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Journal articles on the topic 'Structural optimization. Structural design. Topology'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Min, Seung Jae, and Seung Hyun Bang. "Structural Topology Design Considering Reliability." Key Engineering Materials 297-300 (November 2005): 1901–6. http://dx.doi.org/10.4028/www.scientific.net/kem.297-300.1901.

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In the design optimization process design variables are selected in the deterministic way though those have uncertainties in nature. To consider variances in design variables reliability-based design optimization problem is formulated by introducing the probability distribution function. The concept of reliability has been applied to the topology optimization based on a reliability index approach or a performance measure approach. Since these approaches, called double-loop singlevariable approach, requires the nested optimization problem to obtain the most probable point in the probabilistic design domain, the time for the entire process makes the practical use infeasible. In this work, new reliability-based topology optimization method is proposed by utilizing single-loop singlevariable approach, which approximates searching the most probable point analytically, to reduce the time cost and dealing with several constraints to handle practical design requirements. The density method in topology optimization including SLP (Sequential Linear Programming) algorithm is implemented with object-oriented programming. To examine uncertainties in the topology design of a structure, the modulus of elasticity of the material and applied loadings are considered as probabilistic design variables. The results of a design example show that the proposed method provides efficiency curtailing the time for the optimization process and accuracy satisfying the specified reliability.

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Lewiński, T., S. Czarnecki, G. Dzierżanowski, and T. Sokół. "Topology optimization in structural mechanics." Bulletin of the Polish Academy of Sciences: Technical Sciences 61, no. 1 (2013): 23–37. http://dx.doi.org/10.2478/bpasts-2013-0002.

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Abstract Optimization of structural topology, called briefly: topology optimization, is a relatively new branch of structural optimization. Its aim is to create optimal structures, instead of correcting the dimensions or changing the shapes of initial designs. For being able to create the structure, one should have a possibility to handle the members of zero stiffness or admit the material of singular constitutive properties, i.e. void. In the present paper, four fundamental problems of topology optimization are discussed: Michell’s structures, two-material layout problem in light of the relaxation by homogenization theory, optimal shape design and the free material design. Their features are disclosed by presenting results for selected problems concerning the same feasible domain, boundary conditions and applied loading. This discussion provides a short introduction into current topics of topology optimization

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3

Nowak, M. "Improved aeroelastic design through structural optimization." Bulletin of the Polish Academy of Sciences: Technical Sciences 60, no. 2 (2012): 237–40. http://dx.doi.org/10.2478/v10175-012-0031-8.

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Abstract. The paper presents the idea of coupled multiphysics computations. It shows the concept and presents some preliminary results of static coupling of structural and fluid flow codes as well as biomimetic structural optimization. The model for the biomimetic optimization procedure was the biological phenomenon of trabecular bone functional adaptation. Thus, the presented structural bio-inspired optimization system is based on the principle of constant strain energy density on the surface of the structure. When the aeroelastic reactions are considered, such approach allows fulfilling the mechanical theorem for the stiffest design, comprising the optimizations of size, shape and topology of the internal structure of the wing.

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4

Lee, Eun-Hyung, and Jaegyun Park. "Structural design using topology and shape optimization." Structural Engineering and Mechanics 38, no. 4 (2011): 517–27. http://dx.doi.org/10.12989/sem.2011.38.4.517.

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5

Zhu, Ji-Hong, Yu Li, Wei-Hong Zhang, and Jie Hou. "Shape preserving design with structural topology optimization." Structural and Multidisciplinary Optimization 53, no. 4 (2015): 893–906. http://dx.doi.org/10.1007/s00158-015-1364-3.

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6

Wang, Yong, Guo Niu Zhu, and Zheng Wei Zhu. "Structural Topology Optimization for Street Lamp Bracket." Key Engineering Materials 464 (January 2011): 655–59. http://dx.doi.org/10.4028/www.scientific.net/kem.464.655.

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Structural topology optimization has got a general acceptance in recent years in mechanical design due to its powerful technique for conceptual design. The shortcoming of current development process of mechanical design is discussed and a new approach with structural topology optimization is put forward. The application of the method demonstrates that through innovative utilization of the topology optimization techniques, a multitude of conceptual design proposals based on the design space and design targets can be obtained and then a CAD model with high quality which has a positive impact on the development process is also available.

