Advertisement

Shape Optimization in Contact Problems. 1. Design of an Elastic Body. 2. Design of an Elastic Perfectly Plastic Body

  • J. Haslinger
  • P. Neittaanmäki
  • T. Tiihonen
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 83)

Abstract

The optimal shape design of a two dimensional body on a rigid foundation is analyzed. The problem is how to find the boundary part of the body where the unilateral boundary conditions are assumed in such a way that a certain energy integral (total potential energy, for example) will be minimized. It is assumed that the material of the body is elastic. Some remarks will be given concerning the design of an elastic perfectly plastic body. Numerical examples will be given.

Keywords

Contact Problem Elastic Body Total Potential Energy Shape Optimization Problem Rigid Foundation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    BendsSe, M.P., Olhoff, N. and Sokolowski, J.: Sensitivity analysis of problems of elasticity with unilateral constraints, J. Struct. Mech. 13 (2), 1985, pp. 201–222.CrossRefGoogle Scholar
  2. [2]
    Benedict, R., Sokolowski, J. and Zolesio, J.P.: Shape optimization for contact problems, In System Modelling and Optimization, P. Toft-Cristensen (ed.), LN Control and Information Sciences, Vol. 59, Springer Verlag, 1984, pp. 790–799.Google Scholar
  3. [3]
    Haslinger, J., Hor6k, V. and Neittaanmäki, P.: Shape optimization in contact problem with friction. - Numer. Funct. Anal. and Optimiz., 1986, to appear.Google Scholar
  4. [4]
    Haslinger, J. and Neittaanmäki, P.: On the existence of optimal shapes in contact problems. Numer. Funct. Anal. and Optimiz., Vol. 7, No. 3–4, 1984, pp. 107–124.zbMATHGoogle Scholar
  5. [5]
    Haslinger, J. and Neittaanmäki, P.: Shape optimization of an elastic body in contact with rigid foundation, in Proc. 2nd Int. Confr. on Variational Methods in Engineering (Ed. C.A. Brebbia), Springer Verlag, 1985, pp. 6–31–6–4o.Google Scholar
  6. [6]
    Haslinger, J. and Neittaanmäki, P.: On the existence of optimal shapes in contact problems - perfectly plastic bodies, Univ. Jyväskylä, Dept. Math., Preprint 42, 1986, Comput. Mech., to appear.Google Scholar
  7. [7]
    Haslinger, J. and Neittaanmäki, P.: Shape optimization in contact problems. Approximation and numerical realization, to appear.Google Scholar
  8. [8]
    Haslinger, J., Neittaanmäki, P., Kaarna, A. and Tiihonen, T.: Optimal shape control of the domain in unilateral boundary value problems. Part I. Abstract setting and Dirichlet-Signorini problem. Part II. Design of an elastic body. Lappeenranta University of Technology, Dept. Physics and Mathematics, Reports 4–5, 1986.Google Scholar
  9. [9]
    Haslinger, J., Neittaanmäki, P. and Tiihonen, T.: Shape optimization of an elastic body in contact based on penalization of the state inequality, Apl. Math., 31 (1986), pp. 54–77.zbMATHGoogle Scholar
  10. [10]
    Haug, E.J. and Cea, J. (ed.): Optimization of distributed parameter structures, Nato Advances Study Institute Series, Series E, Alphen aan den Rijn: Sijthoff & Noordhoff, 1981.Google Scholar
  11. [11]
    Pironneau, O.: Optimal shape design for elliptic systems, Springer Series in Computational Physics, Springer Verlag, New York, 1984.CrossRefGoogle Scholar
  12. [12]
    Sokolowski, J. and Zolesio, J.P.: Shape sensitivity analysis of elastic struc-tures, The Danish Center of Applied Mathematics and Mechanics, Report No. 289, 1984.Google Scholar
  13. [13]
    Zolesio, J.P.: The material derivative (or speed) method for shape optimiza-tion, in [10], pp. 1089–1150.Google Scholar
  14. [14]
    Zolesio, J.P.: Shape controlability of free boundaries, as [2], pp. 354–361.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1986

Authors and Affiliations

  • J. Haslinger
    • 1
  • P. Neittaanmäki
    • 2
  • T. Tiihonen
    • 2
  1. 1.Faculty of Mathematics and Physics, KAM MFF UKCharles UniversityPragueCzechoslovakia
  2. 2.Department of MathematicsUniversity of JyväskyläJyväskyläFinland

Personalised recommendations