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Journal articles on the topic 'Constrained Topology Optimization'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Mrzygłód, M. "Multi-constrained topology optimization using constant criterion surface algorithm." Bulletin of the Polish Academy of Sciences: Technical Sciences 60, no. 2 (2012): 229–36. http://dx.doi.org/10.2478/v10175-012-0030-9.

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Abstract. This paper sets out to describe a multi-constrained approach to topology optimization of structures. In the optimization, a constant criterion surface algorithm and the multi-constraint procedure is used. The multi-constraint procedure consists of constraints normalization and equivalent design space assembling. The work is illustrated by an example of the L-shaped domain optimization with the horizontal line support and complex loads. The example takes into consideration stress, fatigue and compliance constraints. The separate and simultaneous application of constraints resulted in

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2

Holmberg, Erik, Bo Torstenfelt, and Anders Klarbring. "Stress constrained topology optimization." Structural and Multidisciplinary Optimization 48, no. 1 (2013): 33–47. http://dx.doi.org/10.1007/s00158-012-0880-7.

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3

Holmberg, Erik, Bo Torstenfelt, and Anders Klarbring. "Fatigue constrained topology optimization." Structural and Multidisciplinary Optimization 50, no. 2 (2014): 207–19. http://dx.doi.org/10.1007/s00158-014-1054-6.

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4

Petersson, Joakim, and Ole Sigmund. "Slope constrained topology optimization." International Journal for Numerical Methods in Engineering 41, no. 8 (1998): 1417–34. http://dx.doi.org/10.1002/(sici)1097-0207(19980430)41:8<1417::aid-nme344>3.0.co;2-n.

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5

Jiang, Yuanteng, Ke Zhan, Jie Xia, and Min Zhao. "Topology Optimization for Minimum Compliance with Material Volume and Buckling Constraints under Design-Dependent Loads." Applied Sciences 13, no. 1 (2023): 646. http://dx.doi.org/10.3390/app13010646.

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Stability is a critical factor in structural design. Although buckling-constrained topology optimization has been investigated in previous work, the problem has not been considered under design-dependent loads. In this study, a model of buckling constraints in topology optimization problems under design-dependent loads was proposed to solve the above problem. First, the Kreisselmeier–Steinhauser aggregation function was employed to reduce multiple constraints to a single constraint. Then, the problem was sequentially approximated using the optimality criteria method tailored to update the vari

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6

Teng, Xiaoyan, Can Wang, Xudong Jiang, and Xiangyang Chen. "Structural Topology Optimization with Local Finite-Life Fatigue Constraints." Mathematics 11, no. 5 (2023): 1220. http://dx.doi.org/10.3390/math11051220.

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To improve the fatigue resistance of engineering structures, topology optimization has always been an effective design strategy. The direct calculation of large-scale local fatigue constraints remains a challenge due to high computational cost. In the past, the constraint aggregation techniques, such as the P-norm method, were often applied to aggregate local fatigue constraints into a global constraint, whereas the resultant optimal solution was not consistent with the original problem. In order to meet the local fatigue constraints accurately and reduce the number of constraints, the augment

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7

Chu, Sheng, Liang Gao, and Mi Xiao. "An Efficient Topology Optimization Method for Structures with Uniform Stress." International Journal of Computational Methods 15, no. 08 (2018): 1850073. http://dx.doi.org/10.1142/s0219876218500731.

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This paper focuses on two kinds of bi-objective topology optimization problems with uniform-stress constraints: compliance-volume minimization and local frequency response–volume minimization problems. An adaptive volume constraint (AVC) algorithm based on an improved bisection method is proposed. Using this algorithm, the bi-objective uniform-stress-constrained topology optimization problem is transformed into a single-objective topology optimization problem and a volume-decision problem. The parametric level set method based on the compactly supported radial basis functions is employed to so

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8

Zhuang, Chungang, Zhenhua Xiong, and Han Ding. "Temperature-constrained topology optimization of nonlinear heat conduction problems." Journal of Computational Design and Engineering 8, no. 4 (2021): 1059–81. http://dx.doi.org/10.1093/jcde/qwab032.

