Solving Multiple Cracks Problem Based On Characteristic Distance Method And Intrinsic Enriched Meshless Method

Multiple cracks are inevitable in engineering structures under the joint action of mechanical and environmental load. These cracks interact with each other, which may finally lead to sudden failure of the components resulting in loss of property and lives. Calculating the stress intensity factor is the key step in predicting structure failure and crack propagation. So, investigations of multiple crack interactions are of practical significance in predicting structural safety and fatigue life. The main achievements in this paper can be concluded as follows:(1) Recent developments of the meshless method are reviewed. Applications of the meshless methods to solve fracture mechanics problem are overviewed. Advantages and disadvantages of meshless methods are concluded.(2) Basic formulae of moving least square shape function and radial point interpolation shape function are derived. Then, three main approaches to model crack problems in meshless methods were introduced, namely modification of the weight function such as the visibility method,the diffraction method and the transparency method, modification of the intrinsic basis to in corporate special functions and methods based on an extrinsic enrichment.(3) Basic formulae of EFGM and RPIM are derived. Afterwards, discrete equations for elastic stationary problem are obtained based on the minimum potential energy principle. Numerical results of a cantilever beam show the accuracy and validity of both methods.(4) A modified intrinsic basis enriched meshless method is presented for solving stress intensity factors of multiple cracks. A modification in the intrinsic enriched basis, which is based on the notation of characteristic distance, has been proposed to incorporate the interaction effect of the neighboring cracks. The mixed-mode stress intensity factors are solved by the interaction integral method. Three test examples are solved under plane stress condition. The results obtained by the modified intrinsic basis enriched meshless method are compared with those obtained by other numerical methods. Numerical examples demonstrate that the proposed method can deal with multiple problems easily and effectively, and are in excellent agreement with the reference solutions without added additional nodes and degrees of freedom.(5) Multiple crack interaction are investigated by the modified intrinsic based enriched EFGM. The programming is implemented by using Matlab software. Numerical tests including one crack in horizontal position and another in inclined position subjected to remote uniform load, three edge cracks, three inner parallel cracks and three pairs of symmetric edge cracks. Numerical results show that the Present method possesses not only feasibility and validity, but also easy to implement, is very suitable for solving multiple cracks interaction.