Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 311, Issue -, Pages 134-150Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2016.08.004
Keywords
Topological derivative; Structural optimization; Topology design; Elastic anisotropy
Funding
- European Research Council under the European Union's Seventh Framework Programme (FP)/ERC [320815]
- ANPCyT (National Agency for Scientific and Technical Promotion) [N PICT 2014-3372]
- PID-UTN (Research and Development Program of the National Technological University) [PID/UTN 2050-2013]
- CONICET (National Council for Scientific and Technical Research) [PIP 2013-631]
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The topological sensitivity analysis for the heterogeneous and anisotropic elasticity problem in two-dimensions is performed in this work. The main result of the paper is an analytical closed-form of the topological derivative for the total potential energy of the problem. This derivative displays the sensitivity of the cost functional (the energy in this case) when a small singular perturbation is introduced in an arbitrary point of the domain. In this case, we consider a small disc with a completely different elastic material. Full mathematical justification for the derived formula, and derivations of precise estimates for the remainders of the topological asymptotic expansion are provided. Finally, the influence of the heterogeneity and anisotropy is shown through some numerical examples of structural topology optimization. (C) 2016 Elsevier B.V. All rights reserved.
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