Shape optimization of a nonlinear elliptic system
Kybernetika (1993)
- Volume: 29, Issue: 3, page 270-283
- ISSN: 0023-5954
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topMyśliński, Andrzej. "Shape optimization of a nonlinear elliptic system." Kybernetika 29.3 (1993): 270-283. <http://eudml.org/doc/28256>.
@article{Myśliński1993,
author = {Myśliński, Andrzej},
journal = {Kybernetika},
keywords = {von Kármán equation; material derivative method; sensitivity analysis; variation of the domain},
language = {eng},
number = {3},
pages = {270-283},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Shape optimization of a nonlinear elliptic system},
url = {http://eudml.org/doc/28256},
volume = {29},
year = {1993},
}
TY - JOUR
AU - Myśliński, Andrzej
TI - Shape optimization of a nonlinear elliptic system
JO - Kybernetika
PY - 1993
PB - Institute of Information Theory and Automation AS CR
VL - 29
IS - 3
SP - 270
EP - 283
LA - eng
KW - von Kármán equation; material derivative method; sensitivity analysis; variation of the domain
UR - http://eudml.org/doc/28256
ER -
References
top- R. A. Adams, Sobolev Spaces, Academic Press, New York 1975. (1975) Zbl0314.46030MR0450957
- N. V. Banichuk, Problems and Methods of Optimal Structural Design, Plenum Press, New York 1983. (1983) MR0715778
- 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. (1967) Zbl0162.56405MR0221808
- 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. (1975) MR0443372
- I. Bock I. Hlaváček, I. Lovíšek, On the optimal control problem governed by the equation of von Kármán, Apl. mat. 30 (1985), 375-392. (1985) MR0806834
- F. Brezzi, Finite element approximation of the von Kármán equations, RAIRO Numer. Anal. 12 (1978), 303-312. (1978) MR0519014
- J. Cea, Opimisation, Theorie et Algorithmes. Dunod, Paгis 1971. (1971) MR0298892
- D. Chenais, On the existence of a solution in a domain identification problem, J. Math. Anal. Appl. 52 (1975), 189-219. (1975) Zbl0317.49005MR0385666
- D. Chenais, Optimal design of midsurface of shells: differentiability proof and sensitivity computation, Appl. Math. Optim. 16 (1987), 93-133. (1987) Zbl0626.73097MR0894807
- 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. (1990) Zbl0708.73033MR1055303
- Ph. Ciarlet, P. Rabier, Les equations de von Kármán, (Lecture Notes in Mathematics 826.) Springer-Verlag, Berlin 1980. (1980) Zbl0433.73019MR0595326
- 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. (1991) Zbl0747.49007MR1132189
- N. Fujii, Necessary conditions for a domain optimization problem in elliptic boundaгy value problems, SIAM J. Contгol Optim. 24 (1986), 346-360. (1986) MR0838044
- E. J. Haug K. K. Choi, V. Komkov, Design Sensitivity Analysis of Structural Systems, Academic Press, New York 1986. (1986) MR0860040
- J. Haslinger, P. Neittaanmäki, Finite Element Approximation for Optimal Shape Design, Theoгy and Applications. J. Wiley, New York 1988. (1988) MR0982710
- T. Masano, N. Fujii, Second order necessary conditions for domain optimization problems in elastic structures, J. Optim. Theory Appl. 72 (1992), 2, 355-401. (1992) MR1143202
- K. Maurin, Functional Analysis, (in Polish). Polish Scientific Publisher, Warsaw 1978. (1978)
- S. G. Michlin, Variational Methods of Mathematical Physics, (in Russian). Mir, Moscow 1970. (1970)
- A. Myslinski, Finite element approximation of a shape optimization problem for von Kármán system, Numer. Funct. Anal. Optim. 10 (1989), 7 &: 8, 691-717. (1989) Zbl0667.73069MR1019489
- 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. (1991) Zbl0756.73063MR1118872
- 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. (1990) MR1070730
- A. Myslinski, J. Sokolowski, Nondifferentiable optimization pгoblems for elliptic systems, SIAM J. Control Optim. 23 (1985), 632-648. (1985) MR0791892
- O. Pironneau, Optimal Shape Design for Elliptic Systems, (Springer Series in Computational Physics.) Springer-Verlag, New York 1984. (1984) Zbl0534.49001MR0725856
- J. Sokolowski, J. P. Zolesio, Introduction to Shape Optimization, Shape Sensitivity Analysis. Springer-Verlag, Berlin 1992. (1992) Zbl0761.73003MR1215733
- J. Sokolowski, J. P. Zolesio, Shape sensitivity analysis of contact, problems with prescribed friction, Nonlinear Theory, Methods, & Applications 12 (1988), 1399-1411. (1988) MR0972408
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