The Application Study Of The Element-Free Galerkin Method To Fatigue Fracture

Meshless methods,which use only a set of nodes and a boundary description of the domain,are a type of new numerical method developed in recent years.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,which simplifies the process of the propagation of crack.So the meshless method is particularly appropriate to solve fatigue crack propagation problems.The Element-free Galerkin method(EFGM),which is based on the moving least-squares(MLS)approximation,is a promising method due to its high accuracy,stability and convergence.Because the MLS approximation does not pass through the nodal data like Finite Element Method or Finite Difference Method,direct implementation of the essential boundary conditions in EFGM becomes difficult.In this paper,the boundary singular kernel method in Reproducing Kernel Paicle Method has been applied to impose the essential boundary conditions in EFGM by revising the MLS shape function.The stress field and the displacement field are analysed by linear elastic theory.The contour integral method is used to calculate the J-integral,then the stress intensity factors of mixed-mode crack is acquired.The correctness and the validity of the method are validated.The results are compared with that of full transformation method.The influential radius influence on the final approximation of the trial function and its gradient greatly. Only the uniform influential radius is needed when nodal arrangements are very regular.It's unworkable to use the uniform influential radius if nodes are randomly scattered,especially for fatigue crack propagation problems. The dynamic influential radius, which is adapted to any kind of node distributing,isutilized in the present paper.The influential radius is adjusted according to the number of node in the influential domain.Fatigue fracture is one of most important form of structural invalidation.In this paper the boundary singular kernel method is used in EFGM 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 Paris' law is applied to analyse the fatigue crack growth rate.The application of EFGM to fatigue crack growth is given.The fatigue crack growth of rectangular plate is presented subjected to cyclic loading.The process of fatigue crack growth is given using EFGM,and then the crack path and fatigue life line are given.