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Topic · Civil and Structural Engineering

Topology Optimization in Engineering

Topology Optimization in Engineering is a research topic within Civil and Structural Engineering. Science Explorer counts 19k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the application of topology optimization in structural engineering, utilizing methods such as level set, sensitivity analysis, and morphology-based filters. It explores topics such as non-linear elastic structures, compliant mechanisms, additive manufacturing, and multi-material optimization using finite element methods and metaheuristic algorithms.

  • Level Set Method
  • Sensitivity Analysis
  • Structural Boundary Design
  • Morphology-based Filters
  • Non-linear Elastic Structures
  • Compliant Mechanisms
  • Additive Manufacturing
  • Multi-material Optimization
  • Finite Element Method
  • Metaheuristic Algorithms
Research works
19k
fractional, since 1950
In the world top 10%
1.9k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+36%
the tick is no change
Largest producer
China
50% of the 10 largest, 2022-now
Topology Optimization in Engineering

Which countries lead Topology Optimization in Engineering research?

By volume, China and the United States publish the most (1.8k and 430 works in 2022-now).

By volume, 2022-now

  1. 1 China 1.8k works
  2. 2 United States 430 works
  3. 3 Japan 237 works
  4. 4 India 237 works
  5. 5 Germany 208 works
  6. 6 Italy 146 works
  7. 7 France 135 works
  8. 8 Türkiye 135 works
  9. 9 United Kingdom 119 works
  10. 10 Iran 116 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 49.9%United States: 12.2%Japan: 6.7%India: 6.7%6 others listed: 24.4%50%largest
China1,753 · 49.9%United States430 · 12.2%Japan237 · 6.7%India237 · 6.7%6 others listed859 · 24.4%

Shares of the rows listed above, not of the whole node.

Which institutions lead Topology Optimization in Engineering research?

By volume in 2022-now, Dalian University of Technology publishes the most Topology Optimization in Engineering research, followed by Northwestern Polytechnical University and Huazhong University of Science and Technology.

By volume, 2022-now

  1. 1 Dalian University of TechnologyChina 102 works
  2. 2 Northwestern Polytechnical UniversityChina 68 works
  3. 3 Huazhong University of Science and TechnologyChina 65 works
  4. 4 Centre National de la Recherche ScientifiqueFrance 52 works
  5. 5 Beihang UniversityChina 36 works
  6. 6 Chinese Academy of SciencesChina 32 works
  7. 7 Beijing Institute of TechnologyChina 32 works
  8. 8 Xi'an Jiaotong UniversityChina 31 works
  9. 9 Shanghai Jiao Tong UniversityChina 31 works
  10. 10 Zhejiang UniversityChina 31 works

Who are the leading researchers in Topology Optimization in Engineering?

The most-cited researchers publishing on Topology Optimization in Engineering include Yi Ping Cui, Kalyanmoy Deb and Seyedali Mirjalili.

  1. 1 Yi Ping Cui United States 261k citations
  2. 2 Kalyanmoy Deb United States 171k citations
  3. 3 Seyedali Mirjalili Australia 154k citations
  4. 4 Stephen Boyd United States 142k citations
  5. 5 Sepp Hochreiter Austria 129k citations
  6. 6 Dierk Raabe Germany 125k citations
  7. 7 Stanley Osher United States 119k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Topology Optimization in Engineering?

The most cited paper in Topology Optimization in Engineering is "Generating optimal topologies in structural design using a homogenization method" (Martin Philip Bendsøe, Noboru Kikuchi, 1988), with 7,508 citations. Next come "Topology Optimization: Theory, Methods, and Applications" (5,759) and "The method of moving asymptotes—a new method for structural optimization" (5,593).

Most cited papers
#PaperReleasedCitations
1 Generating optimal topologies in structural design using a homogenization method Martin Philip Bendsøe, Noboru Kikuchi · Computer Methods in Applied Mechanics and Engineering Nov 1988 7,508
2 Topology Optimization: Theory, Methods, and Applications Martin Philip Bendsøe, Ole Sigmund 17 Sep 2011 5,759
3 The method of moving asymptotes—a new method for structural optimization Krister Svanberg · International Journal for Numerical Methods in Engineering Feb 1987 5,593
4 Finite Element Procedures in Engineering Analysis Klaus‐Jürgen Bathe, Hector Saunders · Journal of Pressure Vessel Technology Open access Nov 1984 5,195
5 Optimal shape design as a material distribution problem Martin Philip Bendsøe · Structural and Multidisciplinary Optimization Dec 1989 4,565
All 100 most cited papers, with filters and sorting

Where is Topology Optimization in Engineering research done?

The largest centres of Topology Optimization in Engineering research in 2022-now are Beijing (China), Xi'an (China), Wuhan (China) and Dalian (China). Among places with at least 20 works in it, it is an unusually large share of all research in Kongens Lyngby, Dalian and Delft.

Largest cities, 2022-now

  1. 1 BeijingChina 241 works
  2. 2 Xi'anChina 144 works
  3. 3 WuhanChina 121 works
  4. 4 DalianChina 121 works
  5. 5 ShanghaiChina 118 works
  6. 6 NanjingChina 74 works
  7. 7 ChangshaChina 71 works
  8. 8 TokyoJapan 67 works
  9. 9 GuangzhouChina 66 works
  10. 10 HangzhouChina 57 works

Where it is the local speciality

  1. Kongens LyngbyDK · 24.6 works10×
  2. DalianCN · 120.8 works9.9×
  3. DelftNL · 25.7 works7.0×
  4. NagoyaJP · 31.9 works6.9×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Topology Optimization in Engineering than the world average.

See Topology Optimization in Engineering on the map

Where is the best place to study Topology Optimization in Engineering?

Among universities, judged by research, Dalian University of Technology, RMIT University and Sejong University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 22.2%fractional works in this field (log) →share of work in the world top 10% →Sejong UniversityRMIT UniversityHuazhong University …Dalian University of…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Dalian University of TechnologyChina 72.815.0%25.9×102 +78.1%
2RMIT UniversityAustralia 72.524.0%13.9×22 +115.0%
3Sejong UniversitySouth Korea 69.537.6%14.5×11 +28.6%
4Huazhong University of Science and TechnologyChina 68.419.0%8.7×65 +59.4%
5Xi'an Jiaotong UniversityChina 65.534.7%4.3×32 +47.8%
6Technical University of DenmarkDenmark 60.222.9%11.1×23 -35.0%
7Northwestern Polytechnical UniversityChina 59.510.7%14.3×68 +21.2%
8Swinburne University of TechnologyAustralia 55.826.4%7.3×9 +30.7%
9Beihang UniversityChina 55.321.4%8.0×36 +12.0%
10Delft University of TechnologyNetherlands 54.110.3%9.0×25 +34.9%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Topology Optimization in Engineering, country by country

Is Topology Optimization in Engineering research growing?

Output in 2022-2025 was 36% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Topology Optimization in Engineering.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Topology Optimization in Engineering as a percentage of every work published that year, 0.018% in 2024.

still counting0.010%0.020%0.030%Topology Optimization in Engineering0.022% in 202519801990200020102020

Fractional works of Topology Optimization in Engineering over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Topology Optimization in Engineering10.2% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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