数值算法

The square root non-optimal algorithm can keep the shape-defining matrixes of the ellipsoids positive definite, so it is also numerically stable.

平方根非最优椭球集员滤波算法能使椭球形状矩阵保持正定性，因而它也具有较好的数值稳定性。

Combined hourglass control in analysis of cold ring rolling process;2. Recent status and development of real-time measurement and online control technology in cold ring rolling ;3. The influence law of feed rate of idle roll on the quality of end face of ring,axial width spread ratio,roll force,roll moment and metal flow characteristic in cold ring rolling process has been explored through the FEM numerical simulation of the ring with rectangular cross-section based on the elastic-plastic dynamic explicit FEM under the Abaqus software environment.

基于Abaqus/Explicit提供的显式动力学有限元算法，对矩形截面环件冷辗扩进行了有限元数值模拟，揭示了芯辊进给速度对环件冷辗扩过程中环件端面质量、轴向宽展率、辗扩力、辗扩力矩以及金属流动特性的影响规律，并从金属塑性成形原理和塑性加工力学等角度对这些规律进行了合理的解释，从而获得了进给速度对冷辗扩成形的影响规律，为环件冷辗扩在实际应用中进给速度的选择提供了依据，对揭示冷辗扩成形机理也具有十分重要的意义。

The influence law of feed rate of idle roll on the quality of end face of ring,axial width spread ratio,roll force,roll moment and metal flow characteristic in cold ring rolling process has been explored through the FEM numerical simulation of the ring with rectangular cross-section based on the elastic-plastic dynamic explicit FEM under the Abaqus software environment.

基于Abaqus/Explicit提供的显式动力学有限元算法，对矩形截面环件冷辗扩进行了有限元数值模拟，揭示了芯辊进给速度对环件冷辗扩过程中环件端面质量、轴向宽展率、辗扩力、辗扩力矩以及金属流动特性的影响规律，并从金属塑性成形原理和塑性加工力学等角度对这些规律进行了合理的解释，从而获得了进给速度对冷辗扩成形的影响规律，为环件冷辗扩在实际应用中进给速度的选择提供了依据，对揭示冷辗扩成形机理也具有十分重要的意义。

In this dissertation the"Penalty"finite element method was employed to compute the velocity of the three-dimensional flow of power-law fluid in a profile die. In order to decrease the needed computer memory and raise the stability of numerical simulation, a set of decoupled methods such as PFEM, pseudo-body force method and transformation of momentum equation to the elliptic equation was developed to establish the general finite element equations to compute the distributions of velocity and viscoelastic stress of the three-dimensional viscoelastic flow of the Phan ThienTanner fluid in a profile die. During numerical simulation of the extrudate swell of the PTT fluid, the flow in the die and out of the die was analyzed separately, which demands less computer memory.

本文建立了求解挤出口模内幂律流体流动速度场的通用三维罚有限元模型；对于非线性粘弹性的Phan Thien-Tanner流体，为了降低模拟计算对计算机硬件的要求，并使模拟计算更加稳定，采用了一种去耦算法，包括罚有限元方法、拟体力方法和动量方程的椭圆类方程转化方法，并建立了求解速度场和粘弹性应力场的总体有限元方程；对于PTT流体的挤出胀大问题，提出了挤出胀大熔体口模内外分离模拟法，这样可以显著降低数值模拟对计算机硬件的要求。

In this dissertation the"Penalty"finite element method was employed to compute the velocity of the three-dimensional flow of power-law fluid in a profile die. In order to decrease the needed computer memory and raise the stability of numerical simulation, a set of decoupled methods such as PFEM, pseudo-body force method and transformation of momentum equation to the elliptic equation was developed to establish the general finite element equations to compute the distributions of velocity and viscoelastic stress of the three-dimensional viscoelastic flow of the Phan ThienTanner fluid in a profile die. During numerical simulation of the extrudate swell of the PTT fluid, the flow in the die and out of the die was analyzed separately, which demands less computer memory. The key techniques used in numerical simulation of the three-dimensional extrusion from dies such as decision of boundary conditions, creation of initial velocity field, selection of penalty factor, high Weissenberg number problem , regeneration of the free surface were studied in detail.

