Flow of a micropolar fluid through two parallel porous boundaries

The present article contains the numerical solution for steady flow of a micropolar fluid between two porous plates using finite element method. The micropolar fluid fills the space inside the porous plates when the rate of suction at one boundary is equal to the rate of injection at the other boundary. The results for the fluid velocity and microrotation are graphically presented and the influence of micropolar fluid parameter K and parameter R is discussed. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

模糊运算和模糊有限元静力控制方程的求解

根据模糊数的区间形式表达和区间运算的性质,给出了模糊数和模糊变量的运算规则.据此并依据区间有限元理论,提出了结构模糊有限元静力控制方程的几种求解方法.方法可根据输入模糊数的隶属函数,给出结构响应量的可能性分布.且计算量小,易于实施.算例分析说明了方法是实用和可行的.     

流体饱和多孔介质中波传播问题的有限元分析

采用基于混合物理论的多孔介质模型,给出流体饱和两相多孔介质波动问题的有限元分析方法·　采用罚方法导出的有限元动力方程,时间积分可采用显式和隐式积分两种方案·　用编制的有限元程序分析了一维柱体在跃阶载荷和脉冲载荷作用下的波传播问题,得到该两种瞬态载荷作用下固体和流体相位移、速度以及固体相有效应力和孔隙压力随时间的变化关系,并对波的传播现象进行了分析·　所得结果与理论相吻合·     

粘性流体两相多孔介质非线性动力问题的罚有限元法

采用基于混合物理论的多孔介质模型,给出粘性流体饱和两相多孔介质非线性动力问题的控制场方程以及相应边值和初值问题的提法,用Galerkin加权残值法导出罚有限元公式,并给出该非线性方程组的迭代求解方法。考虑了体积分数和渗透率与变形相关的情况。用编制的有限元程序计算分析了一维多孔柱体在脉冲载荷作用下的瞬态响应,数值结果表明文中方法正确有效。     

基于内变量理论的电流变液本构关系

研究了电流变液的微结构本构关系.其理论框架是基于内变量理论和机理的分析.电流变液是由高介电常数的颗粒悬浮在某种液体中组成的.在电场作用下,极化的颗粒将沿着电场方向聚集在一起形成链状结构.颗粒聚集体的大小和方向将随外加电场和应变率的变化进行调整,因而可以通过建立起能量守恒方程和力平衡方程来确定颗粒聚集体的大小和方向的变化.那么,一个三维的、清晰的本构关系可以由相互作用能和系统的耗散能导出.具体考虑和讨论了在简单剪切载荷作用下的系统响应,发现电流变液的切变剪薄粘滞系数同系统Mason数之间近似于幂指数∝(Mn)-082的关系.     

A Posteriori Estimators for the FEM: Analysis of the Robustness of the Estimators for the Poisson Equation

This paper is a summary of our study on estimators for the error in the finite element solution given in [4,5,7,9,10]. We will persent the analysis of estimators for finite element solutions of the Poisson equation in the interior of meshes of triangles with straight edges, as well as the analysis at the boundary.     

Guaranteed velocity error control for the pseudostress approximation of the Stokes equations

The pseudostress approximation of the Stokes equations rewrites the stationary Stokes equations with pure (but possibly inhomogeneous) Dirichlet boundary conditions as another (equivalent) mixed scheme based on a stress in H(div) and the velocity in L². Any standard mixed finite element function space can be utilized for this mixed formulation, e.g., the Raviart‐Thomas discretization which is related to the Crouzeix‐Raviart nonconforming finite element scheme in the lowest‐order case. The effective and guaranteed a posteriori error control for this nonconforming velocity‐oriented discretization can be generalized to the error control of some piecewise quadratic velocity approximation that is related to the discrete pseudostress. The analysis allows for local inf‐sup constants which can be chosen in a global partition to improve the estimation. Numerical examples provide strong evidence for an effective and guaranteed error control with very small overestimation factors even for domains with large anisotropy.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1411–1432, 2016     

Technical Note: A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes

We obtain a computable lower bound on the value of the interior penalty parameters sufficient for the existence of a unique discontinuous Galerkin finite element approximation of a second order elliptic problem. The bound obtained is valid for meshes containing an arbitrary number of hanging nodes and elements of arbitrary nonuniform polynomial order. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

多孔介质瞬态分析中非分裂PML及时域有限元实现

在波场的数值模拟中,完全匹配层(perfectly matched layer,PML)已经被证明是一种十分有效的吸收技术,并得到了广泛的应用.为了解决具有无限域的多孔介质中2阶弹性波动方程数值模拟中的吸收边界问题,提出了一种非分裂格式的PML(non-splitting perfectly matched layer,NPML).首先,基于Biot多孔介质波动理论,建立了以固相和流相位移表示的2阶动力控制方程,其中考虑了固体颗粒和孔隙流体的可压缩性、惯性以及孔隙流体的粘性.其次,根据复伸展坐标变换的定义,通过Laplace变换获得了非分裂格式PML的频域表达式.然后,借助辅助函数将该方程变换到时间域内,得到了一种有效的非分裂PML.最后,基于Galerkin近似方法,给出了其时域有限元计算格式.通过数值算例分析了该非分裂格式的PML在饱和介质动力响应分析中的有效性.     