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7

Rozvany, G. I. N. "Topology optimization in structural mechanics." Structural and Multidisciplinary Optimization 21, no. 2 (2001): 89. http://dx.doi.org/10.1007/s001580050173.

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8

Xiong, Yulin, Dingwen Bao, Xin Yan, Tao Xu, and Yi Min Xie. "Lessons Learnt from a National Competition on Structural Optimization and Additive Manufacturing." Current Chinese Science 1, no. 1 (2020): 151–59. http://dx.doi.org/10.2174/2666001601999201006191103.

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Background:: As an advanced design technique, topology optimization has received much attention over the past three decades. Topology optimization aims at finding an optimal material distribution in order to maximize the structural performance while satisfying certain constraints. It is a useful tool for the conceptional design. At the same time, additive manufacturing technologies have provided unprecedented opportunities to fabricate intricate shapes generated by topology optimization. Objective:: To design a highly efficient structure using topology optimization and to fabricate it using additive manufacturing. Method:: The bi-directional evolutionary structural optimization (BESO) technique provides the conceptional design, and the topology-optimized result is post-processed to obtain smooth structural boundaries. Results:: We have achieved a highly efficient and elegant structural design which won the first prize in a national competition in China on design optimization and additive manufacturing. Conclusion:: In this paper, we present an effective topology optimization approach to maximize the structural load-bearing capacity and establish a procedure to achieve efficient and elegant structural designs. : In the loading test of the final competition, our design carried the highest loading and won the first prize in the competition, which demonstrates the capability of BESO in engineering applications.

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9

Kurdi, Mohammad. "A Structural Optimization Framework for Multidisciplinary Design." Journal of Optimization 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/345120.

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This work describes the development of a structural optimization framework adept at accommodating diverse customer requirements. The purpose is to provide a framework accessible to the optimization research analyst. The framework integrates the method of moving asymptotes into the finite element analysis program (FEAP) by exploiting the direct interface capability in FEAP. Analytic sensitivities are incorporated to provide a robust and efficient optimization search. User macros are developed to interface the design algorithm and analytic sensitivity with the finite element analysis program. To test the optimization tool and sensitivity calculations, three sizing and one topology optimization problems are considered. In addition, flutter analysis of a heated panel is analyzed as an example of coupling to nonstructural discipline. In sizing optimization, the calculated semianalytic sensitivities match analytic and finite difference calculations. Differences between analytic designs and numerical ones are less than 2.0% and are attributed to discrete nature of finite elements. In the topology problem, quadratic elements are found robust at resolving checkerboard patterns.

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10

Jaafer, Abdulkhaliq A., Mustafa Al-Bazoon, and Abbas O. Dawood. "Structural Topology Design Optimization Using the Binary Bat Algorithm." Applied Sciences 10, no. 4 (2020): 1481. http://dx.doi.org/10.3390/app10041481.

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In this study, the binary bat algorithm (BBA) for structural topology optimization is implemented. The problem is to find the stiffest structure using a certain amount of material and some constraints using the bit-array representation method. A new filtering algorithm is proposed to make BBA find designs with no separated objects, no checkerboard patterns, less unusable material, and higher structural performance. A volition penalty function for topology optimization is also proposed to accelerate the convergence toward the optimal design. The main effect of using the BBA lies in the fact that the BBA is able to handle a large number of design variables in comparison with other well-known metaheuristic algorithms. Based on the numerical results of four benchmark problems in structural topology optimization for minimum compliance, the following conclusions are made: (1) The BBA with the proposed filtering algorithm and penalty function are effective in solving large-scale numerical topology optimization problems (fine finite elements mesh). (2) The proposed algorithm produces solid-void designs without gray areas, which makes them practical solutions that are applicable in manufacturing.

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11

Zuo, Kong-Tian, Li-Ping Chen, Yun-Qing Zhang, and Jingzhou Yang. "A hybrid topology optimization algorithm for structural design." Engineering Optimization 37, no. 8 (2005): 849–66. http://dx.doi.org/10.1080/03052150500323856.

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12

Bremicker, M., M. Chirehdast, N. Kikuchi, and P. Y. Papalambros. "Integrated Topology and Shape Optimization in Structural Design∗." Mechanics of Structures and Machines 19, no. 4 (1991): 551–87. http://dx.doi.org/10.1080/08905459108905156.

