Готові списки джерел за темами / Multi-Material optimization

Добірка наукової літератури з теми "Multi-Material optimization"

Автор: Grafiati
Опубліковано: 6 липня 2024

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Зміст

  1. Статті в журналах
  2. Дисертації
  3. Книги
  4. Частини книг
  5. Тези доповідей конференцій

Статті в журналах з теми "Multi-Material optimization":

1

Singh, Jaswinder. "Multi-Response Optimization of Manual Material Handling Tasks through Utility Concept." Bonfring International Journal of Industrial Engineering and Management Science 4, no. 2 (May 30, 2014): 83–89. http://dx.doi.org/10.9756/bijiems.6034.

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2

Hvejsel, Christian Frier, Erik Lund, and Mathias Stolpe. "Optimization strategies for discrete multi-material stiffness optimization." Structural and Multidisciplinary Optimization 44, no. 2 (May 7, 2011): 149–63. http://dx.doi.org/10.1007/s00158-011-0648-5.

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3

Chandrasekhar, Aaditya, and Krishnan Suresh. "Multi-Material Topology Optimization Using Neural Networks." Computer-Aided Design 136 (July 2021): 103017. http://dx.doi.org/10.1016/j.cad.2021.103017.

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4

Ramani, Anand. "Multi-material topology optimization with strength constraints." Structural and Multidisciplinary Optimization 43, no. 5 (November 20, 2010): 597–615. http://dx.doi.org/10.1007/s00158-010-0581-z.

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5

MINAMI, Hayato, Akihiro TAKEZAWA, Masanori HONDA, and Mitsuru KITAMURA. "Layout Optimization of Multi-material Beam Elements." Proceedings of Design & Systems Conference 2017.27 (2017): 2107. http://dx.doi.org/10.1299/jsmedsd.2017.27.2107.

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6

SHINTANI, Kohei, Hideyuki AZEGAMI, and Takayuki YAMADA. "Multi-material robust topology optimization considering uncertainty of material properties." Transactions of the JSME (in Japanese) 87, no. 900 (2021): 21–00138. http://dx.doi.org/10.1299/transjsme.21-00138.

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7

Liu, Pai, Litao Shi, and Zhan Kang. "Multi-material structural topology optimization considering material interfacial stress constraints." Computer Methods in Applied Mechanics and Engineering 363 (May 2020): 112887. http://dx.doi.org/10.1016/j.cma.2020.112887.

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8

Hvejsel, Christian Frier, and Erik Lund. "Material interpolation schemes for unified topology and multi-material optimization." Structural and Multidisciplinary Optimization 43, no. 6 (January 27, 2011): 811–25. http://dx.doi.org/10.1007/s00158-011-0625-z.

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9

Zheng, Yongfeng, Zihao Chen, Baoshou Liu, Ping Li, Jiale Huang, Zhipeng Chen, and Jianhua Xiang. "Robust topology optimization for multi-material structures considering material uncertainties." Thin-Walled Structures 201 (August 2024): 111990. http://dx.doi.org/10.1016/j.tws.2024.111990.

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10

Park, Jaejong, and Alok Sutradhar. "A multi-resolution method for 3D multi-material topology optimization." Computer Methods in Applied Mechanics and Engineering 285 (March 2015): 571–86. http://dx.doi.org/10.1016/j.cma.2014.10.011.

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Статті в журналах Дисертації

Дисертації з теми "Multi-Material optimization":

1

Ajayi, Oluwanifemi O. (Oluwanifemi Oluwadara). "Topology optimization with manufacturable multi-material primitives." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/123215.

