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Computer Modeling in Engineering & Sciences 2024年第10期141卷 267-280页

作者： Bingrui Ju Wenxiang Sun wenzhen qu Yan Gu Key Laboratory of Road Construction Technology and Equipment of MOE Chang’an UniversityXi’an710018China School of Mathematics and Statistics Qingdao UniversityQingdao266071China

In this study,we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov(EFK)*** temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolson *** temporal discretization,the generalized finite difference method(GFDM)with supplementary nodes is utilized to address the nonlinear boundary value problems at each time *** supplementary nodes are distributed along the boundary to match the number of boundary *** incorporating supplementary nodes,the resulting nonlinear algebraic equations can effectively satisfy the governing equation and boundary conditions of the EFK *** demonstrate the efficacy of our approach,we present three numerical examples showcasing its performance in solving this nonlinear problem.

关键词： Generalized finite difference method nonlinear extended Fisher-Kolmogorov equation Crank-Nicolson scheme

An Effective Meshless Approach for Inverse Cauchy Problems in 2D and 3D Electroelastic Piezoelectric Structures

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Computer Modeling in Engineering & Sciences 2024年第3期138卷 2955-2972页

作者： Ziqiang Bai wenzhen qu Guanghua Wu School of Automation Qingdao UniversityQingdao266071China School of Mathematics and Statistics Qingdao UniversityQingdao266071China Weifang University of Science and Technology Weifang262700China

In the past decade,notable progress has been achieved in the development of the generalized finite difference method(GFDM).The underlying principle of GFDM involves dividing the domain into multiple *** each sub-domain,explicit formulas for the necessary partial derivatives of the partial differential equations(PDEs)can be obtained through the application of Taylor series expansion and moving-least square approximation ***,the method generates a sparse coefficient matrix,exhibiting a banded structure,making it highly advantageous for large-scale engineering *** this study,we present the application of the GFDM to numerically solve inverse Cauchy problems in two-and three-dimensional piezoelectric *** our preliminary numerical experiments,we demonstrate that the proposed GFDMapproach shows great promise for accurately simulating coupled electroelastic equations in inverse problems,even with 3%errors added to the input data.

关键词： Generalized finite difference method meshless method inverse Cauchy problems piezoelectric problems electroelastic analysis

FAST MULTIPOLE SINGULAR BOUNDARY METHOD FOR LARGE-SCALE PLANE ELASTICITY PROBLEMS

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Acta Mechanica Solida Sinica 2015年第6期28卷 626-638页

作者： wenzhen qu Wen Chen State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Center for Numerical Simulation Software in Engineering and SciencesCollege of Mechanics and MaterialsHohai University Department of Mathematics University of North Carolina

The singular boundary method （SBM） is a recent meshless boundary collocation method that remedies the perplexing drawback of fictitious boundary in the method of fundamental solutions （MFS）. The basic idea is to use the origin intensity factor to eliminate singularity of the fundamental solution at source. The method has so far been applied successfully to the potential and elasticity problems. However, the SBM solution for large-scale problems has been hindered by the operation count of O（N^3） with direct solvers or O（N^2） with iterative solvers, as well as the memory requirement of O（N^2）. In this study, the first attempt was made to combine the fast multipole method （FMM） and the SBM to significantly reduce CPU time and memory requirement by one degree of magnitude, namely, O（N）. Based on the complex variable represen- tation of fundamental solutions, the FMM-SBM formulations for both displacement and traction were presented. Numerical examples with up to hundreds of thousands of unknowns have successfully been tested on a desktop computer. These results clearly illustrated that the proposed FMM-SBM was very efficient and promising in solving large-scale plane elasticity problems.

关键词： fast multipole method singular boundary method meshless boundary collocation method elasticity problems

Solution of Two-Dimensional Stokes Flow Problems Using Improved Singular BoundaryMethod

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Advances in Applied Mathematics and Mechanics 2015年第1期7卷 13-30页

作者： wenzhen qu Wen Chen Department of Engineering Mechanics College of Mechanics and MaterialsHohai UniversityNanjing 210098China

In this paper,an improved singular boundarymethod(SBM),viewed as one kind of modified method of fundamental solution(MFS),is firstly applied for the numerical analysis of two-dimensional(2D)Stokes flow *** key issue of the SBM is the determination of the origin intensity factor used to remove the singularity of the fundamental solution and its *** new contribution of this study is that the origin intensity factors for the velocity,traction and pressure are derived,and based on that,the SBM formulations for 2D Stokes flow problems are *** examples are provided to verify the correctness and robustness of the presented *** numerical results clearly demonstrate the potentials of the present SBM for solving 2D Stokes flow problems.

