Feature-driven topology optimization method with signed distance function

Zhou, Ying; Zhang, Weihong; Zhu, Jihong; Zhao, Xu

doi:10.1016/j.cma.2016.06.027

Cited by 141 publications

(34 citation statements)

References 38 publications

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“…where / , / s , and / t are determined in accordance with Equation (31). According to Equation (12), s / d s i and ∇ s can be calculated as…”

Section: Sensitivity Analysis With Respect To Shape and Topology Varimentioning

confidence: 99%

“…In recent years, great interest arises in a more efficient feature‐driven topology optimization method using implicit features and FE model with fixed mesh. Until now, superellipses, curved skeletons, bars with circular ends, engineering features constructed by means of Boolean operations, and closed B‐spline (CBS) curves have been developed for the definitions of solid and void features. This type of method is a promising approach that reflects the feature design intent of engineers and can easily be implemented in the computer‐aided design (CAD) framework.…”

Section: Introductionmentioning

confidence: 99%

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Concurrent shape and topology optimization involving design‐dependent pressure loads using implicit B‐spline curves

Zhou

Zhang

Zhu

2019

Numerical Meth Engineering

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Summary This work develops a concurrent shape and topology optimization method to solve the design problems of which the pressure loads are applied on designable boundaries. Implicit B‐spline curves including open B‐spline and closed B‐spline are introduced in the form of level‐set functions to act as common design primitives for the description of both moving pressure boundary and inner topology boundaries of a structure. Boolean operations are applied to describe mathematically the shape and topology variations. An artificial nondesignable offset domain of small bandwidth is introduced along the moving pressure boundary to ensure reasonably the imposition of pressure loads on solid materials. The pressure loads are numerically discretized onto the control nodes of finite cell method used for structural analysis with fixed mesh. Sensitivities of design‐dependent pressure loads with respect to both shape and topology design variables are explicitly derived. Numerical problems are finally solved to illustrate the presented method.

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“…where / , / s , and / t are determined in accordance with Equation (31). According to Equation (12), s / d s i and ∇ s can be calculated as…”

Section: Sensitivity Analysis With Respect To Shape and Topology Varimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Concurrent shape and topology optimization involving design‐dependent pressure loads using implicit B‐spline curves

Zhou

Zhang

Zhu

2019

Numerical Meth Engineering

Self Cite

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“…Kang and Wang and Wang et al first introduced design variables (orientation and position variables) defining the layout of embedded components into the level set‐based geometrical representation in topology optimization problems . Recently, several other explicit geometry‐based parameterization schemes have also been studied –. In these methods, the structural geometry is determined by the intersection of some geometry components and is optimized by updating the parameters representing the layout and the shape of these components.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…34,35 Recently, several other explicit geometry-based parameterization schemes have also been studied. [36][37][38][39] In these methods, the structural geometry is determined by the intersection of some geometry components and is optimized by updating the parameters representing the layout and the shape of these components.Despite of the aforementioned advances, the level set-based topology optimization methods still have some limitations that may hinder their applications in engineering structural design. Recently, Sigmund and Maute 3 identified handling multiple constraints as one of the major future challenges of topology optimization (eg, one may need to consider both the material volume constraint and manufacturing constraints 40 ).…”

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confidence: 99%

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A velocity field level set method for shape and topology optimization

Wang

Kang

2018

Numerical Meth Engineering

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Summary In this paper, we propose a new implementation of the level set shape and topology optimization, the velocity field level set method. Therein, the normal velocity field is constructed with specified basis functions and velocity design variables defined on a given set of points that are independent of the finite element mesh. A general mathematical programming algorithm can be employed to find the optimal normal velocities on the basis of the sensitivity analysis. As compared with conventional level set methods, mapping the variational boundary shape optimization problem into a finite‐dimensional design space and the use of a general optimizer makes it more efficient and straightforward to handle multiple constraints and additional design variables. Moreover, the level set function is updated by the Hamilton‐Jacobi equation using the normal velocity field; thus, the inherent merits of the implicit representation is retained. Therefore, this method combines the merits of both the general mathematical programming and conventional level set methods. Integrated topology optimization of structures with embedded components of designable geometries is considered to show the capability of this method to deal with general design variables. Several numerical examples in 2D or 3D design domains illustrate the robustness and efficiency of the method using different basis functions.

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Frequency‐Coded Passive Multifunctional Elastic Metasurfaces

Rong

Zhang

et al. 2020

Adv Funct Materials

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As an emerging material, metasurfaces open the door to a wide range of applications based on ultrasonic and elastic waves. However, most of the existing elastic metasurfaces have a fixed functionality and operate at a fixed frequency, which make them difficult to adapt to changing working requirements and/or environments. Although several recently proposed reconfigurable designs can relax this limitation, they either need laborious tuning or complex active control systems. In this work, by encoding multiple functionalities onto a single metasurface through operation frequencies, passive metasurfaces with switchable multifunctionalities are proposed and realized. Different wave manipulation functions of a single metasurface can be switched from one to another simply by changing the operation frequency. The design of these metasurfaces is realized using a systematic design approach based on topology optimization. Frequency-coded multiple elastic wave manipulation functions, including wave beam steering and focusing, are numerically and experimentally demonstrated. Good agreement between the numerical simulations and experimental measurements is achieved. The proposed design strategy significantly enhances the functionalities and adaptivity of metasurfaces, moving them closer towards real-world applications.

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Feature-driven topology optimization method with signed distance function

Cited by 141 publications

References 38 publications

Concurrent shape and topology optimization involving design‐dependent pressure loads using implicit B‐spline curves

Concurrent shape and topology optimization involving design‐dependent pressure loads using implicit B‐spline curves

A velocity field level set method for shape and topology optimization

Frequency‐Coded Passive Multifunctional Elastic Metasurfaces

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