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13

TSUDA, Akari, Nozomu KOGISO, Takayuki YAMADA, Kazuhiro IZUI, and Shinji NISHIWAKI. "Morphing Wing Structural Design Using Topology Optimization Method." Proceedings of OPTIS 2016.12 (2016): 1206. http://dx.doi.org/10.1299/jsmeoptis.2016.12.1206.

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14

Wang, Cunfu, Min Zhao, and Tong Ge. "Structural topology optimization with design-dependent pressure loads." Structural and Multidisciplinary Optimization 53, no. 5 (2015): 1005–18. http://dx.doi.org/10.1007/s00158-015-1376-z.

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15

Mizobuti, Vinicius, and Luiz C. M. Vieira Junior. "Bioinspired architectural design based on structural topology optimization." Frontiers of Architectural Research 9, no. 2 (2020): 264–76. http://dx.doi.org/10.1016/j.foar.2019.12.002.

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16

Olhoff, Niels, Martin P. Bendsøe, and John Rasmussen. "On CAD-integrated structural topology and design optimization." Computer Methods in Applied Mechanics and Engineering 89, no. 1-3 (1991): 259–79. http://dx.doi.org/10.1016/0045-7825(91)90044-7.

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17

Lee, Edmund, and Joaquim R. R. A. Martins. "Structural topology optimization with design-dependent pressure loads." Computer Methods in Applied Mechanics and Engineering 233-236 (August 2012): 40–48. http://dx.doi.org/10.1016/j.cma.2012.04.007.

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18

Yang, Rui, Yang Liu, and Liang Zhou. "A Topology Optimization Method in Fuselage Flutter Model Design." Advanced Materials Research 199-200 (February 2011): 1297–302. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.1297.

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Airplane flutter scale model should maintain the load transfer characteristics of the original structure. It is a structural inverse problem for proper natural frequencies as well as structural simplification. This inverse problem could be solved by topology optimization. So based on bi-direction evolutionary structural optimization (BESO) method, a topology method for designing fuselage flutter model is presented. Facing porous and irregular shape often appears in topology optimization, a regular shaped grid frame structure consisted of the finite elements is discussed, including its internal mapping relationship and boundary conditions. The ratio criterion for structural modification is raised in this structural topology optimization using frequency sensitivity. Finally, this topology optimization method is applied to cylindrical fuselage flutter model design, result shown that the proposed approach is feasible to achieve given natural frequencies, maintains the character of inner frame structure completely, and the similarity between optimized structure and original structure is achieved.

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19

Chapman, C. D., and M. J. Jakiela. "Genetic Algorithm-Based Structural Topology Design With Compliance and Topology Simplification Considerations." Journal of Mechanical Design 118, no. 1 (1996): 89–98. http://dx.doi.org/10.1115/1.2826862.

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The genetic algorithm (GA), an optimization technique based on the theory of natural selection, is applied to structural topology design problems. After reviewing the genetic algorithm and previous research in structural topology optimization, we detail the chromosome-to-design representation which enables the genetic algorithm to perform structural topology optimization. Extending our prior investigations, this article first compares our genetic-algorithm-based technique with homogenization methods in the minimization of a structure’s compliance subject to a maximum volume constraint. We then use our technique to generate topologies combining high structural performance with a variety of material connectivity characteristics which arise directly from our discretized design representation. After discussing our findings, we describe potential future work.

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20

Zhu, Ji-Hong, and Wei-Hong Zhang. "Structural optimization in ESAC: annals 2011." International Journal for Simulation and Multidisciplinary Design Optimization 5 (2014): A09. http://dx.doi.org/10.1051/smdo/2013013.

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The purpose of this paper is to give an overall introduction of the structural optimization research works in ESAC group in 2011. Four main topics are involved, i.e. 1) topology optimization with multiphase materials, 2) integrated layout and topology optimization, 3) prediction of effective material properties and 4) composite design. More detailed techniques and some numerical results are also presented and discussed here.

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21

Ma, Zheng-Dong, Noboru Kikuchi, Christophe Pierre, and Basavaraju Raju. "Multidomain Topology Optimization for Structural and Material Designs." Journal of Applied Mechanics 73, no. 4 (2005): 565–73. http://dx.doi.org/10.1115/1.2164511.