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Анотація:
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 32-33).
Topology optimization is a field extending to the built environment. Traditionally, optimization focuses mainly on monolithic structures but recently, developments have been made toward determining algorithms for multi-material optimization. A preexisting algorithm is modified to broaden the type of design possible with the method. The algorithm uses a three-phase design problem, a void phase and two other materials, and implements Heaviside Projection Method (HPM) and Rational Approximation of Material Properties (RAMP) method and employs the Method of Moving Asymptotes (MMA) as the gradient based optimizer. Three distinct object projection shapes are proposed, a horizontal, a vertical and a diagonal. The horizontal shaped inclusion enables designs such as, longitudinal reinforced concrete beam design of variable length bars. The vertical shaped inclusion enables designs of columns. The diagonal shaped inclusion allows for design of rebar within more slanted sections of optimized topology. The proposed algorithm is tested on two examples, the cantilever beam and the MBB beam, showing that it works as expected.
by Oluwanifemi O. Ajayi.
M. Eng.
M.Eng. Massachusetts Institute of Technology, Department of Civil and Environmental Engineering
2

Park, Jaejong. "Advanced Topology Optimization Techniques for Engineering and Biomedical Problems." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1534347400733419.

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3

Venugopal, Vysakh. "Design of Multi-Material Lattice Structures with Tailorable Material Properties using Density-Based Topology Optimization." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1553252070840125.

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4

Stern, Brenda G. "Minimizing embodied carbon in multi-material structural optimization of planar trusses." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/119324.

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Анотація:
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 55-56).
In the built environment, there is a growing emphasis on sustainable, energy efficient design that reduces carbon emissions. However, until recently, most efforts have focused only on reducing operational carbon [1]. As a result, the carbon embodied in construction materials, especially in a building's structural system, is becoming a larger contributor to the total carbon impacts of a building. Material type and quantity are important in determining the extent of this contribution because both will affect the amount of carbon emitted from the material production. For example, two common materials for truss structures are timber and steel. While timber's embodied carbon coefficient (kg[subscript CO2e]/kg[subscript material]) and density are lower than that of steel, its much lower strength means that it may not always result in the least-emitting structural design. As a result, the choice of the more sustainable material for any given member is dependent on factors such as the truss span or shape. Multi-material structures offer a solution to create efficient structures with a lower environmental impact. In this thesis, an embodied carbon optimization investigates truss structures of various spans and studies how multi-material and single-material designs compare. This research introduces a new approach for multi-material designs for the optimization of embodied carbon and demonstrates the advantages of using structural optimization and multi-material designs for sustainability. Keywords.: Optimization, embodied carbon, sustainable structures, truss structures
by Brenda G. Stern.
M. Eng.
5

Brister, Kenneth Eugene. "MULTI-OBJECTIVE DESIGN OPTIMIZATION USING METAMODELING TECHNIQUES AND A DAMAGE MATERIAL MODEL." MSSTATE, 2007. http://sun.library.msstate.edu/ETD-db/theses/available/etd-07032007-121410/.

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In this work, the effectiveness of multi-objective design optimization using metamodeling techniques and an internal state variable (ISV) plasticity damage material model as a design tool is demonstrated. Multi-objective design optimization, metamodeling, and ISV plasticity damage material models are brought together to provide a design tool capable of meeting the stringent structural design requirements of today and of the future. The process of implementing this tool are laid out, and two case studies using multi-objective design optimization were carried out. The first was the optimization of a Chevrolet Equinox rear subframe. The optimized subframe was 12% lighter and met design requirements not achieved by the heavier initial design. The second case was the optimization of a Formula SAE front upright. The optimized upright meets all the design constraints and is 22% lighter.
6

Brister, Kenneth Eugene. "Multi-objective design optimization using metamodelling techniques and a damage material model." Master's thesis, Mississippi State : Mississippi State University, 2007. http://library.msstate.edu/etd/show.asp?etd=etd-07032007-121410.

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7

da, Silva de Siqueira Renan [Verfasser]. "Design and Optimization Method for Manufacturable Multi-material Components / Renan da Silva de Siqueira." Garbsen : TEWISS - Technik und Wissen GmbH, 2019. http://d-nb.info/1204212929/34.

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8

Schmidt, Bastian [Verfasser], Michael [Akademischer Betreuer] Stingl, and Jaroslav [Akademischer Betreuer] Haslinger. "Topology Preserving Multi-Layer Shape and Material Optimization / Bastian Schmidt. Gutachter: Michael Stingl ; Jaroslav Haslinger." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2014. http://d-nb.info/1075476747/34.

