After the additionalconstraint equations, the constraint-matrix and its complement-matrix are solved, through multi-body system dynamics theory and numerical analysis theory, the basic dynamics equations aresubtracted and the DAB can be changed into pure differential equations by the constraint-matrix-cut method. Therefore the dynamics algorithm of the ngn-tree-shape mechanical system based onthe Kane-Huston d~pamics theory is obtained.
其次，综合应用多体系统动力学和数值分析理论，在解决附加约束方程、约束矩阵及其正交补等问题的基础上，采用约束矩阵编并法缩减基本运动力学方程、求解微分-代数混合方程组，得出了基于凯恩-休斯敦动力学方法的非树型机械系统运动仿真通用算法。
Spectral method is one of important numerical method for solving differential equations.
谱方法是微分方程数值求解的重要方法之一。
Five novel torsion-mirror optical actuators including double-beam thickness differential structure with single torsional axis, double flexible folded-beam structure with single torsional axis, double-beam vertical torsion comb structure with single torsion axis, four-beam differential compound-micromirror structure with double torsional axis and the combined structure of the four basis forms above, are brought forward. All of these devices could be fabricated by the same silicon micromachining process we have developed. The deformation compensation design with local enhancement for the thin torsional beam which is the key structure of these devices is also put forward to improve the reliability. The three-dimension solid model and two-dimension reduced order model of the torsion-mirror optical actuator are established and then the numerical simulations for evaluating the device characteristics of the statics, dynamics, electrostatic field, mechanical and electrostatic coupling, fluid and solid coupling are carried out to optimize the structure design. Furthermore, three optical fibre clamping structures which could be integrated monolithicly are designed and analyzed to improve the optical coupling capability. 4. Three flexible process flows combined with bulk silicon micromachining and surface silicon micromachining are brought forward to fabricate these novel single-crystal silicon or polysilicon torsion-mirror optical actuators by using the same lithography masks for both SOI wafer and regular silicon wafer. A series of important process experiments are carried out to optimize the process parameters and the process flows. Some novel and typical process phenomena which occurred during the microfabrication are analyzed and then the corresponding solutions are put forward. 5. A MEMS dynamic testing system which exploit blur image synthetic technique, stroboscopic image matching technique, stroboscopic mirau microscopic interferometry technique and microscopic laser dopper vibrometer technique is set up to measure three-dimension and six-freedom micro motions of any MEMS devices with nanometer resolution.
在对硅微机械扭转镜光致动器的光机电特性系统地理论研究的基础上提出了硅微机械扭转镜光致动器的结构设计准则。3、提出了单轴双梁厚度差分结构、单轴双柔性折叠梁结构、单轴双梁垂直扭转梳齿结构、双轴四梁差动复合微镜结构以及以上四种基本结构组合后的衍生结构等五种工艺加工技术兼容的新型的硅微机械扭转镜光致动器，对器件关键结构薄厚度、高耐疲劳扭转梁进行了局部加强的变形补偿设计，建立了器件的三维实体模型以及两维降阶模型，对提出的新结构硅微机械扭转镜光致动器进行了系统的静力学、动力学、静电场、力电耦合和流体固体耦合的建模仿真与优化设计，同时设计并分析了三种可实现单芯片集成的弹性光纤定位夹紧结构。4、提出了组合体硅微加工技术与表面硅微加工技术、兼容同一套光刻版图、可分别基于SOI 晶片和普通Si 晶片、适应于制造提出的各种新结构单晶硅和多晶硅硅微机械扭转镜光致动器的三套柔性加工工艺流程，开展了一系列重要工艺步骤的单项工艺试验，对工艺流程与工艺参数进行了优化，针对加工过程中出现的具有普遍意义的典型工艺问题进行了讨论和分析，并提出了解决方法。5、创新性地将模糊图像合成技术、频闪图像匹配技术、频闪Mirau 显微干涉技术与显微激光多普勒测振技术有机结合，建立起了一套周期运动测量与瞬态运动测量相结合、单点运动测量与全视场运动测量相结合、满足不同MEMS 器件各种动态测试要求的集成的MEMS 三维六自由度微运动精密测量系统。
The particle motion differential equation is analysed detailedly and the three-dimensional direct numerical method of particle motion differential equation is established.
