Numerical analysis for optimal shape design in elliptic boundary value problems

Zdeněk Kestřánek

Aplikace matematiky (1988)

  • Volume: 33, Issue: 4, page 322-333
  • ISSN: 0862-7940

Abstract

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Shape optimization problems are optimal design problems in which the shape of the boundary plays the role of a design, i.e. the unknown part of the problem. Such problems arise in structural mechanics, acoustics, electrostatics, fluid flow and other areas of engineering and applied science. The mathematical theory of such kind of problems has been developed during the last twelve years. Recently the theory has been extended to cover also situations in which the behaviour of the system is governed by partial differential equations with unilateral boundary conditions. In the paper an efficient method of nonlinear programming for solving optimal shape design problems is presented. The effectiveness of the technique proposed is demonstrated by numerical examples.

How to cite

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Kestřánek, Zdeněk. "Numerical analysis for optimal shape design in elliptic boundary value problems." Aplikace matematiky 33.4 (1988): 322-333. <http://eudml.org/doc/15546>.

@article{Kestřánek1988,
abstract = {Shape optimization problems are optimal design problems in which the shape of the boundary plays the role of a design, i.e. the unknown part of the problem. Such problems arise in structural mechanics, acoustics, electrostatics, fluid flow and other areas of engineering and applied science. The mathematical theory of such kind of problems has been developed during the last twelve years. Recently the theory has been extended to cover also situations in which the behaviour of the system is governed by partial differential equations with unilateral boundary conditions. In the paper an efficient method of nonlinear programming for solving optimal shape design problems is presented. The effectiveness of the technique proposed is demonstrated by numerical examples.},
author = {Kestřánek, Zdeněk},
journal = {Aplikace matematiky},
keywords = {finite element method; shape optimization; optimal design; method of nonlinear programming; numerical examples; elliptic boundary value problems; finite element method; Shape optimization; optimal design; method of nonlinear programming; numerical examples},
language = {eng},
number = {4},
pages = {322-333},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Numerical analysis for optimal shape design in elliptic boundary value problems},
url = {http://eudml.org/doc/15546},
volume = {33},
year = {1988},
}

TY - JOUR
AU - Kestřánek, Zdeněk
TI - Numerical analysis for optimal shape design in elliptic boundary value problems
JO - Aplikace matematiky
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 33
IS - 4
SP - 322
EP - 333
AB - Shape optimization problems are optimal design problems in which the shape of the boundary plays the role of a design, i.e. the unknown part of the problem. Such problems arise in structural mechanics, acoustics, electrostatics, fluid flow and other areas of engineering and applied science. The mathematical theory of such kind of problems has been developed during the last twelve years. Recently the theory has been extended to cover also situations in which the behaviour of the system is governed by partial differential equations with unilateral boundary conditions. In the paper an efficient method of nonlinear programming for solving optimal shape design problems is presented. The effectiveness of the technique proposed is demonstrated by numerical examples.
LA - eng
KW - finite element method; shape optimization; optimal design; method of nonlinear programming; numerical examples; elliptic boundary value problems; finite element method; Shape optimization; optimal design; method of nonlinear programming; numerical examples
UR - http://eudml.org/doc/15546
ER -

References

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  4. P. Neittaanmäki T. Tiihonen, Sensitivity Analysis for a Class of Optimal Shape Design Problems, Univ. of Jyväskylä. Dept. of Mathematics, Report 29, 1985. (1985) Zbl0592.49005MR0793016
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  13. I. Hlaváček, Shape optimization of elasto-plastic bodies by the finite element method, Proc. MAFELAP 1987, Academic Press, London. (1987) 
  14. Z. Kestřánek, Optimal Shape Design in Elliptic Boundary Value Problems by Finite Element Method, Proc. MAFELAP 1987, Academic Press, London. (1987) 
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