| Title:
|
Numerical analysis for optimal shape design in elliptic boundary value problems (English) |
| Author:
|
Kestřánek, Zdeněk |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
4 |
| Year:
|
1988 |
| Pages:
|
322-333 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
finite element method |
| Keyword:
|
shape optimization |
| Keyword:
|
optimal design |
| Keyword:
|
method of nonlinear programming |
| Keyword:
|
numerical examples |
| Keyword:
|
elliptic boundary value problems |
| MSC:
|
49A22 |
| MSC:
|
49A29 |
| MSC:
|
49D37 |
| MSC:
|
49J20 |
| MSC:
|
49J40 |
| MSC:
|
49M37 |
| MSC:
|
65K10 |
| MSC:
|
65K99 |
| MSC:
|
65N30 |
| MSC:
|
65N99 |
| idZBL:
|
Zbl 0662.65062 |
| idMR:
|
MR0949252 |
| DOI:
|
10.21136/AM.1988.104312 |
| . |
| Date available:
|
2008-05-20T18:35:03Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104312 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] J. Haslinger P. Neittaanmäki: On Optimal Shape Design of Systems Governed by Mixed Dirichlet-Signorini Boundary Value Problems.Univ. of Jyväskylä, Dept. of Math., Prepr. 22, 1983. |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[13] I. Hlaváček: Shape optimization of elasto-plastic bodies by the finite element method.Proc. MAFELAP 1987, Academic Press, London. |
| Reference:
|
[14] Z. Kestřánek: Optimal Shape Design in Elliptic Boundary Value Problems by Finite Element Method.Proc. MAFELAP 1987, Academic Press, London. |
| Reference:
|
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| Reference:
|
[16] I. Hlaváček: Shape optimization of an elastic-perfectly plastic body.Apl. mat., v. 32, No. 5, 1987, 381-400. MR 0909545 |
| Reference:
|
[17] B. Fraeijs de Veubeke M. Hogge: Dual analysis for heat conduction problems by finite elements.Int. J. Numer. Meth. Engng., 5, 1972, 65-82. 10.1002/nme.1620050107 |
| Reference:
|
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| . |