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A multidomain topology optimization technique (MDTO) is developed, which extends the standard topology optimization method to the realm of more realistic engineering design problems. The new technique enables the effective design of a complex engineering structure by allowing the designer to control the material distribution among the subdomains during the optimal design process, to use multiple materials or composite materials in the various subdomains of the structure, and to follow a desired pattern or tendency for the material distribution. A new algorithm of Sequential Approximate Optimization (SAO) is proposed for the multidomain topology optimization, which is an enhancement and a generalization of previous SAO algorithms (including Optimality Criteria and Convex Linearization methods, etc.). An advanced substructuring method using quasi-static modes is also introduced to condense the nodal variables associated with the multidomain topology optimization problem, especially for the nondesign subdomains. The effectiveness of the new MDTO approach is demonstrated for various design problems, including one of “structure-fixture simultaneous design,” one of “functionally graded material design,” and one of “crush energy management.” These case studies demonstrate the potential significance of the new capability developed for a wide range of engineering design problems.

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22

Li, Jia Chun, Wen Te Tu, Xu Dong Yang, Jian Fu, and Yong Tao Wang. "Heat Conduction Structural Topology Optimization Based on RAMP." Applied Mechanics and Materials 52-54 (March 2011): 1692–97. http://dx.doi.org/10.4028/www.scientific.net/amm.52-54.1692.

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Based on topology optimization techniques of structural mechanics, an effective method for solving the structural design problems of heat transfer is presented in this paper. The topology optimization model of heat conduction is then constructed and the corresponding Optimization Criteria based on density approach is inferred to solve the optimal heat conduction equation of temperature field. A Filtering technique is employed in density field to eliminate numerical instabilities in the process of topology optimization. Some numerical examples are presented to demonstrate the accuracy and the applicability of the present method, theory and algorithm. This research provides a new idea and an access to the structural topology optimization design of temperature field, and is of good engineering application value.

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23

Xu, Jian, Jian Yuan Sun, and Yu Long Shui. "Bi-Directional Evolutionary Structural Optimization in Conceptual Bridge Design." Applied Mechanics and Materials 256-259 (December 2012): 1658–64. http://dx.doi.org/10.4028/www.scientific.net/amm.256-259.1658.

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The principle and procedure of bi-directional evolutionary structural optimization (BESO) are stated in detail. A program based on BESO is introduced in conceptual bridge design. Topology optimizations are achieved for deck arch bridges with different rise-to-span ratios, half-through arch bridge, through tied arch bridge, bridge pier and bridge main beam. The results demonstrate rational structures with well-distributed stress and smooth force transmission, which indicates the efficient of the method.

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24

Xu, Wu Jiao, Lei Zhang, and Wu Hua Li. "Structure Design of Stamping Die Based on Topology Optimization and Shape Optimization." Advanced Materials Research 774-776 (September 2013): 172–75. http://dx.doi.org/10.4028/www.scientific.net/amr.774-776.172.

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To quantitatively analyze the structural topology and control the elastic deformation of die structure in stamping, a new die structure design method was proposed. The forming analysis was conducted based on the die surface mesh generated in the third-party software. Structural analysis models were established according to the die surface mesh and deformation resistance obtained from forming analysis results. And then, the structure analysis and optimization were carried out. This new method for structure design of stamping die has two advantages. First one is the combination of forming analysis and structure analysis makes the structural optimization procedure more practical. Secondly, the coupling of topology optimization and shape optimization makes it possible to fundamentally change the structural topology and it is a new attempt to mold design.

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25

Li, Quhao, Wenjiong Chen, Shutian Liu, and Liyong Tong. "Structural topology optimization considering connectivity constraint." Structural and Multidisciplinary Optimization 54, no. 4 (2016): 971–84. http://dx.doi.org/10.1007/s00158-016-1459-5.

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26

Chapman, C. D., K. Saitou, and M. J. Jakiela. "Genetic Algorithms as an Approach to Configuration and Topology Design." Journal of Mechanical Design 116, no. 4 (1994): 1005–12. http://dx.doi.org/10.1115/1.2919480.

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The genetic algorithm, a search and optimization technique based on the theory of natural selection, is applied to problems of structural topology design. An overview of the genetic algorithm will first describe the genetics-based representations and operators used in a typical genetic algorithm search. Then, a review of previous research in structural optimization is provided. A discretized design representation, and methods for mapping genetic algorithm “chromosomes” into this representation, is then detailed. Several examples of genetic algorithm-based structural topology optimization are provided: we address the optimization of cantilevered plate topologies, and we investigate methods for optimizing finely-discretized design domains. The genetic algorithm’s ability to find families of highly-fit designs is also examined. Finally, a description of potential future work in genetic algorithm-based structural topology optimization is offered.

