The concept of finite element has been developed and applied for centuries ago, for example, the circumference of a circle is obtained by approximating a circle with a polygon (finite number of linear elements), which is an application of the finite element method. Pen, fun, and www.biquge.info

The basic idea is to discretize the structure and express complex objects with a finite number of easily analyzable units.

The elements are connected to each other by a finite number of nodes, which are then comprehensively solved by the deformation coordination condition.

Since the number of elements is finite, the number of nodes is also limited, so it is called the finite element method.

After just a few decades of efforts, with the rapid development and popularization of computer technology, the finite element method has rapidly expanded from structural engineering strength analysis and calculation to almost all scientific and technological fields, and has become a colorful, widely used and practical and efficient numerical analysis method.

It is widely used in elastoplastic mechanics, fracture mechanics, fluid mechanics, heat conduction and other fields, and continues to deepen in the field of engineering, throughout the aerospace industry, nuclear industry, electromechanical, chemical, marine and other industries, is an important means of dynamic and static thermal characteristics analysis of mechanical products.

The application of finite element method in product structure design has made a revolutionary change in the design of mechanical and electrical products, and theoretical design has replaced empirical analogy design.

It can be said that it is the finite element method that makes computer-aided manufacturing possible.

Later generations of finite element analysis software can usually be integrated with general CAD software, that is, after the CAD software completes the modeling design of components and parts, the model can be directly transferred to the CAE software for finite element meshing and analysis and calculation, if the results of the analysis do not meet the design requirements, the design and analysis will be re-carried out until satisfied, thus greatly improving the design level and efficiency.

However, in this era, the finite element method has only been proposed for many years, and most of the research on it at home and abroad is in the theoretical stage, and its application in the field of engineering is very rare.

Yang Weining actually combined the finite element method with CAD software, so that designers can directly use the computer to conduct finite element analysis of the mechanical properties of the product structure they designed, which is an epoch-making event in the history of computer science.

It was not until the mid-to-late nineties that the combination of CAD and finite element became popular around the world, and Yang Weining directly asked it to interview more than ten years in advance, which immediately attracted the attention of Chen Liangwei, Liu Yue, Jing Dongyang and others.

"Xiao Yang, what is the finite element model generator you are talking about?" asked Zhang Weimin, director of the Structure and Strength Design Office.

He is engaged in structural mechanics and is the most sensitive to this technology.

Yang Weining seemed to have known that Zhang Weimin would ask this question, smiled slightly, and said, "Director Zhang, I don't know if you have ever heard of finite element analysis?"

"Finite element analysis?"

Zhang Weimin was slightly stunned, and Chen Liangwei, Liu Yue and Gu Jingyang also looked at each other.

They are accustomed to solving problems from the perspective of engineering practice, and they do not have a deep understanding of these purely theoretical things.

On the side, Professor Kuang Shilin from Huaqing University reacted immediately and said: "Xiao Yang, the finite element analysis you mentioned is a difference method based on the variational principle proposed by Academician Feng Kang, right?"

Yang Weining was slightly stunned, nodded, and said with a smile: "It seems that Professor Kuang, you also know the finite element method?"

Kuang Shilin smiled: "I only have a general understanding, but I don't know the specific details of this technology. ”

Yang Weining nodded: "The essence of finite element analysis is to replace complex problems with simpler problems, and then solve them. It treats the solution domain as consisting of a number of small interconnected subdomains called finite elements, assumes a simpler approximate solution for each element, and then deduces the total satisfaction conditions of this domain, such as the equilibrium condition of the component structure, to obtain the solution to the problem. This solution is not an exact solution, but an approximate solution, because the actual problem is replaced by a simpler one. Because most practical problems are difficult to be solved accurately, finite elements can not only have high calculation accuracy, but also can adapt to various complex shapes, so they can become an effective means of engineering analysis. ”

Yang Weining saw that everyone did not know much about this technology, and continued: "It has only been many years since finite element analysis was really proposed. In 1969, Professor Ray Clough published a paper entitled "ThefiniteElementInplaneStress****ysis", which was the first application of finite element analysis to the field of engineering. ”

In 1967, Professor Zhang Youqi of Hong Kong cooperated with Sinkiewicz to publish the first finite element masterpiece "Finite Element Method of Structural and Continuous Mechanics", which was the pioneer of finite elements, especially plate elements and shell elements, and laid the foundation for semi-analytic solution of finite element method. In the late 50s and early 60s, Academician Feng Kang of the Chinese Academy of Sciences, on the basis of collective research and practice in solving the calculation problem of large dams, independently of the West, created a set of systematic and modern calculation methods for solving differential equation problems. Just a few years ago, Academician Feng Kang established the Poincaré type inequality of discontinuous functions in the discontinuous finite element theory, and on this basis, established the embedding theory of the discontinuous finite element function space, which made a significant contribution to the formation and guidance of China's computational mathematics team. ”

Listening to Yang Weining's contribution of Chinese scientists in the finite element method, everyone at the scene was proud of it, and at the same time, they also secretly admired Yang Weining's erudition.

In this era, the efficiency of communication is extremely low, and most researchers are only interested in some information within the specialty, and as for the progress in other scientific research fields, they are not well understood.

A researcher like Yang Weining, who has shown extremely high standards in the fields of aeronautical engineering, programming, computing science, and applied mathematics, has almost never seen him.

Even Professor Kwong Shilin, who has been tracking the development of CAD technology, is secretly frightened, and he doesn't know where this Xiao Yang came from, he knows too many things, right?

Seeing that everyone still looked like they didn't understand, Yang Weining shook his head and didn't explain too much.

When they get used to it, they will know how powerful the combination of finite element and CAD is.

Professor Yau Chengtong, a famous Fields Medal winner in Tsinghua University, made this evaluation of finite element analysis in a report entitled "My Views on the Development of Chinese Mathematics": "There are three main reasons why modern Chinese mathematics can surpass or keep pace with the West, one is Professor Chern Shiingshen's work in demonstrative classes, one is Professor Hua Luogeng's work in multiple complex functions, and the last one is Professor Feng Kang's work in finite element calculation. ”