A simple and less-costly meshless local Petrov-Galerkin (MLPG) method for the dynamic fracture problem

A simple and less-costly MLPG method using the Heaviside step function as the test function in each sub-domain avoids the need for both a domain integral, except inertial force and body force integral in the attendant symmetric weak form, and a singular integral for analysis of elasto-dynamic deformations near a crack tip. The Newmark family of the methods is applied into the time integration scheme. A numerical example, namely, a rectangular plate with a central crack with plate edges parallel to the crack axis loaded in tension is solved by this method. The results show that the stresses near the crack tip agree well with those obtained from another MLPG method using the weight function of the moving least square approximation as a test function of the weighted residual method. Time histories of dynamic stress intensity factors (DSIF) for mode-I are determined form the computed stress fields.