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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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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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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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基于可拓论的不相容问题求解研究

杨春燕

《中国工程科学》 2007年第9卷第10期页码 36-39

摘要：

以单特征不相容问题及其解变换的研究为基础，探讨多特征不相容问题的结构、判断方法和求解方法，并以在市场营销中的应用为例说明其应用价值。这一研究将为矛盾问题的智能化处理提供新的工具。

关键词：不相容问题相容度函数解变换可拓集合

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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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Operating mechanism and set pair analysis model of a sustainable water resources system

Chaoyang DU,Jingjie YU,Huaping ZHONG,Dandan WANG

《环境科学与工程前沿（英文）》 2015年第9卷第2期页码 288-297 doi: 10.1007/s11783-014-0642-4

摘要： There is no alternative to the world’s water resources, and their increasing scarcity is making it difficult to meet the world population’s water needs. This paper presents a sustainable water resources system (SWRS) and analyzes the operating mechanism that makes it possible to evaluate the status of such a system. A SWRS can be described as a complex coupling system that integrates water resources, social, economic and ecological systems into a whole. The SWRS’s operating mechanism is composed of dynamic, resistance and coordination components, and it interacts with and controls the system’s evolution process. The study introduces a new approach, set pair analysis theory, to measure the state of a SWRS, and an evaluation index system is established using the subsystems and operating mechanism of a SWRS. The evaluation index system is separated into three levels (goal level, criteria level and index level) and divides the index standard into five grades. An evaluation model of the SWRS based on set pair analysis theory is constructed, and an example of SWRS evaluation in Shanghai is presented. The connection degrees of the index in the three levels are calculated, and the connection degree of the goal index is calculated to be 0.342, which classifies the city’s SWRS condition as grade 2. The sustainable use of water resources in the region is determined to be at a relatively adequate level that meets the requirements of sustainable development.

关键词： sustainable water resources system operating mechanism set pair analysis model Shanghai

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Application of python-based Abaqus preprocess and postprocess technique in analysis of gearbox vibration and noise reduction

Guilian YI, Yunkang SUI, Jiazheng DU

《机械工程前沿（英文）》 2011年第6卷第2期页码 229-234 doi: 10.1007/s11465-011-0128-z

摘要：

To reduce vibration and noise, a damping layer and constraint layer are usually pasted on the inner surface of a gearbox thin shell, and their thicknesses are the main parameters in the vibration and noise reduction design. The normal acceleration of the point on the gearbox surface is the main index that can reflect the vibration and noise of that point, and the normal accelerations of different points can reflect the degree of the vibration and noise of the whole structure. The K-S function is adopted to process many points’ normal accelerations as the comprehensive index of the vibration characteristics of the whole structure, and the vibration acceleration level is adopted to measure the degree of the vibration and noise. Secondary development of the Abaqus preprocess and postprocess on the basis of the Python scripting programming automatically modifies the model parameters, submits the job, and restarts the analysis totally, which avoids the tedious work of returning to the Abaqus/CAE for modifying and resubmitting and improves the speed of the preprocess and postprocess and the computational efficiency.

关键词： Abaqus secondary development Python language vibration and noise reduction K-S function vibration acceleration level

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Characteristics of plankton Hg bioaccumulations based on a global data set and the implications for aquatic

《环境科学与工程前沿（英文）》 2022年第16卷第3期 doi: 10.1007/s11783-021-1471-x

摘要：

• Hg bioaccumulation by phytoplankton varies among aquatic ecosystems.

关键词： Plankton Hg bioaccumulation Physiological characteristics A cross-system analysis Nutrient compositions Global data set

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The research on structural damage identification using rough set and integrated neural network

Juelong LI, Hairui LI, Jianchun XING, Qiliang YANG

《机械工程前沿（英文）》 2013年第8卷第3期页码 305-310 doi: 10.1007/s11465-013-0259-5

摘要：

A huge amount of information and identification accuracy in large civil engineering structural damage identification has not been addressed yet. To efficiently solve this problem, a new damage identification method based on rough set and integrated neural network is first proposed. In brief, rough set was used to reduce attributes so as to decrease spatial dimensions of data and extract effective features. And then the reduced attributes will be put into the sub-neural network. The sub-neural network can give the preliminary diagnosis from different aspects of damage. The decision fusion network will give the final damage identification results. The identification examples show that this method can simplify the redundant information to reduce the neural network model, making full use of the range of information to effectively improve the accuracy of structural damage identification.

关键词： rough set integrated neural network damage identification decision making fusion