非均匀Reissner板弯曲的精确元法

本文在阶梯折算法和精确解析法的基础上,提出构造有限元的新方法——精确元法.该方法不用变分原理,可适用于任意变系数正定和非正定偏微分方程.利用该方法,得到Reissuer板弯曲的一个非协调单元,它具有十五个自由度.由于节点位移参数仅含有挠度和转角,因此处理任意边界条件非常容易.文中给出证明,位移和内力均收敛于精确解.由精确元法所得到的单元不仅能用于厚板,也可用于薄板.文末给出四个算例.算例表明,利用本文的方法,可获得满意的结果,并有较高的数值精度.     

An extended beam theory for smart materials applications part I: Extended beam models,duality theory,and finite element simulations

An extended theory for elastic and plastic beam problems is studied. By introducing new dependent and independent variables, the standard Timoshenko beam model is extended to take account of shear variation in the lateral direction. The dynamic governing equations are established via Hamilton's principle, and existence and uniqueness results for the solution of the static problem are proved. Using the theory of convex analysis, the duality theory for the extended beam model is developed. Moreover, the extended theory for rigid-perfectly plastic beams is also established. Based on the extended model, a finite-element method is proposed and numerical results are obtained indicating the usefulness of the extended theory in applications.The work of the first author was supported in part by National Science Foundation under Grant DMS9400565.     

有限元软件中拓扑功能对空心剪力墙的优化设计

利用ANSYS有限元软件中拓扑功能对空心剪力墙进行模拟分析,在保证结构安全的前提下可以大大降低工程制造成本,进一步验证了拓扑功能对结构优化设计的重要作用.     

Numerical simulations of the improved Boussinesq equation

In this study, numerical simulations of the improved Boussinesq equation are obtained using two finite difference schemes and two finite element methods, based on the second‐and third‐order time discretization. The methods are tested on the problems of propagation of a soliton and interaction of two solitons. After the L_∞ error norm is used to measure differences between the exact and numerical solutions, the results obtained by the proposed methods are compared with recently published results. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Numerical solution of a linear elliptic partial differential equation with variable coefficients: A complex variable boundary element approach

This article presents a complex variable boundary element method for the numerical solution of a second order elliptic partial differential equation with variable coefficients. To assess the validity and accuracy of the method, it is applied to solve some specific problems with known solutions. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

On the use of physical spline finite element method for acoustic scattering

This paper presents the comparison of physical spline finite element method (PSFEM), in which differential equations are incorporated into interpolations of basic elements, with least-squares finite element method (LSFEM) and mixed Galerkin finite element method (MGFEM) on the numerical solution of one dimensional Helmholtz equation applied to an acoustic scattering problem. Firstly, all three methods are explained in detail and then it is shown that PSFEM reaches higher precision in a shorter time with fewer nodes than the other methods. It is also observed that this method is well suited for high frequency acoustic problems. Consequently, the results of PSFEM point out better efficiency in terms of number of unknowns and accuracy level.     

引用复变量伪应力函数来解幂硬化材料平面应力问题

本文引用复变量伪应力函数将幂硬化材料平面应力问题的协调方程化为双调和方程,从而使此类有强化材料的弹塑性平面应力问题能像线弹性力学平面问题那样采用复变函数法进行求解.本文推导出了幂硬化材料平面应力问题的应力、应变及位移分量的复变函数表达式,可推广应用于满足全量理论的一股弹塑性平面应力问题.作为算例,文中给出了含圆孔幂硬化材料无限大板单向受拉问题的解答,并和有关文献用摄动法获得的同一问题的渐近解进行了比较.     

Numerical Study of Nonlinear Scattering Characteristics of SH0 Waves Encountering Cracks in Prestressed Plates北大核心CSCD

超声导波因具有传播距离远、能量衰减小等优点在结构健康监测领域中被广泛关注.厘清结构中导波与损伤作用后的散射规律,对于传感器阵列的设计和信号分析均具有重要意义.通过发展的数值方法,研究了受载结构中零阶水平剪切波(SH 0波)与微裂纹作用的接触声非线性作用规律.在双势谱方法的基础上,进一步通过mortar方法将谱单元和有限单元进行了耦合,以充分利用谱元法计算导波传播效率高的优点和有限元在离散复杂结构中的优势.利用该方法计算了板壳结构在自由状态和受载状态下SH 0波与不同角度微裂纹作用的非线性散射场.结果表明,SH 0波与裂纹作用后的二次谐波散射场关于裂纹面近似对称分布,并且单轴预应力不会改变二次谐波散射场的对称性,仍可以通过散射场的分布来确定微裂纹的取向.     

On the problem of superconvergence of finite element method algorithms

The coincidence of an approximate solution to the boundary value problem for an ordinary differential equation with the exact solution at mesh nodes is proved for a certain class of the generalized finite element methods.     

变厚度簿板弯曲问题的任意网格差分解法

本文提出一种求解变厚度薄板弯曲问题的任意网格差分格式,可适应不同边界,各种荷载和复杂形状板.计算实例表明,该方法具有格式简单、通用性强、计算精度高,计算量少等特点.