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1、English for Mechanical Engineering机械工程专业英语常州工学院机电工程学院徐红丽机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimization for Finite Element Applications 一、一、Background InformationnFinite Element Method(有限元法有限元法)The finite element method(FEM)(sometimes referred to as finite element analysis)is a numerical technique for
2、 finding approximate solutions of partial differential equations(PDE)as well as of integral equations.机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimization for Finite Element Applications 一、一、Background InformationnFinite Element Method(有限元法有限元法)The solution approach is based either on eliminating the diffe
3、rential equation completely(steady state problems),or rendering the PDE into an approximating system of ordinary differential equations,which are then numerically integrated using standard techniques such as Eulers method,Runge-Kutta,etc.机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimization for Finite Eleme
4、nt Applications 一、一、Background InformationnFinite Element Method(有限元法有限元法)In solving partial differential equations,the primary challenge is to create an equation that approximates the equation to be studied,but is numerically stable,meaning that errors in the input data and intermediate calculation
5、s do not accumulate and cause the resulting output to be meaningless.There are many ways of doing this,all with advantages and disadvantages.The Finite Element Method is a good choice for solving partial differential equations over complex domains(like cars and oil pipelines),when the domain changes
6、(as during a solid state reaction with a moving boundary),when the desired precision varies over the entire domain,or when the solution lacks smoothness.机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimization for Finite Element Applications 一、一、Background InformationnFinite Element Method(有限元法有限元法)For instanc
7、e,in a frontal crash simulation it is possible to increase prediction accuracy in important areas like the front of the car and reduce it in its rear(thus reducing cost of the simulation);Another example would be the simulation of the weather pattern on Earth,where it is more important to have accur
8、ate predictions over land than over the wide-open sea.机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimization for Finite Element Applications 一、一、Background InformationnFinite Element Method(有限元法有限元法)The finite-element method originated from the need for solving complex elasticity and structural analysis prob
9、lems in civil and aeronautical engineering.Its development can be traced back to the work by Alexander Hrennikoff(1941)and Richard Courant(1942).While the approaches used by these pioneers are dramatically different,they share one essential characteristic:mesh discretization of a continuous domain i
10、nto a set of discrete sub-domains,usually called elements.机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimization for Finite Element Applications 一、一、Background InformationnFinite Element Method(有限元法有限元法)Development of the finite element method began in earnest in the middle to late 1950s for airframe and str
11、uctural analysis and gathered momentum at the University of Stuttgart through the work of John Argyris and at Berkeley through the work of Ray W.Clough in the 1960s for use in civil engineering.By late 1950s,the key concepts of stiffness matrix and element assembly existed essentially in the form us
12、ed today.NASA issued request for proposals for the development of the finite element software NASTRAN in 1965.机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimization for Finite Element Applications 一、一、Background InformationnFinite Element Method(有限元法有限元法)A variety of specializations under the umbrella of the
