Application of meshless local integral equations based on meshless local Petrov-Galerkin (MLPG) method is developed for two dimensional dynamic stress analysis in 2D-FG cylinder with two directional grading patterns. It is assumed that the inner bounding surface of cylinder is excited by mechanical shock loading. The problem is studied in frequency domain by Laplace transformation and then the stresses are transferred to time domain using Talbot techniques. The mechanical properties of FGMs are simulated using a nonlinear model with radial and axial volume fractions. The 2D propagation of stresses are tracked through radial and axial direction in a two dimensional domain for various grading patterns at different time instants. By employing the presented meshless technique, the maximum values of stresses are calculated. The effects of various grading patterns on maximum values of stresses are studied in details. The presented formulations based on MLPG furnish a ground for 2D stress wave propagation in FGMs with two directional grading patterns.

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