Shape optimization for dynamic contact problems

Andrzej Myśliński

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2000)

  • Volume: 20, Issue: 1, page 79-91
  • ISSN: 1509-9407

Abstract

top
The paper deals with shape optimization of dynamic contact problem with Coulomb friction for viscoelastic bodies. The mass nonpenetrability condition is formulated in velocities. The friction coefficient is assumed to be bounded. Using material derivative method as well as the results concerning the regularity of solution to dynamic variational inequality the directional derivative of the cost functional is calculated and the necessary optimality condition is formulated.

How to cite

top

Andrzej Myśliński. "Shape optimization for dynamic contact problems." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 20.1 (2000): 79-91. <http://eudml.org/doc/271445>.

@article{AndrzejMyśliński2000,
abstract = {The paper deals with shape optimization of dynamic contact problem with Coulomb friction for viscoelastic bodies. The mass nonpenetrability condition is formulated in velocities. The friction coefficient is assumed to be bounded. Using material derivative method as well as the results concerning the regularity of solution to dynamic variational inequality the directional derivative of the cost functional is calculated and the necessary optimality condition is formulated.},
author = {Andrzej Myśliński},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {dynamic unilateral problem; shape optimization; sensitivity analysis; necessary optimality condition; dynamic contact; variational inequality},
language = {eng},
number = {1},
pages = {79-91},
title = {Shape optimization for dynamic contact problems},
url = {http://eudml.org/doc/271445},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Andrzej Myśliński
TI - Shape optimization for dynamic contact problems
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2000
VL - 20
IS - 1
SP - 79
EP - 91
AB - The paper deals with shape optimization of dynamic contact problem with Coulomb friction for viscoelastic bodies. The mass nonpenetrability condition is formulated in velocities. The friction coefficient is assumed to be bounded. Using material derivative method as well as the results concerning the regularity of solution to dynamic variational inequality the directional derivative of the cost functional is calculated and the necessary optimality condition is formulated.
LA - eng
KW - dynamic unilateral problem; shape optimization; sensitivity analysis; necessary optimality condition; dynamic contact; variational inequality
UR - http://eudml.org/doc/271445
ER -

References

top
  1. [1] R.A. Adams, Sobolev Spaces, Academic Press, New York 1975. 
  2. [2] G. Duvaut and J.L. Lions, Les inequations en mecanique et en physique, Dunod, Paris 1972. Zbl0298.73001
  3. [3] J. Haslinger and P. Neittaanmaki, Finite Element Approximation for Optimal Shape Design. Theory and Application, John Wiley & Sons, 1988. Zbl0713.73062
  4. [4] E.J. Haug, K.K Choi and V. Komkov, Design Senitivity Analysis of Structural Systems, Academic Press, 1986. 
  5. [5] I. Hlavacek, J. Haslinger, J. Necas and J. Lovisek, Solving of Variational Inequalities in Mechanics (in Russian), Mir, Moscow 1986. Zbl0654.73019
  6. [6] J. Jarusek and C. Eck, Dynamic Contact Problems with Small Coulomb Friction for Viscoelastic Bodies. Existence of Solutions, Preprint 97/01, Universitat Stuttgart 1997. Zbl0938.74048
  7. [7] J. Jarusek, Dynamical Contact Problem with Given Friction for Viscoelastic Bodies, Czech. Math. Journal 46 (1996), 475-487. Zbl0879.73022
  8. [8] A. Klabring and J. Haslinger, On almost Constant Contact Stress Distributions by Shape Optimization, Structural Optimization 5 (1993), 213-216. 
  9. [9] A. Myśliński, Mixed Variational Approach for Shape Optimization of Contact Problem with Prescribed Friction, in: Numerical Methods for Free Boundary Problems, P. Neittaanmaki ed., International Series of Numerical Mathematics, Birkhäuser, Basel 99 (1991), 286-296. 
  10. [10] A. Myśliński, Shape Optimization of Contact Problems Using Mixed Variational Formulation, Lecture Notes in Control and Information Sciences, Springer, Berlin 160 (1992), 414-423. Zbl0790.49038
  11. [11] A. Myśliński, Mixed Finite Element Approximation of a Shape Optimization Problem for Systems Described by Elliptic Variational Inequalities, Archives of Control Sciences 3 (3-4) (1994), 243-257. Zbl0832.73070
  12. [12] J. Necas, Les Methodes Directes en Theorie des Equations Elliptiques, Masson, Paris 1967. 
  13. [13] J. Sokolowski and J.P. Zolesio, Shape sensitivity analysis of contact problem with prescribed friction, Nonlinear Analysis, Theory, Methods and Applications 12 (1988), 1399-1411. Zbl0677.73076
  14. [14] J. Sokolowski and J.P. Zolesio, Introduction to Shape Optimization. Shape Sensitivity Analysis, Springer, Berlin 1992. Zbl0761.73003
  15. [15] J. Telega, Variational Methods in Contact Problems of Mechanics (in Russian), Advances in Mechanics 10 (1987), 3-95. 

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.