Weak Convergence of Finite Element Method for Stochastic Elastic Equation Driven By Additive Noise

In this paper we study the weak convergence of the semidiscrete and full discrete finite element methods for the stochastic elastic equation driven by additive noise, based on $C^0$ or $C^1$ piecewise polynomials. In order to simplify the analysis of weak convergence, we rewrite the stochastic elastic equation in an abstract problem and the solutions of the semidiscrete and full discrete problems in a unified form. We obtain that the weak order is twice the strong order, both in time and in space. Numerical experiments are carried out to verify the theoretical results.     

基于指数上鞅的统计端到端时延分析

借助有效的端到端时延分析可实现大规模网络的QoS控制,运用统计网络演算理论中最小加代数的卷积运算规则计算端到端时延界日益引起人们的重视.随着网络规模的不断扩大,统计端到端时延界应同时具有良好的可扩展性和一定的紧致性,而目前满足这一要求的理论成果还比较少.通过结合最小加代数的卷积运算规则和Doob不等式,并采用矩母函数(Moment Generating Function,MGF)对到达曲线和服务曲线进行描述,文中给出了一种基于指数上鞅的端到端时延界表达式.该时延界不仅可以线性扩展,而且数值分析结果表明,在相同假设条件下,该时延界比现有的线性时延界具有更好的紧致性.     

A Dynamical Multi-level Scheme for the Burgers Equation: Wavelet and Hierarchical Finite Element

Algorithms issued from the NonLinear Galerkin method have been used in many situations and with different discretizations for the resolution of evolutionary nonlinear equations. The main idea of these methods is to use a splitting of the solution in order to model the equation. According to the splitting of the solution, a splitting of the equation is obtained. The modeling principle is to freeze terms which have a small time variation. In this work we use wavelet discretizations of the 2-D Burgers equations and compare the results with the hierarchical finite elements method. The numerical tests indicate that wavelets give better results than finite elements     

A Single-Step Characteristic-Curve Finite Element Scheme of Second Order in Time for the Incompressible Navier-Stokes Equations

In this paper we present a new single-step characteristic-curve finite element scheme of second order in time for the nonstationary incompressible Navier-Stokes equations. After supplying correction terms in the variational formulation, we prove that the scheme is of second order in time. The convergence rate of the scheme is numerically recognized by computational results.     

Research in the Development of Finite Element Software for Creep Damage Analysis

This paper reports the development of finite element software for creep damage analysis. Creep damage deformation and failure of high temperature structure is a serious problem for power generation and it is even more technically demanding under the current increasing demand of power and economic and sustainability pressure. This paper primarily consists of three parts： （1） the need and the justification of the development of in-house software; （2） the techniques in developing such software for creep damage analysis; （3） the validation of the finite element software conducted under plane stress, plane strain, axisymmetric, and 3 dimensional cases. This paper contributes to the computational creep damage mechanics in general.     

水平定向钻钻架有限元建模与分析

钻架是水平定向钻的主要承载部件,其强度和刚度对钻机能否正常工作影响很大.针对钻架传统设计方法存在的问题,提出利用有限元方法对设计进行校核.对水平定向钻钻进工况进行了分析,确定了有限元分析方案,并利用ANSYS软件建立了钻架有限元模型,在此基础上进行了应力应变分析.分析结果表明,钻架的强度能够满足要求,但部分结构需要改进,例如将单排链传动改为双排链传动.结构改进后重新进行分析,发现钻架强度和应力分布有了明显改善.该方法为钻架设计和优化提供了理论依据,有助于提高设计效率.     

Analysis of a Discontinuous Finite Element Method for the Coupled Stokes and Darcy Problems

The coupled Stokes and Darcy flows problem is solved by the locally conservative discontinuous Galerkin method. Optimal error estimates for the fluid velocity and pressure are derived. This revised version was published online in July 2005 with corrected volume and issue numbers.     

纯电动汽车两挡变速器壳体强度分析与改进

在电动汽车变速器优化设计的研究中,变速器壳体的强度对变速器的传动性能有重要影响.纯电动汽车两挡变速器壳体结构较复杂,且受力极不均匀,难以用传统的解析方法对其进行强度计算.针对上述问题,提出利用有限元法对变速器壳体进行强度分析.研究了两挡变速器的结构及工作原理,计算了极限工况下壳体轴承座载荷,建立了壳体的三维实体模型及有限元模型,得到了壳体的应力分布云图,确定了壳体强度的薄弱环节,并据此提出了改进方案.结果表明:改进后的变速器壳体强度得到了改善,并实现了产品的轻量化,为变速器壳体的设计及生产提供了理论依据.     

结合有限元和非刚体运动估计的左心室应变分析

提出一种直观地分析左心室在心脏收缩期的应变情况的方法.首先利用心脏核磁共振图像数据对左心室进行三维实体建模,再进行有限元单元划分;然后,使用非刚体运动估计算法--单位法线及高斯曲率混合算法,在左心室收缩期相邻时刻的有限元模型表面上寻找最相似单元结点作为对应单元结点,计算各对应结点间的位移,并用α剪枝平均对位移过大的可疑结点进行处理;最后,利用弹塑性力学中应变与位移间的几何关系求解左心室表面各单元结点的应变,获得位移和应变的彩色云图.实验结果表明,该方法能直观、有效地反映左心室表面在整个心脏收缩期的形变情况和应变分布.     

股骨NURBS三维实体重建及有限元分析

研究人体股骨是各个分支学科继续发展的需要,能够对人体骨骼进行精确的重建则是研究的基础和关键,股骨的NURBS实体重建有着重大的意义。本文详细介绍了一种通过逆向工程软件Geomagic与三维CAD软件UG相结合,实现股骨从点云到NURBS曲面到实体的三维模型精确重建方法;最后利用ANSYS对重建模型进行了分析,证明了所建模型的正确性与有效性。     

Fully Discrete Analysis of a Discontinuous Finite Element Method for the Keller-Segel Chemotaxis Model

This paper formulates and analyzes fully discrete schemes for the two-dimensional Keller-Segel chemotaxis model. The spatial discretization of the model is based on the discontinuous Galerkin methods and the temporal discretization is based either on Forward Euler or the second order explicit total variation diminishing (TVD) Runge-Kutta methods. We consider Cartesian grids and prove fully discrete error estimates for the proposed methods. Our proof is valid for pre-blow-up times since we assume boundedness of the exact solution.     

基于AWE的立式加工中心床身优化设计

简要介绍运用PROE和ANSYS Workbench进行床身的有限元分析的方法,对床身的位移场和模态进行了分析,并且根据分析的结果对床身进行了轻量化设计,在保持床身变形基本不变的情况下,显著的减轻了床身的重量,床身的低阶频率也有了一定的改善。     

大型塑料模具钢模块淬火工艺的有限元分析

采用有限元软件MSC Marc模拟大型P20钢模块在复杂淬火工艺下的冷却过程,通过分析淬火过程中的温度变化历程及最终组织分布,为厂方生产的P20钢模块制定合理的淬火工艺.     

Convergence and Optimality of the Adaptive Nonconforming Linear Element Method for the Stokes Problem

In this paper, we analyze the convergence and optimality of a standard adaptive nonconforming linear element method for the Stokes problem. After establishing a special quasi-orthogonality property for both the velocity and the pressure in this saddle point problem, we introduce a new prolongation operator to carry through the discrete reliability analysis for the error estimator. We then use a specially defined interpolation operator to prove that, up to oscillation, the error can be bounded by the approximation error within a properly defined nonlinear approximate class. Finally, by introducing a new parameter-dependent error estimator, we prove the convergence and optimality estimates.