Level-set methods for structural topology optimization: a review

Dijk, Nico P. van; Maute, Kurt; Langelaar, Matthijs; Keulen, Fred van

doi:10.1007/s00158-013-0912-y

Cited by 751 publications

(388 citation statements)

References 165 publications

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“…Since its introduction three decades ago [1], this approach has been used to solve a wide variety of problems in various academic and industrial fields. For the recent advancements in TO, please see [2][3][4]. The so-called density-based formulation is the most popular both in academia and in commercial applications.…”

Section: Introductionmentioning

confidence: 99%

Bounds for decoupled design and analysis discretizations in topology optimization

Gupta

Veen

Aragón

et al. 2017

Numerical Meth Engineering

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SUMMARYTopology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non-unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing nonuniqueness.

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Section: Introductionmentioning

confidence: 99%

Bounds for decoupled design and analysis discretizations in topology optimization

Gupta

Veen

Aragón

et al. 2017

Numerical Meth Engineering

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“…Topological functions such as the changes in the boundary, merging of boundaries and formation of new voids are performed on the level-set function. The geometric boundary shape is modified by controlling the motion of the level set according to the physical problem and optimization conditions [26]. It is worth noting that most level-set formulations still rely on finite elements despite the smooth boundary representation.…”

Section: Level-set Methodsmentioning

confidence: 99%

Heat Exchanger Design with Topology Optimization

Manuel¹,

Lin²

2017

Heat Exchangers - Design, Experiment and Simulation

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Topology optimization is proving to be a valuable design tool for physical systems, especially for structural systems. However, its application in the field of heat transfer is less evident but is constantly progressing. In this chapter, we would like to introduce topology optimization in the context of heat exchanger design to the general reader. We also provide a chronological review of available literature to see the current progress of topology optimization in the field of heat transfer and heat exchanger design. We expect that topology optimization will prove to be a valuable tool in heat exchanger design for the coming years.

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“…However, the aforementioned approaches are associated with the solution of a Hamilton-Jacobi-type equation, which may considerably slow down the speed of optimization convergence. New strategies have been implemented in the topology optimization method to solve the Hamilton-Jacobi-type equation [24][25][26][27], aiming at improving the computational efficiency and enhancing the numerical stability [28][29][30]. Recently, Guos group made great progress in parametric level set topology optimization methods, which significantly reduced the number of the design variables and in turn tremendously increase the computational efficiency [31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Topology Description Function Method Based on Modified Sigmoid Function

Yang

Liu

Yang

et al. 2018

Mathematical Problems in Engineering

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Optimal geometries extracted from traditional element-based topology optimization outcomes usually have zigzag boundaries, leading to being difficult to fabricate. In this study, a fairly accurate and efficient topology description function method (TDFM) for topology optimization of linear elastic structures is developed. By employing the modified sigmoid function, a simple yet efficient strategy is presented to tackle the computational difficulties because of the nonsmoothness of Heaviside function in topology optimization problem. The optimization problem is to minimize the structural compliance, with highest stiffness, while satisfying the volume constraint. The design problem is solved by a Sequential Linear Programming method. Convergent, crisp, and smooth final layouts are obtained, which can be fabricated without postprocessing, demonstrated by a series of numerical examples. Further, the proposed method has a rather higher accuracy and efficiency compared with traditional TDFM, when the classical topology optimization methods, such as bidirectional evolutionary structural optimization (BESO) and solid isotropic material with penalization (SIMP) method, are taken as benchmark.

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Level-set methods for structural topology optimization: a review

Cited by 751 publications

References 165 publications

Bounds for decoupled design and analysis discretizations in topology optimization

Bounds for decoupled design and analysis discretizations in topology optimization

Heat Exchanger Design with Topology Optimization

An Efficient Topology Description Function Method Based on Modified Sigmoid Function

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