Parameter Analysis And Structural Fracture Simulation For The Meshless Intervention-point Method

Meshless intervention-point method is a newly developed type of collocation meshless method,the solution process without background grid and numerical integration,and has high accuracy,fast convergence speed and good stability for many advantages,it is a strong kind of promising meshless method.In this paper,development history and current situation of meshless method are analyzed,and advantages and disadvantages of some of the more mature meshless methods are summarized;The knowledge of the meshless method,such as weighted residual method,meshless field function approximation method,treatment of the discontinuity problem and the application of the essential boundary conditions are reviewed and summarized;The principle and procedure of meshless intervention-point method are introduced in detail,and the discrete system equations are derived,and the detailed numerical formula are obtained,At the same time,the feasibility of the meshless intervention-point method is verified by examples.Secondly,the influence of different weight functions on the accuracy of meshless method is discussed;According to the distribution characteristics of the moving least squares core approximation shape functions,the design scheme of local field template is determined,and the validity of the scheme is verified by numerical test,which ensures accuracy and efficiency of the solution of the meshless intervention point method;At the same time,range of the parameters of the local scale of the calculated points is studied furtherly,optimum range of local scale parameters is determined,and rationality of the range is verified by numerical test.Finally,the application of meshless method in fracture mechanics is explored.During the stress intensity factor is solved by the meshless intervention point-direct displacement method,throught meshless intervention-point method program which written in MATLAB language,the positions of the extrapolated nodes,different local encryption schemes for crack tip,the derivative assignment mechanism of the shape function and the influence of different basis functions on the accuracy of the solution are discussed,and the solution of the meshless method is compared with the finite element solution,it is found that the solutions can be well matched.At the same time,the expansion of I crack is simulated,and meshless intervention-point method is used to analyze the crack problem of semi-rigid base course with temperature shrinkage,the results show that the meshless intervention-point method has broad application prospects in solving fracture structures.