Improvement of the Extended-Enriched MLPG Meshless Method by Using Optimal Nodal Points Distribution to Find 3D-SIFs

Subject Areas : Computational Mechanics

B  Ariannezhad ¹ (Department of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran)
Sh  Shahrooi ² (Department of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran)
M  Shishehsaz ³ (Department of Mechanical Engineering, Shahid Chamran University, Ahvaz, Iran)

Received: 2023-05-28 Accepted : 2023-07-02 Published : 2023-09-01

Keywords:

References:

1. Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P., 1996, Meshless methods: an overview andrecent­ developments­,­­ Computer Methods In­applied­ Mechanics and Engineering 139(1-4): 3-47.


2. Liu G.R., Gu Y.T., 2005, An Introduction to Meshfree Methods and Their Programming, Springer Science & Business Media.


3. Li Q., Shen S., Han Z.D., Atluri S.N., 2003, Application of meshless local Petrov-Galerkin (MLPG) to problems with singularities and material discontinuities in 3-D elasticity, Computer Modeling in Engineering and Sciences 4(5): 571-586.


4. Han Z.D., Atluri S.N., 2004, Meshless local Petrov-Galerkin (MLPG) approaches for solving 3D problems in elasto-statics, Computer Modeling in Engineering and Sciences 6: 169-188.


5. Wen P.H., Aliabadi M.H., 2009, Evaluation of mixed-mode stress intensity factors by the mesh-free Galerkin method: static and dynamic,­ The Journal of Strain Analysis for Engineering Design 44(4): 273-286.


6. Liu G.R., GuY., 2001, A point interpolation method for two‐dimensional solids, International Journal for Numerical Methods in Engineering 50(4): 937-951.


7. Wang J.G., Liu G., 2002, A point interpolation meshless method based on radial basis functions, International Journal for Numerical Methods in Engineering54(11): 1623-1648.


8. Zhuang X., 2010, Meshless Methods: Theory and Application in 3D Fracture Modelling with Level Sets, Doctoral Dissertation, Durham University.


9. Gu Y., Wang W., Zhang L.C., Feng X.Q., 2011, An enriched radial point interpolation method (e-RPIM)­ for­ analysis of crack tip­ fields, Engineering Fracture Mechanics 78(1): 175-190.


10. Arzani H., Afshar M.H., 2006, Solving Poisson’s equations by the discrete least square meshless method, Transactions on Modelling and Simulation 42: 23-31.


11.  Firoozjaee A.R., Afshar M.H., 2009, Discrete least squares meshless method with sampling points for the solution of elliptic partial differential equations, Engineering Analysis with Boundary Elements 33(1):83-92.


12. Shobeyri G., Afshar M.H., 2010, Simulating free surface problems using discrete least squares meshless method, Computers & Fluids 39(3): 461-470.


13. Lancaster P., Salkauskas K., 1981, Surfaces generated by moving least squares methods, Mathematics of Computation 37(155): 141-158.


14. Long S., Hu D., 2003, A study on the weight function of the moving least square approximation in the local boundary integral equation method, Acta Mechanica Solida Sinica 3(16): 276-282.


15. Yu-ying Y., Jing L., 2005, A study of weight function in element-free Galerkin method, Journal of Plasticity Engineering 12(4): 5-9.


16. Xu T., Zou P., Xu T., Jiye C., 2010, Study on weight function of meshless method based on B-spline wavelet function, Third International Joint Conference on Computational Science and Optimization 1: 36-40.


17. Wang Y., Luo Z., Zhang N., 2012, Topology optimization using a radial point-based interpolation method, International Conference on Computational Methods University of Queensland.


18. Zhuang X., Cai Y., Augarde C., 2014, A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields,Theoretical and Applied Fracture Mechanics 69: 118-125.


19. Shojaei A., Zaccariotto M., Galvanetto U., 2017, Coupling of 2D discretized Peridynamics with a meshless method based on classical elasticity using switching of nodal behavior, Engineering Computations 34(5): 1334-1366.


20. Karamanli A., 2020, Radial basis Taylor series method and its applications, Engineering Computations 38(5): 2354-2393.


21. Liu G.R., 2009, Meshfree Methods: Moving Beyond the Finite Element Method, CRC press.


22. Krysl P., Belytschko T., 1997, Element-free Galerkin,method: Convergence of the continuous and discontinuous shape functions, Computer Methods in Applied Mechanics and Engineering 148(3-4): 257-277.


23. Wang J.G., Liu G., 2002, On the optimal shape parameters of radial basis functions used for 2-D meshless methods, Computer Methods in Applied Mechanics and Engineering 191(23-24): 2611-2630.


24. Wenterodt C., Von Estorff O., 2009, Dispersion analysis of the meshfree radial point interpolation method for the Helmholtz equation, International Journal for Numerical Methods in Engineering­ 77(12): 1670-1689.


25. Sánchez J.M.M., Gonçalves P.B., 2010, Shape function object modeling for meshfree methods, Mecánica Computacional 29(47): 4753-4767.


26. Razmjoo H., Movahhedi M., Hakimi A., 2010, An efficient meshless method based on a new shape function, International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 23(6): 503-521.


27. Afsari A., Movahhedi M., 2013,Criterion for selecting the shape functions in electromagnetic meshless methods, IET Science, Measurement & Technology 7(3): 157-165.


28. Bozkurt O.Y., Kanber B., AŞIK M.Z., 2013, Assessment of RPIM shape parameters for solution accuracy of 2D geometrically nonlinear problems, ­International Journal of Computational Methods 10(03): 1350003.


29. Moussaoui A., Bouziane T., 2016, Numerical study of the shape parameter dependence of the local radial point interpolation method in linear elasticity, MethodsX 3: 178-187.


30. Ghaffarzadeh H., Barghian M., Mansouri A., Sadeghi M., 2016, Study on meshfree hermite radial point interpolation method for flexural wave propagation modeling and damage quantification, Latin American Journal of Solids and Structures 13: 2606-2627.


31. Shivanian E., 2020, Formulation of pseudospectral meshless radial point Hermit interpolation for the Motz problem and comparison to pseudospectral meshless radial point interpolation, Multidiscipline Modeling in Materials and Structures 16(1): 1-20. 


32. Li Y., Liu G.R., 2019, An element-free smoothed radial point interpolation method (EFS-RPIM) for 2D and 3D solid mechanics problems, Computers & Mathematics with Applications 77(2): 441-465.


33. Ariannezhad B., Shahrooi S., Shishehsaz M., 2022,On applicability of MQ-RPIM and MLPG meshless methods with 3D extended-enriched base functions for estimation of mode I stress intensity factor and fatigue crack growth in cyclic tensile and bending load of an un-notched and notched shaft, The Journal of Strain Analysis for Engineering Design 57(5): 340-359.


34. Carpinteri A., Brighenti R., Vantadori S., 2006, Surface cracks in notched round bars under cyclic tension and bending, International Journal of Fatigue 28(3): 251-260.


35. Hosseini Sh., Soltani B., 2017, Analysis of rectangular stiffness plates based on fstd and meshless collection method, Journal of Solid Mechanics 9(3): 568-586.


36. Eskandari H., Ghanbari M., Mirzadeh F., 2021, Three-dimensional stress analysis for semi-elliptical cracks in the connection of cylinder-hemispherical head for thick-walled cylindrical pressure vessels, Journal of Solid Mechanics 13(1): 1-10.


37. Sharma K., 2014, Crack interaction studies using XFEM technique, Journal of Solid Mechanics 6(4): 410-421.