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Heterogeneous Smoothed Finite Element Method: Convergence/Superconvergence Proof and Its Performance in High-Contrast Composite Materials SCIE
期刊论文 | 2025 , 126 (3) | INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
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Abstract :

Smoothed Finite Element Method (S-FEM) has been widely used in many engineering simulations. However, there are still a lot of theoretical problems to be solved, especially with regard to composite materials and convergence proof. Based on a novel least-squares approximation and conservation property, we extend S-FEM to heterogeneous materials. Firstly, the orthogonality, Softening Effect, and energy function are checked. Secondly, the interpolation error in the maximum norm is estimated in any dimension. Consequently, we get a theoretical convergence rate which has been sought since the year 2010. When restricted to one-dimensional problems, we construct a special test function to prove the superconvergence: (1) S-FEM flux is exact in the meaning of element-wise integral; (2) numerical flux is exact at some point in each element; (3) physical flux can be quadratically approximated at the center of each element. At last, we present two numerical experiments: (1) conventional S-FEM fails in high-contrast composite materials while our new scheme performs well; (2) our flux converges quadratically.

Keyword :

conservative scheme conservative scheme convergence rate convergence rate interpolation error interpolation error smoothed finite element method smoothed finite element method superconvergence superconvergence weighted least-squares weighted least-squares

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GB/T 7714 Chen, Yun , Liu, Guirong , Cui, Junzhi et al. Heterogeneous Smoothed Finite Element Method: Convergence/Superconvergence Proof and Its Performance in High-Contrast Composite Materials [J]. | INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING , 2025 , 126 (3) .
MLA Chen, Yun et al. "Heterogeneous Smoothed Finite Element Method: Convergence/Superconvergence Proof and Its Performance in High-Contrast Composite Materials" . | INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 126 . 3 (2025) .
APA Chen, Yun , Liu, Guirong , Cui, Junzhi , Zhang, Qiaofu , Wang, Ziqiang . Heterogeneous Smoothed Finite Element Method: Convergence/Superconvergence Proof and Its Performance in High-Contrast Composite Materials . | INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING , 2025 , 126 (3) .
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Domain decomposition peridynamic differential operator for solving singularly perturbed reaction-diffusion problems SCIE
期刊论文 | 2025 , 180 | ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
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A domain decomposition peridynamic differential operator (DD-PDDO) method for singularly perturbed reaction-diffusion problems is constructed. The method first uses the background mesh, such as Shishkin mesh here, to divide the computational domain into nonoverlapping subdomains; then uses PDDO to solve the problem in each subdomain independently; finally uses the continuity of the first-order derivative at the interface as a constraint mechanism to combine the solution of subdomains together. Present method overcomes the disadvantages of the weight function in the original PDDO for determining the interaction domain size at the interface transition points which have a large grid ratio. Numerical examples verify that the DD-PDDO method has stronger stability and higher accuracy than the PDDO method under conditions of large grid ratio.

Keyword :

Domain decomposition Domain decomposition Peridynamic differential operator Peridynamic differential operator Reaction-diffusion equation Reaction-diffusion equation Shishkin mesh Shishkin mesh Singular perturbation Singular perturbation

