Shape optimization of thermoviscoelastic contact problems

• Autorzy: Myśliński A.
• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with a shape optimization problem of a viscoelastic body in unilateral dynamic contact with a rigid foundation. The contact with Coulomb friction is assumed to occur at a portion of the boundary of the body. The nonpenetration condition is described in terms of velocities. The thermal deformation is taken into account. Using the material derivative method as well as the results concerning the regularity of solutions to dynamic variational thermoviscoelastic problem the directional derivative of the cost functional is calculated. A necessary optimality condition is formulated.

Słowa kluczowe

EN

dynamic thermoviscoelastic contact problem; shape optimization; sensitivity analysis; necessary optimality condition

PL

optymalizacja kształtu; analiza czułości; warunek konieczny optymalności

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2003
• Tom: Vol. 32, no 3
• Strony: 611--627
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Myśliński A.

• Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01 - 447 Warsaw, Poland,

Bibliografia

• Adams, R.A. (1975) Sobolev Spaces. Academic Press, New York.
• Chudzikiewicz, A. and Myslinski, A. (2002) Augmented Lagrangian Approach for Wheel - Rail Thermoelastic Contact Problem with Friction and Wear. Preprint, Systems Research Institute, Warsaw, Poland.
• Duvaut, G. and Lions, J.L. (1972) Les inequations en mecanique et en physique. Dunod, Paris.
• Denkowski, Z. and Migorski, S. (1998) Optimal Shape Design Problems for a Class of Systems Described by Hemivariational Inequalities. Journal of Global Optimization, 12, 37–59.
• Eck, C. and Jarusek, J. (1999) The solvability of a Coupled Thermoviscoelastic Contact Problem with Small Coulomb Friction and Linearized Growth of Frictional Heat. Mathematical Methods in the Applied Sciences, 22, 1221–1234.
• Gasinski, L. (2000) An Optimal Shape Design Problem for a Hyperbolic Variational Inequalities. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 20, 25–31.
• Goeleven, D., Miettinen, M., and Panagiotopoulos, P. (1999) Dynamic Hemivariational Inequalities and Their Applications. Journal of Optimization Theory and Applications, 103, 567–601.
• Han, W. and Sofonea, M. (2002) Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity. AMS/IP Studies in Advanced Mathematics, 30.
• Haslinger, J. and Neittaanmaki, P. (1988) Finite Element Approximation for Optimal Shape Design. Theory and Application. John Wiley& Sons.
• Haug, E.J., Choi, K.K., and Komkov, V. (1986) Design Sensitivity Analysis of Structural Systems. Academic Press.
• Hlavacek, I., Haslinger, J., Necas, J., and Lovisek, J. (1986) Solving of Variational Inequalities in Mechanics (in Russian). Mir, Moscow.
• Jarusek, J. (1996) Dynamical Contact Problem with Given Friction for Viscoelastic Bodies. Czech. Math. Journal, 46, 475–487.
• Jarusek, J. and Eck, C. (1999) Dynamic Contact Problems with Small Coulomb Friction for Viscoelastic Bodies. Existence of Solutions. Mathematical Modelling and Methods in the Applied Sciences, 9, 11–34.
• Jarusek, J., Krbec, M., Rao, M., and Sokołowski, J. (2002) Conical Differentiability for Evolution Variational Inequalities. To be published in Journal of Differential Equations.
• Klabring, A. and and Haslinger, J. (1993) On almost Constant Contact Stress Distributions by Shape Optimization. Structural Optimization, 5, 213–216.
• Myślinski, A. (1991) Mixed Variational Approach for Shape Optimization of Contact Problem with Prescribed Friction. In: P. Neittaanmaki ed., Numerical Methods for Free Boundary Problems. International Series of Numerical Mathematics, Birkh¨auser, Basel, 99, 286 - 296.
• Myslinski, A. (1994) Mixed Finite Element Approximation of a Shape Optimization Problem for Systems Described by Elliptic Variational Inequalities. Archives of Control Sciences, 3, 3–4, 243–257.
• Myslinski, A. (1992) Shape Optimization of Contact Problems Using Mixed Variational Formulation. Lecture Notes in Control and Information Sciences. Springer, Berlin, 160, 414–423.
• Myslinski, A. (2000) Shape Optimization for Dynamic Contact Problems. Discussiones Mathematicae, Differential Inclusions. Control and Optimization, 20, 79–91.
• Myslinski, A. and Troltzsch, F. (1999) A Domain Optimization Problem for a Nonlinear Thermoelastic System. In: K.H. Hoffmann, G. Leugering, F. Troltzsch eds., Optimal Control of PDE. International Series of Numerical Mathematics, 133. Birkhauser, Basel, Switzerland, 221–230.
• Necas, J. (1967) Les Methodes Directes en Theorie des Equations Elliptiques. Masson, Paris.
• Pawlow, I. and Zochowski, A. (2002) Existence and Uniqueness of Solutions for a Three Dimensional Thermoelastic System. Dissertationes Mathematicae, 406, Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland
• Sokolowski, J. and Zolesio, J.P. (1988) Shape sensitivity analysis of contact problem with prescribed friction. Nonlinear Analysis, Theory, Methods and Applications, 12, 1399–1411.
• Sokolowski, J. and Zolesio, J.P. (1992) Introduction to Shape Optimization. Shape Sensitivity Analysis. Springer, Berlin.
• Telega, J. (1987) Variational Methods in Contact Problems of Mechanics (in Russian). Advances in Mechanics, 10, 3–95