13、 mechanical engineering discipline(such as aeronautical,biomechanical,and automotive industries)commonly use integrated FEM in design and development of their products.Several modern FEM packages include specific components such as thermal,electromagnetic,fluid,and structural working environments.In
14、 a structural simulation,FEM helps tremendously in producing stiffness and strength visualizations and also in minimizing weight,materials,and costs.机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimization for Finite Element Applications 一、一、Background InformationnFinite Element Method(有限元法有限元法)FEM allows deta
15、iled visualization of where structures bend or twist,and indicates the distribution of stresses and displacements.FEM software provides a wide range of simulation options for controlling the complexity of both modeling and analysis of a system.Similarly,the desired level of accuracy required and ass
16、ociated computational time requirements can be managed simultaneously to address most engineering applications.FEM allows entire designs to be constructed,refined,and optimized before the design is manufactured.机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimization for Finite Element Applications 一、一、Backgro
17、und InformationnFinite Element Method(有限元法有限元法)This powerful design tool has significantly improved both the standard of engineering designs and the methodology of the design process in many industrial applications.The introduction of FEM has substantially decreased the time to take products from co
18、ncept to the production line.It is primarily through improved initial prototype designs using FEM that testing and development have been accelerated.In summary,benefits of FEM include increased accuracy,enhanced design and better insight into critical design parameters,virtual prototyping,fewer hard
19、ware prototypes,a faster and less expensive design cycle,increased productivity,and increased revenue.机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimization for Finite Element Applications 一、一、Background InformationnFinite Element Method(有限元法有限元法)General form of the finite element method lChoose a grid.In th
20、e preceding treatment,the grid consisted of triangles,but one can also use squares or curvilinear polygons.lThen,one chooses basis functions.We used piecewise linear basis functions,but it is also common to use piecewise polynomial basis functions.机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimization for Fi
21、nite Element Applications 一、一、Background InformationnFinite Element Method(有限元法有限元法)General form of the finite element method lBy analyzing the response of each finite element of the object to the stress,strain,heat,or other force acting on it,the computer can predict the reaction of the whole objec
22、t.lThere is a trade-off between accuracy and computation time 预备知识预备知识 一、预备知识一、预备知识u有限元法起源于有限元法起源于50年代航空工程中的机构分析矩阵法。为年代航空工程中的机构分析矩阵法。为了解决航空结构设计问题，了解决航空结构设计问题，Turner、Clough等人首次采用等人首次采用三角形和矩形单元，成功地将结构力学中的位移用于平面应三角形和矩形单元，成功地将结构力学中的位移用于平面应力问题的求解，力问题的求解，1960年，首次提出了年，首次提出了“有限元法有限元法”。u有限元法的基本步骤：有限元法的基本步骤：1
23、）结构离散）结构离散-网格划分，关系到有限元网格划分，关系到有限元计算的速度和精度计算的速度和精度2）单元分析：建立各节点位移和节点力）单元分析：建立各节点位移和节点力之间的关系，从而求出单元刚度矩阵之间的关系，从而求出单元刚度矩阵3）等效节点载荷计算）等效节点载荷计算4）整体分析，建立整体刚度方程）整体分析，建立整体刚度方程5）约束条件引入和方程求解）约束条件引入和方程求解Lesson 3 Optimization for Finite Element Applications 机械工程专业英语机械工程专业英语机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimiza
24、tion for Finite Element Applications 一、一、Background InformationnDesign Optimization(优化设计优化设计)Typical engineering systems are described by very large numbers of variables,and it is the designers task to specify appropriate values for these variables.Skilled designers utilize their knowledge,experienc
25、e,and judgment to specify these variables and design effective engineering systems.Because of the size and complexity of the typical design task,however,even the most skilled designers are unable to take into account all of the variables simultaneously.机械工程专业英语机械工程专业英语预备知识预备知识Lesson 3 Optimization f
