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Level set band method: A combination of density-based and level set methods for the topology optimization

Peng WEI, Wenwen WANG, Yang YANG, Michael Yu WANG

《机械工程前沿（英文）》 2020年 第15卷 第3期   页码 390-405 doi: 10.1007/s11465-020-0588-0

摘要： The level set method (LSM), which is transplanted from the computer graphics field, has been successfully introduced into the structural topology optimization field for about two decades, but it still has not been widely applied to practical engineering problems as density-based methods do. One of the reasons is that it acts as a boundary evolution algorithm, which is not as flexible as density-based methods at controlling topology changes. In this study, a level set band method is proposed to overcome this drawback in handling topology changes in the level set framework. This scheme is proposed to improve the continuity of objective and constraint functions by incorporating one parameter, namely, level set band, to seamlessly combine LSM and density-based method to utilize their advantages. The proposed method demonstrates a flexible topology change by applying a certain size of the level set band and can converge to a clear boundary representation methodology. The method is easy to implement for improving existing LSMs and does not require the introduction of penalization or filtering factors that are prone to numerical issues. Several 2D and 3D numerical examples of compliance minimization problems are studied to illustrate the effects of the proposed method.

关键词： level set method     topology optimization     density-based method     level set band    

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XFEM schemes for level set based structural optimization

Li LI, Michael Yu WANG, Peng WEI

《机械工程前沿（英文）》 2012年 第7卷 第4期   页码 335-356 doi: 10.1007/s11465-012-0351-2

摘要：

In this paper, some elegant extended finite element method (XFEM) schemes for level set method structural optimization are proposed. Firstly, two- dimension (2D) and three-dimension (3D) XFEM schemes with partition integral method are developed and numerical examples are employed to evaluate their accuracy, which indicate that an accurate analysis result can be obtained on the structural boundary. Furthermore, the methods for improving the computational accuracy and efficiency of XFEM are studied, which include the XFEM integral scheme without quadrature sub-cells and higher order element XFEM scheme. Numerical examples show that the XFEM scheme without quadrature sub-cells can yield similar accuracy of structural analysis while prominently reducing the time cost and that higher order XFEM elements can improve the computational accuracy of structural analysis in the boundary elements, but the time cost is increasing. Therefore, the balance of time cost between FE system scale and the order of element needs to be discussed. Finally, the reliability and advantages of the proposed XFEM schemes are illustrated with several 2D and 3D mean compliance minimization examples that are widely used in the recent literature of structural topology optimization. All numerical results demonstrate that the proposed XFEM is a promising structural analysis approach for structural optimization with the level set method.

关键词： structural optimization     level set method     extended finite element method (XFEM)     computational accuracy and efficiency    

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Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed

Yingjun WANG,David J. BENSON

《机械工程前沿（英文）》 2016年 第11卷 第4期   页码 328-343 doi: 10.1007/s11465-016-0403-0

摘要：

In this paper, an approach based on the fast point-in-polygon (PIP) algorithm and trimmed elements is proposed for isogeometric topology optimization (TO) with arbitrary geometric constraints. The isogeometric parameterized level-set-based TO method, which directly uses the non-uniform rational basis splines (NURBS) for both level set function (LSF) parameterization and objective function calculation, provides higher accuracy and efficiency than previous methods. The integration of trimmed elements is completed by the efficient quadrature rule that can design the quadrature points and weights for arbitrary geometric shape. Numerical examples demonstrate the efficiency and flexibility of the method.

关键词： isogeometric analysis     topology optimization     level set method     arbitrary geometric constraint     trimmed element    

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Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Manman XU, Shuting WANG, Xianda XIE

《机械工程前沿（英文）》 2019年 第14卷 第2期   页码 222-234 doi: 10.1007/s11465-019-0534-1

摘要： Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises. In this study, we develop an isogeometric analysis (IGA)-based level set model for the formulation and solution of topology optimization in cases with maximum eigenfrequency. The proposed method is based on a combination of level set method and IGA technique, which uses the non-uniform rational B-spline (NURBS), description of geometry, to perform analysis. The same NURBS is used for geometry representation, but also for IGA-based dynamic analysis and parameterization of the level set surface, that is, the level set function. The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material. A modal track method, that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization. The validity and efficiency of the proposed method are illustrated by benchmark examples.