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9

Pfirsching, Marion [Verfasser]. "A multi-scale model for material flow problems based on a non-local conservation law: simulation and optimization / Marion Pfirsching." München : Verlag Dr. Hut, 2018. http://d-nb.info/1162768134/34.

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10

Meisel, Nicholas Alexander. "Design for Additive Manufacturing Considerations for Self-Actuating Compliant Mechanisms Created via Multi-Material PolyJet 3D Printing." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/54033.

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The work herein is, in part, motivated by the idea of creating optimized, actuating structures using additive manufacturing processes (AM). By developing a consistent, repeatable method for designing and manufacturing multi-material compliant mechanisms, significant performance improvements can be seen in application, such as increased mechanism deflection. There are three distinct categories of research that contribute to this overall motivating idea: 1) investigation of an appropriate multi-material topology optimization process for multi-material jetting, 2) understanding the role that manufacturing constraints play in the fabrication of complex, optimized structures, and 3) investigation of an appropriate process for embedding actuating elements within material jetted parts. PolyJet material jetting is the focus of this dissertation research as it is one of the only AM processes capable of utilizing multiple material phases (e.g., stiff and flexible) within a single build, making it uniquely qualified for manufacturing complex, multi-material compliant mechanisms. However, there are two limitations with the PolyJet process within this context: 1) there is currently a dearth of understanding regarding both single and multi-material manufacturing constraints in the PolyJet process and 2) there is no robust embedding methodology for the in-situ embedding of foreign actuating elements within the PolyJet process. These two gaps (and how they relate to the field of compliant mechanism design) will be discussed in detail in this dissertation. Specific manufacturing constraints investigated include 1) "design for embedding" considerations, 2) removal of support material from printed parts, 3) self-supporting angle of surfaces, 4) post-process survivability of fine features, 5) minimum manufacturable feature size, and 6) material properties of digital materials with relation to feature size. The key manufacturing process and geometric design factors that influence each of these constraints are experimentally determined, as well as the quantitative limitations that each constraint imposes on design.
Ph. D.
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Книги з теми "Multi-Material optimization":

1

Zheng, Maosheng, Haipeng Teng, Jie Yu, Ying Cui, and Yi Wang. Probability-Based Multi-objective Optimization for Material Selection. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-3351-6.

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2

Zheng, Maosheng, Jie Yu, Haipeng Teng, Ying Cui, and Yi Wang. Probability-Based Multi-objective Optimization for Material Selection. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-3939-8.

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3

Saravanos, D. A. Multi-objective shape and material optimization of composite structures including damping. [Washington, D.C.]: NASA, 1990.

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4

C, Chamis C., and United States. National Aeronautics and Space Administration., eds. Multi-objective shape and material optimization of composite structures including damping. [Washington, D.C.]: NASA, 1990.

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5

C, Chamis C., and United States. National Aeronautics and Space Administration., eds. Multi-objective shape and material optimization of composite structures including damping. [Washington, D.C.]: NASA, 1990.

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6

Murav'ev, Dmitriy, Aleksandr Rahmangulov, Nikita Osincev, Sergey Kornilov, and Aleksandr Cyganov. The system "seaport - "dry" port". ru: INFRA-M Academic Publishing LLC., 2022. http://dx.doi.org/10.12737/1816639.

