Research On Meshless Method And Its Application

The Element-free Galerkin Method is comparatively maturely applied in linear elastic fracture mechanics in these years.There are two techniques of Element-free Galerkin Method for Near-tip crack field.One is nodal refinement method near crack tip and another one is enriched basis method.The simulation results in this paper show that the enriched basis method is better than the nodal refinement method.The simulation results are sensitive to the arrangement of the refined nodes.The stresses are oscillatory near crack tip when there is an acute change of node density.The reason of the oscillation is discussed.There gives an appropriate scale of support domain from contrasts of some simulation results.Different treatments of discrete region are studied and a reasonable suggestion is put forward.The Local Radial-basis Point Interpolation Meshless Method is applied in liner elastic fracture mechanics the first time in this paper and the feasibility is studied.A Singular Local Radial-basis Point Interpolation Meshless Method(S-LRPIM) is proposed in this paper,which appends a singular functionγ^1/2 to the process of the radial-basis point interpolation.(γ^1/2 is the distance between the crack culmination and the integral point) It is shown that the S-LRPIM predicts the singular stress fields near a crack tip better than the general LRPIM.The Double Gird Meshless Method of Weighted Least Square(DG-MWLS) is proposed in this paper based on the Meshless Method of Weighted Least Square(MWLS) proposed by Zhang Xiong and Breitkopf's Double-Gird Collocation Method.The general MWLS gets inaccurate results because the shape functions' second derivative is needed in its process when a liner basis function is used in the process of moving least square approximation,but DG-MWLS can get comparatively accurate results because it only needs the shape functions' first derivative.Even though a quadratic basis function is used,DG-MWLS is also more accurate than general MWLS.DG-MWLS can get more accurate results than general MWLS as radial-basis point interpolation is adopted for the field function's approximation.