关键词： topology optimization     level set method     isogeometric analysis     eigenfrequency    

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Conceptual design of compliant mechanisms using level set method

Shi-kui CHEN, Michael Yu WANG

《机械工程前沿（英文）》 2006年 第1卷 第2期   页码 131-145 doi: 10.1007/s11465-006-0018-y

摘要： We propose a level set method-based framework for the conceptual design of compliant mechanisms. In this method, the compliant mechanism design problem is recast as an infinite dimensional optimization problem, where the design variable is the geometric shape of the compliant mechanism and the goal is to find a suitable shape in the admissible design space so that the objective functional can reach a minimum. The geometric shape of the compliant mechanism is represented as the zero level set of a one-higher dimensional level set function, and the dynamic variations of the shape are governed by the Hamilton-Jacobi partial differential equation. The application of level set methods endows the optimization process with the particular quality that topological changes of the boundary, such as merging or splitting, can be handled in a natural fashion. By making a connection between the velocity field in the Hamilton-Jacobi partial differential equation with the shape gradient of the objective functional, we go further to transform the optimization problem into that of finding a steady-state solution of the partial differential equation. Besides the above-mentioned methodological issues, some numerical examples together with prototypes are presented to validate the performance of the method.

关键词： splitting     minimum     dimensional optimization     Hamilton-Jacobi     topological    

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A regularization scheme for explicit level-set XFEM topology optimization

Markus J. GEISS, Jorge L. BARRERA, Narasimha BODDETI, Kurt MAUTE

《机械工程前沿（英文）》 2019年 第14卷 第2期   页码 153-170 doi: 10.1007/s11465-019-0533-2

摘要： Regularization of the level-set (LS) field is a critical part of LS-based topology optimization (TO) approaches. Traditionally this is achieved by advancing the LS field through the solution of a Hamilton-Jacobi equation combined with a reinitialization scheme. This approach, however, may limit the maximum step size and introduces discontinuities in the design process. Alternatively, energy functionals and intermediate LS value penalizations have been proposed. This paper introduces a novel LS regularization approach based on a signed distance field (SDF) which is applicable to explicit LS-based TO. The SDF is obtained using the heat method (HM) and is reconstructed for every design in the optimization process. The governing equations of the HM, as well as the ones describing the physical response of the system of interest, are discretized by the extended finite element method (XFEM). Numerical examples for problems modeled by linear elasticity, nonlinear hyperelasticity and the incompressible Navier-Stokes equations in two and three dimensions are presented to show the applicability of the proposed scheme to a broad range of design optimization problems.

关键词： level-set regularization     explicit level-sets     XFEM     CutFEM     topology optimization     heat method     signed distance field     nonlinear structural mechanics     fluid mechanics    

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Concurrent optimization of structural topology and infill properties with a CBF-based level set method

Long JIANG, Yang GUO, Shikui CHEN, Peng WEI, Na LEI, Xianfeng David GU

《机械工程前沿（英文）》 2019年 第14卷 第2期   页码 171-189 doi: 10.1007/s11465-019-0530-5

摘要： In this paper, a parametric level-set-based topology optimization framework is proposed to concurrently optimize the structural topology at the macroscale and the effective infill properties at the micro/meso scale. The concurrent optimization is achieved by a computational framework combining a new parametric level set approach with mathematical programming. Within the proposed framework, both the structural boundary evolution and the effective infill property optimization can be driven by mathematical programming, which is more advantageous compared with the conventional partial differential equation-driven level set approach. Moreover, the proposed approach will be more efficient in handling nonlinear problems with multiple constraints. Instead of using radial basis functions (RBF), in this paper, we propose to construct a new type of cardinal basis functions (CBF) for the level set function parameterization. The proposed CBF parameterization ensures an explicit impose of the lower and upper bounds of the design variables. This overcomes the intrinsic disadvantage of the conventional RBF-based parametric level set method, where the lower and upper bounds of the design variables oftentimes have to be set by trial and error. A variational distance regularization method is utilized in this research to regularize the level set function to be a desired distance-regularized shape. With the distance information embedded in the level set model, the wrapping boundary layer and the interior infill region can be naturally defined. The isotropic infill achieved via the mesoscale topology optimization is conformally fit into the wrapping boundary layer using the shape-preserving conformal mapping method, which leads to a hierarchical physical structure with optimized overall topology and effective infill properties. The proposed method is expected to provide a timely solution to the increasing demand for multiscale and multifunctional structure design.

