Article
MSC:
49A29,
49D29,
49Q10,
65K10,
73K25,
74M15,
74P10 | MR 1709662 | Zbl 1060.49509 | DOI: 10.1023/A:1023013327165
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Keywords:
shape optimization; contact problems; reciprocal variational formulation; sensitivity analysis
shape optimization; contact problems; reciprocal variational formulation; sensitivity analysis
Summary:
The paper deals with a class of optimal shape design problems for elastic bodies unilaterally supported by a rigid foundation. Cost and constraint functionals defining the problem depend on contact stresses, i.e. their control is of primal interest. To this end, the so-called reciprocal variational formulation of contact problems making it possible to approximate directly the contact stresses is used. The existence and approximation results are established. The sensitivity analysis is carried out.
References:
[Benedict, Taylor, 1981] Benedict, R. L. and Taylor, J. E.: Optimal design for elastic bodies in contact. Optimization of Distributed-Parameter Structures, Haug, E. J. and Céa, J. (eds.), Sijthoff and Noordhoff aan den Rijn, Holland, 1981, pp. 1553–1599.
[Correa, Seeger, 1984] Correa, R. and Seeger, A.: Directional derivatives in minimax problems. Numer. Funct. Anal. and Optimiz. 7 (1984), 145–156. DOI 10.1080/01630568508816186 | MR 0767379
[Ekeland, Temam, 1976] Ekeland, I. and Temam, R.: Convex Analysis and Variational Problems. North-Holland, Amsterdam, 1976. MR 0463994
[Hlaváček, Haslinger, Nečas, Lovíšek, 1988] Hlaváček, I., Haslinger, J., Nečas, J. and Lovíšek, J.: Numerical Solution of Variational Inequalities. Springer Series in Applied Mathematical Sciences 66, Springer-Verlag, New York, 1988.
[Haslinger, Klarbring, 1993] Haslinger, J. and Klarbring, A.: Shape optimization in unilateral contact problems using generalized reciprocal energy as objective functional. Nonlinear Analysis, Methods & Appl. 21 (1993), 815–834. MR 1249662
[Haslinger, Neittaanmäki, 1988] Haslinger, J. and Neittaanmäki, P.: Finite Element Approximation for Optimal Shape Design: Theory and Applications. J. Wiley, Chichester-New York, 1988. MR 0982710
[Haslinger, Neittaanmäki, 1996] Haslinger, J. and Neittaanmäki, P.: Finite Element Approximation for Optimal Shape, Material and Topology Design, 2nd Edition. J. Wiley, Chichester-New York, 1996. MR 1419500
[Haslinger, Panagiotopoulos, 1984] Haslinger, J. and Panagiotopoulos, P. D.: Approximation of contact problems with friction by reciprocal variational formulation. Proc. Roy. Soc. Edingburgh 98A (1984), 365–383. MR 0768357
[Kikuchi, Oden, 1988] Kikuchi, N. and Oden, J. T.: Contact Problems in Elasticity: A study of variational inequalities and finite element methods. SIAM, Philadelphia, 1988. MR 0961258
[Klarbring, Haslinger, 1993] Klarbring, A. and Haslinger, J.: On almost constant contact stress distributions by shape optimization. Struct. Opt. 5 (1993), 213–216. DOI 10.1007/BF01743581
[Pironneau, 1984] Pironneau, O.: Optimal Shape Design for Elliptic Systems. Springer series in Computational Physics, Springer-Verlag, New York, 1984. MR 0725856 | Zbl 0534.49001
[Sokolowski, Zolesio, 1992] Sokolowski, J. and Zolesio, J. P.: Introduction to Shape Optimization. Springer-Verlag, 1992. MR 1215733
Search
Partner of
