Volume 51, Number 6, November-December 2017
|Page(s)||2069 - 2092|
|Published online||27 November 2017|
Higher order topological derivatives for three-dimensional anisotropic elasticity
1 POEMS (ENSTA ParisTech, CNRS, INRIA, Université Paris-Saclay), Palaiseau, France.
2 IRMAR, Université Rennes-1, Rennes, France.
Received: 26 May 2016
Revised: 14 February 2017
Accepted: 28 March 2017
This article concerns an extension of the topological derivative concept for 3D elasticity problems involving elastic inhomogeneities, whereby an objective function 𝕁 is expanded in powers of the characteristic size a of a single small inhomogeneity. The O(a6) approximation of 𝕁 is derived and justified for an inhomogeneity of given location, shape and elastic properties embedded in a 3D solid of arbitrary shape and elastic properties; the background and the inhomogeneity materials may both be anisotropic. The generalization to multiple small inhomogeneities is concisely described. Computational issues, and examples of objective functions commonly used in solid mechanics, are discussed.
Mathematics Subject Classification: 35C20 / 45F15 / 74B05
Key words: Topological derivative / asymptotic expansion / volume integral equation / elastostatics
© EDP Sciences, SMAI 2017
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