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27

Cheng, G. D., and X. Guo. "?-relaxed approach in structural topology optimization." Structural Optimization 13, no. 4 (1997): 258–66. http://dx.doi.org/10.1007/bf01197454.

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28

Chirehdast, M., H. C. Gea, N. Kikuchi, and P. Y. Papalambros. "Structural Configuration Examples of an Integrated Optimal Design Process." Journal of Mechanical Design 116, no. 4 (1994): 997–1004. http://dx.doi.org/10.1115/1.2919510.

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Structural optimization procedures usually start from a given design topology and vary proportions or boundary shapes of the design to achieve optimality of an objective under various constraints. This article presents examples of the application of a novel approach for initiating formal structural optimization at an earlier stage, where the design topology is rigorously generated. A three-phase design process is used. In Phase I, an optimal initial topology is created by a homogenization method as a gray-scale image. In Phase II, the image is transformed to a realizable design using computer vision techniques. In Phase III, the design is parameterized and treated in detail by conventional size and shape optimization techniques. Fully-automated procedures for optimization of two-dimensional solid structures are outlined, and several practical design problems for this type of structures are solved using the proposed procedure, including a crane hook and a bicycle frame.

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29

YANG, Rui. "Topology Optimization for Structural Design of Fuselage Flutter Model." Journal of Mechanical Engineering 47, no. 11 (2011): 59. http://dx.doi.org/10.3901/jme.2011.11.059.

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30

TSUDA, Akari, Nozomu KOGISO, Takayuki YAMADA, Kazuhiro IZUI, Shinji NISHIWAKI, and Masato TAMAYAMA. "A Morphing Wing Structural Design Using Topology Optimization Method." Proceedings of the Transportation and Logistics Conference 2017.26 (2017): 1020. http://dx.doi.org/10.1299/jsmetld.2017.26.1020.

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31

OKUMOTO, Yasuhisa, and Takayuki KONISHI. "1108 Structural Design of Steering Knuckle Using Topology Optimization." Proceedings of Conference of Chugoku-Shikoku Branch 2009.47 (2009): 373–74. http://dx.doi.org/10.1299/jsmecs.2009.47.373.

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32

Tseng, K.-Y., C.-B. Zhang, and C.-Y. Wu. "An Enhanced Binary Particle Swarm Optimization for Structural Topology Optimization." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 10 (2010): 2271–87. http://dx.doi.org/10.1243/09544062jmes2128.

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Particle swarm optimization (PSO), a heuristic optimization method, has been successfully applied in solving many optimization problems in real-value search space. The original binary particle swarm optimization (BPSO) uses the concept of bit flipping of the binary string to convert the velocity from a real code into a binary code. However, the conversion process cannot be reversed, and it is difficult to extend this framework to solve certain discrete optimization problems. An enhanced binary particle swarm algorithm is proposed in this study based on pure binary bit-string frameworks to deal with structural topology optimization problems. Further, two enhancement strategies, stress-based strategy and pair-switched strategy, were developed to improve the performance of the proposed algorithm for topology optimization of structure. The results of experimental cases demonstrated in this study show that the proposed enhanced binary particle swarm optimization (EBPSO) with two developed strategies is an efficient population-based approach for finding the optimal design for structural topology optimization problems of minimum compliance design and minimum weight design.

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Jiang, T., and M. Chirehdast. "A Systems Approach to Structural Topology Optimization: Designing Optimal Connections." Journal of Mechanical Design 119, no. 1 (1997): 40–47. http://dx.doi.org/10.1115/1.2828787.

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In this paper, structural topology optimization is extended to systems design. Locations and patterns of connections in a structural system that consists of multiple components strongly affect its performance. Topology of connections is defined, and a new classification for structural optimization is introduced that includes the topology optimization problem for connections. A mathematical programming problem is formulated that addresses this design problem. A convex approximation method using analytical gradients is used to solve the optimization problem. This solution method is readily applicable to large-scale problems. The design problem presented and solved here has a wide range of applications in all areas of structural design. The examples provided here are for spot-weld and adhesive bond joints. Numerous other potential applications are suggested.