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GB/T 7714 Wang, Jun , Ruan, Chunlei , Zhou, Feifei et al. Domain decomposition peridynamic differential operator for solving singularly perturbed reaction-diffusion problems [J]. | ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS , 2025 , 180 .
MLA Wang, Jun et al. "Domain decomposition peridynamic differential operator for solving singularly perturbed reaction-diffusion problems" . | ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 180 (2025) .
APA Wang, Jun , Ruan, Chunlei , Zhou, Feifei , Chen, Yun . Domain decomposition peridynamic differential operator for solving singularly perturbed reaction-diffusion problems . | ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS , 2025 , 180 .
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A theoretical proof of superiority of Smoothed Finite Element Method over the conventional FEM SCIE
期刊论文 | 2024 , 169 | ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
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Numerous simulations have shown that Smoothed Finite Element Method (S-FEM) performs better than the standard FEM. However, there is lack of rigorous mathematical proof on such a claim. This task is challenging since there are so many variants of S-FEM and the standard FEM theory in Sobolev space does not work for S-FEM because of the Smoothed Gradient. Another long-standing open problem is to establish the theory of alpha FEM parameter. The alpha FEM could be the most flexible and fastest S-FEM variant. Its energy is even exact if the parameter is fine-tuned. Sothis problem is practical and interesting. By the help of nonlinear essential boundary (geometry), Weyl inequalities (algebra) and matrix differentiation (analysis), this parameter problem leads us to estimate the eigenvalue-gap and energy-gap between S-FEM and FEM. Consequently, we provide a definite answer to the long-standing S-FEM superiority problem in a unified framework. The essential boundary, eigenvalue and energy are linked together by four new necessary and sufficient conditions which are simple, practical and beyond our expectations. The standard S-FEM source code can be reused so it is convenient to numerically implement. Finally, the cantilever and infinite plate with a circular hole are simulated to verify the proof.

Keyword :

Alpha FEM Alpha FEM Eigenvalue problems Eigenvalue problems Matrix calculus Matrix calculus Smoothed Finite Element Method Smoothed Finite Element Method Weyl inequalities Weyl inequalities

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GB/T 7714 Chen, Yun , Liu, Guirong , Cui, Junzhi et al. A theoretical proof of superiority of Smoothed Finite Element Method over the conventional FEM [J]. | ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS , 2024 , 169 .
MLA Chen, Yun et al. "A theoretical proof of superiority of Smoothed Finite Element Method over the conventional FEM" . | ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 169 (2024) .
APA Chen, Yun , Liu, Guirong , Cui, Junzhi , Zhang, Qiaofu , Wang, Ziqiang . A theoretical proof of superiority of Smoothed Finite Element Method over the conventional FEM . | ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS , 2024 , 169 .
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核电厂乏燃料水池温度影响分析
期刊论文 | 2017 , (22) , 176-177 | 科技视界
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Abstract :

在核电厂乏燃料水池中内贮存着大量从核反应堆中卸出的乏燃料组件,这些组件持续释放大量的衰变热,由核电厂相关冷却系统对其持续冷却,防止乏燃料水池水温超过核电厂技术规范限值。为确保在冷却系统临时中断期间乏燃料水池温度控制在电厂规范要求范围内,文中通过对乏燃料水池温度与衰变热和冷却水温度变化关系进行分析,得到乏燃料水池温度影响一般规律和变化趋势,为核电厂相关维修工作提供重要参考和建议。

Keyword :

乏燃料水池 乏燃料水池 分析 分析 核电厂 核电厂 温度 温度

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GB/T 7714 魏兴 , 陈云 . 核电厂乏燃料水池温度影响分析 [J]. | 科技视界 , 2017 , (22) : 176-177 .
MLA 魏兴 et al. "核电厂乏燃料水池温度影响分析" . | 科技视界 22 (2017) : 176-177 .
APA 魏兴 , 陈云 . 核电厂乏燃料水池温度影响分析 . | 科技视界 , 2017 , (22) , 176-177 .
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Shock responses of nanoporous aluminum by molecular dynamics simulations SCIE
期刊论文 | 2017 , 97 , 24-45 | INTERNATIONAL JOURNAL OF PLASTICITY
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We present systematic investigations examining the shock responses of nanoporous aluminum (np-Al) by nonequilibrium molecular dynamics simulations. The dislocation nucleation sites are observed to be concentrated in the low latitude region near the equator of the spherical void surfaces. We propose a continuum wave reflection theory and a resolved shear stress model to explain the distribution of dislocation nucleation sites. The simulations reveals two mechanisms of void collapse: the plasticity mechanism and the internal jetting mechanism. The plasticity mechanism, which leads to transverse collapse of voids, prevails under relatively weaker shocks; the internal jetting mechanism, which leads to longitudinal filling of the void vacuum, plays a more significant role as the shock intensity increases. In addition, we observed that the temperature rises while the pressure drops for tens of picoseconds in the shocked np-Al. This thermodynamic phenomenon is different from that observed in single-crystal Al, where the temperature and pressure immediately reach the Hugoniot constants. The influences of void collapse on spall fracture of np-Al are studied. Under the same loading velocity, the spall strength of np-Al is observed to be lower than that of single-crystal Al; however, the spall resistance is higher in np-Al than in single-crystal Al. This resistance is explained by the combined influences of thermal dissipation and stress attenuation during shock wave propagation in np-Al. (c) 2017 Elsevier Ltd. All rights reserved.

