; cost functional is second invariant of stress deviator; Banach space; existence of solution; convergence
computer aided design; existence of optimal control; axisymmetric thin elastic shells; constant thickness; meridian curves of middle surfaces taken for designe variable; given volume; own weight loading; hydrostatic pressure of liquid; external or internal pressure; cost functional is second invariant of stress deviator; Banach space; existence of solution; convergence
Summary:
Axisymmetric thin elastic shells of constant thickness are considered and the meridian curves of their middle surfaces taken for the design variable. Admissible functions are smooth curves of a given length, which are uniformly bounded together with their first and second derivatives, and such that the shell contains a given volume. The loading consists of the hydrostatic pressure of a liquid, the shell's own weight and the internal or external pressure.
As the cost functional, the integral of the second invariant of the stress deviator on both surfaces of the shell is chosen. Existence of an optimal design is proved on an abstract level. Approximate optimal design problems are defined and convergence of their solutions studied in detail.
References:
[1] O. C. Zienkiewicz: The finite element method in Engineering Science. Mc Graw Hill, London 1971. MR 0315970 | Zbl 0237.73071
[2] J. Nečas I. Hlaváček: Mathematical theory of elastic and elasto-plastic bodies. Elsevier, Amsterdam 1981.
[3] J. M. Boisserie R. Glowinski: Optimization of the thickness law for thin axisymmetric shells. Computers & Structures, 8 (1978), 331 - 343. DOI 10.1016/0045-7949(78)90176-1
[4] J. H. Ahlberg E. N. Nilson J. L. Walsh: The theory of splines and their applications. Academic Press, New York 1967. (Russian translation - Mir, Moskva 1972.) MR 0239327
[5] Š. B. Stečkin, Ju. N. Subbotin: Splines in numerical mathematics. (Russian). Nauka, Moskva 1976. MR 0455278
[6] J. Céa: Optimisation, théorie et algorithmes. Dunod, Paris 1971. MR 0298892
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