Geodesic
Shape optimization for dynamic contact problems
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 20 (2000) no. 1, pp. 79-91

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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 
Myśliński, Andrzej. Shape optimization for dynamic contact problems. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 20 (2000) no. 1, pp. 79-91. http://geodesic.mathdoc.fr/item/DMDICO_2000_20_1_a5/
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