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Abstract This paper presents topology optimization of nonlinear heat conduction problems with multiple domains and multiple constraints, including regional temperature and material volume for reducing temperature. Maximum approximation temperatures in the constraint regions are accurately and dynamically calculated, though temperature and temperature-dependent thermal conductivity change with the update of material distribution. A temperature measure with constant error to approximate regional maximum temperature is adaptive to different temperature ranges. A strategy of hole nucleation genera

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9

Wang, Bing Qin, Bing Li Wang, and Zhi Yuan Huang. "Topology Optimization for Constrained Layer Damping Plates Using Evolutionary Structural Optimization Method." Advanced Materials Research 894 (February 2014): 158–62. http://dx.doi.org/10.4028/www.scientific.net/amr.894.158.

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The evolutionary structural optimization (ESO) is used to optimize constrained damping layer structure. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, the elements of constrained damping layers and modal loss factor are considered as design variable and objective function, while damping material consumption is considered as a constraint. The sensitivity of modal loss factor to design variable is further derived using modal strain energy analysis method. Numerical example is used to demonstrate the effectiveness of the proposed topol

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10

Liu, Min, Xianmin Zhang, and Sergej Fatikow. "Design of flexure hinges based on stress-constrained topology optimization." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 24 (2016): 4635–45. http://dx.doi.org/10.1177/0954406216671346.

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Stress concentration is one of the disadvantages of flexure hinges. It limits the range of motion and reduces the fatigue life of mechanisms. This article designs flexure hinges by using stress-constrained topology optimization. A weighted-sum method is used for converting the multi-objective topology optimization of flexure hinges into a single-objective problem. The objective function is presented by considering the compliance factors of flexure hinges in the desired and other directions. The stress constraint and other constraint conditions are developed. An adaptive normalization of the P-

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11

Wang, Ming Xu, and Qi Zhi Li. "Dynamic Performance Optimization of Cylindrical Shell with Constrained Damping Layer Using Topology." Advanced Materials Research 479-481 (February 2012): 1209–15. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.1209.

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Topology optimization of the constrained damping cylindrical shell for the maximized modal damping coefficient is studied in this paper. According to the first 3 orders modes, a novel topological optimization model where the volume is taken as the constraint function and the function of the modal damping coefficient as the target function is proposed and analyzed. The reasonable topology configuration was obtained for the damping structure. The results show that this method can be applied to solve the problem of optimization of the constrained damping cylindrical shell with the damping materia

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12

Ivarsson, Niklas, Mathias Wallin, Oded Amir, and Daniel A. Tortorelli. "Plastic work constrained elastoplastic topology optimization." International Journal for Numerical Methods in Engineering 122, no. 16 (2021): 4354–77. http://dx.doi.org/10.1002/nme.6706.

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13

Gu, Jinyu, Zhuo Chen, Kai Long, and Yingjun Wang. "Nonlinear fatigue damage constrained topology optimization." Computer Methods in Applied Mechanics and Engineering 429 (September 2024): 117136. http://dx.doi.org/10.1016/j.cma.2024.117136.

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14

KAMADA, Hiroki, Hiroya HOSHIBA, Junji KATO, and Takashi KYOYA. "STRESS-CONSTRAINED TOPOLOGY OPTIMIZATION OF INFILL STRUCTURE." Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM)) 75, no. 1 (2019): 68–85. http://dx.doi.org/10.2208/jscejam.75.68.

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15

Amstutz, Samuel. "Augmented Lagrangian for cone constrained topology optimization." Computational Optimization and Applications 49, no. 1 (2009): 101–22. http://dx.doi.org/10.1007/s10589-009-9272-3.

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16

Chen, Yanda, Eric Monteiro, Imade Koutiri, and Véronique Favier. "Fatigue-constrained topology optimization using the constrained natural element method." Computer Methods in Applied Mechanics and Engineering 422 (March 2024): 116821. http://dx.doi.org/10.1016/j.cma.2024.116821.

