In this article, the meshless local Petrov�Galerkin method is used to analyze the cracked plate made of functionally graded material. The stress intensity factor of Mode I & II, maximum energy release rate and crack initiation angle are determined under the influence of various nonhomogeneity ratios, crack length, and material gradation angle. To solve discrete dynamic equations, a new effective method is extended and utilized. To find crack initiation angle, a simple and easy to use formula is suggested here. The edge-cracked functionally graded plate is considered under the uniform membrane and fixed grip conditions; also, the center-cracked functionally graded plate is analyzed under the uniform membrane and impact loads.
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