查询词典 equivalent relation

According to the entire theory of plastic mechanics,the relationship between equivalent stress and equivalent strain of circular chamber plastic zone in the complex stress state is deduced from nonlinear softening constitutive relation of rock under uniaxial compression.

依据塑性力学全量理论，将岩体单轴压缩的非线性软化本构关系推广，得到复杂应力状态下圆形硐室围岩塑性区的等效应力与等效应变关系；籍以求得应变非线性软化的圆形硐室围岩塑性区半径、弹塑性区应力、应变和位移；进而求得相应情况下的硐室围岩平衡方程、地应力与硐室周边位移关系以及围岩压力方程。

The second chapter is the main part of this paper, in which the formulation of the Riemann boundary value problem of non-normal type on the real axis, the solution method of homogeneous problem, the relation between the two kinds of different derivatives and the inhomogeneous problem will be thoroughly given. In this paper, the solution and the solvability of the Riemann boundary value problem of non-normal type on the real axis will be given. Furthermore, it is shown that the twokinds of derivatives of the function Ψ are existing and equivalent in the case ofthe solution about the original problem, therefore, we get uniformly Hermite interpolatory polynomial. The relation between the two kinds of different derivativesof the function Ψ are similar for smooth closed contours by means of the same proof.

第二章是本文的主要部分，分别给出了实轴上一类非正则型Riemann边值问题的提法、齐次问题的解法、两种导数的关系及非齐次问题的求解，本文运用杜金元教授[11]的方法获得了实轴上非正则型Riemann边值问题的封闭解及可解性条件，且在问题可解的情况下论证了函数Ψ的非切向极限导数和Peano导数存在且相等，从而获得了统一的Hermite插值多项式，同样关于封闭曲线上非正则型Riemann边值问题，采用本文论证方法证得了函数Ψ的非切向极限导数和Peano导数存在且相等，从而较好地统一了[10]、[11]中的Hermite插值多项式。

The superstructure has used the model of elastical constitutive relation; the pile-group foundation has quoted the soil-pile equivalent compound model. It has been analyzed the constitutive relation for soil-pile equivalent compound which regarded as the transversely isotropic body this construction relations, and determined the corresponding elastic constant.

上部结构采用线弹性本构模型，下部群桩基础引用了桩土等效复合体模型，分析了将桩土等效复合体视为横观各向同性体的本构关系，确定了相应的弹性常数。

By discussing the existent equations of mass-velocity relation, the equivalent polar coordinate equation and its Binet equation of the mass-velocity relation are given, and the expressions of the mass-velocity relation and mass-energy relation are given too, which include the forms of superluminal motion.

摘 要：通过讨论已有质速关系的方程形式，给出质速关系的等效极坐标方程及其 Binet 方程，进而给出质速关系及质能关系的几个较为具体的方程形式，包括超光速运动形式。

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。

Satellite ; Layout ; Optimization Algorithm ; Symmetric Group ; Equivalent Relation ; Isomorphism.

人造卫星；布局；最优化算法；对称群；等价关系；同构

This article mainly simulates gradually damage destruction process of rock, major in determinationg the definition of rock three-dimensional damage tensor, simplify to the damage tensor and obtain its engineering calculation method, and obtains the basic expression form of equivalent stress by equivalent stress assumption, symmetrization to the actual stress, thus obtains construction relation of the festival principle of three-dimensional damage rock mass, finally couples elasticity- plasticity with damage in the finite element equation, with reference to elasticity-plasticity gradually degenerated method thought, simulates rock damage to advance gradually the destruction process in finite element method, draws up elasticity - plasticity and damage coupling two-dimension finite element procedure with the C language in the VC contact surface, by simulating experiment destroyed process, acquires destruction image and the axial load distortion curve of model, agreement with the experimental result.

本文主要模拟岩石渐进损伤破坏过程，确定岩石三维损伤张量的定义，对损伤张量进行简化计算并得出其工程计算方法，采用等效应力假设得出有效应力的基本表达形式，对有效应力进行对称化，得出节理损伤岩体的三维本构关系，在有限元方程中实现弹塑性和损伤耦合；借鉴弹塑性渐进退化方法的思想，采用有限元的方法模拟岩石损伤渐进破坏过程，用C++语言在VC界面编制了弹塑性和损伤耦合的二维有限元程序，通过模拟已有的实验破坏过程，得出模型的破坏图像和轴向荷载变形曲线，与实验结果基本一致。

This paper briefs the basic principles of " transitive closure " cluster analysis based on fuzzy equivalent relation and fuzzy ISODATA cluster analysis based on soft division technique, and advances a classification and recognition method by combining K-L transformation and the two fuzzy cluster methods above, which makes full use of the advantages of both cluster methods.

介绍了基于模糊等价关系的"传递包"聚类和基于软划分的模糊ISODATA聚类2种模糊聚类分析方法的基本原理，充分利用2种方法的优点，提出了一种将K-L变换与上述2种模糊聚类方法相结合的分类识别方法。

In the second part, the theory of numerical simulation is introduced, including description of body configuration, elastic-plastic large deformation constitutive equation and finite element formula. It is followed by the derivation of equation from the basic theory of elastic-plastic deformation. The solution to temperature field, thermal stress, thermal strain, equivalent effective stress and equivalent strain is achieved then. In addition, we exposit the relation between machine load and thermal load in coupling analysis.

介绍了物体的构形及其描述，弹塑性大变形的本构方程、有限元列式；并进一步论述了弹塑性变形的基本理论，推导了弹塑性方程组；阐述了温度场的求解、热应力及热应变的理论概要，说明了等效应力与等效应变，并进一步阐明了在热力耦合分析中，机械负荷与温度负荷之间的关系；此外，还简介了Marc AutoForge程序结构的特点。

In the second part we have deduced the microRNA cladograms of 18 species byconstructing fuzzy equivalent relation based on Pearson correlation coefficient,Spearman correlation coefficient and a new definition of sequence distance betweenspecies.

第二部分分别运用Pearson相关系数，Spearman相关系数和物种距离定义构建模糊等价矩阵，由此得到18个物种的分子进化树。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。