关键词： Singular boundary method origin intensity factor Stokes flow fundamental solution.

EVALUATION OF SINGULAR AND NEARLY SINGULAR INTEGRALS IN THE BEM WITH EXACT GEOMETRICAL REPRESENTATION＊

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Journal of Computational Mathematics 2013年第4期31卷 355-369页

作者： Yaoming Zhang wenzhen qu Yan Gu Institute of Applied Mathematics Shandong University of Technology Zibo 255039 China State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology Dalian 116024 China Center for Numerical Simulation software in Engineering and Sciences Department of Engineering Mechanics Hohai University Nanjing 210098 China

The geometries of many problems of practical interest are created from circular or ellip- tic arcs. Arc boundary elements can represent these boundaries exactly, and consequently, errors caused by representing such geometries using polynomial shape functions can be removed. To fully utilize the geometry of circular boundary, the non-singular boundary integral equations （BIEs） and a general nonlinear transformation technique available for arc elements are introduced to remove or damp out the singular or nearly singular proper- ties of the integral kernels. Several benchmark 2D elastostatic problems demonstrate that the present algorithm can effectively handle singular and nearly singular integrals occur- ring in the boundary element method （BEM） for boundary layer effect and thin-walled structural problems. Owing to the employment of exact geometrical representation, only a small number of elements need to be divided along the boundary and high accuracy can be achieved without increasing other more computational efforts.

关键词： BEM Singular integrals Nearly singular integrals Boundary layer effect Thinwalled structures Exact geometrical representation.

Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals

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Advances in Applied Mathematics and Mechanics 2021年第6期13卷 1398-1417页

作者： wenzhen qu Hongwei Gao Yan Gu School of Mathematics and Statistics Qingdao UniversityQingdaoShandong 266071China Institute of Mechanics for Multifunctional Materials and Structures Qingdao UniversityQingdaoShandong 266071China

In this paper,a high-accuracy numerical scheme is developed for long-time dynamic simulations of 2D and 3D wave propagation *** the derivation of the present approach,the second order time derivative of the physical quantity in the wave equation is treated as a substitution *** on the temporal discretization with the Krylov deferred correction(KDC)technique,the original wave problem is then converted into the modified Helmholtz *** transformed boundary value problem(BVP)in space is efficiently simulated by using the meshless generalized finite difference method(GFDM)with Taylor series after truncating the second and fourth order *** developed scheme is finally verified by four numerical experiments including cases with complicated domains or the temporally piecewise defined source *** results match with the analytical solutions and results by the COMSOL software,which demonstrates that the developed KDC-GFDM can allow large time-step sizes for wave propagation problems in longtime intervals.

关键词： Wave equation Krylov deferred correction technique large time-step long-time simulation,generalized finite difference method

Boundary Element Analysis forModeⅢCrack Problems of Thin-Walled Structures from Micro-to Nano-Scales

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Computer Modeling in Engineering & Sciences 2023年第9期 2677-2690页

作者： Bingrui Ju wenzhen qu Yan Gu School of Mathematics and Statistics Qingdao UniversityQingdao266071China Institute of Mechanics for Multifunctional Materials and Structures Qingdao UniversityQingdao266071China

This paper develops a new numerical framework for modeⅢcrack problems of thin-walled structures by integrating multiple advanced techniques in the boundary element *** details of special crack-tip elements for displacement and stress are *** exponential transformation technique is introduced to accurately calculate the nearly singular integral,which is the key task of the boundary element simulation of thin-walled *** numerical experiments with different types of cracks are provided to verify the performance of the present numerical *** results demonstrate that the present scheme is valid for modeⅢcrack problems of thin-walled structures with the thickness-to-length ratio in the microscale,even nanoscale,regime.