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The monograph presents an approach to solving the problem of increasing the throughput and processing capacity of seaports in conditions of limiting their territorial dislocation and increasing the unevenness of external and internal cargo flows. The basis of the approach is the proposed system of the main parameters of the dry port and the methodology of simulation modeling of the functioning of the system "seaport - dry port". The material is illustrated with examples of the implementation of the developed approach, including model scenarios of multi-agent optimization of the parameters of the system under study. The proposed approach and the developed methodology can be used to justify management decisions on the balanced development of transport and logistics infrastructure of the regions hosting sea and dry ports. It is intended for specialists of transport and logistics companies, engineering and technical workers engaged in solving problems in the field of logistics, supply chain management and transport infrastructure design. In addition, it is recommended to students in the following programs: postgraduate studies 23.06.01 "Land transport engineering and technology" (focus "Transport and transport-technological systems of the country, its regions and cities, organization of production in transport") and 27.06.01 "Management in technical systems" (focus "Management of transportation processes"); master's degree 23.04.01 "Technology of transport processes" (profile "Organization of transportation and management in a single transport system"); bachelor's degree 38.03.02 "Management" (profile "Logistics") and 23.03.01 "Technology of transport processes".
7

Yu, Jie, Yi Wang, Maosheng Zheng, Haipeng Teng, and Ying Cui. Probability-Based Multi-Objective Optimization for Material Selection. Springer, 2022.

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8

Multi-objective shape and material optimization of composite structures including damping. [Washington, D.C.]: NASA, 1990.

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Частини книг з теми "Multi-Material optimization":

1

Shintani, Kohei, Yu-Chin Chan, and Wei Chen. "Robust Multi-material Topology Optimization for Lattice Structure Under Material Uncertainties." In Advances in Structural and Multidisciplinary Optimization, 1110–23. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67988-4_84.

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2

Zheng, Maosheng, Haipeng Teng, Jie Yu, Ying Cui, and Yi Wang. "Introduction to Multi-objective Optimization in Material Selections." In Probability-Based Multi-objective Optimization for Material Selection, 7–20. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3351-6_2.

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3

Zheng, Maosheng, Jie Yu, Haipeng Teng, Ying Cui, and Yi Wang. "Introduction to Multi-objective Optimization in Material Selections." In Probability-Based Multi-objective Optimization for Material Selection, 7–21. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-3939-8_2.

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4

Zheng, Maosheng, Jie Yu, Haipeng Teng, Ying Cui, and Yi Wang. "Robustness Evaluation with Probability-Based Multi-objective Optimization." In Probability-Based Multi-objective Optimization for Material Selection, 47–59. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-3939-8_4.

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5

Zheng, Maosheng, Jie Yu, Haipeng Teng, Ying Cui, and Yi Wang. "Treatment of Multi-objective Shortest Path Problem by Means of Probability-Based Multi-objective Optimization." In Probability-Based Multi-objective Optimization for Material Selection, 169–78. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-3939-8_12.

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6

Zheng, Maosheng, Jie Yu, Haipeng Teng, Ying Cui, and Yi Wang. "Fuzzy-Based Probabilistic Multi-objective Optimization for Material Selection." In Probability-Based Multi-objective Optimization for Material Selection, 125–34. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-3939-8_8.

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7

de Wit, A. J., A. Lipka, E. Ramm, and F. van Keulen. "Multi-level optimization of material and structural layout." In III European Conference on Computational Mechanics, 738. Dordrecht: Springer Netherlands, 2006. http://dx.doi.org/10.1007/1-4020-5370-3_738.

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8

Zheng, Maosheng, Haipeng Teng, Jie Yu, Ying Cui, and Yi Wang. "Correction to: Probability-Based Multi-objective Optimization for Material Selection." In Probability-Based Multi-objective Optimization for Material Selection, C1. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3351-6_11.

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9

Zheng, Maosheng, Haipeng Teng, Jie Yu, Ying Cui, and Yi Wang. "Extension of Probability-Based Multi-objective Optimization in Condition of the Utility with Interval Number." In Probability-Based Multi-objective Optimization for Material Selection, 43–51. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3351-6_4.

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10

Zheng, Maosheng, Haipeng Teng, Jie Yu, Ying Cui, and Yi Wang. "History and Current Status of Material Selection with Multi-objective Optimization." In Probability-Based Multi-objective Optimization for Material Selection, 1–6. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3351-6_1.

