Topological sensitivity analysis in heterogeneous anisotropic elasticity problem. Theoretical and computational aspects

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 t...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2016-11, Vol.311, p.134-150
Main Authors: Giusti, S.M., Ferrer, A., Oliver, J.
Format: Article
Language:English
Subjects:
Anisotropia
Anisotropy
Asymptotic properties
Asymptotic series
COMP-DES-MAT Project
COMPDESMAT Project
Economic models
Elastic anisotropy
Elasticitat
Elasticity
Enginyeria civil
Exact solutions
Heterogeneity
Materials i estructures
Mathematical models
Models matemàtics
Perturbation methods
Potential energy
Sensitivity analysis
Singular perturbation
Structural optimization
Topological derivative
Topology design
Topology optimization
Àrees temàtiques de la UPC
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Summary: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. •Topological derivative of elastic anisotropic and heterogeneous 2D problem.•Novel, extremely simple closed formula for the topological sensitivity.•Full mathematical justifications for the obtained formulas.•Potential applications to structural topology design.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2016.08.004