Inclusions, Control and Optimization 20 (2000) 79-91
System Research Institute
01-447 Warsaw, ul. Newelska 6, Poland
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.
Keywords: dynamic unilateral problem, shape optimization, sensitivity analysis, necessary optimality condition.
1991 Mathematics Subject Classification: 35B30, 49B50, 73C60, 73K40.
|||R.A. Adams, Sobolev Spaces, Academic Press, New York 1975.|
|||G. Duvaut and J.L. Lions, Les inequations en mecanique et en physique, Dunod, Paris 1972.|
|||J. Haslinger and P. Neittaanmaki, Finite Element Approximation for Optimal Shape Design. Theory and Application, John Wiley & Sons, 1988.|
|||E.J. Haug, K.K Choi and V. Komkov, Design Senitivity Analysis of Structural Systems, Academic Press, 1986.|
|||I. Hlavacek, J. Haslinger, J. Necas and J. Lovisek, Solving of Variational Inequalities in Mechanics (in Russian), Mir, Moscow 1986.|
|||J. Jarusek and C. Eck, Dynamic Contact Problems with Small Coulomb Friction for Viscoelastic Bodies. Existence of Solutions, Preprint 97/01, Universitat Stuttgart 1997.|
|||J. Jarusek, Dynamical Contact Problem with Given Friction for Viscoelastic Bodies, Czech. Math. Journal 46 (1996), 475-487.|
|||A. Klabring and J. Haslinger, On almost Constant Contact Stress Distributions by Shape Optimization, Structural Optimization 5 (1993), 213-216.|
|||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.|
|||A. Myśliński, Shape Optimization of Contact Problems Using Mixed Variational Formulation, Lecture Notes in Control and Information Sciences, Springer, Berlin 160 (1992), 414-423.|
|||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.|
|||J. Necas, Les Methodes Directes en Theorie des Equations Elliptiques, Masson, Paris 1967.|
|||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.|
|||J. Sokolowski and J.P. Zolesio, Introduction to Shape Optimization. Shape Sensitivity Analysis, Springer, Berlin 1992.|
|||J. Telega, Variational Methods in Contact Problems of Mechanics (in Russian), Advances in Mechanics 10 (1987), 3-95.|
Received 18 November 1999
Revised 3 March 2000