Application And Analysis Of Meshless Methods In Fracture Mechanics

Both the Meshless methods and finite element methods are similarly based on the weighted residual method and variation principle. Meshless methods approximate the function only by a series of nodes. It needs nodes information and description to inside and outside border condition. So Meshless methods can be thorough or partly have removed the element. Thereby, Meshless methods have avoided element partition and heavy structure complicated process, which have clear superiority in problems such as element distortion, element displacement. Therefore, this method has important research value and applies value.Radial basis function include global radial basis function and compactly supported radial basis function, they have form merit such as simple, isotropy. With radial basis function for the approximation function and Galerkin weighted residual method, developing one kind of new application method-radial basis function Meshless method. Meanwhile, global radial basis function Meshless method was used to compute plane elastic mechanics problems and Fracture Mechanics problems, and compared with the Finite Element Method results, having ascertained its feasibility and calculation accuracy. The value range of the global radial basis function parameter in cantilever beam problem was obtained; The compactly supported radial basis function is used to simulate finite board crack problem, and the Fracture Mechanics parameter factors are gained.The element-free Glerkin method is used to investigate crack problems of the finite width plane. improved and expanded approximation function used in Fracture Mechanics, which include how to deal with the discontinuous in the modified moving least square approximation function, and expand the radix function of shape function to improve calculation accuracy, and first to rectify the state power weight function for the weight function. having simulated out the finite plane problems with I type crack, mixed type crack and a group of cracks. calculated the stress intensity factors with different crack length, and compared with Finite Element Method results. The element-free Glerkin method is used to investigate crack problems of the pipe, compared integral accuracy of regulation background cells with integral accuracy of nodes. The results indicate that precisely to simulate stress concentrates phenomenon and calculate stress intensity factor of the pipe under the condition of cracks.It is effective to take advantage of the Meshless methods to analyse the Fracture Mechanics problems. According to the analysis in this text, some valuable conclusions are obtained as follows: global radial basis function Meshless method resolves the plane elastic mechanics problems with higher accuracy than, problems of fracture mechanics; compactly supported radial basis function Meshless method simulates the fracture mechanics problems with high accuracy; the stress intensity correction factor of a series of cracks is smaller than one of crack; The longer the crack length, the bigger the stress intensity correction factor; It is precise to calculate the stress intensity factor of mixed type crack by stress method; The integral accuracy of regulate background cells is a bit minor than nodes integral of the thin-wall pipe cracks; All the results of this text have certain reference value to Meshless method calculation of Fracture Mechanics problems.