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Chen, Shikui, Michael Yu Wang, and Ai Qun Liu. "Shape feature control in structural topology optimization." Computer-Aided Design 40, no. 9 (2008): 951–62. http://dx.doi.org/10.1016/j.cad.2008.07.004.

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Du, Yi Xian, Wei Wang, Qi Hua Tian, and Jin Run Hu. "Research on Techniques of Structural Topology Optimization Using Cellular Automaton." Advanced Materials Research 308-310 (August 2011): 987–93. http://dx.doi.org/10.4028/www.scientific.net/amr.308-310.987.

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By integrating cellular automaton (CA) theory into topology optimization of continuum, the local rule is defined for sensitivity analysis and updating of the design variable, according to the analysis of the structural mechanical response. Topology optimization design of loaded structure is conducted using minimal compliance as the optimization objective. The optimal distribution of material in the design domain is finally obtained. Comparing to other algorithms, the local rule has proved to be computationally efficient to solve structural topology optimization problems. The resulting optimal structures are free of numerical instabilities such as the checkerboard patterns and mesh dependency.

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Wu, Yong Hai. "Optimization Design of Vehicle Frame Based on ANSYS." Advanced Materials Research 590 (November 2012): 341–45. http://dx.doi.org/10.4028/www.scientific.net/amr.590.341.

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A special vehicle frame as the research object, its topology optimization mathematical model and its algorithm is established based on variable density method. Topology optimization method of continuum structures is applied to the frame structural design of this special vehicle using Optistruct solver. Take the least flexibility of frame as design goal; topology optimization design of frame structure was carried under the condition of flexure, torsion and flexure-torsion. New structural model of frame was determined according to results of topology optimization and engineering experience. The calculation of the stress, deformation and the volume for optimization results was conducted with ANSYS software, and compared with the data before optimization. The results showed that the safety performance of optimized frame improved, and the weight reduced.

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Yildiz, Ali Riza. "Optimal Structural Design of Vehicle Components Using Topology Design and Optimization." Materials Testing 50, no. 4 (2008): 224–28. http://dx.doi.org/10.3139/120.100880.

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Zhou, Hui, Gang Yan Li, Yuan Zhang, and Le Li. "Structure Topology Optimization Design for Compression Box of Horizontal Preloading Domestic Waste Transfer Station." Applied Mechanics and Materials 475-476 (December 2013): 1382–86. http://dx.doi.org/10.4028/www.scientific.net/amm.475-476.1382.

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Horizontal preloading domestic waste transfer station is the core equipment for domestic waste disposal. Compression equipment is the elementary equipment of horizontal preloading domestic waste transfer station, which should be ensured its mechanical properties and structural lightweight. According to the compression box structure in this paper, structural topology optimization model is established. By using HyperWorks software, the result of structural topology optimization result of compression box is obtained. Based on the result of topology optimization, the structural improvement design model of compression box is established, and the number, location, size of strengthening rib for bottom plate, top plate, side plate are optimal designed so as to realize structural lightweight.

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Tomšič, Pavel, and Jože Duhovnik. "Simultaneous Topology and Size Optimization of 2D and 3D Trusses Using Evolutionary Structural Optimization with regard to Commonly Used Topologies." Advances in Mechanical Engineering 6 (January 1, 2014): 864807. http://dx.doi.org/10.1155/2014/864807.

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One of many optimization techniques is the evolutionary structural optimization (ESO), based on the idea that an optimal structure can be achieved by gradually removing ineffectively used materials from the design domain. Production of a multistage optimization is often proposed to reach the best overall solution. In the first stage, the structure is optimized according to a topology criterion, and, in the second stage, sizing optimization is carried out. The efficiency of such an approach is questionable as a fixed topology, for the second stage optimization may not be the most favorable before sizing optimization is carried out. In this paper, the simultaneous topology and size optimization of trusses using the ESO algorithm are discussed. A number of numerical examples are presented to research capacity to achieve optimal solutions for a structural problem. The topology design of the initial design domain is based on commonly used designs for multistorey trusses constructed from straight members. Therefore, the cases are of a slender shape and made from a combination of presented internal designs. The case studies will present an evaluation to show whether the described optimization approach can be beneficial in structural design for the purpose of steel framework designs.

