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Title: Optimization of the shape of axisymmetric shells (English)
Author: Hlaváček, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 28
Issue: 4
Year: 1983
Pages: 269-294
Summary lang: English
Summary lang: Czech
Summary lang: Russian
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Category: math
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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. (English)
Keyword: computer aided design
Keyword: existence of optimal control
Keyword: axisymmetric thin elastic shells
Keyword: constant thickness
Keyword: meridian curves of middle surfaces taken for designe variable
Keyword: given volume
Keyword: own weight loading
Keyword: hydrostatic pressure of liquid
Keyword: external or internal pressure
Keyword: cost functional is second invariant of stress deviator
Keyword: Banach space
Keyword: existence of solution
Keyword: convergence
MSC: 49H05
MSC: 73K15
MSC: 73k40
MSC: 74K15
MSC: 74P99
MSC: 74S05
MSC: 90C48
MSC: 90C90
idZBL: Zbl 0529.73078
idMR: MR0710176
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Date available: 2008-05-20T18:22:41Z
Last updated: 2015-06-18
Stable URL: http://hdl.handle.net/10338.dmlcz/104037
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Reference: [1] O. C. Zienkiewicz: The finite element method in Engineering Science.Mc Graw Hill, London 1971. Zbl 0237.73071, MR 0315970
Reference: [2] J. Nečas I. Hlaváček: Mathematical theory of elastic and elasto-plastic bodies.Elsevier, Amsterdam 1981.
Reference: [3] J. M. Boisserie R. Glowinski: Optimization of the thickness law for thin axisymmetric shells.Computers & Structures, 8 (1978), 331 - 343. 10.1016/0045-7949(78)90176-1
Reference: [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
Reference: [5] Š. B. Stečkin, Ju. N. Subbotin: Splines in numerical mathematics.(Russian). Nauka, Moskva 1976. MR 0455278
Reference: [6] J. Céa: Optimisation, théorie et algorithmes.Dunod, Paris 1971. MR 0298892
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