26、or Finite Element Applications 一、一、Background InformationnDesign Optimization(优化设计优化设计)In mathematics,optimization,or mathematical programming,refers to choosing the best element from some set of available alternatives.Optimization methodologies can be applied during the product development stage to
27、 ensure that the finished design will have the high performance,high reliability,low weight,and/or low cost.Alternatively,optimization methods can be applied to existing products to identify potential design improvements.机械工程专业英语机械工程专业英语预备知识预备知识 一、预备知识一、预备知识Lesson 3 Optimization for Finite Element A
28、pplications u最优化问题：希望在可能的条件下用最少的付出最优化问题：希望在可能的条件下用最少的付出得最满意的效果。得最满意的效果。u最优化设计：借助最优化数值计算方法和计算机最优化设计：借助最优化数值计算方法和计算机技术，求取工程问题的最优设计方案。技术，求取工程问题的最优设计方案。-用数学方用数学方法解决设计问题的设计方法。法解决设计问题的设计方法。u最优化设计的数学模型：最优化设计的数学模型：由设计变量、目标函数和约束条件组成由设计变量、目标函数和约束条件组成optimization 7Cptimai5zeiFen7Cptimai5zeiFen n.优化，优选（法）优化，优选（
29、法）finite element analysis5fainait5fainait5elimEnt5elimEnt E5nAlEsisE5nAlEsis n.有限元分析有限元分析iterative 5itErEtiv5itErEtiv adj.反复的反复的 迭代的迭代的alternative C:C:l l5 5tE:nEtivtE:nEtiv n.二中择一二中择一,可供选择的办法可供选择的办法,事事物物 adj.交替的交替的 可供选择的可供选择的manual 5mAnjuEl5mAnjuEl adj.手工的，人工的手工的，人工的trial-and-error 反复试验反复试验 试凑法试凑法b
30、ias 5baiEs5baiEs n.偏向（重、差）偏向（重、差）vt.使存偏见使存偏见a desktop platform 桌面平台桌面平台 词词 汇汇 二、词汇二、词汇Lesson 3 Optimization for Finite Element Applications 机械工程专业英语机械工程专业英语 二、词汇二、词汇Lesson 3 Optimization for Finite Element Applications 机械工程专业英语机械工程专业英语constrain(t)kEn5streinEn5strein n.vt.强制强制 约束约束response ris5pCnsri
31、s5pCns n.反应反应 灵敏度灵敏度parameter pE5rAmitEE5rAmitE n.参数，参量参数，参量 parametric 7pArE5metrik7pArE5metrik adj.mesh meFmeF n.网格网格 vt.以网捕捉，啮合，编织，以网捕捉，啮合，编织，vi.落网，落网，相啮合相啮合capability 7keipE5biliti7keipE5biliti n.能力，性能，容量能力，性能，容量loop lu:plu:p n.循环循环 closed loop闭环闭环 open loop 开环开环pose pEuzpEuz vt.摆出摆出.姿态，提出姿态，提出m
32、odel 5mCdl5mCdl n.模型，样品模型，样品词词 汇汇displacement dis5pleismEnt5pleismEnt n.位移，排量，替换位移，排量，替换buckling 5bQkliN5bQkliN n.弯曲，翘曲，挠度弯曲，翘曲，挠度factor 5fA5fA ktEktE n.因素因素gradient 5greidiEnt5greidiEnt n.梯度，倾斜度，坡度，倾斜的梯度，倾斜度，坡度，倾斜的flux flQksflQks n.通量，流量，通量，流量，vi.溶化，流出溶化，流出 vt.使溶融，用使溶融，用焊剂处理焊剂处理 multidisciplinary 7
33、mQlti5disiplinEri7mQlti5disiplinEri adj.多学科的多学科的 deflection di5flekFEndi5flekFEn n.偏转，挠曲偏转，挠曲objective function 目标函数目标函数 preprocesspri:5prEusespri:5prEuses 预处理预处理词词 汇汇 二、词汇二、词汇Lesson 3 Optimization for Finite Element Applications 机械工程专业英语机械工程专业英语 As engineers work with increasingly complex structure
34、s,they need rational,reliable,fast,and economical design tools.Over the past two decades,finite element analysis has proven to be the most frequently used method of identifying and solving the problems associated with these complicated designs.课文分析课文分析Lesson 3 Optimization for Finite Element Applica
35、tions 机械工程专业英语机械工程专业英语As engineers work with increasingly complex structures,they need rational,reliable,fast,and economical design tools.课文分析课文分析当工程师们需要求解越来越复杂的结构问题时，他们当工程师们需要求解越来越复杂的结构问题时，他们需要合理的、可靠的、快速而经济的设计工具。需要合理的、可靠的、快速而经济的设计工具。Over the past two decades,finite element analysis has proven to be
36、 the most frequently used method of identifying and solving the problems associated with these complicated designs.过去二十年里，有限元分析已经成为确定和解决涉及过去二十年里，有限元分析已经成为确定和解决涉及这些复杂设计问题时的最常用方法。这些复杂设计问题时的最常用方法。Lesson 3 Optimization for Finite Element Applications 机械工程专业英语机械工程专业英语 Because most of the design tasks in
37、engineering are quantifiable,computers have revolutionized the highly iterative design process,particularly the procedures for quickly finding alternative designs.But even now,many engineers still follow a manual trial and error approach,Such all approach makes designing even for seemingly simple ta