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Qiu, Guang Yu, Ping Hu, and Wei Zhou. "Two-Dimensional Structural Topology Optimization Based on Isogeometric Analysis." Applied Mechanics and Materials 472 (January 2014): 475–79. http://dx.doi.org/10.4028/www.scientific.net/amm.472.475.

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In this paper, the isogeometric analysis is applied to two-dimensional structural topology optimization instead of traditional finite element analysis. By treating the corresponding element density of knot spans as design variables, the topology optimization model is formulated based on SIMP method. Then the optimization problem is solved using the method of moving asymptotes. As demonstrated by examples, the proposed method can be used for two-dimensional topology optimization. And the results show that checkerboard patterns can be controlled.

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Choi, S. H., J. Y. Park, I. S. Shin, and Seok Young Han. "Topology Optimization of a Vehicle’s Hood Using Evolutionary Structural Optimization." Key Engineering Materials 326-328 (December 2006): 1217–20. http://dx.doi.org/10.4028/www.scientific.net/kem.326-328.1217.

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Topology optimization of the inner reinforcement for a vehicle’s hood has been performed by evolutionary structural optimization (ESO) method. The purpose of this study is to obtain optimal topology of the inner reinforcement for a vehicle’s hood considering static stiffness and natural frequency simultaneously. To do this, the multiobjective design optimization technique was implemented. From several combinations of weighting factors, a Pareto-optimal solution was obtained. Optimal topologies were obtained by the ESO method, i.e., by eliminating the elements having the lowest efficiency from the structural domain. As the weighting factor of the elastic strain efficiency goes from 1 to zero, it is found that the optimal topologies transmits from the optimal topology of static stiffness problem to that of natural frequency problem. Therefore, it was concluded that ESO method is effectively applied to topology optimization of the inner reinforcement of a vehicle’s hood.

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Mi, Da Hai, Rui Yang, Liang Zhou, Yang Liu, and Dong Ming Guo. "Optimal Structural Frequency Design of Stiffened Shell." Applied Mechanics and Materials 157-158 (February 2012): 1636–39. http://dx.doi.org/10.4028/www.scientific.net/amm.157-158.1636.

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Frequency-aimed optimal structural design of stiffened shell is concerned. It is a reverse design problem for the first several modal frequencies to converge to a set of target value. A design method combined modified bi-directional evolutionary structural optimization (BESO) and size optimization is presented. Optimization model consists of skin and regular grid frame structure. To solve irregular branches and holes that often exist in ordinary topology optimization results, instead of elements, the existence states of ribs in the frame are used as design variables and sensitivity of the rib is discussed. Detailed design is conducted by size optimization. Example shows that frequency requirements are achieved. And the optimum structure is regular and clear, the localized modes problem is avoid. This is very suitable for designing airplane wind tunnel flutter test models.

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Xue, Hongjun, Haiyang Yu, Xiaoyan Zhang, and Qi Quan. "A Novel Method for Structural Lightweight Design with Topology Optimization." Energies 14, no. 14 (2021): 4367. http://dx.doi.org/10.3390/en14144367.

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Topological optimization is an innovative method to realize the lightweight design. This paper proposes a hybrid topology optimization method that combines the SIMP (solid isotropic material with penalization) method and genetic algorithm (GA), called the SIMP-GA method. In the method, SIMP is used to update the chromosomes, which can accelerate convergence. The filtering scheme in the SIMP method can filter unconnected elements to ensure the connectivity of the structure. We studied the influence of varying the filtering radius on the optimized structure. Simultaneously, in the SIMP-GA method, each element is regarded as a gene, which controls the population number to a certain extent, reduces the amount of calculation, and improves the calculation efficiency. The calculation of some typical examples proves that the SIMP-GA method can obtain a better solution than the gradient-based method. Compared with the conventional genetic algorithm and GA-BESO (Bi-directional Evolutionary Structural Optimization) method, the calculation efficiency of the proposed method is higher and similar results are obtained. The innovative topology optimization method could be an effective way for structural lightweight design.

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Yao, S. G., and Hang Li. "Structural Topology Optimization of the Column of Form Grinding Machine." Key Engineering Materials 455 (December 2010): 397–401. http://dx.doi.org/10.4028/www.scientific.net/kem.455.397.

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Based on Topology optimization method of continuum the structural dynamic model has been built by constraint condition of volume and objective function of column natural frequency. In order to improve precision the dynamic characteristics of non-design region have been considered in optimization process. The column of structural optimization design has been done by applying topology optimization. The quality has not only reduced, but also the dynamic characteristic of the column has been improved. Thus the design effect has been reached.

