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

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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

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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

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  1. G. Anzellotti, A class of non-coercive functionals and masonry-like materials, Ann. Inst. H. Poincaré 2 (1985), 261-307. (1985) MR0801581
  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, Researches on the equilibrium of masonry structures, Arch. Rational Mech. Anal. 88 (1985), 359-392. (1985) MR0781597
  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

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