Mechanical design problems with unilateral contact
ESAIM: Modélisation mathématique et analyse numérique, Tome 32 (1998) no. 3, pp. 255-281. 
@article{M2AN_1998__32_3_255_0,
     author = {Ko\v{c}vara, Michal and Zibulevsky, Michael and Zowe, Jochem},
     title = {Mechanical design problems with unilateral contact},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {255--281},
     publisher = {Elsevier},
     volume = {32},
     number = {3},
     year = {1998},
     mrnumber = {1627151},
     zbl = {0901.73055},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1998__32_3_255_0/}
}
TY  - JOUR
AU  - Kočvara, Michal
AU  - Zibulevsky, Michael
AU  - Zowe, Jochem
TI  - Mechanical design problems with unilateral contact
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1998
SP  - 255
EP  - 281
VL  - 32
IS  - 3
PB  - Elsevier
UR  - http://www.numdam.org/item/M2AN_1998__32_3_255_0/
LA  - en
ID  - M2AN_1998__32_3_255_0
ER  - 
%0 Journal Article
%A Kočvara, Michal
%A Zibulevsky, Michael
%A Zowe, Jochem
%T Mechanical design problems with unilateral contact
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1998
%P 255-281
%V 32
%N 3
%I Elsevier
%U http://www.numdam.org/item/M2AN_1998__32_3_255_0/
%G en
%F M2AN_1998__32_3_255_0
Kočvara, Michal; Zibulevsky, Michael; Zowe, Jochem. Mechanical design problems with unilateral contact. ESAIM: Modélisation mathématique et analyse numérique, Tome 32 (1998) no. 3, pp. 255-281. http://www.numdam.org/item/M2AN_1998__32_3_255_0/

[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. | MR

[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. | MR | Zbl

[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. | MR | Zbl

[5] K. J. Bathe and E. L. Wilson. Numerical Methods in Finite Element Analysis. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1976. | Zbl

[6] A. Ben-Tal and M. Bendsøe. A new iterative method for optimal truss topology design. SIAM J. Optimization, 3: 322-358, 1993. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[11] M. P. Bendsøe . Optimization of Structural Topology, Shape and Material, Springer-Verlag, Heidelberg, 1995. | MR | Zbl

[12] J. Cea. Lectures on Optimization. Springer-Verlag, Berlin, 1978.

[13] P. G. Ciarlet. The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, New York, Oxford, 1978. | MR | Zbl

[14] I. Ekeland and R. Temam. Convex Analysis and Variational Problems. North-Holland, Amsterdam, 1976. | MR | Zbl

[15] E. J. Haug and J. S. Arora Applied Optimal Design. Wiley, New York, 1979.

[16] I. Hlaváček, J. Haslinger, J. Nečas and J. Lovíšek Solution of Variational Inequalities in Mechanics. Springer-Verlag, New-York, 1988. | MR | Zbl

[17] F. Jarre, M. Kočvara and J. Zowe. Interior point methods for mechanical design problems. SIAM J. Optimization. To appear.

[18] A. Klarbring, J. Petersson and M. Rönnquist . Truss topology optimization involving unilateral contact. J. Optimization Theory and Applications, 87, 1995. | Zbl

[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. | Zbl

[20] J. Petersson On stiffness maximization of variable thickness sheet with unilateral contact. Quarterly of Applied Mathematics, 54: 541-550, 1996. | MR | Zbl

[22] J. Petersson and J. Haslinger. An approximation theory for optimum sheet in unilateral contact. Quarterly of Applied Mathematics. To appear. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[25] R. Polyak. Modified barrier fonctions: Theory and methods. Mathematical Programming, 54: 177-222, 1992. | MR | Zbl

[26] R. T. Rockafellar A dual approach to solving nonlinear programming problems by unconstrained optimization. Mathematical Programming, 5: 354-373, 1973. | MR | Zbl

[27] R. T. Rockafellar Convex Analysis. Princeton University Press, Princeton, New Jersey, 1970. | MR | Zbl

[28] P. Tseng and D. P. Bertsekas On the convergence of the exponential multiplier method for convex programming. Mathematical Programming, 60: 1-19, 1993. | MR | Zbl