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ARTICLE

Analysis of Elastodynamic Deformations near a Crack/Notch Tip by the Meshless Local Petrov-Galerkin (MLPG) Method

by R. C. Batra¹, H.-K. Ching¹

1 Department of Engineering Science and Mechanics, MC 0219
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061

Computer Modeling in Engineering & Sciences 2002, 3(6), 717-730. https://doi.org/10.3970/cmes.2002.003.717

Abstract

The Meshless Local Petrov-Galerkin (MLPG) method is used to analyze transient deformations near either a crack or a notch tip in a linear elastic plate. The local weak formulation of equations governing elastodynamic deformations is derived. It results in a system of coupled ordinary differential equations which are integrated with respect to time by a Newmark family of methods. Essential boundary conditions are imposed by the penalty method. The accuracy of the MLPG solution is established by comparing computed results for one-dimensional wave propagation in a rod with the analytical solution of the problem. Results are then computed for the following two problems: a rectangular plate with a central crack with plate edges parallel to the crack axis loaded in tension, and a double edge-notched plate with the edge between the notches loaded by compressive tractions. Stresses at points near the crack/notch tip computed from the MLPG solution are found to agree well with those obtained from either the analytical or the finite element solution of the same problem. The index of stress singularity is ascertained from a plot of log (stress) vs. log(r) where r is the distance from the crack tip. It is found that, for the double-edge notched plate, the mode-mixity of deformations near a notch-tip in an orthotropic plate can be adjusted by suitably varying the in-plane moduli of the material of the plate. The variation of shear stress with r exhibits a boundary layer effect near r = 0.

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