The Solution And Application Of The Elastic Fracture Analysis Based On Meshless Galerkin Method(EFG)

As a rising numerical analysis method in the last ten years, Meshless Method gains the academia's recognition and attention due to its novel numerical ideas and advanced numerical technique. The shape function of meshless method is built on a series of discrete points, which is different from the finite element method. And it doesn't need to use a grid, which is not restrained by the nodes of grid, and free of the unit grid generation of the finite, leading to the decrease of the difficulty caused by the mesh distortion. Meshless Method has unique advantages in the aspect of analyzing the discontinuous problems of the crack. Moreover, Meshless Galerkin Method(EFG) method is one of the most promising method, due to its high precision, good stability and fast convergence speed and so on. And EFG is adopted to analyze the linear problems and fracture problems in this paper.1. Fracture numerical method of the continuous and discontinuous medium are summarized, and the research progress of meshless method at home and abroad is expounded, using the analysis of linear elastic force.2. Based on the basic theory of the weighted residual method,the several common interpolation methods of the Meshless Method are expounded and their respective advantages and disadvantages are also introduced. Moreover, the moving least squares method(MLS) of interpolation methods are mainly described. On this basis, the shape function matrix singularity situation is given the solution and different types of weight function has been calculated and analyzed.3. According to the linear elastic fracture mechanics, the body mechanics behavior of the crack is described, from the two aspects of stress intensity factors and energy release rate. Based on meshless galerkin method(EFG),the stress intensity factor of the linear elastic fracture mechanics numerical calculation methods is analyzed.4. The four numerical analysis methods for dealing with discontinuous numerical problem of the EFG method are summarized, which provides a reference basis for the selection principle of discontinuous problems. The innovation of this article is to analyze the expansion shape function and the EFG method is improved and establishes meshless galerkin method of approximate displacement function based on the thought of the partition of unity and describes in detail some key problems in the program design and draw up program flow chart and the corresponding main program is given.5. Based on MATLAB software, the programs to improve meshless galerkin method is written, which calculates the accuracy of MLS approximation, analysis the effective linear elastic problem and one dimensional bar is calculated and two-dimensional cantilever deep is solved and the change rule of the parameter, simulates the fracture problem of stress concentration phenomenon, and calculates the stress intensity factor. The influence on the precision and the change law of weight function, node distribution density and influence domain expansion coefficient are also discussed. Moreover, the accuracy of the program is verified by the examples.