A novel subdomain level set method for structural topology optimization and its application in graded cellular structure design

Hui, Lam; Zong, Hongming; Tian, Ye; Ma, Qingping; Wang, Michael Yu

doi:10.1007/s00158-019-02318-3

Cited by 47 publications

(9 citation statements)

References 70 publications

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“…The first-order forward Euler's method is employed to solve the evolution equation numerically. Liu et al (2019) developed a subdomain parameterized level-set topology optimization framework using RBFs, where the global design domain is divided into a number of subdomains. In this way, the parameterization and evolution of level-set functions can be conducted in each subdomain separately.…”

Section: Level-set Methodsmentioning

confidence: 99%

“…To generate structural designs made of bars, Smith and Norato (2020) developed a MATLAB code for the topology optimization of 2D and 3D problems using the geometry projection method. The basic idea behind the geometry projection is to take a high-level parametric description of a given geometric top_levelset (Challis, 2010) Standard code: top88 (Andreassen et al, 2011) TOPRBF (Wei et al, 2018) Sub_LSM (Liu et al, 2019) levelset88 (Otomori et al, 2015) filter_based_ levelset (Yaghmaei et al, 2020) Standard code: top99 (Sigmund, 2001) Discrete level-set method Parameterized level-set method Reaction-diffusion-based approach Another topology optimization approach using the discrete geometric components is the MMC (and MMB) method. The MMC method proposed by Guo et al (2014) aims to conduct topology optimization in an explicit and geometrical way using a set of morphable components.…”

Section: Geometric Component Approachesmentioning

confidence: 99%

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A comprehensive review of educational articles on structural and multidisciplinary optimization

Wang

Zhao

Zhou

et al. 2021

Struct Multidisc Optim

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Ever since the publication of the 99-line topology optimization MATLAB code (top99) by Sigmund in 2001, educational articles have emerged as a popular category of contributions within the structural and multidisciplinary optimization (SMO) community. The number of educational papers in the field of SMO has been growing rapidly in recent years. Some educational contributions have made a tremendous impact on both research and education. For example, top99 (Sigmund in Struct Multidisc Optim 21(2):120-127, 2001) has been downloaded over 13,000 times and cited over 2000 times in Google Scholar. In this paper, we attempt to provide a systematic and comprehensive review of educational articles and codes in SMO, including topology, sizing, and shape optimization and building blocks. We first assess the papers according to the adopted methods, which include density-based, level-set, ground structure, and more. We then provide comparisons and evaluations on the codes from several key aspects, including techniques, efficiency, usability, readability, environment, and compatibility. In addition, we conduct numerical experiments on the reviewed codes using the benchmark cantilever beam example to provide feedback on the overall user experience. With a systematic review and comparison, this paper aims to offer insights on the educational values and practicality for employing these codes. We try to provide not only guidance for beginners to approach various optimization methods, but also a dictionary to direct readers to effectively target the relevant codes and building blocks based on their demands. Finally, based on the findings in this review paper, we provide some perspectives and recommendations for future educational contributions.

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Section: Level-set Methodsmentioning

confidence: 99%

Section: Geometric Component Approachesmentioning

confidence: 99%

A comprehensive review of educational articles on structural and multidisciplinary optimization

Wang

Zhao

Zhou

et al. 2021

Struct Multidisc Optim

View full text Add to dashboard Cite

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“…Gao 等 [9] 对多尺度复合结构进行了研究, 并编写了相应的代码. Liu 等 [10] 提出一种基于径向基函数(radial basis function, RBF)的水平集微结构拓扑优化方法.…”

Section: 计算机辅助设计与图形学学报unclassified

An Improved Topology Optimization Method for Suppressing Gray Elements

Gao¹,

Wang²,

Du³

2020

J Comput-Aided Design Comput Graphics

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The topology optimization structure obtained by the SIMP (solid isotropic material with penalization) method or RAMP (rational approximation of material properties) method has a large number of gray elements, and the existing Heaviside function has the problem of calling the density matrix frequently, so the computational efficiency is relatively low. Aiming at this problem, an improved topology optimization method for suppressing gray elements is proposed in this paper. Firstly, a topology optimization model with minimizing the structural compliance as design objective is established; then, the Young's modulus is calculated by the SIMP method or RAMP method; finally, gray element is suppressed by the Heaviside projection function, and the topology optimization problem is solved by the OC (optimality criteria) method. The numerical simulation results show that: the two Heaviside projection functions proposed in this paper can suppress gray elements stably and effectively, and they can notably improve the definition and stiffness of the structure obtained by the SIMP method and RAMP method respectively.

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“…Similar methods in the general multiscale TO field accomplish connected heterogeneous designs without the above simplifications by: (1) sharing finite elements and design variables at interfaces (Liu et al, 2019), (2) adding connectivity constraints (Du et al, 2018;Garner et al, 2019), (3) controlling the change in the properties of intermediate microstructures (Zhou et al, 2019), (4) creating geometric gradations during pre-or post-processing (Sanders et al, 2021;Zhou et al, 2019;Zobaer and Sutradhar, 2020), and (5) interpolating random field representations of microstructures (Kumar et al, 2020). Of these, Liu et al (2019), Garner et al (2019), and Sanders et al (2021) concurrently design the macrostructure as well as the distributions of multiple microstructures, and only Luo et al (2021) also optimized the graded volume fractions. Moreover, many do not scale well with the number of classes.…”

Section: Introductionmentioning

confidence: 99%

Remixing Functionally Graded Structures: Data-Driven Topology Optimization with Multiclass Shape Blending

Chan,

Da,

Wang

et al. 2021

Preprint

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To create heterogeneous, multiscale structures with unprecedented functionalities, recent topology optimization approaches design either fully aperiodic systems or functionally graded structures, which compete in terms of design freedom and efficiency. We propose to inherit the advantages of both through a data-driven framework for multiclass functionally graded structures that mixes several families, i.e., classes, of microstructure topologies to create spatially-varying designs with guaranteed feasibility. The key is a new multiclass shape blending scheme that generates smoothly graded microstructures without requiring compatible classes or connectivity and feasibility constraints. Moreover, it transforms the microscale problem into an efficient, low-dimensional one without confining the design to predefined shapes. Compliance and shape matching examples using common truss geometries and diversitybased freeform topologies demonstrate the versatility of our framework, while studies on the effect of the number and diversity of classes illustrate the effectiveness. The generality of the proposed methods supports future extensions beyond the linear applications presented.

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A novel subdomain level set method for structural topology optimization and its application in graded cellular structure design

Cited by 47 publications

References 70 publications

A comprehensive review of educational articles on structural and multidisciplinary optimization

A comprehensive review of educational articles on structural and multidisciplinary optimization

An Improved Topology Optimization Method for Suppressing Gray Elements

Remixing Functionally Graded Structures: Data-Driven Topology Optimization with Multiclass Shape Blending

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