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Тези доповідей конференцій з теми "Multi-Material optimization":

1

Roper, Stephen, Garrett Vierhout, Daozhong Li, Balbir Sangha, Manish Pamwar, and Il Yong Kim. "Multi-Material Topology Optimization and Multi-Material Selection in Design." In WCX SAE World Congress Experience. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2019. http://dx.doi.org/10.4271/2019-01-0843.

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2

Hardman, Andrew, Tim Sirola, Yuhao Huang, Zane Morris, Yifan Shi, Il Yong Kim, Manish Pamwar, and Balbir Sangha. "Multi-Material Topology Optimization Considering Crashworthiness." In WCX SAE World Congress Experience. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2023. http://dx.doi.org/10.4271/2023-01-0030.

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<div class="section abstract"><div class="htmlview paragraph">There is an increasing need for lightweight structures in the transportation industry, and within these lightweight structures occupant safety is continually important to all stakeholders. Standard single and multi-material topology optimization (MMTO) techniques are effective for designing lightweight structures subjected to linear objectives and constraints but cannot consider crashworthiness. Crashworthiness must be evaluated using explicit dynamic simulation techniques, as a crash event contains geometric and material nonlinearities which cannot be captured by linear static finite element simulations. Explicit dynamic simulations prevent the calculation of sensitivity derivatives required for conventional gradient-based structural optimization strategies. This paper describes a design tool for multi-material topology optimization considering crashworthiness using the equivalent static load (ESL) method. The ESL method is used to generate linear static sub-problems which replicate the dynamic structural response of explicit dynamic crash simulations in the linear regime. The ESL sub-problems are input to a standard MMTO, optimized results from which are used as input for subsequent crash analyses to update the ESLs for additional sub-problems. The ESLs evolve as the design changes – convergence occurs when the design does not change significantly between subsequent sub-problem optimizations. The objective of this paper is to demonstrate a methodology for an efficient design tool for MMTO considering crashworthiness. Firstly, the ESL and competing methods for crashworthiness optimization are introduced and compared. Next a discussion of the tool’s operation flow as well as the sensitivity equations are presented along with two academic examples demonstrating its implementation. The design tool generates optimized multi-material designs which outperform single-material optimized designs in terms of mass by 7.5% and 17.6% in 2D and 3D models respectively when subjected to crash load cases.</div></div>
3

Shi, Yifan, Yuhao Huang, Zane Morris, Mira Teoli, Daniel Tameer, and Il Yong Kim. "Stress-Constrained Multi-Material Topology Optimization." In WCX SAE World Congress Experience. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2024. http://dx.doi.org/10.4271/2024-01-2458.

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<div class="section abstract"><div class="htmlview paragraph">The study and application of Topology Optimization (TO) has experienced great maturity in recent years, presenting itself as a highly influential and sought-after design tool in both the automotive and aerospace industries. TO has experienced development from single material topology optimization (SMTO) to multi-material topology optimization (MMTO), where material selection is simultaneously optimized with material existence. Today, MMTO for standard structural optimization responses are well supported. An additional and vital response in the design of structures is that of stress. Stress-driven or stress-controlled optimization techniques for SMTO are well understood and have been well-documented, evidenced by both published works and its availability in multiple commercial solvers. However, its integration into MMTO frameworks has not yet achieved reliable levels of accuracy and flexibility. The principal limitation of existing stress-constrained MMTO methodologies is the inability to consider candidate material-specific stress limits. Another limitation is that candidate materials cannot have different Poisson’s ratios. Herein, the study of stress-constrained MMTO is extended to consider material-specific yield stresses by introducing a novel stress limit interpolation scheme on P-norm aggregation scheme. Moreover, a stress correction method is extended from SMTO to MMTO, to avoid the stress overestimation issue. In support of the discussion on the constraint and its characteristics, its sensitivities are derived. The proposed method is examined on both 2D and 3D models, including the comparison to the results obtained by the existing commercial solver and on models with more than one million elements or multiple load cases to present the effectiveness of the proposed method.</div></div>
4

Lund, Erik, Leon Johansen, Christian Hvejsel, and Esben Olesen. "Multi-Criteria Multi-Material Topology Optimization of Laminated Composite Structures." In 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-5897.

