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Computer Modeling in Engineering & Sciences 2024年第2期138卷 1277-1299页

作者： Haonan Li WeiWang Quan Shen linquan yao School of Rail Transportation Soochow UniversitySuzhou215131China Soochow College Soochow UniversitySuzhou215006China

The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational *** to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy ***, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.

关键词： 8-node plane hybrid element Hellinger-Reissner variational principle locking behaviors structural mechanics problems

NEW TREATMENT OF ESSENTIAL BOUNDARY CONDITIONS IN EFG METHOD BY COUPLING WITH RPIM

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Acta Mechanica Solida Sinica 2013年第3期26卷 302-316页

作者： Yang Cao linquan yao Yu Yin School of Mathematical Sciences Soochow University School of Urban Rail Transportation Soochow University

One of major difficulties in the implementation of meshfree methods using the mov- ing least square （MLS） approximation, such as element-free Galerkin method （EFG）, is the im- position of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of meshfree methods based on the radial basis point interpola- tion can satisfy the essential boundary conditions exactly since its approximation function passes through each node in an influence domain and thus its shape functions possess the properties of delta function. In this paper, a coupled element-free Galerkin（EFG）-radial point interpola- tion method （RPIM） is proposed to enhance their advantages and avoid their disadvantages. Discretized equations of equilibrium are obtained in the RPIM region and the EFG region, respectively. Then a collocation approach is introduced to couple the RPIM and the EFG method. This method satisfies the linear consistency exactly and can maintain the stiffness matrix symmetric. Numerical tests show that this method gives reasonably accurate results consistent with the theory.

关键词： meshfree method moving least-squares (ntis) approximation radial point inter-polation method (rpim) coupled method collocation approach

IMPROVED RELAXED POSITIVE-DEFINITE AND SKEW-HERMITIAN SPLITTING PRECONDITIONERS FOR SADDLE POINT PROBLEMS

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Journal of Computational Mathematics 2019年第1期37卷 95-111页

作者： Yang Cao Zhiru Ren linquan yao School of Transportation Nantong UniversityNantong 226019China School of Statistics and Mathematics Central University of Finance and Economics Beijing 100081China School of Urban Rail Transportation Soochow UniversitySuzhou 215006China

We establish a class of improved relaxed positive-definite and skew-Hermitian splitting (IRPSS)preconditioners for saddle point *** preconditioners are easier to be implemented than the relaxed positive-definite and skew-Hermitian splitting (RPSS) preconditioner at each step for solving the saddle point *** study spectral properties and the minimal polynomial of the IRPSS preconditioned saddle point matrix.A theoretical optimal IRPSS preconditioner is also obtained,Numerical results show that our proposed IRPSS preconditioners are convergence rate of the GMRES method superior to the existing ones in accelerating the for solving saddle point problems.

关键词： Saddle point problems Preconditioning RPSS preconditioner Eigenvalues Krylov subspace method

A RELAXED HSS PRECONDITIONER FOR SADDLE POINT PROBLEMS FROM MESHFREE DISCRETIZATION＊

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Journal of Computational Mathematics 2013年第4期31卷 398-421页

作者： Yang Cao linquan yao Meiqun Jiang Qiang Niu School of Transportation Nantong University Nantong 226019 China School of Urban Rail Transportation Soochow University Suzhou 215006 China School of Mathematical Sciences Soochow University Suzhou 215006 China Mathematics and Physics Center Xi 'an Jiaotong-L iverpool University Suzhou 215123 China

In this paper, a relaxed Hermitian and skew-Hermitian splitting （RHSS） preconditioner is proposed for saddle point problems from the element-free Galerkin （EFG） discretization method. The EFG method is one of the most widely used meshfree methods for solving partial differential equations. The RHSS preconditioner is constructed much closer to the coefficient matrix than the well-known HSS preconditioner, resulting in a RHSS fixed-point iteration. Convergence of the RHSS iteration is analyzed and an optimal parameter, which minimizes the spectral radius of the iteration matrix is described. Using the RHSS pre- conditioner to accelerate the convergence of some Krylov subspace methods （like GMRES） is also studied. Theoretical analyses show that the eigenvalues of the RHSS precondi- tioned matrix are real and located in a positive interval. Eigenvector distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are obtained. A practical parameter is suggested in implementing the RHSS preconditioner. Finally, some numerical experiments are illustrated to show the effectiveness of the new preconditioner.

