| Title:
|
Shape optimization of a nonlinear elliptic system (English) |
| Author:
|
Myslinski, Andrzej |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
29 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
270-283 |
| . |
| Category:
|
math |
| . |
| MSC:
|
35J45 |
| MSC:
|
35J60 |
| MSC:
|
49K20 |
| MSC:
|
49Q10 |
| MSC:
|
73K10 |
| MSC:
|
73k40 |
| MSC:
|
74K20 |
| MSC:
|
74P99 |
| idZBL:
|
Zbl 0787.73049 |
| idMR:
|
MR1231872 |
| . |
| Date available:
|
2009-09-24T18:40:39Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125101 |
| . |
| Reference:
|
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| Reference:
|
[2] N. V. Banichuk: Problems and Methods of Optimal Structural Design.Plenum Press, New York 1983. MR 0715778 |
| Reference:
|
[3] M. S. Berger: On von Kármán's equations and the buckling of a thin elastic plate. I. The clamped plate.Comm. Pure Appl. Math. 20 (1967), 687-719. Zbl 0162.56405, MR 0221808 |
| Reference:
|
[4] D. Begis, R. Glowinski: Application de la metode des elements finis a ľapproximation ďun probleme de domaine optimal.Appl. Math. Optim. 2 (1975), 130-169. MR 0443372 |
| Reference:
|
[5] I. Bock I. Hlaváček, I. Lovíšek: On the optimal control problem governed by the equation of von Kármán.Apl. mat. 30 (1985), 375-392. MR 0806834 |
| Reference:
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[6] F. Brezzi: Finite element approximation of the von Kármán equations.RAIRO Numer. Anal. 12 (1978), 303-312. MR 0519014 |
| Reference:
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[7] J. Cea: Opimisation.Theorie et Algorithmes. Dunod, Paгis 1971. MR 0298892 |
| Reference:
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[8] D. Chenais: On the existence of a solution in a domain identification problem.J. Math. Anal. Appl. 52 (1975), 189-219. Zbl 0317.49005, MR 0385666 |
| Reference:
|
[9] D. Chenais: Optimal design of midsurface of shells: differentiability proof and sensitivity computation.Appl. Math. Optim. 16 (1987), 93-133. Zbl 0626.73097, MR 0894807 |
| Reference:
|
[10] D. Chenais, B. Rousselet: Dependence of the buckling load of a nonshallow arch with respect to the shape of its midcurve.RAIRO Modél. Math. Anal. Numér. 24 (1990), 3, 307-341. Zbl 0708.73033, MR 1055303 |
| Reference:
|
[11] Ph. Ciarlet, P. Rabier: Les equations de von Kármán.(Lecture Notes in Mathematics 826.) Springer-Verlag, Berlin 1980. Zbl 0433.73019, MR 0595326 |
| Reference:
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[12] M. C. Delfour, J. P. Zolesio: Velocity method and Lagrangian formulation for the computation of the shape hessian.SIAM J. Control Optim. 29 (1991), 6, 1414-1442. Zbl 0747.49007, MR 1132189 |
| Reference:
|
[13] N. Fujii: Necessary conditions for a domain optimization problem in elliptic boundaгy value problems.SIAM J. Contгol Optim. 24 (1986), 346-360. MR 0838044 |
| Reference:
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[14] E. J. Haug K. K. Choi, V. Komkov: Design Sensitivity Analysis of Structural Systems.Academic Press, New York 1986. MR 0860040 |
| Reference:
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[15] J. Haslinger, P. Neittaanmäki: Finite Element Approximation for Optimal Shape Design.Theoгy and Applications. J. Wiley, New York 1988. MR 0982710 |
| Reference:
|
[16] T. Masano, N. Fujii: Second order necessary conditions for domain optimization problems in elastic structures.J. Optim. Theory Appl. 72 (1992), 2, 355-401. MR 1143202 |
| Reference:
|
[17] K. Maurin: Functional Analysis.(in Polish). Polish Scientific Publisher, Warsaw 1978. |
| Reference:
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[18] S. G. Michlin: Variational Methods of Mathematical Physics.(in Russian). Mir, Moscow 1970. |
| Reference:
|
[19] A. Myslinski: Finite element approximation of a shape optimization problem for von Kármán system.Numer. Funct. Anal. Optim. 10 (1989), 7 &: 8, 691-717. Zbl 0667.73069, MR 1019489 |
| Reference:
|
[20] A. Myslinski: Mixed variational approach for shape optimization in contact problem with prescribed friction.In: Numerical Methods in Free Boundary Problems (P. Neittaanmäki ed.), Birkhäuser, Basel 1991, pp. 286-296. Zbl 0756.73063, MR 1118872 |
| Reference:
|
[21] A. Myslinski: Minimax shape optimization problem for von Kármán system.In: Analysis and Optimization of Systems (A. Bensoussan and J. L. Lions, eds., Lecture Notes in Control and Information Sciences 144), Springer-Verlag, Beгlin 1990, pp. 164-173. MR 1070730 |
| Reference:
|
[22] A. Myslinski, J. Sokolowski: Nondifferentiable optimization pгoblems for elliptic systems.SIAM J. Control Optim. 23 (1985), 632-648. MR 0791892 |
| Reference:
|
[23] O. Pironneau: Optimal Shape Design for Elliptic Systems.(Springer Series in Computational Physics.) Springer-Verlag, New York 1984. Zbl 0534.49001, MR 0725856 |
| Reference:
|
[24] J. Sokolowski, J. P. Zolesio: Introduction to Shape Optimization.Shape Sensitivity Analysis. Springer-Verlag, Berlin 1992. Zbl 0761.73003, MR 1215733 |
| Reference:
|
[25] J. Sokolowski, J. P. Zolesio: Shape sensitivity analysis of contact, problems with prescribed friction.Nonlinear Theory, Methods, & Applications 12 (1988), 1399-1411. MR 0972408 |
| . |
