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求解奇异摄动问题混合有限元的最优一致收敛的统一方法_英文_

有限元分析法英文简介

The finite element analysis Finite element method, the solving area is regarded as made up of many small in the node connected unit (a domain), the model gives the fundamental equation of sharding (sub-domain) approximation solution, due to the unit (a domain) can be divided into various shapes and sizes of different size, so it can well adapt to the complex geometry, complex material properties and complicated boundary conditions Finite element model: is it real system idealized mathematical abstractions. Is composed of some simple shapes of unit, unit connection through the node, and under a certain load. Finite element analysis: is the use of mathematical approximation method for real physical systems (geometry and loading conditions were simulated. And by using simple and interacting elements, namely unit, can use a limited number of unknown variables to approaching infinite unknown quantity of the real system. Linear elastic finite element method is a ideal elastic body as the research object, considering the deformation based on small deformation assumption of. In this kind of problem, the stress and strain of the material is linear relationship, meet the generalized hooke's law; Stress and strain is linear, linear elastic problem boils down to solving linear equations, so only need less computation time. If the efficient method of solving algebraic equations can also help reduce the duration of finite element analysis.

有限元分析英文文献

The Basics of FEA Procedure有限元分析程序的基本知识 2.1 Introduction This chapter discusses the spring element, especially for the purpose of introducing various concepts involved in use of the FEA technique. 本章讨论了弹簧元件，特别是用于引入使用的有限元分析技术的各种概念的目的 A spring element is not very useful in the analysis of real engineering structures; however, it represents a structure in an ideal form for an FEA analysis. Spring element doesn’t require discretization (division into smaller elements) and follows the basic equation F = ku. 在分析实际工程结构时弹簧元件不是很有用的;然而,它代表了一个有限元分析结构在一个理想的形式分析。弹簧元件不需要离散化(分裂成更小的元素)只遵循的基本方程F = ku We will use it solely for the purpose of developing an understanding of FEA concepts and procedure. 我们将使用它的目的仅仅是为了对开发有限元分析的概念和过程的理解。 2.2 Overview概述 Finite Element Analysis (FEA), also known as finite element method (FEM) is based on the concept that a structure can be simulated by the mechanical behavior of a spring in which the applied force is proportional to the displacement of the spring and the relationship F = ku is satisfied. 有限元分析(FEA),也称为有限元法(FEM)，是基于一个结构可以由一个弹簧的力学行为模拟的应用力弹簧的位移成正比,F = ku切合的关系。 In FEA, structures are modeled by a CAD program and represented by nodes and elements. The mechanical behavior of each of these elements is similar to a mechanical spring, obeying the equation, F = ku. Generally, a structure is divided into several hundred elements, generating a very large number of equations that can only be solved with the help of a computer. 在有限元分析中,结构是由CAD建模程序通过节点和元素建立。每一个元素的力学行为类似于机械弹簧,遵守方程,F =ku。一般来说,一个结构分为几百元素,生成大量的方程,只能在电脑的帮助下得到解决。 The term ‘finite element’ stems from the procedure in which a structure is divided into small but finite size elements (as opposed to an infinite size, generally used in mathematical integration).“有限元”一词源于一个结构分为小而有限大小元素的过程(而不是无限大小,通常用于数学集成) The endpoints or corner points of the element are called nodes. 元素的端点或角点称为节点。 Each element possesses its own geometric and elastic properties. 每个元素拥有自己的几何和弹性。