关键词： concurrent topology optimization     parametric level set method     cardinal basis function     shell-infill structure design     conformal mapping    

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Isogeometric analysis based on geometric reconstruction models

《机械工程前沿（英文）》 2021年 第16卷 第4期   页码 782-797 doi: 10.1007/s11465-021-0648-0

摘要： In isogeometric analysis (IGA), the boundary representation of computer-aided design (CAD) and the tensor-product non-uniform rational B-spline structure make the analysis of three-dimensional (3D) problems with irregular geometries difficult. In this paper, an IGA method for complex models is presented by reconstructing analysis-suitable models. The CAD model is represented by boundary polygons or point cloud and is embedded into a regular background grid, and a model reconstruction method is proposed to obtain the level set function of the approximate model, which can be directly used in IGA. Three 3D examples are used to test the proposed method, and the results demonstrate that the proposed method can deal with complex engineering parts reconstructed by boundary polygons or point clouds.

关键词： isogeometric analysis     reconstruction model     level set function     trimmed element     point cloud    

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Calculations of narrow-band transimissities and the Planck mean absorption coefficients of real gasesusing line-by-line and statistical narrow-band models

Huaqiang CHU, Mingyan GU, Huaichun ZHOU, Fengshan LIU

《能源前沿（英文）》 2014年 第8卷 第1期   页码 41-48 doi: 10.1007/s11708-013-0292-4

摘要： Narrow-band transmissivities in the spectral range of 150 to 9300 cm and at a uniform resolution of 25 cm were calculated using the statistical narrow-band (SNB) model with the band parameters of Soufiani and Taine, the more recent parameters of André and Vaillon, and the line-by-line (LBL) method along with the HITEMP-2010 spectroscopic database. Calculations of narrow-band transmissivity were conducted for gas columns of different lengths and containing different isothermal and non-isothermal CO -H O-N mixtures at 1 atm. Narrow-band transmissivities calculated by the SNB model are in large relative error at many bands. The more recent SNB model parameters of André and Vaillon are more accurate than the earlier parameters of Soufiani and Taine. The Planck mean absorption coefficients of CO , H O, CO, and CH in the temperature range of 300 to 2500 K were calculated using the LBL method and different versions of the high resolution transmission (HITRAN) and high-temperature spectroscopic absorption parameters (HITEMP) spectroscopic databases. The SNB model was also used to calculate the Planck mean absorption coefficients of these four radiating gases. The LBL results of the Planck mean absorption coefficient were compared with the classical results of Tien and those from the SNB model.

关键词： transimissity     HITEMP     HITRAN     Planck mean absorption coefficients    

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国外光纤光纤带和带状光缆技术的最新发展

刘良炎

《中国工程科学》 2001年 第3卷 第9期   页码 86-94

摘要：

综合介绍了近年国外关于低衰耗的色散补偿光纤，非零色散位移光纤，用于恶劣环境的碳涂覆和氮化硅涂覆光纤的研究；光纤带制造技术包括光纤带的结构、涂层、性能、生产工艺，大芯数光纤带状光缆包括层绞式松管、中心松管式、骨架式、干缆芯带状光缆的设计制造技术的最新进展。

关键词： 光纤通信     低衰耗光纤     光纤带     光纤带状光缆    

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between office workers’ staying and workstation attributes in a non-territorial office using ultra wide band