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17

Wang, Michael Yu, and Li Li. "Shape equilibrium constraint: a strategy for stress-constrained structural topology optimization." Structural and Multidisciplinary Optimization 47, no. 3 (2012): 335–52. http://dx.doi.org/10.1007/s00158-012-0846-9.

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18

Lu, Jianan, and Yonghua Chen. "Manufacturable mechanical part design with constrained topology optimization." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 226, no. 10 (2012): 1727–35. http://dx.doi.org/10.1177/0954405412457643.

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19

Mirzendehdel, Amir M., and Krishnan Suresh. "Support structure constrained topology optimization for additive manufacturing." Computer-Aided Design 81 (December 2016): 1–13. http://dx.doi.org/10.1016/j.cad.2016.08.006.

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20

da Silva, Gustavo Assis, André Teófilo Beck, and Ole Sigmund. "Stress-constrained topology optimization considering uniform manufacturing uncertainties." Computer Methods in Applied Mechanics and Engineering 344 (February 2019): 512–37. http://dx.doi.org/10.1016/j.cma.2018.10.020.

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21

Stolpe, M., and K. Svanberg. "A note on stress-constrained truss topology optimization." Structural and Multidisciplinary Optimization 25, no. 1 (2003): 62–64. http://dx.doi.org/10.1007/s00158-002-0273-4.

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22

Guo, X., G. D. Cheng, and K. Yamazaki. "A note on stress-constrained truss topology optimization." Structural and Multidisciplinary Optimization 27, no. 1-2 (2004): 136–37. http://dx.doi.org/10.1007/s00158-003-0370-z.

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23

Lee, Edmund, Kai A. James, and Joaquim R. R. A. Martins. "Stress-constrained topology optimization with design-dependent loading." Structural and Multidisciplinary Optimization 46, no. 5 (2012): 647–61. http://dx.doi.org/10.1007/s00158-012-0780-x.

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24

Deng, Shiguang, and Krishnan Suresh. "Multi-constrained topology optimization via the topological sensitivity." Structural and Multidisciplinary Optimization 51, no. 5 (2014): 987–1001. http://dx.doi.org/10.1007/s00158-014-1188-6.

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25

De Leon, Daniel M., Joe Alexandersen, Jun S. O. Fonseca, and Ole Sigmund. "Stress-constrained topology optimization for compliant mechanism design." Structural and Multidisciplinary Optimization 52, no. 5 (2015): 929–43. http://dx.doi.org/10.1007/s00158-015-1279-z.

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26

Liu, Jikai, Qian Chen, Xuan Liang, and Albert C. To. "Manufacturing cost constrained topology optimization for additive manufacturing." Frontiers of Mechanical Engineering 14, no. 2 (2019): 213–21. http://dx.doi.org/10.1007/s11465-019-0536-z.

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27

Salazar de Troya, Miguel A., and Daniel A. Tortorelli. "Adaptive mesh refinement in stress-constrained topology optimization." Structural and Multidisciplinary Optimization 58, no. 6 (2018): 2369–86. http://dx.doi.org/10.1007/s00158-018-2084-2.

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28

Belblidia, F., and S. Bulman. "Constrained adaptive topology optimization for vibrating shell structures." Structural and Multidisciplinary Optimization 22, no. 2 (2001): 167–76. http://dx.doi.org/10.1007/s001580100134.

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29

Liu, Jikai, Jingjing Yan, and Huangchao Yu. "Stress-constrained topology optimization for material extrusion polymer additive manufacturing." Journal of Computational Design and Engineering 8, no. 3 (2021): 979–93. http://dx.doi.org/10.1093/jcde/qwab028.

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Abstract This paper presents a comprehensive numerical and experimental study on stress-constrained topology optimization for Fused Deposition Modeling (FDM) additive manufacturing. The qp method is employed to avoid the singularity issue of stress-constrained problems. The P-norm function with stability transformation is adopted to build the global stress constraint with iterative corrections to eliminate the gap between the maximum local stress and the P-norm stress. The Heaviside projection is employed to generate clear-cut 0–1 designs. Two benchmark examples have been studied with the nume

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30

Ling, Zheng, Xie Ronglu, Wang Yi, and Adel El-Sabbagh. "Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach." Shock and Vibration 18, no. 1-2 (2011): 221–44. http://dx.doi.org/10.1155/2011/830793.

