The Homogenization Method for Topology Optimization of Structures: Old and New

Allaire, Grégoire; Cavallina, Lorenzo; Miyake, Nobuhito; Oka, Tomoyuki; Yachimura, Toshiaki

doi:10.4036/iis.2019.b.01

Cited by 10 publications

(7 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Depending on the objective to reach, a variety of optimization problems have been investigated. Including use of conventional density-based topology optimization procedure, which is a promising tool that allows reducing weight and achieving optimal performance simultaneously (Dong et al , 2017; Langelaar, 2017; Allaire et al , 2019).…”

Section: Resultsmentioning

confidence: 99%

A bibliometric indicators analysis of additive manufacturing research trends from 2010 to 2020

Jemghili

Taleb

Mansouri

2021

RPJ

View full text Add to dashboard Cite

Purpose Although many researchers have widely studied additive manufacturing (AM) as one of the most important industrial revolutions, few have presented a bibliometric analysis of the published studies in this area. This paper aims to evaluate AM research trends based on 4607 publications most cited from year 2010 to 2020. Design/methodology/approach The research methodology is bibliometric indicators and network analysis, including analysis based on keywords, citation analysis, productive journal, related published papers and authors indicators. Two free available software were employed VOSviewer and Bibexcel. Findings Keywords analysis results indicate that among the AM processes, Selective Laser Melting and Fused Deposition Modeling techniques, are the two processes ranked on top of the techniques employed and studied with 35.76% and 20.09% respectively. The citation analysis by VOSviewer software, reveals that the medical applications field and the fabrication of metal parts are the areas that interest researchers greatly. Different new research niches, as pharmaceutical industry, digital construction and food fabrication are growing topics in AM scientific works. This study reveals that journals “Materials & design”, “Advanced materials”, “Acs applied materials & interfaces”, “Additive manufacturing”, “Advanced functional materials” and “Biofabrication” are the most productive and influential in AM scientific research. Originality/value The results and conclusions of this work can be used as indicators of trends in AM research and/or as prospects for future studies in this area.

show abstract

Section: Resultsmentioning

confidence: 99%

A bibliometric indicators analysis of additive manufacturing research trends from 2010 to 2020

Jemghili

Taleb

Mansouri

2021

RPJ

View full text Add to dashboard Cite

show abstract

“…The most challenging part of the solution of the TO problem is the calculation of the elastic modulus. The homogenization theory uses an effective elasticity tensor to describe the mesotropic properties of a structure [19]. The above formulation of a discrete TO problem resulted in the known "checkerboard" structural problem [20].…”

Section: The General Structural Optimization Problem and The Simp Appmentioning

confidence: 99%

“…Allaire, et al [19] argue that SIMP is an over-simplified version of the initial homogenization theory and does not consider anisotropy. Despite this fact, the SIMP method is broadly implemented due to its simplicity.…”

Section: The General Structural Optimization Problem and The Simp Appmentioning

confidence: 99%

Optimization of Brake Calipers Using Topology Optimization for Additive Manufacturing

2021

View full text Add to dashboard Cite

The weight optimization of a structure can be conducted by using fewer and downsized components, applying lighter materials in production, and removing unwanted material. Topology optimization (TO) is one of the most implemented material removal processes. In addition, when it is oriented towards additive manufacturing (AM), it increases design flexibility. The traditional optimization approach is the compliance optimization, where the material layout of a structure is optimized by minimizing its overall compliance. However, TO, in its current state of the art, is mainly used for design inspiration and not for manufacturing due to design complexities and lack of accuracy of its design solutions. The authors, in this research paper, explore the benefits and the limitations of the TO using as a case study the housings of a front and a rear brake caliper. The calipers were optimized for weight reduction by implementing the aforementioned optimization procedure. Their housings were topologically optimized, partially redesigned, prepared for 3D printing, validated, and 3D printed in titanium using selective laser melting (SLM). The weight of the optimized calipers reduced by 41.6% compared to commercial calipers. Designers interested in either TO or in automotive engineering can exploit the findings in this paper.

show abstract

“…As far as this problem, in the former paper [1,2], it has proven difficult to achieve using traditional topology optimization methods which consist of the using homogenization [3][4][5][6][7][8][9][10][11], density method [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

The Outstanding Excellences of Interactive Energy Density Topology Change Method

Yang,

Sasaki,

Abe

et al. 2024

IJMEA

View full text Add to dashboard Cite

It has not been solved that the fruits, vegetables, strawberries, cells, blood and a bottle of liquor are damaged, broken during transportation. It is the greatest factor in this situation that there is a danger vibration frequency band where these are easy to scratch and are prone to death. If there are eigen frequencies within this danger frequency band, it needs that those eigen frequencies within this danger frequency band are moved out of the band. In the former paper, it was shown difficult to apply the existing topology optimization methods using homogenization method or density method to control plural eigen frequencies for solving this problem. Therefore in the former paper, it was proposed the so called “Interactive Energy Density Topology (IEDT) change method” that is a new high precision and high efficiency method for controlling plural eigen frequencies simultaneously referring to the kinetic and the strain energy density distributions. Here it is discussed more about the IEDT change method and show that it is sometimes difficult for the traditional methods to get solutions because especially in the dynamic problem, eigen frequencies may go up or down depending on its size even if reinforcement or hall for change topology is applied at the same location. But with the proposed IEDT change method, always it can be realized because the proposed method has wider solution spaces than the traditional one. Lastly, it is shown that this IEDT method is also very effective to reduce the integral value of response curve by frequency.

show abstract

The Homogenization Method for Topology Optimization of Structures: Old and New

Abstract: We differentiate t → j(t),Since t = 0 is a minimum point of j, we have a(u, v) = L(v) for all v ∈ V .

Cited by 10 publications

References 26 publications

A bibliometric indicators analysis of additive manufacturing research trends from 2010 to 2020

A bibliometric indicators analysis of additive manufacturing research trends from 2010 to 2020

Optimization of Brake Calipers Using Topology Optimization for Additive Manufacturing

The Outstanding Excellences of Interactive Energy Density Topology Change Method

Contact Info

Product

Resources

About