Analysis Of The Crack Propagation Problems By The Meshless Method

The meshless method which is a new kind of calculation method has attracted considerable attention of researcher in the past two decades due to the flexibility of locating nodes. It possesses many advantages in many scientific research and application fields. Among them the most outstanding superiority is to overcome the dependence of meshes and thoroughly or partly eliminate meshing. The meshless method is better than methods based on meshes, such as FDM and FEM. It has broad application prospect to solve super-large deformation problems, moving boundary problems, crack propagation problems and high velocity impact problems etc.Firstly, this paper very briefly reviews the development on meshless methods and introduces application of MLPG method in solid mechanics problems. The MLPG formulation including construction of the moving least squares method, the choice of the weight function, the local symmetric weak form and the discretization equation are expounded in detail. Several numerical examples are demonstrated to validate the code and the range of parameters.Secondly, the MLPG method is used to investigate several kinds of fracture mechanics problems. The basis function of the MLS approximation is enriched by the singular function which can rightly capture1/(?)r stress-singularity in the linear-elastic fracture mechanics problem. A visibility criterion and a diffraction method are employed to solve non-continuity of field. The stress intensity factors computed with the equivalent domain agree well with analytical solution. Stress field and crack growth of I mode are simulated respectively.Lastly, the MLPG method is used to analyze elastodynamic problem. The local weak formulation of equations governing elastodynamic deformations is derived. The spatial domain is discreted by the moving least squares and the time domain is discreted by the Newmark implicit method. Essential boundary conditions are imposed by the penalty method. The accuracy of the MLPG solution is established by comparing computed results for vibration of clamped beam with the analytical solution of the problem. Time histories of the dynamic stress intensity factors (DSIF), the stress field around the crack tip and the deformation are computed for a center cracked plate and a double edge notched plate under an impulsive load. The results are compared with FEM and so on. Numerical results show that the present method possesses fantastic feasibility and validity to solve static and dynamic fracture mechanics problems.