中文题名聚合物异型材口模挤出三维流动研究副题名外文题名 Study on three-dimensional flow of polymer melts during the process of profile extrusion from dies 论文作者涂志刚导师柳和生包忠诩教授学科专业材料加工工程研究领域\研究方向学位级别博士学位授予单位南昌大学学位授予日期2001 论文页码总数148页关键词挤出成型聚合物材料挤出口模聚合物异型材馆藏号BSLW /2003 /TQ320 /9 本文建立了求解挤出口模内幂律流体流动速度场的通用三维罚有限元模型；对于非线性粘弹性的Phan Thien-Tanner流体，为了降低模拟计算对计算机硬件的要求，并使模拟计算更加稳定，采用了一种去耦算法，包括罚有限元方法、拟体力方法和动量方程的椭圆类方程转化方法，并建立了求解速度场和粘弹性应力场的总体有限元方程；对于PTT流体的挤出胀大问题，提出了挤出胀大熔体口模内外分离模拟法，这样可以显著降低数值模拟对计算机硬件的要求。

In the first part, the SIMPLE algorithm is used to solve the MHD equations and the solutions of MHD equations are presented for the whole free-burning arc, excluding the electrodes. The SIMPLE algorithm has been revised in order to solve MHD equations, and the flow chart is showed.

第一部分：采用标准SIMPLE算法，并作了一些修正，给出了具体的计算步骤和流程图，将其应用于磁流体动力学方程进行数值求解。

The discussion on the gauge problem which is the point at issue in 3D eddy current computation suggests that the FE solution from 〓, V-ψ formulation without gauge is unique.

本文以RFEC缺损响应和检测机理的电磁场数值分析方法为研究对象，在数学模型、算法和计算技术上进行了研究和探讨。

The mechanism of some typical hexapods has been discussed, the advantages and backwards of it have also been analyzed. 2 Workspace analysis is a very important aspect of mechanism analysis.

工作空间是并联机器人机床的重要指标，为了方便、快速地求得并联机构的工作空间，提出了基于并联机构运动学逆解的工作空间极限边界数值搜索算法。

First, we introduce and discuss the various methods of multivariate polynomial interpolation in the literature. Based on this study, we state multivariate Lagrange interpolation over again from algebraic geometry viewpoint:Given different interpolation nodes A1,A2 .....,An in the affine n-dimensional space Kn, and accordingly function values fi(i = 1,..., m), the question is how to find a polynomial p K[x1, x2,...,xn] satisfying the interpolation conditions:where X=(x1,X2,....,xn). Similarly with univariate problem, we have provedTheorem If the monomial ordering is given, a minimal ordering polynomial satisfying conditions (1) is uniquely exsisted.Such a polynomial can be computed by the Lagrange-Hermite interpolation algorithm introduced in chapter 2. Another statement for Lagrange interpolation problem is:Given monomials 1 ,2 ,.....,m from low degree to high one with respect to the ordering, some arbitrary values fi(i= 1,..., m), find a polynomial p, such thatIf there uniquely exists such an interpolation polynomial p{X, the interpolation problem is called properly posed.

文中首先对现有的多元多项式插值方法作了一个介绍和评述，在此基础上我们从代数几何观点重新讨论了多元Lagrange插值问题：给定n维仿射空间K~n中两两互异的点A_1，A_2，…，A_m，在结点A_i处给定函数值f_i(i=1，…，m)，构造多项式p∈K[X_1，X_2，…，X_n]，满足Lagrange插值条件：p=f_i，i=1，…，m (1)其中X=(X_1，X_2，…，X_n)，与一元情形相似地，本文证明了定理满足插值条件(1)的多项式存在，并且按&序&最低的多项式是唯一的，上述多项式可利用第二章介绍的Lagrange-Hermite插值算法求出，Lagrange插值另一种描述是：按序从低到高给定单项式ω_1，ω_2，…，ω_m，对任意给定的f_1，f_2，…，f_m，构造多项式p，满足插值条件：p=sum from i=1 to m=Ai=f_i，i=1，…，m (2)如果插值多项式p存在且唯一，则称插值问题适定。

Base on these functions,we develop nonlinear rescaling methods and carry out the numerical experiments.

数值结果表明该类算法是有效的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。