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Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the

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31

Juárez-Castillo, Efrén, Héctor-Gabriel Acosta-Mesa, and Efrén Mezura-Montes. "Adaptive boundary constraint-handling scheme for constrained optimization." Soft Computing 23, no. 17 (2018): 8247–80. http://dx.doi.org/10.1007/s00500-018-3459-4.

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32

Zhong, Yuhai, Huashan Feng, Hongbo Wang, Runxiao Wang, and Weiwei Yu. "A bionic topology optimization method with an additional displacement constraint." Electronic Research Archive 31, no. 2 (2022): 754–69. http://dx.doi.org/10.3934/era.2023037.

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<abstract><p>Displacement is an important measure of stiffness, and its constraint must be considered in many real engineering designs. However, traditional volume-constrained compliance minimization methods for load-bearing structures do not deal with displacements of practical importance directly. Based on this situation, the paper extends an improved bionic topology optimization method to solve the topology optimization problem with an additional displacement constraint. The updates of density design variables are based on an improved bone remodeling algorithm rather than gradie

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33

Zhou, Hong, and Kwun-Lon Ting. "Shape and Size Synthesis of Compliant Mechanisms Using Wide Curve Theory." Journal of Mechanical Design 128, no. 3 (2005): 551–58. http://dx.doi.org/10.1115/1.2180809.

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A wide curve is a curve with width or cross section. This paper introduces a shape and size synthesis method for compliant mechanisms based on free-form wide curve theory. With the proposed method, detailed dimensions synthesis can be performed to further improve the performance after the topology is selected. Every connection in the topology is represented by a parametric wide curve in which variable shape and size are fully described and conveniently controlled by the limited number of parameters. The shape and size synthesis is formulated as the optimization of the control parameters of wid

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34

Liu, Wenchang, Chaohua Wu, and Xingan Chen. "An Eigenfrequency-Constrained Topology Optimization Method with Design Variable Reduction." Strojniški vestnik - Journal of Mechanical Engineering 70, no. 3-4 (2024): 159–69. http://dx.doi.org/10.5545/sv-jme.2023.739.

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The dynamic response of structures heavily relies on eigenfrequency, so the optimization of eigenfrequency is valuable in various working conditions. The bi-directional evolutionary structural optimization (BESO) method has been widely applied due to its ability to eliminate grayscale elements. Based upon BESO, this paper introduces a topology optimization method that incorporates eigenfrequency constraints and reduces the number of design variables. In this method, the optimization objective was to minimize compliance. The Lagrange multiplier was used to introduce eigenfrequency constraints,

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35

Ni, Yun, Jinqing Zhan, and Min Liu. "Topological design of continuum structures with global stress constraints considering self-weight loads." Electronic Research Archive 31, no. 8 (2023): 4708–28. http://dx.doi.org/10.3934/era.2023241.

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<abstract> <p>This paper proposes an approach for the topological design of continuum structures with global stress constraints considering self-weight loads. The rational approximation of material properties is employed to describe the material distribution for overcoming the parasitic effect for low densities. The structure volume is used as the objective function to be minimized. The local stress constraints for all elements are aggregated into a global stress constraint using the improved <italic>P</italic>-norm method. A model for the stress-constrained topology op

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36

Amir, Oded. "Efficient stress‐constrained topology optimization using inexact design sensitivities." International Journal for Numerical Methods in Engineering 122, no. 13 (2021): 3241–72. http://dx.doi.org/10.1002/nme.6662.

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37

Zhuang, Chungang, and Zhenhua Xiong. "Temperature-Constrained Topology Optimization of Transient Heat Conduction Problems." Numerical Heat Transfer, Part B: Fundamentals 68, no. 4 (2015): 366–85. http://dx.doi.org/10.1080/10407790.2015.1033306.

