Study On The Application Of Natural Element Method In Linear-Elastic Fracture Mechanics

Facture problem is a difficulty in numerical calculation . There are some staple methods such as finite element method,boundary element method and methless method to solve it . Methless method is now far ranging used in discontinuum problem . Since no element connectivity data is required , burdensome meshing or remeshing characteristic of the traditional numerical methods is avoided . A growthing crack can be modelled by simply extending the free crack surfaces or free crack lines corresponding to the crack . This method simplifies the process of the propagation of crack . So the meshless method is particularly appropriate to solve fatigue crack propagation problems .Nature element method is a new type of methless method .It use natural neighbour interpolation to structure shape function . The natural neighbour interpolation is a multivariable interpolation scheme based on Voronoi diagram of scattered nodes . The approximation scheme is used in natureal element method and natural neighbour Galerkin method successfully . The Laplace interpolation is a kind of natural neighbour interpolation developed relatively recently , and proved to be more efficient . As the Laplace interpolation is a interpolant in stead of fitting , methless methods based on it can impose the essential boundary condition directly .In this paper , Laplace interpolation is first used to structure shape function to approximate simple problems , such as square plate which is beared stretching force and socle beam which is beared concentrated force.Gauss integral is used in delaunay triangle during computational process . The result of numerical calculation is very precise , and very match up to the exact solution . This prove the correctness and feasibility of the method and the procedure .Fracture is one of the most important form of body invalidation . In this paper, the Laplace interpolation is used in NEM to impose the essential boundary conditions exactly . The discrete equations of plane problem in elasticity are acquired by weak variation form.Crack propagation is simulated by successive linear increments and the equivalent stress intensity factor is given according to maximum principal stress criterion . The application of NEM to crack growth is given . The crack growth of rectangular plate is presented subjected to cyclic loading .The process of compound crack growth are given using NEM , and then the crack path and fatigue life line are given.