The Problems Of Discontinuity In EFG Methods

Recently, the meshfree methods developed quickly, and have been paid much attention in international computational fields. Unlike the finite element method, the approximation function in the meshfree method is constructed on a series of points, independent of meshes. So it has the obvious advantage in some aspects such as impact, fracture and matel formation et al. The meshfree method is a good companion of the finite element method in these particular fields.At present, many meshfree methods have been advanced. Their distinctions consist in the choice of test function and the counterpart of the differential equation. In this paper, the well developed EFG method is used. The EFG method has not the property ofδfunction, this makes the imposition of essential boundary conditions more complicated than that in the finite element method. Several techniques have been developed to enforce essential boundary conditions, including Lagrange multipliers, modified variational principles, etc.To simulate crack, the visibility criterion is often used. However, this criterion will bring discontinuity at the crack tip. In order to avoid this shortcoming, the diffraction criterion is used to deal with the discontinuity. In this paper, we wrote a program of two dimensions so that it can deal with the edge crack. And we construct a new array of the background cells which simplify the program. At last, we studied the problems of interface and material inhomogeniety, which may provide some information for further study.