What Is the FE Exam?

In mathematics, the Finite Element Method (FEM) is a numerical technique for solving approximate solutions of partial differential equation boundary value problems. When solving the entire problem area, each sub-area becomes a simple part. This simple part is called a finite element.

English: Finite Element

Solve the finite element equation to get the displacement. Here, according to

Overview:

With the rapid development of computer technology, in the field of engineering, finite element analysis (FEA) is increasingly used in simulations to solve real engineering problems. Over the years, more and more engineers, applied mathematicians, and physicists have proven that this method of solving partial differential equations (PDE) can solve many

China's CAE technology research, development and application can be said to be ups and downs, following a very difficult development path. The late Chinese famous mathematician Feng Kang proposed the basic idea of the finite element method in the 1950s, which is almost synchronous with foreign countries. In the mid-1960s, some units and scholars who studied finite element methods also appeared in China. However, due to the constraints of computer hardware conditions and the influence of the political and social environment such as the Cultural Revolution, China s CAE technology has been impacted for a long time. However, in response to the national call, researchers devoted themselves to the calculation of the stress and strain of the dam of the hydropower station. Finally, Xie Qianquan and Li Jianhua of the Hunan Institute of Computing Technology, independently invented China under the circumstances of isolation from foreign countries. The 3D finite element method and engineering software were successfully applied to the engineering projects of the Yellow River Water Conservancy Commission in 1973, and the paper "Finite Element Method for 3D Elasticity Problems" was published in 1975 ^[2] , and then in the 1970s to the first half of the 1980s Ye, applied to the calculation of large-scale dams nationwide, has saved a lot of funds for the country ^[3] ; it is worth emphasizing that according to the rigorous review of this article ^[4] , Xie Qianquan and Li Jianhua cooperated to overcome the three-dimensional finite element program is 1972 Successfully commissioned in 1973, used for the project of the Yellow River Water Conservancy Commission in 1973. Out: This article was submitted in 1973, finalized in 1974, and officially published in 1975 ^[2] . They are available in chronological order. They discovered the three-dimensional finite element superconvergence in 1973, far ahead of foreign experts. The conclusion that the world's first three-dimensional finite element superconvergence was discovered was publicly acknowledged in academic papers by world-renowned finite element expert MICHAL KRIZEK ^[5] , which is the first discovery in China that has surpassed foreign countries in the field of finite element. In 2000, the Li Jianhua and Xie Qianquan couples first discovered the cloak of stealth in the world, and it is a achievable double-layer stealth cloak that does not exceed the speed of light. Not only has it maintained its leading position in the field of computing science, but it has also pioneered the world's first super-scientific Concept ^[6-9] .

In the mid-1970s, Dalian University of Technology developed DDJ, JIGFEX finite element analysis software, and DDDU structure optimization software; Professor Li Mingrui of Beijing Agricultural University developed FEM software; in the mid-1980s, Professor Yuanmingwu of Peking University adopted a transplant of foreign SAP software And major transformation, developed the SAP-84; due to the needs of the aviation industry, the Ministry of Aviation Industry has also organized the development of HAJIF (I, II, III), YIDOYU, COMPASS since the early 1970s, and has won many national awards and many more. Compared with similar foreign products, these domestic CAE software have many characteristics in core algorithms and certain functions, reflecting the results obtained by Chinese scholars in the study of computational mechanics, fully considering the actual conditions of China's computer hardware, and in national infrastructure. Both construction and engineering structure design have played an important role and have a wide range of applications.

Since the 1990s, the country has stepped up its efforts to open up, and a large number of foreign software has poured into the Chinese market, which has accelerated the promotion of CAE technology in China, which has undoubtedly improved the design level of China's equipment manufacturing industry. At the same time, the software we developed independently was strongly challenged. Especially pirated foreign software has hit the CAE software independently developed in China. For a period of time, the sound of independent development of CAE software was hardly heard, and the strength of relevant management departments to support the development of domestic software dropped significantly. The department that supports basic research believes that CAE software development cannot raise basic scientific issues, and the department that supports scientific and technological research and high-tech development believes that CAE software development must take a market-oriented path and seek funding in the market. The independent development of CAE software has encountered many difficulties in terms of human, financial and material resources. ^[10]

The CAE software condenses the research results of technical science, and the situation facing the independent development of CAE software is similar to that of technical science in China. At the recent academician conference of the Chinese Academy of Sciences and Chinese Academy of Sciences, Comrade Hu Jintao emphasized the "need to attach great importance to the development of technology and science" in response to the tendency to ignore technology and science, which greatly encouraged us. In fact, the achievements of these softwares with China's independent intellectual property rights are indelible. These software not only solve a large number of problems raised by the national economic construction, but also generate direct and indirect economic benefits. The development and application process has cultivated a large number of Talents engaged in CAE R & D and application; the existence of these software has also broken the barriers to us in western countries, forcing foreign products to significantly reduce prices, and they have made an inestimable contribution to national GDP directly or indirectly.