微观经济学试题英文版

Managerial Economics

Part 1: 1. The price of good A goes up. As a result the demand for good B shifts to the left. From this we can infer that: a. good A is a normal good. b. good B is an inferior good. c. goods A and B are substitutes. d. goods A and B are complements. e. none of the above. Choose: d) the definition os complements 2. Joe's budget line is 15F + 45C = 900. When Joe chooses his most preferred market basket, he buys 10 units of C. therefore, he also buys : a. 10 units of F b. 30 units of F c. 50 units of F d. 60 units of F e. None of the above Choose: b) We assume that Joe will spend all his income. If C = 10, then 15F =900 – 45(10) =450, so F = 450/15 =30. 3. Kim only buys coffee and compact discs. Coffee costs $0.60 per cup, and CDs cost $12.00 each. She has $18 per week to spend on these two goods. If Kim is maximizing her utility, her marginal rate of substitution of coffee for CDs is: a. 0.05 b. 20 c. 18 d. 1.50 e. None of the above Choose: a) At Kim's most preferred market basket, her MRS equals the price ratio (Pcoffee/PCD), which equals 0.6/12 or 0.05. 4. The bandwagon effect corresponds best to which of the following? a. snob effect. b. external economy. c. negative network externality. d. positive network externality. Choose: d) 5. A Giffen good a. is always the same as an inferior good. b. is the special subset of inferior goods in which the substitution effect dominates the income effect. c. is the special subset of inferior goods in which the income effect dominates the substitution effect. d. must have a downward sloping demand curv e. Choose: c) the definition of Giffen good 6. An Engel curve for a good has a positive slope if the good is : a. an inferior good. b. a Giffen good. c. a normal goo d. d. a, b, and c are tru e. e. None of the above is true. Choose: c) Inferior and Giffen goods have negatively sloped Engel curves. 7. The price of beef and quantity of beef traded are P* and Q*, respectively. Given

有限元分析作业报告英文版

有限元分析及应用上机实验报告学院：机电工程学院专业：机械工程班级：硕士1606班姓名：钱树生学号：163712160 指导教师：李毅波日期：2016.12.02

1.Question Fig.1.Schematic diagram of herringbone roof truss. Question:The geometric dimensions of the chevron roof is shown in Fig.1,you should analyze it by statics，as a result you should give the displacement and axial force and axial force diagram of the deformation diagram. Conditions:The ends of the roof truss were fixed,the sectional area of the truss is 0.01m2,elastic modulus is2.0×1011 N/m2,poisson's ratio is 0.3. 2.The software used ANSYS Finite element software(APDL 15.0) 3.Solving process Point1 was choosed as the Coordinate point, horizontal to the right was the X axis，the upright direction is choosed as the Yaxis to create a coordinate system. The nodes was numberedas shown in Figure 1，node 1 and node 5 was fixed，and the force on node 6,7,8was is 1k N，the direction is opposite to the Y-axis 3.1 The preparatory work before analysis （1）Specify the new file name. Select Utility>Menu> File>Change Jobname, then pop-up the dialog box Change Jobname,inputthe the working file name ‘2D-sp’ in the Enter New Jobname, click OK to finish the difinition, as shown in Fig.2. Fig.2.The difinition of working file name. （2）Specify a new title.Select Utility>Menu>File>Change Title，then pop-up the dialog box Change Title,inputthe the file name ‘2D-sp pro’ in the Enter New Title,click OK to finish the difinition, as shown in Fig.3.

微观经济学原理(第七版)-曼昆-名词解释(带英文)

微观经济学原理曼昆名词解释 1.需求价格弹性(price elasticity of demand)： 2.蛛网模型（）：对于生产周期较长的商品供给的时滞性，需求的不是动态模型分类，画图 3.边际效用递减（diminishing marginal utility）——基数效用论不违反边际效用递减规律。因为边际效用是指物品的消费量每增加(或减少)一个单位所增加(或减少)的总效用的量。这里的“单位”是指一完整的商品单位，这种完整的商品单位，是边际效用递减规律有效性的前提。比如，这个定律适用于一双的鞋子，但不适用于单只的鞋子。对于四轮车而言，必须是有四个轮子的车才成为一单位。三个轮子不能构成一辆四轮车，因而每个轮子都不是一个有效用的物品，增加一个轮子，才能使车子有用。因此，不能说第四个轮子的边际效用超过第三个轮子 4.无差异曲线(indifference curve)：一条表示给消费者相同满足程度的消费组合的曲线。

（2）特征：凸向原点越远越大不相交 5.边际替代率(marginal rate of substitution.MRS)：——序数效用论

6.预算线（Budget line/ budget constraint） 7.吉芬物品(Giffen good)：价格上升引起需求量增加的物品。 8.柯布道格拉

