几何边界条件

RCS of facets of targets coated RAM was resolved by combining Impedance Boundary Condition and Geometric Optics and RCS of those edges were approximated by computing the RCS of edges of impedance wedge through Method of Equivalent Currents.

其中，涂覆目标面元的散射场是通过结合阻抗边界条件和几何光学法而得到；而涂覆目标棱边的散射场则是通过等效电磁流法求解阻抗劈的边缘绕射场近似得到的。

By introducing reasonable fundamental assumptions and the Green strain in orthogonal curvilinear coordinates,geometric equations expressed by the Green strain tensor for solving thin shells with large deformation are derived in this paper.

将正交曲线坐标下的格林应变张量引入到薄壳大变形分析，通过建立恰当的基本假设，直接导出了用格林应变张量表示的壳体变形几何方程，将该方程代入到本构方程，由能量原理得到了小应变非线性变形平衡方程、内力方程和边界条件，在此基础上提出了大应变变形的简化分析方法。

The new schemes hold the main advantages of the DG finite element method: the method can easily handle complicated geometries and the boundary conditions; the method is highly parallelizable.

格式保持了DG有限元方法的优点：易处理复杂的几何区域和边界条件，具有高度的并行性。

Thirdly, according to the development of the frozen soil, the coupling model of single freezing pipe of axial symmetry of temperature field, stress field and moisture migration is put forward firstly. Then, by means of the progressing principle of potential field, the coupling model of temperature field, stress field and moisture migration which is under the condition of the multi-freezing pipes is extended. At last, the energy balance equation, stress balance equation, quality balance equation, geometric equation, physical equation, initial and boundary conditions etc are adopted to give the analytic solution to the problem of plane axial symmetry of single freezing pipe.

第三，在对室内试验和现场实测结果研究的基础上，分析了土体冻结过程中温度场、应力场、水分场耦合原理，并按照冻土体形成发展过程，首先建立了单一冷源冻结轴对称温度、应力、水分场耦合模型；接着利用势场的迭加原理，将单一冷源情况的三场耦合问题推广到多冷源情况的三场耦合；最后根据能量守恒平衡方程、应力平衡方程、质量守恒平衡方程、几何方程、物理方程、初始及边界条件，解出了单一冷源平面轴对称问题的解析解。

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

Considering the real wheel/rail geometry and boundary condition, the distribution of elastic-plastic stress in the rail-joint, the effect of the inclusion and crack in the rail surface on the distribution of elastic-plastic stress in railhead are analyzed by using software ANSYS.

本文以大型有限元软件ANSYS为分析工具，同时考虑车轮和钢轨真实的几何形状及边界条件，分析了钢轨接头位置弹塑性应力场、钢轨表面点状缺陷和条纹状钢轨表面缺陷对钢轨接触应力场的影响。

Using geometrical method to calculate the gravitational deflection of light ray in the static spherically symmetric gravitational field;2. The reflection formulas of the ordinary and extraordinary light are given for determining their reflecting orientation of the wave normal and the light ray .

基于电磁波边界条件，从几何光学的角度，对单轴晶体内表面上光的反射规律进行了分析和讨论，给出了寻常光和非常光波法线和光线反射的公式同时指出了上述结果与由费马原理导出的结果是一致

Establishing a geometric model of pump shaft with Three-dimensional modeling software and considering force condition to determine the boundary Conditions, after a reasonable simplification, then the modeling is inputted for ANSYS strength analysis combined with the traditional strength theoretical calculations of the shaft to get the result of stress and strain calculations and static stress and strain diagram.

应用三维造型软件建立了泵轴的几何模型，经过合理的简化，分析受力情况确定边界条件，在ANSYS软件中进行分析，结合传统的强度理论计算对泵轴的强度进行了计算和求解，得到了应力和应变的计算结果。

For the special boundary condition and geometry profile of meandering river, when water going into together with sediment, the former character will change, such as the superelevation of water surface and the difference of pressure in the centripetal direction.

由于弯道特有的几何特征和边界条件，使得弯道中水流产生水面超高现象，从而在向心方向上产生压力差。

With an actual gymnasium of a long-span spatial steel-cable-membrane hybrid structure as the cal- culation model,both static and dynamic analyses were performed by employing the global analysis for the whole hybrid structure,and the substructural analysis for the truss arch substructure,and the cable-membrane substructure etc.,and the stresses and displacements of structural members were compared during global and substructural analyses.

在复杂的混合结构体系中，结构形态呈三维状态，在荷载作用下具有三维受力特征并呈空间工作'，，〕，结构之间的相互作用越来越不直观。同时，由于一些大跨度空间结构中包含了柔性部分，使结构的几何非线性行为成为必须考虑的因素，从而结构构件的内力改变与边界条件、荷载的变化关系就更加难以估计。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。