关键词： Meshfree method Element-free Galerkin method Saddle point problems Pre-conditioning HSS preconditioner Krylov subspace method.

强电场作用下简支压电层合梁的非线性动力分析

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固体力学学报 2008年第4期29卷 341-347页

作者：姚林泉王伟苏州大学数学科学学院苏州215006 南京铁道职业技术学院苏州校区苏州215031

研究可移简支压电弯曲层合梁在交变强电场作用下的非线性动力学行为.考虑材料的电致伸缩和电致弹性压电效应以及几何非线性导出压电层合梁的数学模型.导出简支压电执行器的弯曲振动控制方程,并得到它的刚度是关于时间的慢变函数关系.利... 详细信息

研究可移简支压电弯曲层合梁在交变强电场作用下的非线性动力学行为.考虑材料的电致伸缩和电致弹性压电效应以及几何非线性导出压电层合梁的数学模型.导出简支压电执行器的弯曲振动控制方程,并得到它的刚度是关于时间的慢变函数关系.利用非定常振动的渐近理论和Galerkin方法对具有慢变系数的非线性动力方程进行求解,得到了可移简支压电层合梁的动力特征.最后得到了可移压电简支梁的共振频率、固有频率和电场频率三者之间的变化关系以及谐振幅度与作用电场强度的关系.

关键词：压电结构强电场层合梁渐进理论非线性动力分析

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非线性压电效应下压电层合板的弯曲

应用力学学报 2005年第1期22卷 107-110页

作者：姚林泉丁睿苏州大学苏州215006

考虑非线性压电效应,即电致弹性和电致伸缩效应情况下压电层合板的弯曲。从非线性压电方程和几何方程导出了压电层合板合应力、合力矩与应变之间的广义本构关系,这些关系关于电场是非线性的。利用Ritz法和双傅立叶级数得到四边简支对称... 详细信息

考虑非线性压电效应,即电致弹性和电致伸缩效应情况下压电层合板的弯曲。从非线性压电方程和几何方程导出了压电层合板合应力、合力矩与应变之间的广义本构关系,这些关系关于电场是非线性的。利用Ritz法和双傅立叶级数得到四边简支对称压电层合板在高电场作用下的非线性解并进行计算。结果表明,只考虑线性压电效应只能适应于作用电场较低或基础层的刚度比压电层的刚度要大得多的情况。

关键词：电致弹性电致伸缩层合板非线性压电效应压电材料

考虑几何与压电非线性行为压电层合轴对称圆板的精确解

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应用力学学报 2007年第4期24卷 633-636页

作者：姚林泉沈纪苹苏州大学苏州215006

研究可移简支及夹支边界条件下,轴对称压电层合圆板在强电场和机械荷载联合作用下的非线性变形。考虑电致伸缩的非线性压电效应及几何非线性的影响,导出轴对称压电层合圆板的控制方程。通过调整坐标轴的位置对控制方程进行简化,得到关... 详细信息

研究可移简支及夹支边界条件下,轴对称压电层合圆板在强电场和机械荷载联合作用下的非线性变形。考虑电致伸缩的非线性压电效应及几何非线性的影响,导出轴对称压电层合圆板的控制方程。通过调整坐标轴的位置对控制方程进行简化,得到关于挠度和径向力的4阶非线性控制方程。再通过简单的积分并引入无量刚变量将控制方程等价地化为2阶非线性耦合微分方程组。利用幂级数法得到可移简支及夹支边界条件下强电场和均布荷载共同作用时的挠度、径向力及径向位移的幂级数精确解。通过对双、单压电晶片执行器的数值计算及分析,得到电场、外载对于位移、径向力的影响关系。

