The Study Of Meshless Method Based On The Interpolation Theory Of Shape Function

Meshless method is a kind of calculation, analysis method which has developed rapidly in recent years. And there is a growing interest in the development of meshless methods as the meshless characteristic has distinctive advantages to deal with high-speed impact, industrial forming, extremely large deformation, fracture and fragmentation problems, etc. It offers the tremendous value in theory and potential in industrial application.However, because the meshless methods are relatively new, there exist the following technical problems:1. Complexity in algorithms for computing the interpolation functions;2. Difficulties in the implementation of essential boundary conditions;3. The difficulty to select the size of influence domain;4. The need of assistance mesh for integration damage the meshless characteristic. In this article, the principle and method of meshless method was introduced andsystemized from the construction of shape functions. Through the comparison with FEM, the reason of the above problems are found, which is the shape functions are constructed by fitting method, but not by interpolation method; So the dissertation mainly studied the meshless method based on the theory of interpolation .The point interpolation method (PIM) is a kind of new meshless method based on the theory of interpolation, its shape function is constructed by interpolation method. In this article, the thinking of point interpolation function is used in the method of Weighted Residuals (WRM), so the PIFWRM is presented, and the numerical examples show its validity.The point assembly method (PAM) is another new meshless method based on the theory of interpolation, and at the same time, on the moving element. The shape function is obtained in the same way as the in the finite element method. In the method, the influence domain is looked as a moving mesh, the shape function is constructed in it, and at the same time, integration is also calculated in the mesh. A PAM program has been developed in FORTRAN. Examples are also presented to demonstrate the efficiency and accuracy of the present method compared with analytical solutions.In addition, the dissertation also shows some studying directions of meshless methods.