In recent years, there has been an extensive research interest on the functionally graded materials (FGMs). FGMs, unlike laminated or layered composites, provide continuously varying properties in a definable direction. From the viewpoint of continuum mechanics, FGMs are nonhomogeneous. Though numerous papers are concerned with design, fabrication, and simulation of FGMs [1,2], theoretical analysis is still lack due to the complexity of the problem. Erdogan and co-workers [3-5] studied the crack problem for the nonhomogeneous elastic medium under mechanical loadings. They assumed that the Poission's ratio of the medium was constant and the Young's modulus E varied exponentially with the coordinate parallel to the crack. Noda, Jin and Batra [6,7] considered the temperature field and thermal stresses by further assuming exponential variations of thermal properties. In these works, the stress intensity factors were obtained using integral transformation and integral equation method.
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