关键词：几何非线性材料非线性电致伸缩压电层合圆板

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热环境中旋转功能梯度纳米环板的振动分析

应用数学和力学 2020年第11期41卷 1224-1236页

作者：刘旭姚林泉苏州大学轨道交通学院江苏苏州215131

基于非局部弹性理论和Kirchhoff薄板理论,研究了旋转功能梯度纳米环板在热环境中的振动频率.首先,通过Hamilton原理,得到在温度变化和由旋转运动引起的面力作用下旋转功能梯度纳米环板的径向和横向耦合运动微分方程,并以此为依据得到了... 详细信息

基于非局部弹性理论和Kirchhoff薄板理论,研究了旋转功能梯度纳米环板在热环境中的振动频率.首先,通过Hamilton原理,得到在温度变化和由旋转运动引起的面力作用下旋转功能梯度纳米环板的径向和横向耦合运动微分方程,并以此为依据得到了热环境下旋转功能梯度纳米环板的横向振动问题;接着,通过平面应力问题,得到在沿径向分布的离心惯性力和温度应力作用下环板的轴对称中面内力;然后,通过微分求积法对变系数微分方程进行离散并求解;最后,通过数值计算结果分析内外径比、功能梯度参数、旋转速度、非局部参数以及温度对环板无量纲固有频率的影响关系.

关键词：非局部理论功能梯度材料纳米环板微分求积法固有频率

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弹性边界径向功能梯度压电环板面内振动

振动与冲击 2018年第8期37卷 225-237页

作者：胡统号沈纪苹姚林泉苏州大学城市轨道交通学院江苏苏州215131

基于二维线弹性体理论,推导了弹性边界径向功能梯度压电(FGPM)环板面内自由振动的控制微分方程,利用微分求积法(DQM)将控制微分方程和边界条件离散化,得到求解频率的特征方程。假设材料的物性参数按幂函数形式变化,通过数值求解得到了径... 详细信息

基于二维线弹性体理论,推导了弹性边界径向功能梯度压电(FGPM)环板面内自由振动的控制微分方程,利用微分求积法(DQM)将控制微分方程和边界条件离散化,得到求解频率的特征方程。假设材料的物性参数按幂函数形式变化,通过数值求解得到了径向FGPM环板面内自由振动的无量纲频率。考虑了弹性边界和电学开路组合边界条件下径向FGPM环板的梯度指数p、内外径比η、弹性边界的弹性刚度k和压电效应对无量纲频率的影响,最后研究了径向FGPM环板模态特性。

关键词：弹性支撑边界功能梯度环板面内自由振动微分求积法模态特性

钢轨波磨不平顺对弹性车轮车辆动力学的影响分析

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机械设计与制造工程 2023年第3期52卷 1-5页

作者：徐磊吴兵姚林泉苏州大学轨道交通学院江苏苏州215131

为了研究地铁弹性车轮车辆通过钢轨波磨不平顺处的动力学行为,建立了弹性车轮车辆和轨道模型。基于多刚体动力学理论建立车辆系统模型,在传统刚性车轮车辆-轨道耦合模型的基础上,将弹性车轮简化为轮辋与轮芯双质量块,轮箍与轮芯的橡胶... 详细信息

为了研究地铁弹性车轮车辆通过钢轨波磨不平顺处的动力学行为,建立了弹性车轮车辆和轨道模型。基于多刚体动力学理论建立车辆系统模型,在传统刚性车轮车辆-轨道耦合模型的基础上,将弹性车轮简化为轮辋与轮芯双质量块,轮箍与轮芯的橡胶层用弹簧-阻尼进行建模。推导了矩阵形式的车辆-轨道运动方程,分别调查了刚性车轮及弹性车轮经过钢轨波磨处动力学行为。结果表明:短波长波磨比长波长波磨对车辆运行的平稳性影响更大,在特定条件下,轮轨力比长波长波磨增大了约75.8%;在钢轨波磨波长为0.04~0.05 m时轮轨力会有极大值;钢轨波磨波深与轮轨力呈自相关;弹性车轮相较普通刚性车轮有更好的动力学性能。

关键词：弹性车轮钢轨波磨动力学轮轨力加速度

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