Xinnan ZHANG, Takashi IZATO, Junzo MUNENOTO, Daisuke MATSUSHITA, Tetsu YOSHIDA

《结构与土木工程前沿（英文）》 2010年 第4卷 第4期   页码 438-449 doi: 10.1007/s11709-010-0076-4

摘要： This paper investigates the staying and moving characteristics of office workers in a non-territorial office using an ultra wide band (UWB) impulse radio sensor network. The differences between office workers’ staying and moving are clarified according to the individual workstation type that they select. The study determines the characteristics of each type of workstation. By clarifying office workers’ preference for staying and moving with regard to individual workstation types and office worker post, the reasons why office workers in different posts tended to select different types of workstations were revealed. Specifically, leaders tended to select workstations at the “inner meeting corner side” most frequently, as they had a greater need to stay in other areas. In contrast, ordinary staff needed to visit office workers in other areas less often, and as such, they tended to select individual workstations at the “middle meeting corner side.” Barring this, they tended to select individual workstations at the “middle corridor side” or “outer-meeting corner side.” Temporary staff members had little need to visit or stay at other places so they tended to select individual workstations at the “window side,” which is seldom visited or stayed at by other office workers and they could be disturbed less often from their solo work.

关键词： workplace     non-territorial office     staying behavior     ultra wide band (UWB)     sensor network    

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Fluorene-based narrow-band-gap copolymers for red light-emitting diodes and bulk heterojunction photovoltaic

SUN Mingliang, WANG Li, XIA Yangjun, DU Bin, LIU Ransheng, CAO Yong

《化学科学与工程前沿（英文）》 2008年 第2卷 第3期   页码 257-264 doi: 10.1007/s11705-008-0052-x

摘要： A series of narrow band-gap conjugated copolymers (PFO-DDQ) derived from 9,9-dioctylfluorene (DOF) and 2,3-dimethyl-5,8-dithien-2-yl-quinoxalines (DDQ) is prepared by the palladium-catalyzed Suzuki coupling reaction with the molar feed ratio of DDQ at around 1%, 5%, 15%, 30% and 50%, respectively. The obtained polymers are readily soluble in common organic solvents. The solutions and the thin solid films of the copolymers absorb light from 300–590 nm with two absorbance peaks at around 380 and 490 nm. The intensity of 490 nm peak increases with the increasing DDQ content in the polymers. Efficient energy transfer due to exciton trapping on narrow-band-gap DDQ sites has been observed. The PL emission consists exclusively of DDQ unit emission at around 591–643 nm depending on the DDQ content in solid film. The EL emission peaks are red-shifted from 580 nm for PFO-DDQ1 to 635 nm for PFO-DDQ50. The highest external quantum efficiency achieved with the device configuration ITO/PEDOT/PVK/PFO-DDQ15/Ba/Al is 1.33% with a luminous efficiency 1.54 cd/A. Bulk heterojunction photovoltaic cells fabricated from composite films of PFO-DDQ30 copolymer and [6,6]-phenyl C butyric acid methyl ester (PCBM) as electron donor and electron acceptor, respectively in device configuration: ITO/PEDOT:PSS/PFO-DDQ30:PCBM/PFPNBr/Al shows power conversion efficiencies of 1.18% with open-circuit voltage () of 0.90 V and short-circuit current density () of 2.66 mA/cm under an AM1.5 solar simulator (100 mW/cm). The photocurrent response wavelengths of the PVCs based on PFO-DDQ30/PCBM blends covers 300–700 nm. This indicates that these kinds of low band-gap polymers are promising candidates for polymeric solar cells and red light-emitting diodes.

关键词： simulator     Efficient     band-gap     PFO-DDQ50     intensity    

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Maximum independent set in planning freight railway transportation

Gainanov Damir N., Mladenovic NENAD, Rasskazova V. A.

《工程管理前沿（英文）》 2018年 第5卷 第4期   页码 499-506 doi: 10.15302/J-FEM-2018031

摘要：

This work is devoted to the problem of planning of freight railway transportation. We define a special conflict graph on the basis of a set of acceptable train routes. The investigation aims to solve the classical combinatorial optimization problem in relation to the maximum independent set of vertices in undirected graphs. The level representation of the graph and its tree are introduced. With use of these constructions, the lower and upper bounds for the number of vertices in the maximum independent set are obtained.

