Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side

Ivan Hlaváček; Michal Křížek

Applications of Mathematics (1992)

  • Volume: 37, Issue: 3, page 201-240
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Hlaváček, Ivan, and Křížek, Michal. "Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side." Applications of Mathematics 37.3 (1992): 201-240. <http://eudml.org/doc/15711>.

@article{Hlaváček1992,
abstract = {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.},
author = {Hlaváček, Ivan, Křížek, Michal},
journal = {Applications of Mathematics},
keywords = {existence; masonry dam; hydrostatic pressure; penalty method; convergence; shape optimization; weight minimization; finite elements; existence; masonry dam; hydrostatic pressure; penalty method; convergence},
language = {eng},
number = {3},
pages = {201-240},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side},
url = {http://eudml.org/doc/15711},
volume = {37},
year = {1992},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 3
SP - 201
EP - 240
AB - 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.
LA - eng
KW - existence; masonry dam; hydrostatic pressure; penalty method; convergence; shape optimization; weight minimization; finite elements; existence; masonry dam; hydrostatic pressure; penalty method; convergence
UR - http://eudml.org/doc/15711
ER -

References

top
  1. G. Anzellotti, 10.1016/S0294-1449(16)30398-5, Ann. Inst. H. Poincaré 2 (1985), 261-307. (1985) MR0801581DOI10.1016/S0294-1449(16)30398-5
  2. S. Bennati A. M. Genai C. Padovani, Trapezoidal gravity dams in pure compression, CNUCE - C.N.R., Internal Rep. C88-22, May 1988. (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. (1988) 
  4. R. A. Brockman, 10.1002/cnm.1630030609, Comm. Appl. Numer. Methods 3 (1987), 495-499. (1987) Zbl0623.73081MR0937760DOI10.1002/cnm.1630030609
  5. M. Giaquinta G. Giusti, 10.1007/BF00250872, Arch. Rational Mech. Anal. 88 (1985), 359-392. (1985) MR0781597DOI10.1007/BF00250872
  6. I. Hlaváček, Optimization of the shape of axisymmetric shells, Apl. Mat. 28 (1983), 269-294. (1983) MR0710176
  7. I. Hlaváček, Inequalities of Korn's type, uniform with respect to a class of domains, Apl. Mat. 34 (1989), 105-112. (1989) Zbl0673.49003MR0990298
  8. I. Hlaváček R. Mäkinen, On the numerical solution of axisymmetric domain optimization problems, Appl. Math. 36 (1991), 284-304. (1991) MR1113952
  9. J. Nečas I. Hlaváček, Mathematical Theory of Elastic and Elasto-Plastic Bodies. An Introduction, Elsevier, Amsterdam, 1981. (1981) MR0600655
  10. O. Pironneau, Optimal Shape Design for Elliptic Systems, Springer-Verlag, New York, 1983. (1983) MR0725856

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.