Higher order topological derivatives for three-dimensional anisotropic elasticity
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 justi...
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| Published in | ESAIM Mathematical Modelling and Numerical Analysis Vol. 51; no. 6; pp. 2069 - 2092 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Les Ulis
EDP Sciences
01.11.2017
Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP |
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| ISSN | 0764-583X 2822-7840 1290-3841 1290-3841 2804-7214 |
| DOI | 10.1051/m2an/2017015 |
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| Abstract | 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. |
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| AbstractList | 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. This article concerns an extension of the topological derivative concept for 3D elasticity problems involving elastic inhomogeneities, whereby an objective function ?? is expanded in powers of the characteristic size a of a single small inhomogeneity. The O(a6) approximation of ?? 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. 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(a 6) 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. |
| Author | Cornaggia, Rémi Bonnet, Marc |
| Author_xml | – sequence: 1 givenname: Marc surname: Bonnet fullname: Bonnet, Marc organization: POEMS (ENSTA ParisTech, CNRS, INRIA, Université Paris-Saclay), Palaiseau, France – sequence: 2 givenname: Rémi surname: Cornaggia fullname: Cornaggia, Rémi organization: IRMAR, Université Rennes-1, Rennes, France |
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| Cites_doi | 10.1023/A:1023940025757 10.1137/S0363012902406801 10.1002/pssb.200572719 10.1093/qjmam/hbu025 10.1007/978-94-011-9306-1 10.1016/j.ijsolstr.2011.07.013 10.1002/(SICI)1097-0207(19980815)42:7<1215::AID-NME406>3.0.CO;2-5 10.1137/1.9781611972597 10.1016/j.enganabound.2010.08.007 10.1081/SME-100105654 10.1016/0093-6413(93)90032-J 10.1137/S0036139902414379 10.1007/978-3-642-61631-0 10.1016/j.ijsolstr.2010.07.004 10.1137/100812501 10.1002/9781118578469 10.1080/00029890.2001.11919820 10.1093/qjmam/hbt018 10.1088/0266-5611/21/2/008 10.1007/978-0-387-70914-7 10.1007/978-3-540-68545-6 10.1088/0266-5611/29/7/075012 10.1007/s11075-014-9953-6 10.1137/S0363012900369538 10.1016/j.jcp.2005.12.015 10.1088/0266-5611/6/3/009 10.1088/0266-5611/24/3/035022 10.1177/1081286511433082 10.1098/rspa.1957.0133 10.1177/1081286515588636 10.1016/0022-5096(75)90012-5 10.1016/j.ijsolstr.2010.01.011 |
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| SubjectTerms | 35C20 45F15 74B05 asymptotic expansion Computer Science Elastic anisotropy Elastic properties Elasticity elastostatics Inhomogeneity Modeling and Simulation Solid mechanics Topological derivative Topology volume integral equation |
| Title | Higher order topological derivatives for three-dimensional anisotropic elasticity |
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