Keyword :

Aluminum Aluminum Dislocations Dislocations Porous material Porous material Shock Shock Void collapse Void collapse

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GB/T 7714 Xiang, Meizhen , Cui, Junzhi , Yang, Yantao et al. Shock responses of nanoporous aluminum by molecular dynamics simulations [J]. | INTERNATIONAL JOURNAL OF PLASTICITY , 2017 , 97 : 24-45 .
MLA Xiang, Meizhen et al. "Shock responses of nanoporous aluminum by molecular dynamics simulations" . | INTERNATIONAL JOURNAL OF PLASTICITY 97 (2017) : 24-45 .
APA Xiang, Meizhen , Cui, Junzhi , Yang, Yantao , Liao, Yi , Wang, Kun , Chen, Yun et al. Shock responses of nanoporous aluminum by molecular dynamics simulations . | INTERNATIONAL JOURNAL OF PLASTICITY , 2017 , 97 , 24-45 .
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数学类本科专业校企合作模式研究
期刊论文 | 2016 , (20) , 37-38 | 高教学刊
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Abstract :

文章从校企合作的意义与模式入手,分析我校数学类本科专业的校企合作现状,提出校企合作的设想及实践。

Keyword :

实践 实践 数学类本科专业 数学类本科专业 校企合作 校企合作 现状 现状 设想 设想

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GB/T 7714 姜永 , 林玉蕊 , 温永仙 et al. 数学类本科专业校企合作模式研究 [J]. | 高教学刊 , 2016 , (20) : 37-38 .
MLA 姜永 et al. "数学类本科专业校企合作模式研究" . | 高教学刊 20 (2016) : 37-38 .
APA 姜永 , 林玉蕊 , 温永仙 , 林鸿钊 , 连海峰 , 黄习培 et al. 数学类本科专业校企合作模式研究 . | 高教学刊 , 2016 , (20) , 37-38 .
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一种高效的CFD/CSD耦合飞行器多学科优化设计方法 CSCD PKU
期刊论文 | 2014 , 29 (12) , 2898-2904 | 航空动力学报
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Abstract :

建立了一种基于CFD/CSD(computational fluid dynamics/computational structure dynamics)耦合的多学科优化设计方法.该方法采用结构有限元方程进行结构特性分析,同时采用数值求解N-S方程方法获得气动载荷,保证了设计结果的可信性,并采用基于代理模型的优化设计方法解决了采用高精度模型后计算量太大的问题.采用RBF(径向基函数)插值方法进行流固耦合界面数据插值,保证了传递过程中的能量守恒.利用建立的优化设计方法对一典型的翼身组合体进行了气动和结构优化设计,算例表明在满足约束条件的前提下优化后阻力和质量分别减小了5.0%和4.2%,证明了该方法的有效性.

