通过将该半解析解与忽略扩散的数值解进行对比分析，讨论了数值弥散代替物理扩散的条件。
Then this paper studied the effect of diffusion coefficient on concentration distribution and the conditions of substitution with numerical dispersion for physical diffusion.
通过对CRCP微分单元的分析，推导了考虑钢筋与混凝土间及混凝土与地基间非线性粘结-滑移关系的温度应力通用解析解。
Based on the analysis of CRCP differential cell, a general analytic solution considering nonlinear bond-slip relation between steel bar and concrete and that between concrete and base is deducted.
最后，在S-PLUS中进行以上两种回归分析计算，并进行了比较，给出复印机维修信息系统统计解析的结果，得到了数学模型的解。
Finally, I proceed regression analysis with such two method in the S-PLUS, gain the analysis result from the Duplicator Maintaining Information System, and get the solution of the mathematics model.
说明采用七自由度单元的有限元法进行矩形截面简支梁的弯翘分析，有很高的精度，可以代替繁琐的解析解。
The result shows seven-freedom unit finite element method has high precision to analyse simple beam of rectangular section, it can replace complex analytic solution.
基于理论分析建立了第三类边界条件下的煤粒瓦斯扩散方程，并给出了解析解。
The differential equations of coal particle gas diffusion under the third kind boundary condition and its analytical solution have obtained on the basis of theoretical analysis.
分析了梅花形卸线的运动规律；得出了轨迹的解析解，为卸线机的结构设计提供了依据。
Analyze the law of movement of blossom-form unloading wire machine, obtain the analytical solution of locus, the results can be used for designing the construction of the unloaders.
本文用解析法和有限元法分析了连续多支承压杆的稳定性及其近似解与精确解。
This paper analyzes the stability of continuous and multi-support compressed pillars using analysing method and finite element method.
将解析解应用于通行能力分析，结果表明，超车换道率对通行能力的影响较大，为交通管理中某些路段禁止超车换道提供了理论依据。
Applying the analytical solution to analyze the passing capacity, the result indicates that the over taking rate influences the passing capacity, which is .
采用可变长度单摆的力学模型对秋千振荡给出初等分析，采用微扰近似法导出了秋千的非线性参数共振解析解，并进行了讨论。
A variable length simple pendulum model is introduced, elementary analysis and perturbation analytic solution of nonlinear differential equation for parametric resonance are presented.
用简易坐标投影法计算了其位置分析的正、逆解析解。
The forward and inverse analytical solutions of its positional analysis were computed by the use of simple and easy coordinative projection.
运用球面解析理论分析了球面机构的位置正反解，并举例说明输入和输出之间的关系。
The forward and reverse position are analyzed by using the spherical analytic theory, and corresponding numerical examples are also given to show the relations between the inputs and the outputs.
给出了具有抛物形电导率分布的电弧螺旋不稳定性的一个简化线性分析，得到了显式解析解。
A simplified linear analysis of the helical instability of arc plasmas is given. Explicit analytic results are obtained.
通过分析，针对混凝土材料，提出了可给出弹体减速度时间历程解析解的法向膨胀理论。
For concrete material, a normal expansion theory was proposed by which some deceleration about time history of the projectile can be analytically given.
给出了板状介质在重复率泵浦和连续泵浦情况下的温度分布和应力状态的解析解，对板的热效应进行了分析与讨论。
Analytic solutions of temperature and stress distributions in condition of CW and pulse pumping are given. We have analyzed and discussed the thermal distortion in the slab.
一个精确的重富立叶级数解析解用于分析四边形自由的点支横观各向异性平行四边形板的自由振动、屈曲和弯曲。
The accurate double Fourier series analytical solutions are obtained for the free vibration, buckling and bending of Point Supported Anisotropic Skew Plates with four free edges.
通过实例计算，将数值解结果与解析解结果进行比较，数值解结果具有较高精度，为工程实际中的无损检测提供了理论和计算分析依据。
Compared with the analytical results, the numerical results have attained a high precision. The study provides a basis for a theoretical and numerical analysis on defectoscopy.
利用此基本解并考虑桩土位移协调条件，提出了层状地基中单桩扭转变形分析的解析方法；
These solutions are then combined with the displacement compatibility between the pile and the surrounding soil to analyze the torsional behaviour of a single pile.
阐述利用最新提出的同伦分析方法求解有正阻尼的强非线性振动方程，得到了该方程的六阶近似解析解。
In this paper, the sixth-order approximate analytical solutions of the strong nonlinear oscillation with positive damping are obtained by using newly developed homotopy analysis method.
这些结果可直接应用于围岩—支护相互作用分析的已有解析解中，并通过控制围岩边界位移量进行锚杆支护参数设计。
The improved rock mass parameters have been applied to the support action analysis of tensioned and grouted bolts by using the existing analytical solutions.
本文介绍了一种求解地下水流问题的有限分析法，该方法将解析解结合到数值方法中，从而提高了计算精度，改善了稳定性。
This paper introduces a finite analytic method of solving groundwater flow. This method combines analytic solution with numerical method, and can rise computational accuracy and improve the stability.
通过分析，得到了运动学逆解的解析公式。
Analytical expression of inverse solution for kinematics equation is solved.
通过一个有解析解的双层有损同轴绝缘结构模型，验证了方法的有效性。最后，分析了一个换流变压器阀侧绕组典型绝缘结构的极性反转电场变化过程。
The proposed method was verified by a simple model, which has analytical solutions, and used to analyze the pr process of a typical oil-paper insulation structure of converter transformer.
具有一定精度的近似解析解有助于方便分析船舶非线性横摇运动及其稳定性。
An approximate analytical solution with comparative accuracy is helpful in investigating nonlinear rolling of ships and its stability.
在不同地震波作用下，将动液压力解析解与地震荷载同时作用于储罐外墙，进行动力响应分析。
Under the action of the different seismic waves, the analytic solution dynamic fluid pressure and seismic loads acting on the tank wall at the same time to carry out dynamic response analysis.
运用泛函分析和积分方程理论，证明了系统解的存在性与唯一性，得到系统解的解析表达式。
Applying the theory of integral equation and functional analysis, we prove the existence and uniqueness of the system solution to the equation, and get the analytical expression of the solution.
本文采用有限元数值分析方法计算多层圆管的温度场，并把解析解与有限元相结合，提出一种求解其热应力的计算方法。
This paper used the finite element method to compute the temperature field, and combined finite element with analytic solution to develop a calculation of thermal stresses.
把数值解与解析解进行比较，分析了误差及其产生的原因。
The numerical solution and the analytical solution were compared, absolute errors as well as reasons of the errors were analyzed.
应用谐波平衡法对系统三阶非线性微分方程组解析分析，与数值解比较验证了解析解的正确性和有效性。
The method of harmonic balance is applied to study the non-linear dynamic response of the third-order nonlinear partial differentiation system.
本文在分析二阶绕射势产生机理的基础上，提出了二阶绕射势的解析解，从而得到了作用于大直径圆柱上二阶波浪力的协调表达。
On the basis of analysing the mechanism of generation of second-or-der diffraction potential, an exact solution is proposed in this paper.
本文在分析二阶绕射势产生机理的基础上，提出了二阶绕射势的解析解，从而得到了作用于大直径圆柱上二阶波浪力的协调表达。
On the basis of analysing the mechanism of generation of second-or-der diffraction potential, an exact solution is proposed in this paper.
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