The Reasearch And Application Of The Coupled Meshless-Finite Element Method

Being one of the most effective project numerical analysis tool established in the 20th century, the Element Finite Method not only developed in its own theory largely, but also be received the engineering value day by day. Since the limitation of mesh generation, it's application and popularization are restricted. With the appearance of Meshless Method(MLM), a new way of numerical analysis is worked out.This paper studies the basic theory of Meshless and the Element -free Galerkin Method(EFG), along with the study and the analysis of the two main Coupled Meshless-Finite Element Method has been established, the author establishes the Coupled Meshless-Finite Element Method based on Transition Element. Meanwhile ,through the analysis of the essence difference the Meshless Method from the Finite Element, the concept Generalized Element has been proposed, and the Coupled Meshless-Finite Element Method based on Generalized Element has been proposed, then the author use this method to solve the Contact Question. The corresponding program by FORTRAN language is carried out. Trough result of the numerical -example, mainly draws the conclusion:1. After the transition element established, the new transient function is established, meanwhile the corresponding program by FORTRAN language is carried out and the cantilever beam is calculated as example to show the coupling method had higher computation precision than FEM.2. Meshless Method is inferior to FEM in processing the boundary condition, therefore it is extremely essential to study the coupled method of them.3. The concept of Generalized Element is proposed after the contract of the essence difference the Meshless Method from the Finite Element and the coupled method base on Generalized Element is established. This method does not need the Transition Element in the border of FEM and MLM, and only needs to establish the public point, so the program is simplified as well as the computation process.4. The generalized unit coupling - linear programming Method base on linear programming Method is proposed to solve Contact Question, through the example of the column and the rigid plane Contact Question, confirms that the method is feasible.The Coupled Meshless-Finite Element Method and its achievements proposed in this paper are helpful to the further development and research of Meshless Method.