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Rong, Jian Hua, Wei Xiang Li, and Bing Feng. "A Structural Topological Optimization Method Based on Varying Displacement Limits and Design Space Adjustments." Advanced Materials Research 97-101 (March 2010): 3609–16. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.3609.

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In the proposed topology optimization method, the whole optimization process is divided into two phases. Firstly，an optimization model dealing with varying displacement limits and design space adjustment approaches， after the combination of structural discrete topology variable condition and the original objective， are built. Secondly，incorporating smooth optimization algorithm，a procedure is proposed to solve the optimization problem of the first optimization adjustment phase. This design space adjustment capability is automatic when the design domain needs expansion or reduction, and it will not affect the property of mathematical programming method convergences. The structural topology approaches to the vicinity of the optimum topology when the first optimization adjustment phase ends. Then, a heuristic algorithm is given to make the topology of the design structure be of solid/empty property and the optimum topology is obtained during the second optimization adjustment phase. The simulation shows that the topologies obtained by the proposed method are of very good 0-1 distribution property, the proposed method is robust and efficient.

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Han, Haitao, Yuchen Guo, Shikui Chen, and Zhenyu Liu. "Topological constraints in 2D structural topology optimization." Structural and Multidisciplinary Optimization 63, no. 1 (2020): 39–58. http://dx.doi.org/10.1007/s00158-020-02771-5.

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Niu, Fei, Shengli Xu, and Gengdong Cheng. "A general formulation of structural topology optimization for maximizing structural stiffness." Structural and Multidisciplinary Optimization 43, no. 4 (2010): 561–72. http://dx.doi.org/10.1007/s00158-010-0585-8.

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Wang, Ping, Zhou Lan, and Xiao Yang Shen. "Weight Reduction Design of Gear Drive Based on Parameter and Structural Optimization." Advanced Materials Research 139-141 (October 2010): 1406–10. http://dx.doi.org/10.4028/www.scientific.net/amr.139-141.1406.

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. For a medium or large-sized gear drive, in order to achieve the optimum weight reduction effect, an approach of weight reduction design is proposed that multi-objective optimization of gear parameters is carried out firstly, and then structural optimization is adopted to design the gear former. The rational design parameters of a gear drive are determined by the multi-objective optimization with minimizing the sum of gear volumes and the equivalent moment of inertia of input shaft (EMI) synchronously. Conceptual design of the former is given by structural topology optimization of the gear, and the reasonability of topology optimization can be demonstrated by static and dynamic analysis. The results indicate that for a double-reduction gearbox of 500KW co-rotating twin screw pulping extruder, the EMI of the gear drive reduces by 20.88% through the multi-objective optimization of gear parameters, and the moment of inertia of a bull gear reduces by 38.86% through structural topology optimization.

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Sun, Jian Xiang, Ye Yang, and Jing Yi Tian. "Structural Topology Optimization for Improvements of some Shell Structures' Rib Design Process." Applied Mechanics and Materials 385-386 (August 2013): 1927–32. http://dx.doi.org/10.4028/www.scientific.net/amm.385-386.1927.

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In order to overcome the shortcoming of traditional mathematical model of topology optimization which aims to the continuum structures, a new implementation combined with TOSCA Structure software is presented. To examine the accuracy of optimal topology of this kind of structural, the programming scheme for the conceptual design of one shell structure using topological optimization approaches is set firstly, then build up a new topology optimization design method of the shell structure rib model. Through the FE simulation calculations from Project 1 to Project 4, different improvement results of maximum displacements are obtained. These results demonstrate the validity and reliability of the method.

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Tang, Ji Wu, Mike Xie, and Peter Felicetti. "Topology Optimization of Building Structures Considering Wind Loading." Applied Mechanics and Materials 166-169 (May 2012): 405–8. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.405.

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The latest developments in structural topological optimization have been integrated with CFD for the optimization of building structures considering wind loading. Wind loads on a building are numerically simulated in ANSYS CFX and then transferred to ANSYS Static to get the structural response of the building in wind. The bi-directional evolutionary structural optimization (BESO) algorithm has been applied to buildings for an automatic structural topological optimization considering wind loading. The proposed approach is demonstrated by examples of the optimum structural design of exterior bracing system of a high-rise building.

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