论文对颗粒运动微分方程进行详细的分析讨论，建立了三维颗粒运动微分方程的直接模拟数值方法。
This paper is devoted to the application of the parallel multistep hybrid method to the numerical solution for a class of Index-2 differential algebraic equations, and the errors are estimated, it has obtained the extremely ideal result.
将并行多值混合方法应用于一类2-指标微分代数方程的数值处理，并进行误差估计，获得了十分理想的结果。
Four bands Runge - Kutta method for ordinary differential equations, numerical algorithm of the function subroutine.
4阶龙格库塔方法求常微分方程的数值算法的函数子程序。
Setting up mathematic model of slipper pair lubrication film formation through squeezing and making quantificational study Pressure-flow analytical formulas of lubrication film of slipper pairs on LSHT hydraulic motors are put forward on the basis of numerical calculation of Reynolds equation of steady state by finite differential method. The bottom surface of slipper pairs is rectangle, and the effect of squeeze flow and pressure differential flow is considered. The dynamic process of lubrication film formation through squeezing is numerical studied by computer simulation.
本论文的主要研究内容：1、建立了滑靴副油膜挤压形成过程的数学模型和进行了定量分析在数值求解雷诺方程分析矩形平板底面稳态压力场分布规律的基础上，推导出了考虑压差效应和挤压效应的曲轴连杆式低速大扭矩液压马达滑靴副矩形投影底面的压力流量关系，计算机模拟仿真了润滑油膜的挤压形成过程。
Cavities are formed by differential weathering between sandstone and mudstone and they can cause collapse of slopes. Firstly, mechanism of collapse of high slopes is studied from the aspects, such as the topographical features, lithologic characters, combination of structural surfaces, effects of rainfall and the weathering effects. Differential weathering is the main reason for the collapse of high slopes. Secondly, according to field surveys, failure mechanisms of high slope collapse are classified into toppling, sliding, creeping-tension, cantilever-tension and staggered breaking. Sketch maps of failure were generalized according to the failure mechanism. Forming process of collapse is determined by the numerical simulation. The failure process of collapse is mudstone spalling, cavity, sandstone crack opening, tilting of dangerous rock mass, toppling cillapse and rockfall deposite. Lastly, supporting measures were put forward against all the failure modes of high cutting slopes in the Three Gorges area.
由于泥、砂岩风化速度的不同而产生的崩塌灾害现象是三峡库区最为常见的一种地质灾害，首先，从地形地貌、地层岩性、结构面组合、降雨作用和风化作用等方面对软硬互层高切坡的崩塌形成原因进行研究，软硬岩的差异性风化而造成的软岩空腔和硬岩中的结构面组合是造成崩塌的主要原因；其次，基于野外调查的地质现象分析，得到了软硬互层高切坡崩塌主要有倾倒、滑移、塑流拉裂、悬臂拉裂、错断等破坏机制，并概化出了各类破坏示意图；通过离散元数值模拟，对泥砂岩软硬互层高切坡崩塌的形成破坏过程进行了再现和分析，其破坏过程为泥岩剥落-岩腔-砂岩裂隙张开-危岩体弯曲-倾倒崩塌-堆积坡脚；最后，在三峡库区高切坡各类破坏机制的基础上，提出了相应的处治对策。
This book discusses the theory of elliptic differential equations and numerical processing.
本书论述了椭圆型微分方程的理论与数值处理。
ABSTRACT Based on analyzing the flow and heat transfer features of vertical pipe in quench chamber, a numerical model is first presented per to multi-phase turbulent flow theory. The partial differential equations are deduced in detail. The QUICK scheme on uniform grid is employed in discretising these equations and boundary condition.
本文在分析煤气化炉激冷室下降管工作特点的基础上，利用气固两相湍流理论建立了激冷室下降管的数学模型，推导出控制方程组，应用QUICK均分网格格式对控制方程和边界条件进行离散，编制了能进行气固两相流的计算程序。
This program is the numerical differential line drawing algorithm.
本程序实现的是数值微分画线算法。
Numerical and vectorial analysis Differential calculus: multivariable functions.
