Evaluation and optimization of meshless methods to estimation of the 3D-stress intensity factors in mode I–III for fatigue life prediction cracked shaft under uni and multi-axial cyclic loading

In this research, in order to estimate 3D-Stress Intensity Factors in mode I–III, fatigue crack growth and fatigue life prediction of a cracked shaft under various cyclic loading, meshless methods are evaluated and the most appropriate method is selected. For better results, the Base Functions (BFs) are first identified and their performance and efficiency are compared with each other. In addition, while enriching the BFs in all methods and study the effect of increasing the number of sentences of Polynomial-BFs (m = 4, 7,10) and their Linearity or Quadraticity in the accuracy of calculations, two sets of Extend-Enriched-RBFs including the Multi-Quadrics and Gaussian RBFs are used in MQ-RPIM and EXP-RPIM methods. To optimize the shape parameters in the RPIM method and determine the Penalty Factor in the MLPG method, Uni and Multi-objective PSO algorithm was used. Then, a shaft with an initial semi-elliptic surface crack as a 3D-meshless domain for discretizing the weak differential equations was selected and modeled under a fixed latitude tensile, bending, and torsional cyclic loads. Changing the standard values of the shape parameters and estimating their optimal values by the PSO algorithm and comparison of findings with the results of Experimental, MLPG, PIM, FEM, and XFEM methods, has led to the best answer from the applied methods for calculation of; displacement, strain and stress fields, and the SIFs in Mode I–III. Finally, based on the results of uniaxial cyclic load analysis and selection of the MQ-RPIM method, the Multi-axial Cyclic load analysis has been performed on 3D-domain. During this analysis, the Paris Parametric equation along with the Elliptic equation and Liu’s Virtual Strain Energy (VSE) model was used to estimate the fatigue crack growth and fatigue life prediction of a submersible cracked shaft of a pump used in water pumping stations.