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Topological derivative

About: Topological derivative is a research topic. Over the lifetime, 480 publications have been published within this topic receiving 27626 citations.


Papers
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Journal ArticleDOI
TL;DR: In this article, the authors present a methodology for optimal shape design based on homogenization, which is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, i.i.
Abstract: Optimal shape design of structural elements based on boundary variations results in final designs that are topologically equivalent to the initial choice of design, and general, stable computational schemes for this approach often require some kind of remeshing of the finite element approximation of the analysis problem. This paper presents a methodology for optimal shape design where both these drawbacks can be avoided. The method is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, i~otropic material, with the requirement that the resulting structure can carry the given loads as well as satisfy other design requirements. The computation of effective material properties for the anisotropic material is carried out using the method of homogenization. Computational results are presented and compared with results obtained by boundary variations.

5,858 citations

Book
17 Sep 2011
TL;DR: In this article, the authors proposed a topology optimization by distribution of isotropic material for truss structures with anisotropic materials, based on the topology design of truss structure.
Abstract: 1 Topology optimization by distribution of isotropic material- 2 Extensions and applications- 3 Design with anisotropic materials- 4 Topology design of truss structures- 5 Appendices- 6 Bibliographical notes- References- Author Index

4,881 citations

Journal ArticleDOI
TL;DR: A new approach to structural topology optimization that represents the structural boundary by a level set model that is embedded in a scalar function of a higher dimension that demonstrates outstanding flexibility of handling topological changes, fidelity of boundary representation and degree of automation.

2,404 citations

Journal ArticleDOI
TL;DR: A new numerical method based on a combination of the classical shape derivative and of the level-set method for front propagation, which can easily handle topology changes and is strongly dependent on the initial guess.

2,176 citations

Journal ArticleDOI
TL;DR: An overview, comparison and critical review of the different approaches to topology optimization, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.
Abstract: Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsoe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary” and several others. The paper gives an overview, comparison and critical review of the different approaches, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.

1,816 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20221
202137
202024
201926
201834
201738