38、sks more difficult because it usually takes longer,requires extensive human machine interaction,and tends to be biased by the design groups experience.课文分析课文分析Lesson 3 Optimization for Finite Element Applications 机械工程专业英语机械工程专业英语Because most of the design tasks in engineering are quantifiable,comput
39、ers have revolutionized the highly iterative design process,particularly the procedures for quickly finding alternative designs.课文分析课文分析因为工程实践中的大多数设计任务都是可量化因为工程实践中的大多数设计任务都是可量化的，计算机彻底改变了繁琐的重复设计过程，的，计算机彻底改变了繁琐的重复设计过程，特别是有了快速找到比较设计方案的程序。特别是有了快速找到比较设计方案的程序。Lesson 3 Optimization for Finite Element Appli
40、cations adj.可以计量的，可以计量的，可计量的可计量的itrtivadj.重复的重复的,迭代的迭代的机械工程专业英语机械工程专业英语But even now,many engineers still follow a manual trial-and-error approach,Such all approach makes designing even for seemingly simple tasks more difficult because it usually takes longer,requires extensive human machine interact
41、ion,and tends to be biased by the design groups experience.课文分析课文分析但是，即使是现在，许多工程师仍然使用人工试凑法。但是，即使是现在，许多工程师仍然使用人工试凑法。这种方法使得设计过程、即使是很简单的设计任务也这种方法使得设计过程、即使是很简单的设计任务也变得困难，因为通常它要花更长的时间，需要广泛的变得困难，因为通常它要花更长的时间，需要广泛的人人机交流，且设计质量取决于设计人员的经验。机交流，且设计质量取决于设计人员的经验。Lesson 3 Optimization for Finite Element Applicatio
42、ns 试凑法试凑法取决于取决于机械工程专业英语机械工程专业英语 Design optimization,which is based on a rational mathematical approach to modifying designs too complex for the engineer to modify,automates the design cycle.课文分析课文分析优化设计是以合理的数学推倒方法为基础，改进那些优化设计是以合理的数学推倒方法为基础，改进那些对于工程师来说过于复杂无法改进的设计，使设计过对于工程师来说过于复杂无法改进的设计，使设计过程自动化。程自动化。
43、If automated optimization can be done on a desktop platform,it can save a lot of time and money.如果在如果在台计算机就能实现自动优化设计，台计算机就能实现自动优化设计，那就可以节省大量的时间和金钱那就可以节省大量的时间和金钱Lesson 3 Optimization for Finite Element Applications 机械工程专业英语机械工程专业英语 The goal of optimization is to minimize or maximize an objective,such
44、 as weight or fundamental frequency that is subject to constraints on response and design parameters.课文分析课文分析优化设计的目的就是要将设计目标最大化或最小化，优化设计的目的就是要将设计目标最大化或最小化，例如，重量或基频这些受到频响和设计参数方向的约例如，重量或基频这些受到频响和设计参数方向的约束的对象。束的对象。The size and/or shape of the design determine the optimization approach.尺寸和尺寸和(或或)结构形状决定着
45、优化设计的方法。结构形状决定着优化设计的方法。Lesson 3 Optimization for Finite Element Applications 机械工程专业英语机械工程专业英语 Looking at optimization as part of the design process makes it easier to understand.The first step includes preprocessing,analysis,and postprocessing,just as ii1 customary finite element analysis(REA)and co
46、mputer aided design(CAD)program applications(the difference in CAD lies in building the problems geometry in terms of the design parameters).In the second step,the optimization objective and response constraints are defined.And in the last step,the repetitive task of design adjustment is automated.课
47、文分析课文分析Lesson 3 Optimization for Finite Element Applications 机械工程专业英语机械工程专业英语 Looking at optimization as part of the design process makes it easier to understand.课文分析课文分析优化过程看作设计过程的一部分，使它变得更容易理解优化过程看作设计过程的一部分，使它变得更容易理解 The first step includes preprocessing,analysis,and postprocessing,just as in cust
48、omary finite element analysis(FEA)and computer aided design(CAD)program applications(the difference in CAD lies in building the problems geometry in terms of the design parameters).第一步，包括前处理、分析和后处理，正像通常使用的第一步，包括前处理、分析和后处理，正像通常使用的有限元分析有限元分析(FEA)和计算机辅助设计和计算机辅助设计(CAD)程序应用。程序应用。(CAD的特点在于根据设计参数建立了问题的几何图形
49、的特点在于根据设计参数建立了问题的几何图形)。Lesson 3 Optimization for Finite Element Applications 机械工程专业英语机械工程专业英语 In the second step,the optimization objective and response constraints are defined.课文分析课文分析第二步，定义优化目标和响应约束。第二步，定义优化目标和响应约束。And in the last step,the repetitive task of design adjustment is automated.而最后而最后步，
50、自动化的重复设计过程。步，自动化的重复设计过程。Lesson 3 Optimization for Finite Element Applications 机械工程专业英语机械工程专业英语 Optimization programs should allow engineers to monitor the progress of the design,stop it if necessary,change the design conditions,and restart.The power of an optimization program depends on the availabl