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,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,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,预备知识,Lesson 3 Optimization for Finite Element Applications,一、,Background Information,Finite Element Method(,有限元法,),The finite element method(FEM)(sometimes referred to as finite element analysis)is a,numerical technique,for finding approximate solutions of,partial differential equations,(PDE)as well as of,integral equations,.,机械工程专业英语,预备知识,Lesson 3 Optimization for Finite Element Applications,一、,Background Information,Finite Element Method(,有限元法,),The solution approach is based either on eliminating the differential 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,预备知识,Lesson 3 Optimization for Finite Element Applications,一、,Background Information,Finite Element Method(,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 calculations 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(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,预备知识,Lesson 3 Optimization for Finite Element Applications,一、,Background Information,Finite Element Method(,有限元法,),For instance,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 accurate predictions over land than over the wide-open sea.,机械工程专业英语,预备知识,Lesson 3 Optimization for Finite Element Applications,一、,Background Information,Finite Element Method(,有限元法,),The finite-element method originated from the need for solving complex,elasticity,and,structural analysis,problems 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 into a set of discrete sub-domains,usually called elements.,机械工程专业英语,预备知识,Lesson 3 Optimization for Finite Element Applications,一、,Background Information,Finite Element Method(,有限元法,),Development of the finite element method began in earnest in the middle to late 1950s for,airframe,and,structural 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 used 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,预备知识,Lesson 3 Optimization for Finite Element Applications,一、,Background Information,Finite Element Method(,有限元法,),A variety of specializations under the umbrella of the 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 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,预备知识,Lesson 3 Optimization for Finite Element Applications,一、,Background Information,Finite Element Method(,有限元法,),FEM allows detailed 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 associated 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,预备知识,Lesson 3 Optimization for Finite Element Applications,一、,Background Information,Finite Element Method(,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 s
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