Keyword :

CFD/CSD耦合 CFD/CSD耦合 RBF插值 RBF插值 代理模型 代理模型 多学科优化设计 多学科优化设计 翼身组合体 翼身组合体

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GB/T 7714 左英桃 , 王晓鹏 , 陈云 et al. 一种高效的CFD/CSD耦合飞行器多学科优化设计方法 [J]. | 航空动力学报 , 2014 , 29 (12) : 2898-2904 .
MLA 左英桃 et al. "一种高效的CFD/CSD耦合飞行器多学科优化设计方法" . | 航空动力学报 29 . 12 (2014) : 2898-2904 .
APA 左英桃 , 王晓鹏 , 陈云 , 陈刚 , 高正红 . 一种高效的CFD/CSD耦合飞行器多学科优化设计方法 . | 航空动力学报 , 2014 , 29 (12) , 2898-2904 .
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Dynamic thermo-mechanical coupled response of random particulate composites: A statistical two-scale method SCIE CSCD
期刊论文 | 2014 , 23 (7) | CHINESE PHYSICS B
WoS CC Cited Count: 6
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Abstract :

This paper focuses on the dynamic thermo-mechanical coupled response of random particulate composite materials. Both the inertia term and coupling term are considered in the dynamic coupled problem. The formulation of the problem by a statistical second-order two-scale (SSOTS) analysis method and the algorithm procedure based on the finite-element difference method are presented. Numerical results of coupled cases are compared with those of uncoupled cases. It shows that the coupling effects on temperature, thermal flux, displacement, and stresses are very distinct, and the micro-characteristics of particles affect the coupling effect of the random composites. Furthermore, the coupling effect causes a lag in the variations of temperature, thermal flux, displacement, and stresses.

Keyword :

numerical algorithm numerical algorithm random particulate composites random particulate composites statistical second-order two-scale (SSOTS) analysis method statistical second-order two-scale (SSOTS) analysis method thermo-mechanical coupling effect thermo-mechanical coupling effect

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GB/T 7714 Yang Zi-Hao , Chen Yun , Yang Zhi-Qiang et al. Dynamic thermo-mechanical coupled response of random particulate composites: A statistical two-scale method [J]. | CHINESE PHYSICS B , 2014 , 23 (7) .
MLA Yang Zi-Hao et al. "Dynamic thermo-mechanical coupled response of random particulate composites: A statistical two-scale method" . | CHINESE PHYSICS B 23 . 7 (2014) .
APA Yang Zi-Hao , Chen Yun , Yang Zhi-Qiang , Ma Qiang . Dynamic thermo-mechanical coupled response of random particulate composites: A statistical two-scale method . | CHINESE PHYSICS B , 2014 , 23 (7) .
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一种高效的CFD/CSD耦合飞行器多学科优化设计方法 CQVIP
期刊论文 | 2014 , 29 (12) , 2898-2904 | 航空动力学报
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Abstract :

建立了一种基于CFD/CSD(computational fluid dynamics/computational structure dynamics)耦合的多学科优化设计方法.该方法采用结构有限元方程进行结构特性分析,同时采用数值求解N-S方程方法获得气动载荷,保证了设计结果的可信性,并采用基于代理模型的优化设计方法解决了采用高精度模型后计算量太大的问题.采用RBF(径向基函数)插值方法进行流固耦合界面数据插值,保证了传递过程中的能量守恒.利用建立的优化设计方法对一典型的翼身组合体进行了气动和结构优化设计,算例表明在满足约束条件的前提下优化后阻力和质量分别减小了5.0%和4.2%,证明了该方法的有效性.

Keyword :

CFD/CSD耦合 CFD/CSD耦合 RBF插值 RBF插值 代理模型 代理模型 多学科优化设计 多学科优化设计 翼身组合体 翼身组合体

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GB/T 7714 Zuo, Ying-Tao , Wang, Xiao-Peng , Chen, Yun et al. 一种高效的CFD/CSD耦合飞行器多学科优化设计方法 [J]. | 航空动力学报 , 2014 , 29 (12) : 2898-2904 .
MLA Zuo, Ying-Tao et al. "一种高效的CFD/CSD耦合飞行器多学科优化设计方法" . | 航空动力学报 29 . 12 (2014) : 2898-2904 .
APA Zuo, Ying-Tao , Wang, Xiao-Peng , Chen, Yun , Chen, Gang , Gao, Zheng-Hong . 一种高效的CFD/CSD耦合飞行器多学科优化设计方法 . | 航空动力学报 , 2014 , 29 (12) , 2898-2904 .
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