数值和矢量分析微分：多变量函数。
In order to make a thorough comprehension on the wave filed of complex topography, this dissertation reviewed the relative studies and achievements before at first, followed by a theoretical study on the reflection character of seismic wave from rough interface. Reflection wave field from rough interface is numerically simulated by the finite differential method with high accuracy, as well as that of the complex surface case. On the basis of the comprehensive study, some imaging methods are discussed and a few of proposals are given.
中文题名粗糙界面和复杂地表的地震反射特征研究与数值模拟副题名外文题名 Seismic reflection of rough interface and complex surface and numerical simulation 论文作者孙成禹导师杜世通教授学科专业地球探测与信息技术研究领域研究方向地球物理探测方法与技术学位级别博士学位授予单位石油大学学位授予日期2001 论文页码总数99页关键词粗糙界面复杂地形地震成像地震勘探馆藏号BSLW /2003 /P631.4 /24 为了加深对复杂地表区地震波场的结构、类型和传播规律的了解，探索提高地震成像精度的有效途径，本文在分析国内外已有研究成果的基础上，对于地震波在粗糙界面上的反射特征进行了初步研究；并利用高精度有限差分方法，对其进行了数值模拟和特征分析；随后对复杂地表情况下的地震波场进行数值模拟和综合分析，对成像方法进行了讨论，提出了自己的建议。
They are used to numerical solutions of multiple-dimensionalsingular partial differential equations with different singularities, such as degeneratingcoefficients, singular boundary values and singular source terms.
近年来许多代数学者利用Hopf代数的导出与上导出函子研究分裂积代数与分裂余积余代数，Hopf代数的导出与上导出函子均与不动函子有伴随关系。
The paper applied highorder differential numerical simulation to perform a series of forward numerical simulations for various caves with different sizes and filling material different velocit...
应用高阶差分数值模拟方法，对一系列不同尺度、不同充填物的溶洞模型进行了系列的正演数值模拟，并对具地震反射特征及反射波振幅进行了综合分析。
The elevational images could be obtained by resolving camera parameters and correcting digital images with numerical differential. Throughout image processing, the marks on the undercarriage wheels and airframe were high-accurately tracked and identified based on sub-pixel. The trace, velocity and other parameters of the undercarriage were gained by data processing.
同时，应用摄影测量原理，通过对摄影机的标校，获得了摄影机的参数；利用图像的数字微分纠正原理，对所摄图像进行修正和重建，得到摄影机的正摄影像，进而利用图像处理方法对起落架机轮及机身测量标志进行基于亚像素的跟踪判读；对判读数据进行处理，得到了飞机着陆道面段的运动轨迹、速度等数据。
The Differential Quadrature Method and the Differential Quadrature Element Method are numerical methods developed recently and still under developing. The theory and applications of these two methods in Structural Mechanics are systematically studied in this dissertation. The principles and properties of these two methods are described, studied, and summarized in detail. It is shown that DQM is equivalent to a special kind of mixed collocation method. It is also shown for the first time that DQEM could be regarded as the combinations of the sub-domain method with the special mixed collocation method. The effects of the application of boundary conditions and the selection of grid points on the final results are investigated.
中文题名微分求积法和微分求积单元法副题名外文题名 Differential quadrature method and differential quadrature element method-theory and application 论文作者王永亮导师刘人怀院士学科专业固体力学研究领域研究方向板壳力学计算方法学位级别博士学位授予单位南京航空航天大学学位授予日期2001 论文页码总数142页关键词薄壳薄板结构力学微分求积单元法微分求积法馆藏号BSLW /2003 /O302 /1 微分求积法和微分求积单元法是在近年里发展起来，并正在进一步发展的一种数值计算方法，本文对这两种方法的原理和它们在结构力学中的应用进行了较深入系统地研究。
Introduced Ordinary Differential numerical method, such as Euler, Runge solution, and so on.
主要介绍的常微分方程的数值解法，如欧拉，龙格解法等等。
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。
In this project, we develop the numerical model of the differential quadrature element analysis of beam problems considering the effects of shear deformations. The results demonstrate this method.
在这个计画中我们开发剪变形梁问题的数值积分表示微分元素分析的数值模式，并做数值计算，证明此种方法的优越性。