关键词： Boundary element nearly singular integral thin-walled structure mode III crack

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正交各向异性弹性问题的规则化边界元法

固体力学学报 2012年第6期33卷 644-654页

作者：张耀明刘召颜屈文镇山东理工大学理学院淄博255049 大连理工大学工业装备结构分析国家重点实验室大连116024 北京理工大学力学系北京100081

论文致力于平面正交各向异性弹性问题的规则化边界元法研究,提出了新的规则化边界元法的理论和方法.对问题的基本解的特性进行了研究,确立基本解的积分恒等式,提出一种基本解的分解技术,在此基础上,结合转化域积分方程为边界积分方程的... 详细信息

论文致力于平面正交各向异性弹性问题的规则化边界元法研究,提出了新的规则化边界元法的理论和方法.对问题的基本解的特性进行了研究,确立基本解的积分恒等式,提出一种基本解的分解技术,在此基础上,结合转化域积分方程为边界积分方程的极限定理,建立了新颖的规则化边界积分方程.和现有方法比,论文不必将问题变换为各向同性的去处理,从而不含反演运算,也有别于Galerkin方法,无需计算重积分,因此所提方法不仅效率高,而且程序设计简单.特别是,所建方程可计算任何边界位移梯度,进而可计算任意边界应力,而不仅限于面力.数值实施时,采用二次单元和椭圆弧精确单元来描述边界几何,使用不连续插值逼近边界函数.数值算例表明,论文算法稳定、效率高,所取得的边界量数值结果与精确解相当接近.

关键词：边界元法正交各向异性弹性问题间接变量边界积分方程(Indirect Boundary Integral Equation IBIEs) 规则化IBIEs

钛合金球头镀类金刚石碳膜人工髋关节磨屑分析

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解放军医学院学报 2015年第12期36卷 1217-1221页

作者：屈文振廖伟雄张浩李冀王克涛杨以萌李众利解放军总医院骨科北京100853

目的分析钛合金球头镀类金刚石碳（diamond-like carbon,DLC）膜人工髋关节的磨屑特征。方法实验设置3组：进口关节组（A）,钴铬钼合金球头对超高分子量聚乙烯（ultra-high molecular weight polyethylene,UHMWPE）臼杯（CoCrMo-UHMWPE,... 详细信息

目的分析钛合金球头镀类金刚石碳（diamond-like carbon,DLC）膜人工髋关节的磨屑特征。方法实验设置3组：进口关节组（A）,钴铬钼合金球头对超高分子量聚乙烯（ultra-high molecular weight polyethylene,UHMWPE）臼杯（CoCrMo-UHMWPE,Zimmer,America）;镀膜关节组（B）,镀类金刚石碳膜钛合金球头对超高分子量聚乙烯臼杯（Ti-DLC-UHMWPE,京航,中国）;国产关节组（C）,钴铬钼合金球头对超高分子量聚乙烯臼杯（CoCrMo-UHMWPE,京航,中国）。髋关节模拟机运行0.33×10^6转后,收集含有磨屑的小牛血清润滑液,经酸消解过滤后,用扫描电镜-能量色散X线分析仪鉴定滤膜上的磨屑。采用Image-Pro Plus 6.0对电镜图片进行图像分析获取颗粒大小、形状、数量信息,比较各组的差异。结果能量色散X线分析显示磨屑的元素峰主要为碳（C）峰,未见明显的钴（Co）、铬（Cr）、钼（Mo）、钛（Ti）等金属元素峰。各组磨屑60%以上为类球状颗粒,粒径为0.1～40μm,0.1～1μm的颗粒数量较多,1μm以上的颗粒所占体积百分比大;B组滤膜上的磨屑数量少于另外两组。结论实验产生的磨屑主要为超高分子量聚乙烯颗粒;钛合金球头镀类金刚石碳膜人工髋关节可减少磨屑的数量。

关键词：髋假体超高分子量聚乙烯类金刚石碳磨屑

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镁合金压铸用热作模具钢高温磨损特性研究

特种铸造及有色合金 2007年第7期27卷 525-528页

作者：李文珍曲楠清华大学机械工程系

用GWY-2000高温摩擦磨损试验机研究了镁合金压铸常用的热作模具钢DIEVAR、DAC和自主开发的热作模具钢TFHS-1的高温摩擦磨损特性。结果表明,在550℃高温干摩擦情况下,磨损机制以氧化磨损为主,同时伴随着少量粘着磨损、磨粒磨损;TFHS-1钢... 详细信息

用GWY-2000高温摩擦磨损试验机研究了镁合金压铸常用的热作模具钢DIEVAR、DAC和自主开发的热作模具钢TFHS-1的高温摩擦磨损特性。结果表明,在550℃高温干摩擦情况下,磨损机制以氧化磨损为主,同时伴随着少量粘着磨损、磨粒磨损;TFHS-1钢的抗磨损性能要优于DIEVAR和DAC钢;热处理工艺对TFHS-1钢的高温磨损性能有重要影响,回火温度越高,抗磨损性能越好。

关键词：高温磨损氧化磨损热作模具钢镁合金压铸