Modelling of topological derivatives for contact problems |
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Authors: | J Soko?owski A ?ochowski |
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Institution: | (1) Institut Elie Cartan, Laboratoire de Mathématiques, Université Henri Poincaré Nancy I, B.P. 239, 54506 Vandoeuvre lès Nancy Cedex, France;(2) Systems Research Institute of the Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland |
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Abstract: | The problem of topology optimization is considered for free boundary problems of thin obstacle types. The formulae for the
first term of asymptotics for energy functionals are derived. The precision of obtained terms is verified numerically. The
topological differentiability of solutions to variational inequalities is established. In particular, the so-called outer asymptotic expansion for solutions of contact problems in elasticity with respect to singular perturbation of geometrical domain depending on
small parameter are derived by an application of nonsmooth analysis. Such results lead to the topological derivatives of shape functionals for contact problems. The topological derivatives are used in numerical methods of simultaneous shape
and topology optimization.
Partially supported by the grant 4 T11A 01524 of the State Committee for the Scientific Research of the Republic of Poland |
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Keywords: | 49Q10 49Q12 35J05 35J50 35B37 |
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