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5

I., Sabotin, Tristo G., Bissacco G., and Valentinčič J. "Optimization of a Bottom Grooved Micromixer Design." In 8th International Conference on Multi-Material Micro Manufacture. Singapore: Research Publishing Services, 2011. http://dx.doi.org/10.3850/978-981-07-0319-6_233.

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6

Grzegorz, Janczyk, Bieniek Tomasz, Dumania Piotr, and Wymysłowski Artur. "Development of Multiscale, Multicriteria Optimization of SiP Design Methods." In 10th International Conference on Multi-Material Micro Manufacture. Singapore: Research Publishing Services, 2013. http://dx.doi.org/10.3850/978-981-07-7247-5-347.

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Huang, Yuhao, Yifan Shi, Zane Morris, Mira Teoli, Daniel Tameer, and Il Yong Kim. "Multi-Material and Multi-Objective Topology Optimization Considering Crashworthiness." In WCX SAE World Congress Experience. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2024. http://dx.doi.org/10.4271/2024-01-2262.

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<div class="section abstract"><div class="htmlview paragraph">Recently, topology optimization (TO) has seen increased usage in the automotive industry as a numerical tool, greatly enhancing the accessibility and production-readiness of optimal, lightweight solutions. By natural extension of classic single material TO (SMTO), a wealth of research has been completed in multi-material TO (MMTO), enabling simultaneous determination of material selection and existence. MMTO is effective for linear static analyses, making use of structural responses that are continuously differentiable, giving itself to efficient gradient-based optimization engines. A structural response that is inherently nonlinear and transient, thus providing difficulty to the mainstay MMTO process, is that of crashworthiness. This paper presents a multi-objective MMTO framework considering crashworthiness using the equivalent static load (ESL) method. The ESL method uses a series of linear static sub-models to approximate the transient crashworthiness model. Then, the sub-models can be optimized sequentially, using a conventional MMTO program. The limitations of the existing framework are: (1) its sole focus on intrusion minimization using displacement constraints, (2) some results have checkerboard patterns despite the use of a filter. In this paper, an improved framework aims to support the weighted sum of multiple objectives such as compliance and aggregated stress, which would affect multiple performance metrics, such as intrusion, deceleration, and energy absorption. Also, the ESL load generation method is updated to reduce checkerboarding. Firstly, the MMTO theory and ESL method are introduced. Second, the operational flow of the framework is discussed. Finally, the multi-objective solutions of an example academic model are compared using Pareto Frontiers. The optimized results show 6.4% reduction of maximum intrusion and 1.5% reduction of maximum deceleration.</div></div>
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Mirzendehdel, Amir M., and Krishnan Suresh. "Multi-Material Topology Optimization for Additive Manufacturing." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46268.

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Additive manufacturing (AM) and topology optimization strongly complement each other in that the complex and optimal designs created through the latter can directly be fabricated through AM, leading to reduced design and fabrication time. As AM expands into multi-material fabrication, there is a natural need for efficient multi-material topology optimization methods, where one must simultaneously optimize the topology, and the distribution of various materials within the topology. In this paper we generalize the single-material Pareto tracing method of topology optimization to multiple materials, and discuss its implementation using assembly-free finite element analysis, and first-order element-sensitivity. The effectiveness of the algorithm is demonstrated through illustrative examples.
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Shah, Vishrut, Kiarash Kashanian, Manish Pamwar, Balbir Sangha, and Il Yong Kim. "Multi-Material Topology Optimization Considering Manufacturing Constraints." In WCX SAE World Congress Experience. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2020. http://dx.doi.org/10.4271/2020-01-0628.

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Reis Amaral, Rodrigo, and Herbert Gomes. "MULTI-MATERIAL TOPOLOGY OPTIMIZATION WITH STRESS CONSTRAINTS." In 26th International Congress of Mechanical Engineering. ABCM, 2021. http://dx.doi.org/10.26678/abcm.cobem2021.cob2021-0435.

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