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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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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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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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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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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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Application of random set method in a deep excavation: based on a case study in Tehran cemented alluvium

Arash SEKHAVATIAN, Asskar Janalizadeh CHOOBBASTI

《结构与土木工程前沿（英文）》 2019年 第13卷 第1期   页码 66-80 doi: 10.1007/s11709-018-0461-y

摘要： The design of high-rise buildings often necessitates ground excavation, where buildings are in close proximity to the construction, thus there is a potential for damage to these structures. This paper studies an efficient user-friendly framework for dealing with uncertainties in a deep excavation in layers of cemented coarse grained soil located in Tehran, Iran by non-deterministic Random Set (RS) method. In order to enhance the acceptability of the method among engineers, a pertinent code was written in FISH language of FLAC2D software which enables the designers to run all simulations simultaneously, without cumbersome procedure of changing input variables in every individual analysis. This could drastically decrease the computational effort and cost imposed to the project, which is of great importance especially to the owners. The results are presented in terms of probability of occurrence and most likely values of the horizontal displacement at top of the wall at every stage of construction. Moreover, a methodology for assessing the credibility of the uncertainty model is presented using a quality indicator. It was concluded that performing RS analysis before the beginning of every stage could cause great economical savings, while improving the safety of the project.

关键词： uncertainty     reliability analysis     deep excavations     random set method     finite difference method    

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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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A three-dimensional two-level gradient smoothing meshfree method for rainfall induced landslide simulations

Dongdong WANG, Jiarui WANG, Junchao WU, Junjun DENG, Ming SUN

《结构与土木工程前沿（英文）》 2019年 第13卷 第2期   页码 337-352 doi: 10.1007/s11709-018-0467-5

摘要： A three-dimensional two-level gradient smoothing meshfree method is presented for rainfall induced landslide simulations. The two-level gradient smoothing for meshfree shape function is elaborated in the three-dimensional Lagrangian setting with detailed implementation procedure. It is shown that due to the successive gradient smoothing operation without the requirement of derivative computation in the present formulation, the two-level smoothed gradient of meshfree shape function is capable of achieving a given influence domain more efficiently than the standard gradient of meshfree shape function. Subsequently, the two-level smoothed gradient of meshfree shape function is employed to discretize the weak form of coupled rainfall seepage and soil motion equations in a nodal integration format, as provides an efficient three-dimensional regularized meshfree formulation for large deformation rainfall induced landslide simulations. The exponential damage and pressure dependent plasticity relationships are utilized to describe the failure evolution in landslides. The plastic response of soil is characterized by the true effective stress measure, which is updated according to the rotationally neutralized objective integration algorithm. The effectiveness of the present three-dimensional two-level gradient smoothing meshfree method is demonstrated through numerical examples.

关键词： meshfree method     landslide     rainfall     three-dimensional two-level gradient smoothing     nodal integration    

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Reliability assessment of three-dimensional bearing capacity of shallow foundation using fuzzy set theory

Rajarshi PRAMANIK, Dilip Kumar BAIDYA, Nirjhar DHANG

《结构与土木工程前沿（英文）》 2021年 第15卷 第2期   页码 478-489 doi: 10.1007/s11709-021-0698-8

摘要： The aim of this study is to investigate the applicability of reliability theory on surface square/rectangular footing against bearing capacity failure using fuzzy set theory in conjunction with the finite element method. Soil is modeled as a three-dimensional spatially varying medium, where its parameters (cohesion, friction angle, unit weight, etc.) are considered as fuzzy variables that maintain some membership functions. Soil is idealized as an elastic-perfectly plastic material obeying the Mohr–Coulomb failure criterion, where both associated and non-associated flow rules are considered in estimating the ultimate bearing capacity of the footing. The spatial variability of the soil is incorporated for both isotropic and anisotropic fields, which are determined by the values of scales of fluctuation in both the horizontal and vertical directions. A new parameter namely, limiting applied pressure at zero failure probability is proposed, and it indirectly predicts the failure probability of the footing. The effect of the coefficient of variation of the friction angle of the soil on the probability of failure is analyzed, and it is observed that the effect is significant. Furthermore, the effect of the scale of fluctuation on the probability of failure is investigated, and the necessity for considering spatial variability in the reliability analysis is well proven.

