Abstract
In this chapter variational inequalities are considered from the point of view of topological sensitivity analysis. We concentrate on the specific class of problems with the unilateral boundary conditions. This class of variational inequalities includes the frictionless contact problems in linearized elasticity. For the contact problems in two and three spatial dimensions the linearized nonpenetration condition is imposed for the normal displacements in the potential contact zone including crack problems [52, 103, 108, 109, 110, 111, 112, 113]. Topological derivatives for unilateral problems are obtained in [208, 209].
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© 2013 Springer-Verlag Berlin Heidelberg
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Novotny, A.A., Sokołowski, J. (2013). Topological Derivatives for Unilateral Problems. In: Topological Derivatives in Shape Optimization. Interaction of Mechanics and Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35245-4_11
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DOI: https://doi.org/10.1007/978-3-642-35245-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35244-7
Online ISBN: 978-3-642-35245-4
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