Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition

Zhou, Shiwei; Wang, Michael Yu

doi:10.1007/s00158-006-0035-9

Cited by 228 publications

(118 citation statements)

References 34 publications

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“…Among the several methods that appeared in the literature, such as SIMP (Solid Isotropic Material with Penalization) method [14,49,16], the homogenization method [3,13,15], the phase field method [18,41,51,17] or the Soft Kill Option [31,23], the level-set method for shape and topology optimization [10,11,35,38,44] seems to fulfill industrial requirements in a satisfying way. Using a level-set function to describe implicitly the boundary of a shape [36,37] allows topological changes to appear in an easy way, while the geometric nature of the method is a benefit for the study of problems where the position of the interface plays a significant role (stress constraints, thermal problems with flux across the boundary, etc.).…”

Section: Introductionmentioning

confidence: 99%

Molding Direction Constraints in Structural Optimization via a Level-Set Method

Allaire

Jouve

Michailidis

2016

Variational Analysis and Aerospace Engineering

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Section: Introductionmentioning

confidence: 99%

Molding Direction Constraints in Structural Optimization via a Level-Set Method

Allaire

Jouve

Michailidis

2016

Variational Analysis and Aerospace Engineering

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“…Currently, the most used techniques for topology design of continuum structures using heterogeneous or multiple materials are: 1) Material interpolation schemes (Yin and Ananthasuresh 2001, Huang and Xie 2009, Gao et al 2010, Luo et al 2012, Blasques and Stolpe 2012; 2) Level-set models (Yulin and Xiaoming 2004, Zhuang et al 2007; and 3) Phase-field schemes (Bourdin and Chambolle 2000, Jung and Gea 2006, Zhou and Wang 2007.…”

Section: Topology Design With Multi-materials Techniquesmentioning

confidence: 99%

“…The material may be solid or liquid of two or more phases. The usual problem is to characterize the stability of such a system and to describe the interface between the phases while the system undergoes a physical process to reach its stability (Zhou and Wang 2007). In spite of the fact that there is a clear relationship between the problem of topology optimization of a solid multi-material structure and a phase transition system of material phases, the use of these schemes has not yet become popular.…”

Section: Topology Design With Multi-materials Techniquesmentioning

confidence: 99%

“…A three-phase material model for topology optimization was derived to accommodate two conflicting design objectives: 1) Minimize the mean compliance; and 2) Maximize the strain energy for energy absorption. Zhou and Wang (2007) Interpolation Model (UIM) were considered. Ramani (2010) presented an algorithm which uses material as a discrete variable in multi-material topology optimization and thus provides an alternative to traditional methods using material interpolation and level-set approaches.…”

Section: Introductionmentioning

confidence: 99%

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Layout optimization of multi-material continuum structures with the isolines topology design method

Querin

Victoria

Díaz

et al. 2014

Engineering Optimization

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ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. A heterogeneous or multi-material object is one made from different materials which are distributed continuously or discontinuously and where its properties can be adjusted by controlling the material composition, microstructure and geometry of the object. The development of manufacturing technologies such as rapid prototyping can eliminate the high cost of tooling and can offer the possibility to make multi-materials structures. However the ability to design them is not a trivial task and requires the development or modifications of optimization algorithms to take into consideration the different aspects of these problems. This article presents an enhancement to the ITD Osvaldo M. Querin, Mariano Victoria, Concepción Díaz, and Pascual Martí 2 algorithm which allows it to obtain multi-material designs. Four examples of the topology design of 2D continuum structures are presented to demonstrate that the ITD algorithm is an efficient and reliable method to carry out the layout optimization of multimaterial continuum structures.

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“…Many articles have been published on this topic in the framework of the SIMP (Solid Isotropic Material with Penalization) method (see [10,11,16] and the references therein). Several interpolation schemes have been proposed for the construction of the smooth Hooke's tensor and the penalization of intermediate densities.…”

Section: Introductionmentioning

confidence: 99%

Structural and Multi-Functional Optimization Using Multiple Phases and a Level-Set Method

Allaire¹,

Jouve²,

Michailidis³

2014

Proceedings of the 3rd South-East European Conference on Computational Mechanics (SEECCM III)

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Abstract. In this work we adress the problem of structural and multi-functional shape and topology optimization using several elastic materials in a fixed working domain. The description and the evolution of the interfaces between the different phases is done using the level-set method. We use a smooth Hooke's tensor, instead of a discontinuous one. The continuous case can be seen as an approximation of the sharp interface case, and in this context, the signed distance function corresponding to each interface is used for modeling the smooth Hooke's tensor. A directional shape derivative is calculated for the objective function to minimize. We show 2d results for compliance minimization, as well as an example of multi-functional optimization, coupling structural and thermal problems. 639

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Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition

Cited by 228 publications

References 34 publications

Molding Direction Constraints in Structural Optimization via a Level-Set Method

Molding Direction Constraints in Structural Optimization via a Level-Set Method

Layout optimization of multi-material continuum structures with the isolines topology design method

Structural and Multi-Functional Optimization Using Multiple Phases and a Level-Set Method

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