解析法

Advanced numerical simulations were introduced in soil water research,such as finite analysis method,characteristic finite element method,and alternating direction finite element method.

土壤水研究的数值模拟方法也有一些突破，如有限解析法、特征有限元法、交替方向有限元法等。

The basic approach of protecting people from being hurt or killed in an accident is to improve crashworthiness of vehicles. This paper starts with discussing theories and methods for vehicle passive safety design, which included experiential methods, analytic methods, multi-body dynamics methods, crash test methods and the finite element method. Emphasis will be paid to the basic FEM theories and algorithms of impact problems. Topics discussed include the governing equation, element discretization, hourglass control, time integration, material model, shell element algorithms and contact-impact algorithms. For more reliable simulation results, this paper then conducts study on how to accurately get material model parameters by combining the FEM method with experimental method, and develops relevant material test machine and parameter calculating software. Based on that, basic typical impact simulation and test validation study are conducted. On the basis of the above work, the paper studies the thin-shell structures'crashworthiness, which was affected by the following factors: spot-weld features, shell thickness, cross-section and pre-deformation. As to vehicle parts'crashworthiness, the paper conducts simulation study of designing energy-absorbing steering system and adaptive airbag system. A practical energy-absorbing steering wheel is designed as an example. In further depth research, the paper suggests several inverse quantificational methods for vehicle crashworthiness design based on the ideal crash characteristics. The above theories and methods are applied with good results through several practical vehicles' crashworthiness design and improvement.

文中对汽车碰撞安全性的设计理论和方法进行了归类和总结，其中包括经验法、解析法、多刚体动力学法、试验法以及有限元方法等；重点介绍了碰撞有限元法的基本理论和有关算法，涉及到有限元求解控制方程、单元离散、沙漏模态控制、时间积分、材料模型和应力修正、薄壳单元算法以及接触碰撞界面算法等，探讨了有限元计算中的材料模型参数获取技术，开发了相应的材料试验装置及材料模型参数反求软件，在此基础上进行了基本的碰撞仿真算例和试验对比研究；文中通过应用有限元方法研究了薄壁构件的碰撞吸能特性，指出了设计薄壁吸能构件时需要考虑的几个主要影响因素，即焊点、壁厚、横截面和预变形等；在关于车辆部件的碰撞安全性能设计中进行了吸能转向机构和自适应安全气囊的仿真研究，提出了吸能转向机构和自适应安全气囊的仿真研究方法；文中最后探讨了整车碰撞性能的设计与改进方法，提出了以理想碰撞特性为目标，采用分段加速度或者根据碰撞时间进行设计的反推设计法、部件吸能仿真优化设计法等量化设计方法，并通过综合应用文中所讨论的相关技术进行了整车碰撞性能的设计与改进实例研究，所选定的车型是大众化的普通轿车和碰撞安全性基础较差的微型面包车，研究结果表明，本文所提出的设计与改进方法是适用而有效的，具有重要的工程实用意义和价值。

Comprehensively making use of the basic theory, such as Space Analytic Geometry, Gear Meshing Engagement Theory, Method of Mathematical Calculation, Theory for Error Analyzing and Data Processing, the author has established the mathematical models of the new method, which has included the analytic mathematical model for precision orientation, the mathematical model for the ball's diameter and the measuring diameter, the mathematical model about the ball's centre, the calculation model for tooth alignment diviations and the model for tooth alignment error evaluation.

本文综合应用空间解析几何学、啮合原理、计算方法、误差理论与数据处理等有关基础理论，推导建立了新方法的数学模型，包括：确定定位关系的解析法数学模型，测球直径与测量半径的数学模型，测球球心的数学模型，齿向偏差的计算模型以及齿向误差的评定数学模型等。

Many typical problems are studied and compared with boundary collocation method, traditional finite element method and analytical methods. The results indicate that the method is accurate and simple for stress intensity factor computation and is easy to be used in practical engineering.

文中作了大量的裂纹应力强度因子计算，与边界配置法、传统有限元法以及解析法进行了系统的比较，结果表明该方法用于应力强度因子计算不但精度较高，而且简便易行，便于工程实际应用。

Model of water supply networks dynamic simulation is finished through analysis of parameter simulation and characteristic of big city.

深入分析了供水管网动态模型校核方法和影响模型精度的各种影响因素，探讨了简化模型校核过程的原则和方法，在深入剖析灵敏度分析法、解析法和解非线性方程组法等校核方法优缺点的基础上，提出了"最优化方法"作为供水管网系统动态模拟模型校核的基本方法，并以天津市供水管网170个实测点的实测数据对模型进行了校核，使模型达到了预定的精度要求，同时也证实了模型校核方法的适用性。

This semi-analytical method is more accurate then the numerical methods. And it overcome the disadvantage of analysis methods such as conformal mapping, the position of cracks can be random.

此方法属于一种半解析半数值的方法，由于充分利用了解析的结果，因而具有比较高的精度，同时又克服了保角变换等解析法的局限，各裂纹位置可以是任意的。

The present research status of heterotaxy by the excavation of tunnel is introduced, including empirical formula method, numerical method, analytical method and so on.

然后概述了隧道开挖引起地层变位的研究现状，主要包括经验公式法、数值计算法、解析法及其他一些方法。

In this paper the progress in analysis on slope stability by limit equilibrium and finite element methods was introduced.

本文介绍近年在用极限平衡法与有限单元法，分析边坡稳定性方面的一些进展，在基于极限平衡的解析法上，我们导出了多阶斜坡的稳定安全系数与滑裂面角度的计算公式。

The advantages and limitations of every kind of methods for calculating the failure probability is reviewed. The frist order reliability method, the second order reliability method and many kinds of boundary method have achieved remarkable success and formed nature fields of reliability. However, the precision of these methods decrease as the increase of complexity of problem. The numrical methods are versatile, except numerical intergration is only adaptable to special problems which have small number variables and regular intergral domain. Particularly, the advanced variance reduction techniques own the following character: high precision and a small amount computation. But some questions remain to study in the future because only an initial work about these techniqes is developed.

全面评述了计算失效概率各种方法的优点和局限性，其中经典的解析法包括一次可靠性方法、二次可靠性方法、一阶边界法、Vanmarcke上边界、PENT上边界和Ditlevsen二阶窄边界法，这些方法对于多设计点、变量较多且相关、密度函数不是正态以及极限状态方程较复杂的情况，其计算精度较差；而已有的数值方法却是具有较好的通用性，其中除数值积分法只对变量较少、积分域较规则的特殊问题适用外，各种数值模拟方法均具有较广的适应性，特别是各种改进的方差减小技术，精度高、计算量小，但由于其处在研究的初级阶段，还有许多问题有待于解决。

Because of the method of Hamilton semi-analysis solution of the thermo-elastic problem of composite laminates has not any assumptions in the direction of thickness, the continuous conditions of the interlaminated stress and deformation are content. The interlaminated stress and the deformation of the laminates can be obtained through solve the state equations by analysis.

由于复合材料层合板热弹性问题的Hamilton半解析法，在板厚度方向不引入任何假定，保证了层合板层间应力和位移的连续性，通过对状态方程解析求解得到层合板的层间应力和位移。

The reasons of iron ions content overproof in grade Ⅱ desalting water system,such as variation water quality,contamination of regenerant , operation adjustment of pretreatment system and switching operation of bed were discussed.

对二级脱盐水系统中铁离子含量超标的原因，如来水水质发生波动、再生剂受到污染、预处理系统操作调整、床体运行切换等进行了论述。

You were hired to drum up new business, so go and do it.

公司雇你招徕新业务，你就做你的事好了。