斯生产函数稀缺性（scarcity）：社会资源的有限性。经济学(economics)：研究社会如何管理自己的稀缺资源。效率(efficiency)：社会能从其稀缺资源中得到最多东西的特性。平等(equality)：经济成果在社会成员中公平分配的特性。机会成本(opportunity cost)：为了得到某种东西所必须放弃的东西。理性人(rational people)：系统而有目的地尽最大努力实现起目标的人。边际变动(marginal change)：对行动计划微小的增量调整。激励(incentive)：引起一个人做出某种行为的某种东西。市场经济(market economy)：当许多企业和家庭在物品与劳务市场上相互交易时，通过他们的分散决策配置资源的经济。产权（property rights）：个人拥有并控制稀缺资源的能力。市场失灵(market failure)：市场本身不能有效配置资源的情况。外部性(externality)：

车架有限元分析英文翻译

附件9：华南理工大学广州汽车学院本科生毕业设计（论文）翻译英文原文名FINITE ELEMENT ANALYSIS AND OPTIMIZATION OF A HEA VY TRUCK FRAME 中文译名重型货车汽车车架的有限元分析及优化设计系别汽车系专业班级车辆六班学生姓名马俊指导教师李利平填表日期2012年5月4日二00 年月

英文原文版出处：译文成绩：指导教师（导师组）签名：译文：重型货车汽车车架的有限元分析及优化设计摘要本文针对某重型汽车厂载货汽车车架在实际使用过程中出现的破坏等现象，利用美国大型有限元分析软件ANSYS对其进行静、动态分析，找出车架破坏的主要原因，并提出结构改进方案，通过对各方案的分析对比，提出合理的结构改进，对改进后的结构进行优化设计，最后根据优化结果生产样车，进行试验验证。本文所取得的主要研究成果如下。对车架及平衡悬架进行有限元仿真。根据车架结构特点，采用壳单元建立车架的有限元模型。采用弹簧单元COMBIN14和刚性杆单元MPC184，利用节点耦合的办法来模拟平衡架与车架的连接，目前有关模拟平衡悬架的报道还不多见。通过对车架在各种工况下的静态分析，得出载荷作用下车架的四个大应力区，这些区域与车架在实际使用过程中曾发生过破坏的位置相吻合。对车架进行动态特性分析得出车架的各阶段固有频率及振型。确定了路面不平度及发动机的激励频率范围，计算在此激励下车架的响应，得出大应力点在外界激励时其应力响应幅值较大的结论。在分析车架破坏的主要原因基础上，提出改进车架结构的若干方案，通过对各方案进行分析对比，得出通过增高车架纵梁的高度以及加长车架长度

经济学原理__英文版复习题

复习题：一、True or False： 1. Government policies that improve equality usually increase efficiency at the same time. 2. A rational decisionmaker takes an action if and only if the marginal cost exceeds the marginal benefit. 3.Trade allows each person to specialize in the activities he or she does best, thus increasing each individual's productivity. 4. the production possibilities frontier shows the opportunity cost of one good as measured in terms of the other good. 5. When a production possibilities frontier is bowed outward, the opportunity cost of the first good in terms of the second good increases as more of the second good is produced. 6. For a country producing two goods, the opportunity cost of one good will be the inverse of the opportunity cost of the other good. 7. If a country has the comparative advantage in producing a product, then that country must also have the absolute advantage in producing that product. 8.An increase in the price of pizza will shift the demand curve for pizza to the left. 9. A decrease in supply shifts the supply curve to the right. 10. The demand for gasoline will respond more to a change in price over a period of five weeks than over a period of five years. 11. Suppose that when the price rises by 10% for a particular good, the quantity demanded of that good falls by 30%. The price elasticity of demand for this good is equal to 1/3. 12. Demand is inelastic if the price elasticity of demand is greater than 1. 13.A price ceiling is a legal minimum on the price at which a good or service can be sold. 14. A price floor set above the equilibrium price is not binding. 15 .The equilibrium of supply and demand in a market maximizes the total benefits to buyers and sellers of participating in that market. 16. Efficiency is related to the size of the economic pie, whereas equality is related to how the pie gets sliced and distributed. 17. When markets fail, public policy can potentially remedy the problem and increase economic efficiency. 18. As the size of a tax increases, the government's tax revenue rises, then falls. 19.Because the supply of land is perfectly elastic, the deadweight loss of a tax on land is very large. 20.In principle, trade can make a nation better off, because the gains to the winners exceed the losses to the losers.

