Mechanical design problems with unilateral contact
Michal Kočvara; Michael Zibulevsky; Jochem Zowe
- Volume: 32, Issue: 3, page 255-281
- ISSN: 0764-583X
Access Full Article
topHow to cite
topKočvara, Michal, Zibulevsky, Michael, and Zowe, Jochem. "Mechanical design problems with unilateral contact." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 32.3 (1998): 255-281. <http://eudml.org/doc/193874>.
@article{Kočvara1998,
author = {Kočvara, Michal, Zibulevsky, Michael, Zowe, Jochem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {rigid obstacles; truss topology problem; elastic bodies; general multi-load formulations; discretization; iterative optimization algorithm; penalty-barrier methods},
language = {eng},
number = {3},
pages = {255-281},
publisher = {Dunod},
title = {Mechanical design problems with unilateral contact},
url = {http://eudml.org/doc/193874},
volume = {32},
year = {1998},
}
TY - JOUR
AU - Kočvara, Michal
AU - Zibulevsky, Michael
AU - Zowe, Jochem
TI - Mechanical design problems with unilateral contact
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1998
PB - Dunod
VL - 32
IS - 3
SP - 255
EP - 281
LA - eng
KW - rigid obstacles; truss topology problem; elastic bodies; general multi-load formulations; discretization; iterative optimization algorithm; penalty-barrier methods
UR - http://eudml.org/doc/193874
ER -
References
top- [1] W. ACHTZIGER. Truss topology design under multiple loading. DFG Report 367, Math. Institut, Univ. of Bayreuth, 1992.
- [2] W. ACHTZIGER. Minimax compliance truss topology subject to multiple loadings. In M. BendsØe and C. Mota-Soares, editors, Topology optimization of trusses, pages 43-54. Kluwer Academic Press, Dortrecht, 1993. MR1250189
- [3] W. ACHTZIGER, A. BEN-TAL, M. BENDSØE and J. ZOWE. Equivalent displacement based formulations for maximum strength truss topology design. IMPACT of Computing in Science and Engineering, 4: 315-345, 1992. Zbl0769.73054MR1196354
- [4] G. ALLAIRE and R. KOHN. Optimal design for minimum weight and compliance in plane stress using extremal microstructures. European J. on Mechanics (A/Solids) 12: 839-878, 1993. Zbl0794.73044MR1343090
- [5] K. J. BATHE and E. L. WILSON. Numerical Methods in Finite Element Analysis. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1976. Zbl0387.65069
- [6] A. BEN-TAL and M. BENDSØE. A new iterative method for optimal truss topology design. SIAM J. Optimization, 3: 322-358, 1993. Zbl0780.90076MR1215447
- [7] A. BEN-TAL, M. BENDSØE and J. ZOWE. Optimization methods for truss geometry and topology design. Structural Optimization, 7: 141-159, 1994.
- [8] A. BEN-TAL, I. YUZEFOVICH and M. ZIBULEVSKY. Penalty/barrier multiplier methods for minmax and constrained smooth convex programs. Research report 9/92, Optimization Laboratory, Technion-Israel Institute of Technology, Haifa, 1992.
- [9] A. BEN-TAL and M. ZIBULEVSKY. Penalty/barrier multiplier methods: a new class of augmented lagrangian algorithms for large scale convex programming problems. SIAM J. Optimization, 7, 1997. Zbl0872.90068MR1443623
- [10] M. BENDSØE, J. GUADES, R. HABER, P. PEDERSEN and J. TAYLOR. An analytical model to predict optimal material properties in the context of optimal structural design. J. Applied Mechanics, 61: 930-937, 1994. Zbl0831.73036MR1327483
- [11] M. P. BENDSØE. Optimization of Structural Topology, Shape and Material, Springer-Verlag, Heidelberg, 1995. Zbl0822.73001MR1350791
- [12] J. CEA. Lectures on Optimization. Springer-Verlag, Berlin, 1978. Zbl0409.90050
- [13] P. G. CIARLET. The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, New York, Oxford, 1978. Zbl0383.65058MR520174
- [14] I. EKELAND and R. TEMAM. Convex Analysis and Variational Problems. North-Holland, Amsterdam, 1976. Zbl0322.90046MR463994
- [15] E. J. HAUG and J. S. ARORAApplied Optimal Design. Wiley, New York, 1979.
- [16] I. HLAVÁČEK, J. HASLINGER, J. NEČAS and J. LOVÍŠEKSolution of Variational Inequalities in Mechanics. Springer-Verlag, New-York, 1988. Zbl0654.73019MR952855
- [17] F. JARRE, M. KOČVARA and J. ZOWE. Interior point methods for mechanical design problems. SIAM J. Optimization. To appear. Zbl0912.90231
- [18] A. KLARBRING, J. PETERSSON and M. RÖNNQUIST. Truss topology optimization involving unilateral contact. J. Optimization Theory and Applications, 87, 1995. Zbl0841.73046
- [19] M. KOČVARA and J. ZOWE. How mathematics can help in design of mechanical structures. In. D.F. Griffiths and G.A. Watson, eds., Numerical Analysis 1995, Longman, Harlow, 1996, pp. 76-93. Zbl0858.73059
- [20] J. PETERSSONOn stiffness maximization of variable thickness sheet with unilateral contact. Quarterly of Applied Mathematics, 54: 541-550, 1996. Zbl0871.73046MR1402408
- [22] J. PETERSSON and J. HASLINGER. An approximation theory for optimum sheet in unilateral contact. Quarterly of Applied Mathematics. To appear. Zbl0960.74051MR1622499
- [23] J. PETERSSON and A. KLARBRING. Saddle point approach to stiffness optimization of discrete structures including unilateral contact. Control and Cybernetics, 3: 461-479, 1994. Zbl0820.73053MR1303365
- [24] J. PETERSSON and M. PATRIKSSON. Topology optimization of sheets in contact by a subgradient method. International Journal for Numerical Methods in Engineerings. To appear. Zbl0890.73046MR1449228
- [25] R. POLYAK. Modified barrier fonctions: Theory and methods. Mathematical Programming, 54: 177-222, 1992. Zbl0756.90085MR1158819
- [26] R. T. ROCKAFELLARA dual approach to solving nonlinear programming problems by unconstrained optimization. Mathematical Programming, 5: 354-373, 1973. Zbl0279.90035MR371416
- [27] R. T. ROCKAFELLARConvex Analysis. Princeton University Press, Princeton, New Jersey, 1970. Zbl0193.18401MR274683
- [28] P. TSENG and D. P. BERTSEKASOn the convergence of the exponential multiplier method for convex programming. Mathematical Programming, 60: 1-19, 1993. Zbl0783.90101MR1231274
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.