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SIMP‐ALL: A generalized SIMP method based on the topological derivative concept

SIMP-ALL: a generalized SIMP method based on the topological derivative concept
Authors: Ferrer, A.;

SIMP‐ALL: A generalized SIMP method based on the topological derivative concept

Abstract

SummaryTopology optimization has emerged in the last years as a promising research field with a wide range of applications. One of the most successful approaches, the SIMP method, is based on regularizing the problem and proposing a penalization interpolation function. In this work, we propose an alternative interpolation function, the SIMP‐ALL method that is based on the topological derivative concept. First, we show the strong relation in plane linear elasticity between the Hashin‐Shtrikman (H‐S) bounds and the topological derivative, providing a new interpretation of the last one. Then, we show that the SIMP‐ALL interpolation remains always in between the H‐S bounds regardless the materials to be interpolated. This result allows us to interpret intermediate values as real microstructures. Finally, we verify numerically this result and we show the convenience of the proposed SIMP‐ALL interpolation for obtaining auto‐penalized optimal design in a wider range of cases. A MATLAB code of the SIMP‐ALL interpolation function is also provided.

Keywords

:74 Mechanics of deformable solids::74P Optimization [Classificació AMS], Engineering, Civil, Engineering, Multidisciplinary, Hashin-Shtrikman bounds, Structural optimization, 510, topological derivative, Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia, Topology optimization, Engineering, Ocean, Engineering, Aerospace, Engineering, Biomedical, topology optimization, Classificació AMS::74 Mechanics of deformable solids::74P Optimization, Optimització d'estructures, Computer Science, Software Engineering, Engineering, Marine, 004, Engineering, Manufacturing, Engineering, Mechanical, Topological methods for optimization problems in solid mechanics, Optimization of shapes other than minimal surfaces, Compliance or weight optimization in solid mechanics, Engineering, Industrial, Topological derivative, SIMP, :Matemàtiques i estadística::Topologia [Àrees temàtiques de la UPC]

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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