有限元分析软件ANSYS命令流中英文对照

有限元分析软件ANSYS命令流中文说明 Command VSBV, NV1, NV2, SEPO, KEEP1, KEEP2 —Subtracts volumes from volumes，用于2个solid相减操作，最终目的是要nv1-nv2=?通过后面的参数设置，可以得到很多种情况：sepo项是2个体的边界情况，当缺省的时候，是表示2个体相减后，其边界是公用的，当为sepo的时候，表示相减后，2个体有各自的独立边界。keep1与keep2是询问相减后，保留哪个体？当第一个为keep时，保留nv1,都缺省的时候，操作结果最终只有一个体，比如：vsbv,1,2,sepo,,keep,表示执行1-2的操作，结果是保留体2，体1被删除，还有一个1-2的结果体，现在一共是2个体（即1-2与2），且都各自有自己的边界。如vsbv,1,2,,keep,,则为1-2后，剩下体1和体1-2，且2个体在边界处公用。同理，将v换成a及l是对面和线进行减操作！ mp,lab, mat, co, c1,…….c4 定义材料号及特性 lab: 待定义的特性项目（ex,alpx,reft,prxy,nuxy,gxy,mu,dens） ex: 弹性模量 nuxy: 小泊松比 alpx: 热膨胀系数 reft: 参考温度 reft: 参考温度 prxy: 主泊松比 gxy: 剪切模量 mu: 摩擦系数

dens: 质量密度 mat: 材料编号（缺省为当前材料号） co: 材料特性值，或材料之特性，温度曲线中的常数项 c1-c4: 材料的特性-温度曲线中1次项，2次项，3次项，4次项的系数定义DP材料：首先要定义EX和泊松比：MP，EX，MAT，…… MP，NUXY，MAT，…… 定义DP材料单元表（这里不考虑温度）：TB，DP，MAT 进入单元表并编辑添加单元表：TBDATA，1，C TBDATA，2，ψ TBDATA，3，…… 如定义：EX=1E8，NUXY=0.3，C=27，ψ=45的命令如下： MP，EX，1，1E8 MP，NUXY，1，0.3 TB，DP，1 TBDATA，1，27 TBDATA，2，45这里要注意的是，在前处理的最初，要将角度单位转化到“度”，即命令：*afun,deg VSEL, Type, Item, Comp, VMIN, VMAX, VINC, KSWP Type，是选择的方式，有选择（s）,补选（a），不选(u)，全选(all)、反选（inv）等,其余方

微观经济学高级版英文原版课件

Chapter1:Key concepts February19,2013 1Introduction Economics is the study of choice under scarcity.Typically,consumers want more goods and services than they can a?ord to buy.Similarly,businesses face constraints in terms what funds and resources that they can https://www.wendangku.net/doc/0d13009432.html,ernments and countries also face the same type of problem:a government might want to address a large number of social problems,but they have limited resources with which to do so.Economics is about understanding how a party deals with the fact that when they use their resources to pursue one option,they cannot use those resources to do something else.And so,a consumer may have to choose between a new pair of shoes or a textbook,a?rm may have to choose between developing a new product or launching a marketing campaign, and the government may have to choose between improving education or targeting crime. To understand these issues,economics has developed a set of tools that can be used to analyze these problems.This book provides an introduction to those tools.They can be used to help understand economic problems wherever they arise,be it businesses understanding the markets they compete in,or governments trying to develop social policy,or families trying to manage their households.These tools are not meant to capture everything that is occurring in any given situation.Rather,they are designed to simplify(or to model)a complicated and potentially messy real-world issue into a tractable form that can provide valuable insights. Given that resources are limited,the key questions that an economy needs to‘decide’are:(a)what to produce;(b)how to produce it;and(c)who should get what is made.In modern economies,the answers to these questions are largely determined by the market –that is,by the interaction of sellers and buyers in the market.1Sometimes,however, the government also helps determine the answer to these questions,by regulating or intervening in the market.Consequently,our focus in this microeconomics text will be on the study of individuals(consumers,?rms,and governments)and their interaction in markets. This chapter provides a few key concepts that underpin the analysis in the rest of the book,as well as economics analysis in general. 1By‘market’,we simply mean a place where buyers and sellers of a particular good or service meet, such as a traditional bazaar or an online trading site. 1