Shape optimization in contact problems based on penalization of the state inequality

Jaroslav Haslinger; Pekka Neittaanmäki; Timo Tiihonen

Aplikace matematiky (1986)

  • Volume: 31, Issue: 1, page 54-77
  • ISSN: 0862-7940

Abstract

top
The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.

How to cite

top

Haslinger, Jaroslav, Neittaanmäki, Pekka, and Tiihonen, Timo. "Shape optimization in contact problems based on penalization of the state inequality." Aplikace matematiky 31.1 (1986): 54-77. <http://eudml.org/doc/15435>.

@article{Haslinger1986,
abstract = {The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.},
author = {Haslinger, Jaroslav, Neittaanmäki, Pekka, Tiihonen, Timo},
journal = {Aplikace matematiky},
keywords = {frictionless plane contact; linear-elastic sheet; rigid foundation; shape optimization; contact boundary curve; minimization of the total potential energy; family of penalized state problems; existence; convergence; nonlinear programming problem; box constraints; linear inequality constraints; linear equality constraint; frictionless plane contact; linear-elastic sheet; rigid foundation; shape optimization; contact boundary curve; minimization of the total potential energy; family of penalized state problems; existence; convergence; nonlinear programming problem; box constraints; linear inequality constraints; linear equality constraint},
language = {eng},
number = {1},
pages = {54-77},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Shape optimization in contact problems based on penalization of the state inequality},
url = {http://eudml.org/doc/15435},
volume = {31},
year = {1986},
}

TY - JOUR
AU - Haslinger, Jaroslav
AU - Neittaanmäki, Pekka
AU - Tiihonen, Timo
TI - Shape optimization in contact problems based on penalization of the state inequality
JO - Aplikace matematiky
PY - 1986
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 1
SP - 54
EP - 77
AB - The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.
LA - eng
KW - frictionless plane contact; linear-elastic sheet; rigid foundation; shape optimization; contact boundary curve; minimization of the total potential energy; family of penalized state problems; existence; convergence; nonlinear programming problem; box constraints; linear inequality constraints; linear equality constraint; frictionless plane contact; linear-elastic sheet; rigid foundation; shape optimization; contact boundary curve; minimization of the total potential energy; family of penalized state problems; existence; convergence; nonlinear programming problem; box constraints; linear inequality constraints; linear equality constraint
UR - http://eudml.org/doc/15435
ER -

References

top
  1. D. Begis R. Glowinski, 10.1007/BF01447854, Appl. Math. Optim., 2, (1975), 130-169. (1975) MR0443372DOI10.1007/BF01447854
  2. M. P. Bendsoe N. Olhoff J. Sokolowski, Sensitivity analysis of problems of elasticity with unilateral constraints, MAT-report 1984-10, Matematisk institut, Danmarks Tekniske Hojskole, 1984. (1984) MR0802916
  3. R. L. Benedict J. E. Taylor, Optimal design for elastic bodies in contact, in [13], 1553-1569. 
  4. R. L. Benedict J. Sokolowski J. P. Zolesio, Shape optimization for contact problems, In: Proceedings of 11th IFIP Conference on System Modelling and Optimization (P. Thoft-Cristensen ed.), Springer Verlag, Berlin, LN in Contr. and Inform. Sci. 59, 1984, 790-799. (1984) MR0769714
  5. R. H. Gallagher O. C. Zienkiewicz ed., Optimum Structural Design II, John Wiley & Sons, New York, 1983. (1983) MR0718335
  6. P. E. Gill W. Murray M. H. Wright, Practical Optimization, Academic Press, London, 1981. (1981) MR0634376
  7. R. Glowinski, Numerical Methods for Nonlinear Variational Problems, Springer Series in Computational Physics, Springer-Verlag, New York, 1984. (1984) Zbl0536.65054MR0737005
  8. J. Haslinger P. Neittaanmäki, 10.5802/afst.594, Ann. Fac. Sci. Tolouse, Vol. V, 1983, 199-216. (1983) MR0747190DOI10.5802/afst.594
  9. J. Haslinger P. Neittaanmäki, On optimal shape design of systems governed by mixed Dirichlet - Signorini boundary value problem, Math. Meth. Appl. Sci. 9, (1985) (to appear). (1985) MR0845923
  10. J. Haslinger P. Neittaanmäki, On the existence of optimal shape in contact problems, Numer. Funct. Anal. and Optimiz., 7 (2&3), 107-124, 1984-85. (1984) MR0767377
  11. J. Haslinger P. Neittaanmäki T. Tiihonen, On optimal shape of an elastic body on a rigid foundation, in: Proceedings of MAFELAP V, (J. R. Whitcman ed.) Academic Press. 
  12. E. J. Haug J. S. Arora, Applied optimal design, mechanical and structural systems, Wiley - Interscience Publ., New York, 1979. (1979) 
  13. E. J. Haug J. Cea ed., Optimization of Distributed Parameter Structures, Nato Advanced Study Institutes Series, Series E, Alphen aan den Rijn: Sijthoff & Noordhoff, 1981. (1981) 
  14. E. J. Haug B. Rousselet, Design sensitivity analysis of eigenvalue variations, in [13], 1371 to 1396. MR0690999
  15. I. Hlaváček I. Bock J. Lovíšek, Optimal control of variational inequalities with applications to structural analysis, Part I, Optimal design of a beam with unilateral supports. Part II, Local optimization of the stress of a beam. Part III, Optimal design of an elastic plate, Appl. Math. Optimiz. 
  16. I. Hlaváček J. Haslinger J. Nečas J. Lovíšek, Numerical solution of variational inequalities, (in Slovak), ALFA, SNTL, 1982, English translation, (to appear). (1982) MR0755152
  17. I. Hlaváček J. Nečas, Optimization of the domain in elliptic unilateral boundary value problems by finite element method, R.A.I.R.O., Num. Anal., 16 (1982), 351-373. (1982) MR0684830
  18. V. Komkov, ed., Sensitivity of Functionals with Applications to Engineering Sciences, Lecture Notes in Mathematics, 1086, Springer Verlag, Berlin 1984. (1984) Zbl0539.00022MR0791769
  19. P. Neittaanmäki T. Tiihonen, Sensitivity analysis for a class of shape design problems, Ber. Univ. Jyväskylä Math. Inst., (to appear). MR0793016
  20. O. Pironneau, Optimal shape design for elliptic systems, Springer Series in Comput. Physics, Springer Verlag, New York, 1984. (1984) Zbl0534.49001MR0725856
  21. J. Sokolowski, Sensitivity analysis of a class of variational inequalities, in [13], 1600-1605. MR0691007
  22. J. Sokolowski J. P. Zolesio, Shape sensitivity analysis for variational inequalities, in: Proceedings of 10th IFIP Conference, (P. Thoft-Christensen, ed.). Springer-Verlag, Berlin, LN in Contr. and Inform. Sci., 38, 1982, 399-407. (1982) MR1215733
  23. J. Р. Zolesio, The material derivative (or speed) method for shape optimization, in [13], 1089-1151. Zbl0517.73097MR0690991
  24. J. A. Nitsche, On Korn's inequality, R.A.I.R.O. Analyse numérique/Numerical analysis, vol. 15, No 3, 1981, 237-248. (1981) MR0631678

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.