The dilemma facing the development of domestic CAE software is the epitome of the difficulties faced by most technologies and products of our country s independent intellectual property rights. In the field of technical economics in China, some experts believe that the main contribution of national economic growth since the reform and opening up has come from opening up. , Rather than technological innovation with independent intellectual property rights, which contributes very little to GDP. Such a statement may be valid, because in real life we can see that quite a large number of domestic enterprises use complete sets of technology, complete sets of equipment and large-scale software on imported production lines from abroad, the production process and the intellectual property rights of many products are For foreign companies. Because of the many years of experience in developing complete sets of technologies, equipment, products, and market expansion in western developed countries, although our independent innovations are technologically superior to each other, they often lack sufficient economic advantages to eliminate each other. Such a statement should arouse the reflection of our vast number of science and technology workers and management departments, how to accelerate our technological innovation activities with independent intellectual property rights, and how to turn these achievements into realistic productivity as soon as possible. However, we should emphasize that it is very one-sided to measure the contribution of China s scientific and technological progress to the country s economic construction and social progress in terms of direct contribution to GDP; we cannot ignore the direct contribution to GDP Innovation. As Comrade Jiang Zemin pointed out, innovation is the soul of a nation.

Fortunately, despite facing many difficulties, China still survives a group of research teams dedicated to CAE technology. The chief scientist of meta-computing and the research team of Liang Guoping from the Institute of Mathematics and Systems Science of the Chinese Academy of Sciences, after eight years of intensive research, have created the world-leading automatic generation system of finite element programs (FEPG). FEPG uses the advanced software design of componentized thinking and finite element language to provide an extremely powerful tool for solving finite element problems in various fields and aspects. Using FEPG can be completed in days or even hours. Programming labor that can be completed in months or even years. FEPG is one of the few CAE software that has survived. This is also due to the flexibility of FEPG software, which can solve many finite element problems that cannot be solved by foreign commercial software. FEPG software is more practical, but easier to use than foreign commercial software. Poor, which is also the reason why many novice users find it difficult to learn FEPG. After years of accumulation, it has been used by more than 300 research institutes and enterprises. Has become the largest finite element software platform in China. However, compared with the degree of marketization of foreign software, there is still a certain gap, and some work needs to be done in terms of software ease of use.

In order to provide domestic users with application-oriented finite element analysis systems, Dr. Qian Huashan of the original FEPG team organized the establishment of Beijing Supercomputing Technology Co., Ltd. and developed the supercomputing finite element analysis system SciFEA. SciFEA software has formed a series of stand-alone version, network version (iSciFEA), cluster parallel version, GPU parallel version (SciFEA-GPU). There are nearly 500 domestic users of SciFEA software, and more than 20,000 users have downloaded trial versions. SciFEA has abandoned the traditional CAE software complex structure system design mode and adopted an independent module development method that is directly oriented to user needs. The usual computing functions in terms of functions are already available. Further expansion of the computing model is yet to be developed.

In addition to the FEPG software and SciFEA software, which are relatively large-scale, the PKPM software of the China Institute of Architectural Design and Research also has a wide range of applications in the construction field, while the software of Dalian University of Technology is mainly used to solve structural optimization; there are also some domestic finite element software, Chinese agriculture The finite element developed by the university focuses on the calculation of beam plates and shells, but its development is slow and it is difficult to see it on the market. In the 2011 plan, the United States considered simulation calculations as one of the five basic industries in future planning. It can be seen that the impact of finite elements on the development of society, and most of our country uses foreign finite element software, and in some military industries or In terms of cutting-edge finite element analysis modules, exports to China are strictly restricted. This requires more finite element software with domestic independent intellectual property rights.

Finite element methods of fluid mechanics include velocity pressure method, flow function-vortex function method and flow function method.