Finite Block Method with Chebyshev Polynomials Applied to Cracked Plate in Functional Graded Materials

The Finite Block Method (FBM) with Chebyshev polynomials is developed in this paper for the Functionally Graded Material (FGM) of two-dimensional fracture problem. The main idea is to divide domain into few blocks. By introducing the mapping technique, a block of quadratic type is transformed from Cartesian coordinate to normalised coordinate with 8 seeds two dimensions. The differential matrices in physical domain are determined from that in the normalised transformed system. The accuracy of the FBM with Chebyshev polynomials is demonstrated with two examples and comparisons have been implemented with different numerical approaches.