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Published in:
2006 | OriginalPaper | Chapter
Topological Derivatives for Contact Problems
Conical Differentiability and Asymptotic Analysis
Authors : Jan Sokołowski, Antoni Żochowski
Published in: IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials
Publisher: Springer Netherlands
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Numerical methods of evaluation of topological derivatives are proposed for contact problems in two dimensional elasticity. Problems of topology optimisation are investigated for free boundary problems of boundary 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 with respect to singular perturbation of geometrical domain depending on small parameter are obtained by an application of nonsmooth analysis. The topological derivatives can be used in numerical methods of simultaneous shape and topology optimisation, in particular, in the level set type methods.