关键词： independent set     algorithm     planning of transportation     two-sided estimate    

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Controlling nested wrinkle morphology through the boundary effect on narrow-band thin films

Hanyang XU, Tielin SHI, Guanglan LIAO, Qi XIA

《机械工程前沿（英文）》 2019年 第14卷 第2期   页码 235-240 doi: 10.1007/s11465-017-0458-6

摘要： We describe the formation of nested wrinkles created by the thermal mismatch between a narrow-band thin film and a compliant substrate. When a film is described as “narrow-band”, it literally means that the film band width is much shorter than its length; more precisely, it means that the width is comparable with the wavelength of the wrinkles. A silicon mask was used during film sputtering to create narrow-band films on poly (dimethylsiloxane) substrate, thus creating regular boundaries to steer local stresses and control wrinkle morphology. Disordered nano-scale wrinkles were found nested within highly ordered micro-scale sinusoidal wrinkles. The formation of nested wrinkles was explained through the amplitude and wavelength saturation of nano-scale wrinkles. The disordered morphology of nano-scale wrinkles and the highly ordered morphology of micro-scale wrinkles were explained by using the boundary effect.

关键词： nested and hierarchical wrinkles     morphology     amplitude saturation     boundary effect    

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Existence of complete band gaps in 2D steel-water phononic crystal with square lattice

Cunfu HE, Huanyu ZHAO, Ruiju WEI, Bin WU

《机械工程前沿（英文）》 2010年 第5卷 第4期   页码 450-454 doi: 10.1007/s11465-010-0105-y

摘要： This paper theoretically and experimentally studies the existence of complete band gaps in two-dimensional (2D) phononic crystal consisting of parallel steel rods in water with square lattice. The band structure of phononic crystal is calculated by a plane wave expansion (PWE) method. Based on the well-known ultrasonic immersion transmission technique, the overlapping transmission spectra of acoustic waves, a complete band gap, is experimentally measured along the two high-symmetry directions of the first irreducible Brillouin zone. There is a very good agreement between the experimental result and the range of frequencies of the complete band gap.

关键词： phononic crystal     plane wave expansion (PWE) method     experimental study    

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标题 作者 时间 类型 操作

Level set band method: A combination of density-based and level set methods for the topology optimization

Peng WEI, Wenwen WANG, Yang YANG, Michael Yu WANG

期刊论文

XFEM schemes for level set based structural optimization

Li LI, Michael Yu WANG, Peng WEI

期刊论文

Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed

Yingjun WANG,David J. BENSON

期刊论文

Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Manman XU, Shuting WANG, Xianda XIE

期刊论文

Conceptual design of compliant mechanisms using level set method

Shi-kui CHEN, Michael Yu WANG

期刊论文

A regularization scheme for explicit level-set XFEM topology optimization

Markus J. GEISS, Jorge L. BARRERA, Narasimha BODDETI, Kurt MAUTE

期刊论文

Concurrent optimization of structural topology and infill properties with a CBF-based level set method

Long JIANG, Yang GUO, Shikui CHEN, Peng WEI, Na LEI, Xianfeng David GU

期刊论文

Isogeometric analysis based on geometric reconstruction models

期刊论文

Calculations of narrow-band transimissities and the Planck mean absorption coefficients of real gasesusing line-by-line and statistical narrow-band models

Huaqiang CHU, Mingyan GU, Huaichun ZHOU, Fengshan LIU

期刊论文

国外光纤光纤带和带状光缆技术的最新发展

刘良炎

期刊论文

between office workers’ staying and workstation attributes in a non-territorial office using ultra wide band

Xinnan ZHANG, Takashi IZATO, Junzo MUNENOTO, Daisuke MATSUSHITA, Tetsu YOSHIDA

期刊论文

Fluorene-based narrow-band-gap copolymers for red light-emitting diodes and bulk heterojunction photovoltaic

SUN Mingliang, WANG Li, XIA Yangjun, DU Bin, LIU Ransheng, CAO Yong

期刊论文

Maximum independent set in planning freight railway transportation

Gainanov Damir N., Mladenovic NENAD, Rasskazova V. A.

期刊论文

Controlling nested wrinkle morphology through the boundary effect on narrow-band thin films

Hanyang XU, Tielin SHI, Guanglan LIAO, Qi XIA

期刊论文

Existence of complete band gaps in 2D steel-water phononic crystal with square lattice

Cunfu HE, Huanyu ZHAO, Ruiju WEI, Bin WU

期刊论文