求解

The convergence of the traditional nonlinear equations is related to the selected initial value, but the convergence of the fixed point method is not related to it.

传统的非线性有限元方程组的数值求解法（牛顿-拉普森迭代法与共轭梯度法）只能求解单值性有限元方程，且其收敛行为与初始值的选择有关，而不动点方法在求解非线性方程组时的收敛行为不受初始值选择的影响，在大范围内是一致收敛的。

Next, we developed direct calculation solvers and flamelet solvers based on OpenFOAM and used them to study and analyzed exactness and limitations of flamelet model in multi-dimensional CFD.

此后，基于OpenFOAM程序开发出多维流场中燃烧问题的直接求解器和火焰面模型求解器，分析了火焰面模型在多维燃烧CFD中的准确性和局限性。

Firstly, dynamic equations?mathematics modal of a fighter and a bomber has been built and some solutions of the dynamic equations have been acquired in the paper. Secondly, a flight simulation vision system has been set up which can display flight status and flight parameters of the simulated airplane.

首先，本文建立某歼击机及某轰炸机的六自由度运动方程的数学模型，并做了一些求解运动方程方法的探讨，在完成运动方程求解的基础上创建模拟视景系统，用于显示飞机的即时位置及飞行姿态和各种飞行参数。

The balancing condition of plane joint-force system is that force polygon must be closed.The graphic solution and AUTO CAD tool of computer can be applied to obtain two forces on a nodepoint fast and accurately,then internal force of truss can be obtained.

摘 要 一个平面汇交力系的平衡条件是其力多边形必须闭合，依其条件，利用图解法和计算机中的AUTO CAD绘图工具，迅速准确地求解一个结点上的两个未知力，并以其类推求解桁架各杆内力。

Overcoming the inability of Forcing Decoupling method, this paper presents a new method-To-Step-Additional-Stiffness method to calculate the translation-torsion coupling seismic response of tile symmetric structures with asymmetrically viscous dampers.

摘要克服强行解耦法不能求解对称结构由于不对称安装粘滞消能器而产生平扭耦合地震作用的不足，提出了一种求解该种情况下的平扭耦合地震反应的新方法－两步附加刚度法。

Then, the differential equations are solved by the Fourier expanding and Hankel integral transform method. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media are obtained. Furthermore, a systematic study on Lamb's problems in transversely isotropic saturated half-space is performed. Integral solutions for surface radial, vertical and tangentical displacements are obtained both in the case of drained surface and in the case of undrained surface excited by vertical and tangentical harmonic resources respectively. Numerical results show the obvious difference between the model of isotropic saturated poroelastic media and that of transversely isotropic saturated poroelastic media.

其次，基于Biot波动理论，在圆柱坐标系下求解了横观各向同性饱和土的Biot波动方程：通过引入位移函数，在圆柱坐标系下将横观各向同性饱和土的Biot波动方程转化为两个解耦的6阶和2阶控制方程，然后根据方位角的Fourier展开和径向Hankel变换，求解波动方程，得到以土骨架位移和孔隙水压力为基本未知量的积分形式一般解，并用一般解给出了饱和土总应力分量的表达式；再以基本解为基础，系统地研究了横观各向同性饱和半空间体的Lamb问题，考虑表面排水或不排水两种情况后，首次得到横观各向同性饱和半空间体在表面竖向和水平谐振力作用的下径向、竖向和周向位移的解析解。

The equation is a Fredholm integral equation of the first kind which is extremely unstable. The solution of this equation is the brightness temperature of target.

本文建立天线模型得到天线温度方程，它是病态的第一类Fredholm积分方程，求解目标亮度温度也即求解这个积分方程。

In the second part,we have mainly discussed the error es-timates of the numerical methods for solving ill-posed problem,including the error estimate of finite-dimensional regulariza-tion method in Chapter 5,and the error estimate of regulariza-tion-spline method for solving Fredholm integral equation ofthe first kind.

在第二部分，我们主要讨论了不适定问题数值方法的误差估计，包括有限维正则化方法求解不适定问题的误差估计以及用样条正则化方法求解第一类Fredholm积分方程的误差估计，两者均是目前还未有的结果。

Finally, based on the fundamental solutions of Biots consolidation of transversely isotropic saturated multi-layered soils, the Fredholm integral equation of second kind for the interaction between transversely isotropic saturated multi-layered soils and rectangular piles is established, the relevant numerical analysis is also carried out.

最后，基于横观各向同性层状饱和地基Biot固结问题的基本解答，建立了横观各向同性层状饱和地基与方形单桩、群桩共同作用问题的第二类Fredholm积分方程，并进行了数值分析与计算；通过将矩形刚性基础基底划分成若干个大小相等的矩形网格，用矩形均布荷载表示网格的基底反力，并利用已获得的横观各向同性层状饱和地基Biot固结问题的基本解来求解每个矩形网格的柔度系数，然后根据刚性基础与层状饱和地基的接触条件和其本身的静力平衡条件，求解分析了横观各向同性层状饱和地基与刚性矩形板的共同作用问题。

In this dissertation, two methods were adopted to build dynamics model for vehicle ride comfort analysis: one is eight freedom vehicle ride comfort differential equation model in which lateral movement of driver and vehicle body was considered. Combined with time domain model of random road input, we got the driver and vehicles moving displacement.

本文采用两种方法建立了车辆平顺性分析的动力学模型：8自由度车辆平顺性分析的微分方程模型，考虑了驾驶员和车体的侧倾，结合随机路面激励的时域模型，在B级路面输入条件下，进行了时域仿真求解，得到车辆和驾驶员在汽车坐标系中各个方位上随时间历程的运动位移；利用ADAMS软件建立的福田小卡汽车，共计596个自由度的三维实体整车虚拟汽车模型，全面地考虑了影响平顺性的各种因素，然后通过对路面功率谱的变换生成适合于ADAMS／Tire的路面文件，实现了整车虚拟样机在随机输入激励下，车辆振动模型的时域仿真求解。

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。