查询词典 coulomb

Fourier analysis is used to cast the considered non-linear wave problem with unilateral Coulomb frictional boundaries to a set of algebraic equations with a simple form.

利用Fourier分析方法将非线性Coulomb摩擦接触边界波动问题化为一组代数方程。

Biot's consolidation theory was used to serve as a frame working with the nonlinear elastic model or with elasto-plastic model in the program. Nonlinear elastic model includes Duncan-Zhang model, Gong Xiannan Ko consolidation model and the model proposed in chapter 2. Elasto-plastic model in the program includes Mohr-Coulomb model, Drucker-Prager model and the bounding surface model developed in chapter 3. The program can be used in cases of plane problem and axisymmtric problem.

FOR，针对软土地基的变形特点，该程序以Biot固结理论为框架，可以进行线弹性，非线性弹性和弹塑性的有限元计算，在非线性弹性模型中包括了Duncan—Chang模型、龚晓南Ko固结模型和本文建立的非线性模型，弹塑性模型中包拓了Mohr—Coulomb模型，Drucker—Prager模型以及本文中建立的边界面模型，该程序可以考虑平面问题也可以考虑轴对称问题。

The fine structure Hamiltonian for Hydrogen-like atoms is derived using the nonrelativistic approximation of the Dirac equation for one electron moving in the Coulomb field.

从Coulomb场中运动的电子的Dirac方程出发，取其非相对论极限导出了类氢离子的精细结构哈密顿的表达式。

All the work done is as follows:Firstly, given the impact of the soil gravidity stress on the scale of the vertical drain disturbance, Vesic's column cavity expansion theorem is mended. Then the radius of the plastic zone, the ultimate crowding stress and the soil displacement in the intersection of plastic and elastic areas are deduced when Mohr-Coulomb surrender criterion is adopted. The result of which caters better to the real situation.

本文针对竖井地基的施工扰动效应及固结可靠性做了如下一些工作：首先，考虑土体自重应力对竖井扰动范围的影响，对Vesic圆柱形孔扩张弹塑性理论解进行了修正，采用Mohr-Coulomb屈服准则，得到了弹塑性交界处土体位移、塑性区半径以及最终挤土应力等理论计算公式，修正以后的结果能更好地符合竖井施工的实际情况。

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

On the basis of the achieved result and the effect of stress such as minor principal stress, intermediate principal stress, hydrostatic pressure, stress Lode degree, a generalized hyperbolic failure function adapted naturally with the envelope form of Mohr-Coulomb criterion is proposed for brittle rocks; and a smooth failure function acquired by Yu Maohong is also presented. Thus, a generalized polyaxial strain energy strength criterion is created.

在分析脆性岩石强度的静水压力、中间主应力、最小主应力以及应力Lode角等4种效应的基础上，提出子午面上与Mohr-Coulomb准则包络线自然衔接的广义双曲线型破坏函数及八面体偏平面上光滑角隅型破坏函数，从而建立非线性广义多轴应变能强度准则。

Based on the description of Mohr-Coulomb and Drucker-Prager yield criteria with invariant of stress, a formula for error estimation of unit strain energy between the two stress states is established in the deviatoric plane of the principal stress space, which satisfies M-C and D-P yield criteria respectively. A general procedure to transform M-C material parameters to D-P analysis parameters is obtained.

基于应变比能的概念，在偏平面内建立了分别进入Mohr-Coulomb和Drucker-Prager屈服面时所需形状改变比能的差值公式，获得M-C材料参数向D-P计算参数等效的统一性方案。

In spherical polar coordinates, DRSC potential have supersymmetry and shape invariance for θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrodinger equation with double ring-shaped Coulomb potential are presented. The normalized angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.

本文研究了双环形Coulomb势Schrdinger方程的束缚态精确解，所采用的方法是首先对双环形Coulomb势的Schrdinger方程在球坐标系中进行分离变量，得到相应的角向方程和径向方程；证明双环形Coulomb势在角向和径向具有超对称性和形不变性；根据超对称性和形不变性的性质，获得了角动量量子化条件和束缚态的能谱方程，并将归一化角向波函数用Jacobi多项式表示，将归一化径向波函数用Laguerre多项式函数表示。

According to penetration mechanism of jacked pile, the expansion of a series of spherical cavities in semi-infinite space is used to simulate the process of pile installation; and soil is assumed as Mohr-Coulomb material.

根据静压桩的贯入机制，将沉桩过程模拟为半无限土体中一系列球形孔的连续扩张，土体假定为Mohr-Coulomb材料。

The mechanism of cohesion in the generation of ice rubble and ice ridging, the main factors arc demonstrated and analyzed elementarily. Considering three sea ice ridging process. the cohesion is set up as a function of initial ice thickness, total ice thickness, temperature and salinity, respectively. The theoretic expressions of sea ice cohesion were determined and to be introduced into the Mohr-Coulomb yield criterion.

考虑三种不同情况下的海冰堆积过程，将粘结力分别设为初始冰厚、当前堆积冰厚和海冰温盐的函数，分别建立了海冰粘结力的理论表达式，并将其应用到Mohr-Coulomb屈服准则中，建立了考虑粘结力影响的粘弹-塑性海冰动力学本构模型。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