Geodesic
Optimization of the shape of axisymmetric shells
Applications of Mathematics, Tome 28 (1983) no. 4, pp. 269-294

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/AM.1983.104037
Classification : 49H05, 73K15, 73k40, 74K15, 74P99, 74S05, 90C48, 90C90
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 
@article{10_21136_AM_1983_104037,
     author = {Hlav\'a\v{c}ek, Ivan},
     title = {Optimization of the shape of axisymmetric shells},
     journal = {Applications of Mathematics},
     pages = {269--294},
     publisher = {mathdoc},
     volume = {28},
     number = {4},
     year = {1983},
     doi = {10.21136/AM.1983.104037},
     mrnumber = {0710176},
     zbl = {0529.73078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104037/}
}
TY  - JOUR
AU  - Hlaváček, Ivan
TI  - Optimization of the shape of axisymmetric shells
JO  - Applications of Mathematics
PY  - 1983
SP  - 269
EP  - 294
VL  - 28
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104037/
DO  - 10.21136/AM.1983.104037
LA  - en
ID  - 10_21136_AM_1983_104037
ER  - 
%0 Journal Article
%A Hlaváček, Ivan
%T Optimization of the shape of axisymmetric shells
%J Applications of Mathematics
%D 1983
%P 269-294
%V 28
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104037/
%R 10.21136/AM.1983.104037
%G en
%F 10_21136_AM_1983_104037
Hlaváček, Ivan. Optimization of the shape of axisymmetric shells. Applications of Mathematics, Tome 28 (1983) no. 4, pp. 269-294. doi: 10.21136/AM.1983.104037

Cité par Sources :