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38

Zhu, Xuefeng, Chao Zhao, Xuan Wang, Yu Zhou, Ping Hu, and Zheng-Dong Ma. "Temperature-constrained topology optimization of thermo-mechanical coupled problems." Engineering Optimization 51, no. 10 (2019): 1687–709. http://dx.doi.org/10.1080/0305215x.2018.1554065.

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39

Emmendoerfer, Hélio, Eduardo Alberto Fancello, and Emílio Carlos Nelli Silva. "Stress-constrained level set topology optimization for compliant mechanisms." Computer Methods in Applied Mechanics and Engineering 362 (April 2020): 112777. http://dx.doi.org/10.1016/j.cma.2019.112777.

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40

Svanberg, Krister, and Mats Werme. "Sequential integer programming methods for stress constrained topology optimization." Structural and Multidisciplinary Optimization 34, no. 4 (2007): 277–99. http://dx.doi.org/10.1007/s00158-007-0118-2.

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41

Kočvara, Michal, and Michael Stingl. "Solving stress constrained problems in topology and material optimization." Structural and Multidisciplinary Optimization 46, no. 1 (2012): 1–15. http://dx.doi.org/10.1007/s00158-012-0762-z.

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42

Suresh, Krishnan, and Meisam Takalloozadeh. "Stress-constrained topology optimization: a topological level-set approach." Structural and Multidisciplinary Optimization 48, no. 2 (2013): 295–309. http://dx.doi.org/10.1007/s00158-013-0899-4.

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43

Takaki, Tomohiro, and Junji Kato. "Volume constrained topology optimization using multi-phase-field method." Proceedings of The Computational Mechanics Conference 2017.30 (2017): 332. http://dx.doi.org/10.1299/jsmecmd.2017.30.332.

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44

Yang, Dixiong, Hongliang Liu, Weisheng Zhang, and Shi Li. "Stress-constrained topology optimization based on maximum stress measures." Computers & Structures 198 (March 2018): 23–39. http://dx.doi.org/10.1016/j.compstruc.2018.01.008.

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45

Cai, Shouyu, and Weihong Zhang. "Stress constrained topology optimization with free-form design domains." Computer Methods in Applied Mechanics and Engineering 289 (June 2015): 267–90. http://dx.doi.org/10.1016/j.cma.2015.02.012.

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46

Dalklint, Anna, Mathias Wallin, and Daniel A. Tortorelli. "Eigenfrequency constrained topology optimization of finite strain hyperelastic structures." Structural and Multidisciplinary Optimization 61, no. 6 (2020): 2577–94. http://dx.doi.org/10.1007/s00158-020-02557-9.

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47

Wang, Cunfu, and Xiaoping Qian. "Heaviside projection-based aggregation in stress-constrained topology optimization." International Journal for Numerical Methods in Engineering 115, no. 7 (2018): 849–71. http://dx.doi.org/10.1002/nme.5828.

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48

Bruggi, M., and P. Venini. "A mixed FEM approach to stress-constrained topology optimization." International Journal for Numerical Methods in Engineering 73, no. 12 (2008): 1693–714. http://dx.doi.org/10.1002/nme.2138.

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49

da Silva, Gustavo Assis, and Hélio Emmendoerfer. "Fail-safe stress-constrained manufacturing error tolerant topology optimization." Computer Methods in Applied Mechanics and Engineering 421 (March 2024): 116817. http://dx.doi.org/10.1016/j.cma.2024.116817.

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50

Okamoto, Yoshifumi, Hiroshi Masuda, Yutaro Kanda, Reona Hoshino, and Shinji Wakao. "Improvement of topology optimization method based on level set function in magnetic field problem." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 2 (2018): 630–44. http://dx.doi.org/10.1108/compel-12-2016-0528.

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PurposeThe purpose of this paper is the improvement of topology optimization. The scope of the paper is focused on the speedup of optimization. Design/methodology/approachTo achieve the speedup, the method of moving asymptotes (MMA) with constrained condition of level set function is applied instead of solving the Hamilton–Jacobi equation. FindingsThe acceleration of convergence of objective function is drastically improved by the implementation of MMA. Originality/valueNormally, the level set method is solved through the Hamilton–Jacobi equation. However, the possibility of introducing mathem

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