关键词： finite element method     square footing     reliability analysis     fuzzy set theory     coefficient of variation     spatial variability    

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M-LFM: a multi-level fusion modeling method for shape−performance integrated digital twin of complex

《机械工程前沿（英文）》 2022年 第17卷 第4期 doi: 10.1007/s11465-022-0708-0

摘要： As a virtual representation of a specific physical asset, the digital twin has great potential for realizing the life cycle maintenance management of a dynamic system. Nevertheless, the dynamic stress concentration is generated since the state of the dynamic system changes over time. This generation of dynamic stress concentration has hindered the exploitation of the digital twin to reflect the dynamic behaviors of systems in practical engineering applications. In this context, this paper is interested in achieving real-time performance prediction of dynamic systems by developing a new digital twin framework that includes simulation data, measuring data, multi-level fusion modeling (M-LFM), visualization techniques, and fatigue analysis. To leverage its capacity, the M-LFM method combines the advantages of different surrogate models and integrates simulation and measured data, which can improve the prediction accuracy of dynamic stress concentration. A telescopic boom crane is used as an example to verify the proposed framework for stress prediction and fatigue analysis of the complex dynamic system. The results show that the M-LFM method has better performance in the computational efficiency and calculation accuracy of the stress prediction compared with the polynomial response surface method and the kriging method. In other words, the proposed framework can leverage the advantages of digital twins in a dynamic system: damage monitoring, safety assessment, and other aspects and then promote the development of digital twins in industrial fields.

关键词： shape−performance integrated digital twin (SPI-DT)     multi-level fusion modeling (M-LFM)     surrogate model     telescopic boom crane     data fusion    

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市场智能经济控制中的统一集方法初探

包极峰,刘扬,贺仲雄

《中国工程科学》 2005年 第7卷 第5期   页码 84-89

摘要： 由于统一集包容了Fuzzy set，Vague set，Extension set，SPA，FEEC等学科，将这些学科中的方法融合起来，提出统一集市场智能经济控制的初步设想，并给出几个应用实例。

关键词： 市场经济     大系统与统一集     控制方法探讨     应用实例    

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Achieving air pollutant emission reduction targets with minimum abatement costs: An enterprise-levelallocation method with constraints of fairness and feasibility

《环境科学与工程前沿（英文）》 2022年 第16卷 第2期 doi: 10.1007/s11783-021-1459-6

摘要：

• Quantification of efficiency and fairness of abatement allocation are optimized.

关键词： Pollutant emission reduction allocation     Emission reduction measures     Total abatement cost     Economic efficiency     Abatement space    

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基于Rough集理论的模糊神经网络构造方法

黄显明,易继锴

《中国工程科学》 2004年 第6卷 第4期   页码 44-50

摘要：

提出了在模糊神经网络中使用Rough集理论进行网络结构设计的方法。由于Rough集理论有强大的数值分析能力，而模糊神经网络具有准确的逼近收敛能力和较高的精度，所以通过两者的结合，可以得到一种可理解性好、计算简单、收敛速度快的神经网络模型。这种网络构造方法的主要过程为：首先，利用Rough集理论对给定数据集进行规则获取；然后，根据这些规则构造模糊神经网络各层的神经元个数及相关参数初始值；最后，用BP算法迭代求出网络的各种参数，完成网络的设计。给出了一个二维非线性函数拟合的实例，进一步验证了方法的正确性。

关键词： 模糊神经网络     Rough集     规则获取     函数拟合    

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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

Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Manman XU, Shuting WANG, Xianda XIE

期刊论文

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

Yingjun WANG,David J. BENSON

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

Conceptual design of compliant mechanisms using level set method

Shi-kui CHEN, Michael Yu WANG

期刊论文

Application of random set method in a deep excavation: based on a case study in Tehran cemented alluvium

Arash SEKHAVATIAN, Asskar Janalizadeh CHOOBBASTI

期刊论文

Isogeometric analysis based on geometric reconstruction models

期刊论文

A three-dimensional two-level gradient smoothing meshfree method for rainfall induced landslide simulations

Dongdong WANG, Jiarui WANG, Junchao WU, Junjun DENG, Ming SUN

期刊论文

Reliability assessment of three-dimensional bearing capacity of shallow foundation using fuzzy set theory

Rajarshi PRAMANIK, Dilip Kumar BAIDYA, Nirjhar DHANG

期刊论文

M-LFM: a multi-level fusion modeling method for shape−performance integrated digital twin of complex

期刊论文

市场智能经济控制中的统一集方法初探

包极峰,刘扬,贺仲雄

期刊论文

Achieving air pollutant emission reduction targets with minimum abatement costs: An enterprise-levelallocation method with constraints of fairness and feasibility

期刊论文

基于Rough集理论的模糊神经网络构造方法

黄显明,易继锴

期刊论文