Modeling and analysis of crack in plane stressproblems by discrete least squares meshless methodbased on transparency theorem

Meshless methods because of using figure functions with high connection rate needpreparations in producing figure functions in confronting with convex boundaries anddiscontinuities. In this study, transparency method is used to create continuous figurefunctions around the crack tip. In transparency method, the surface or discontinuities linesare defined to discontinuities tip using a function with diverse transparency. In this case thediscontinuities tip is considered completely transparent and by getting away from the cracktip the transparency decreases. Finally, efficiency and high accuracy of the discrete leastsquares method will be shown by solving standard questions and comparison the results ofthe numerical solution with analysis results and the results of the finite element analysis.

Keywords:

crack , meshless method , discrete least squares method , transparency method