Geodesic
Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side
Applications of Mathematics, Tome 37 (1992) no. 3, pp. 201-240
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its own weight and to the hydrostatic presure. Existence of an optimal shape is proved. Using a penalty method and finite element technique, approximate solutions are proposed and their convergence is analyzed.
Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its own weight and to the hydrostatic presure. Existence of an optimal shape is proved. Using a penalty method and finite element technique, approximate solutions are proposed and their convergence is analyzed.
DOI : 10.21136/AM.1992.104504
Classification : 49Q10, 65K10, 65N30, 73C99, 73V20, 73k40, 74P10, 74P99, 74S05, 74S30
Keywords: existence; masonry dam; hydrostatic pressure; penalty method; convergence; shape optimization; weight minimization; finite elements 
@article{10_21136_AM_1992_104504,
     author = {Hlav\'a\v{c}ek, Ivan and K\v{r}{\'\i}\v{z}ek, Michal},
     title = {Weight minimization of elastic bodies weakly supporting tension. {I.} {Domains} with one curved side},
     journal = {Applications of Mathematics},
     pages = {201--240},
     year = {1992},
     volume = {37},
     number = {3},
     doi = {10.21136/AM.1992.104504},
     mrnumber = {1157456},
     zbl = {0767.73047},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1992.104504/}
}
TY  - JOUR
AU  - Hlaváček, Ivan
AU  - Křížek, Michal
TI  - Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side
JO  - Applications of Mathematics
PY  - 1992
SP  - 201
EP  - 240
VL  - 37
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1992.104504/
DO  - 10.21136/AM.1992.104504
LA  - en
ID  - 10_21136_AM_1992_104504
ER  - 
%0 Journal Article
%A Hlaváček, Ivan
%A Křížek, Michal
%T Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side
%J Applications of Mathematics
%D 1992
%P 201-240
%V 37
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1992.104504/
%R 10.21136/AM.1992.104504
%G en
%F 10_21136_AM_1992_104504
Hlaváček, Ivan; Křížek, Michal. Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side. Applications of Mathematics, Tome 37 (1992) no. 3, pp. 201-240. doi: 10.21136/AM.1992.104504

[1] G. Anzellotti: A class of non-coercive functionals and masonry-like materials. Ann. Inst. H. Poincaré 2 (1985), 261-307. | DOI | MR

[2] S. Bennati A. M. Genai C. Padovani: Trapezoidal gravity dams in pure compression. CNUCE - C.N.R., Internal Rep. C88-22, May 1988.

[3] S. Bennati M. Lucchesi: The minimal section of a triangular masonry dam. Мессаniса J. Ital. Assoc. Theoret. Appl. Mech. 23 (1988), 221-225.

[4] R. A. Brockman: Geometric sensitivity analysis with isoparametric finite elements. Comm. Appl. Numer. Methods 3 (1987), 495-499. | DOI | MR | Zbl

[5] M. Giaquinta G. Giusti: Researches on the equilibrium of masonry structures. Arch. Rational Mech. Anal. 88 (1985), 359-392. | DOI | MR

[6] I. Hlaváček: Optimization of the shape of axisymmetric shells. Apl. Mat. 28 (1983), 269-294. | MR

[7] I. Hlaváček: Inequalities of Korn's type, uniform with respect to a class of domains. Apl. Mat. 34 (1989), 105-112. | MR | Zbl

[8] I. Hlaváček R. Mäkinen: On the numerical solution of axisymmetric domain optimization problems. Appl. Math. 36 (1991), 284-304. | MR

[9] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies. An Introduction. Elsevier, Amsterdam, 1981. | MR

[10] O. Pironneau: Optimal Shape Design for Elliptic Systems. Springer-Verlag, New York, 1983. | MR

Cité par Sources :