| Title:
|
Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side (English) |
| Author:
|
Hlaváček, Ivan |
| Author:
|
Křížek, Michal |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1992 |
| Pages:
|
201-240 |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
existence |
| Keyword:
|
masonry dam |
| Keyword:
|
hydrostatic pressure |
| Keyword:
|
penalty method |
| Keyword:
|
convergence |
| Keyword:
|
shape optimization |
| Keyword:
|
weight minimization |
| Keyword:
|
finite elements |
| MSC:
|
49Q10 |
| MSC:
|
65K10 |
| MSC:
|
65N30 |
| MSC:
|
73C99 |
| MSC:
|
73V20 |
| MSC:
|
73k40 |
| MSC:
|
74P10 |
| MSC:
|
74P99 |
| MSC:
|
74S05 |
| MSC:
|
74S30 |
| idZBL:
|
Zbl 0767.73047 |
| idMR:
|
MR1157456 |
| DOI:
|
10.21136/AM.1992.104504 |
| . |
| Date available:
|
2008-05-20T18:43:38Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104504 |
| . |
| Reference:
|
[1] G. Anzellotti: A class of non-coercive functionals and masonry-like materials.Ann. Inst. H. Poincaré 2 (1985), 261-307. MR 0801581, 10.1016/S0294-1449(16)30398-5 |
| Reference:
|
[2] S. Bennati A. M. Genai C. Padovani: Trapezoidal gravity dams in pure compression.CNUCE - C.N.R., Internal Rep. C88-22, May 1988. |
| Reference:
|
[3] S. Bennati M. Lucchesi: The minimal section of a triangular masonry dam.Мессаniса J. Ital. Assoc. Theoret. Appl. Mech. 23 (1988), 221-225. |
| Reference:
|
[4] R. A. Brockman: Geometric sensitivity analysis with isoparametric finite elements.Comm. Appl. Numer. Methods 3 (1987), 495-499. Zbl 0623.73081, MR 0937760, 10.1002/cnm.1630030609 |
| Reference:
|
[5] M. Giaquinta G. Giusti: Researches on the equilibrium of masonry structures.Arch. Rational Mech. Anal. 88 (1985), 359-392. MR 0781597, 10.1007/BF00250872 |
| Reference:
|
[6] I. Hlaváček: Optimization of the shape of axisymmetric shells.Apl. Mat. 28 (1983), 269-294. MR 0710176 |
| Reference:
|
[7] I. Hlaváček: Inequalities of Korn's type, uniform with respect to a class of domains.Apl. Mat. 34 (1989), 105-112. Zbl 0673.49003, MR 0990298 |
| Reference:
|
[8] I. Hlaváček R. Mäkinen: On the numerical solution of axisymmetric domain optimization problems.Appl. Math. 36 (1991), 284-304. MR 1113952 |
| Reference:
|
[9] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies. An Introduction.Elsevier, Amsterdam, 1981. MR 0600655 |
| Reference:
|
[10] O. Pironneau: Optimal Shape Design for Elliptic Systems.Springer-Verlag, New York, 1983. MR 0725856 |
| . |
