Titlebook: Topological Derivatives in Shape Optimization; Antonio André Novotny,Jan Sokołowski Book 2013 Springer-Verlag Berlin Heidelberg 2013 Appli

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Topological Derivatives for Unilateral Problems,d elasticity. For the contact problems in two and three spatial dimensions the linearized nonpenetration condition is imposed for the normal displacements in the ... 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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1860-6245 um of examples and techniques for.learning how to use the mo.The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusio

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Introduction, the insertion of holes, inclusions, source-terms or even cracks. The topological derivative was rigorously introduced by Sokołowski & Żochowski 1999 [204]. In particular, it can be seen as a mathematical justification for the so-called bubble method [53] (see for instance [136]).

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Topological Derivative Evaluation with Adjoint States,The evaluation of the topological derivative for a general class of shape functionals is presented in this chapter. The method is applied to a modified energy shape functional associated with the steady-state heat conduction problem.