| Title:
|
Shape optimization in contact problems based on penalization of the state inequality (English) |
| Author:
|
Haslinger, Jaroslav |
| Author:
|
Neittaanmäki, Pekka |
| Author:
|
Tiihonen, Timo |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
31 |
| Issue:
|
1 |
| Year:
|
1986 |
| Pages:
|
54-77 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established. (English) |
| Keyword:
|
frictionless plane contact |
| Keyword:
|
linear-elastic sheet |
| Keyword:
|
rigid foundation |
| Keyword:
|
shape optimization |
| Keyword:
|
contact boundary curve |
| Keyword:
|
minimization of the total potential energy |
| Keyword:
|
family of penalized state problems |
| Keyword:
|
existence |
| Keyword:
|
convergence |
| Keyword:
|
nonlinear programming problem |
| Keyword:
|
box constraints |
| Keyword:
|
linear inequality constraints |
| Keyword:
|
linear equality constraint |
| MSC:
|
49J40 |
| MSC:
|
49M30 |
| MSC:
|
73T05 |
| MSC:
|
73k40 |
| MSC:
|
74A55 |
| MSC:
|
74M15 |
| MSC:
|
74P99 |
| MSC:
|
74S05 |
| idZBL:
|
Zbl 0594.73109 |
| idMR:
|
MR0836802 |
| DOI:
|
10.21136/AM.1986.104184 |
| . |
| Date available:
|
2008-05-20T18:29:18Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104184 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] R. L. Benedict J. E. Taylor: Optimal design for elastic bodies in contact.in [13], 1553-1569. |
| Reference:
|
[4] R. L. Benedict J. Sokolowski J. P. Zolesio: Shape optimization for contact problems.In: Proceedings of 11th IFIP Conference on System Modelling and Optimization (P. Thoft-Cristensen ed.), Springer Verlag, Berlin, LN in Contr. and Inform. Sci. 59, 1984, 790-799. MR 0769714 |
| Reference:
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| Reference:
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[6] P. E. Gill W. Murray M. H. Wright: Practical Optimization.Academic Press, London, 1981. MR 0634376 |
| Reference:
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| Reference:
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[8] J. Haslinger P. Neittaanmäki: Penalty method in design optimization of systems governed by mixed Dirichlet - Signorini boundary value problem.Ann. Fac. Sci. Tolouse, Vol. V, 1983, 199-216. MR 0747190, 10.5802/afst.594 |
| Reference:
|
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| Reference:
|
[10] J. Haslinger P. Neittaanmäki: On the existence of optimal shape in contact problems.Numer. Funct. Anal. and Optimiz., 7 (2&3), 107-124, 1984-85. MR 0767377 |
| Reference:
|
[11] J. Haslinger P. Neittaanmäki T. Tiihonen: On optimal shape of an elastic body on a rigid foundation.in: Proceedings of MAFELAP V, (J. R. Whitcman ed.) Academic Press. |
| Reference:
|
[12] E. J. Haug J. S. Arora: Applied optimal design, mechanical and structural systems.Wiley - Interscience Publ., New York, 1979. |
| Reference:
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[13] E. J. Haug J. Cea ed.: Optimization of Distributed Parameter Structures.Nato Advanced Study Institutes Series, Series E, Alphen aan den Rijn: Sijthoff & Noordhoff, 1981. |
| Reference:
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[14] E. J. Haug B. Rousselet: Design sensitivity analysis of eigenvalue variations.in [13], 1371 to 1396. MR 0690999 |
| Reference:
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[15] I. Hlaváček I. Bock J. Lovíšek: Optimal control of variational inequalities with applications to structural analysis.Part I, Optimal design of a beam with unilateral supports. Part II, Local optimization of the stress of a beam. Part III, Optimal design of an elastic plate, Appl. Math. Optimiz. |
| Reference:
|
[16] I. Hlaváček J. Haslinger J. Nečas J. Lovíšek: Numerical solution of variational inequalities.(in Slovak), ALFA, SNTL, 1982, English translation, (to appear). MR 0755152 |
| Reference:
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[17] I. Hlaváček J. Nečas: Optimization of the domain in elliptic unilateral boundary value problems by finite element method.R.A.I.R.O., Num. Anal., 16 (1982), 351-373. MR 0684830 |
| Reference:
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[18] V. Komkov, ed.: Sensitivity of Functionals with Applications to Engineering Sciences.Lecture Notes in Mathematics, 1086, Springer Verlag, Berlin 1984. Zbl 0539.00022, MR 0791769 |
| Reference:
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[19] P. Neittaanmäki T. Tiihonen: Sensitivity analysis for a class of shape design problems.Ber. Univ. Jyväskylä Math. Inst., (to appear). MR 0793016 |
| Reference:
|
[20] O. Pironneau: Optimal shape design for elliptic systems.Springer Series in Comput. Physics, Springer Verlag, New York, 1984. Zbl 0534.49001, MR 0725856 |
| Reference:
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[21] J. Sokolowski: Sensitivity analysis of a class of variational inequalities.in [13], 1600-1605. MR 0691007 |
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| . |
