# Optimization of the shape of axisymmetric shells

Aplikace matematiky (1983)

- Volume: 28, Issue: 4, page 269-294
- ISSN: 0862-7940

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topHlaváček, Ivan. "Optimization of the shape of axisymmetric shells." Aplikace matematiky 28.4 (1983): 269-294. <http://eudml.org/doc/15306>.

@article{Hlaváček1983,

abstract = {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.},

author = {Hlaváček, Ivan},

journal = {Aplikace matematiky},

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},

language = {eng},

number = {4},

pages = {269-294},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Optimization of the shape of axisymmetric shells},

url = {http://eudml.org/doc/15306},

volume = {28},

year = {1983},

}

TY - JOUR

AU - Hlaváček, Ivan

TI - Optimization of the shape of axisymmetric shells

JO - Aplikace matematiky

PY - 1983

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 28

IS - 4

SP - 269

EP - 294

AB - 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.

LA - eng

KW - 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

UR - http://eudml.org/doc/15306

ER -

## References

top- O. C. Zienkiewicz, The finite element method in Engineering Science, Mc Graw Hill, London 1971. (1971) Zbl0237.73071MR0315970
- J. Nečas I. Hlaváček, Mathematical theory of elastic and elasto-plastic bodies, Elsevier, Amsterdam 1981. (1981) Zbl0448.73009
- J. M. Boisserie R. Glowinski, 10.1016/0045-7949(78)90176-1, Computers & Structures, 8 (1978), 331 - 343. (1978) Zbl0379.73090DOI10.1016/0045-7949(78)90176-1
- 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.) (1967) Zbl0158.15901MR0239327
- Š. B. Stečkin, Ju. N. Subbotin, Splines in numerical mathematics, (Russian). Nauka, Moskva 1976. (1976) MR0455278
- J. Céa, Optimisation, théorie et algorithmes, Dunod, Paris 1971. (1971) Zbl0211.17402MR0298892

## Citations in EuDML Documents

top- Jan Chleboun, Optimal design of an elastic beam on an elastic basis
- Ján Lovíšek, Optimal control of variational inequality with applications to axisymmetric shells
- Petr Salač, Shape optimization of elastic axisymmetric plate on an elastic foundation
- Jan Brandts, Michal Křížek, Ivan Hlaváček is seventy-five
- Ivan Hlaváček, Michal Křížek, Weight minimization of elastic bodies weakly supporting tension. II. Domains with two curved sides
- Ivan Hlaváček, Raino Mäkinen, On the numerical solution of axisymmetric domain optimization problems
- Ivan Hlaváček, Michal Křížek, Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side

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