THE EXACT ANALYTICAL SOLUTION OF THE BENDING ANALYSIS OF THICK FUNCTIONALLY GRADED BEAMS WITH HIGHER ORDER SHEAR DEFORMATION THEORY USING DIFFERENTIAL TRANSFORM METHOD

In this paper, we have developed the static analysis of the bending of a functionally graded beam theory using refined shear deformation. The governing equations, obtained using the principle of virtual work, are found to be a differential equations system which has been expressed in terms of displacements. Thus, by performing differential transformation method (DTM) on this system, we have elaborated the exact general analytical solution assuming that it's a Taylor´s series expansion. The final exact analytical form of this solution is given for simplysupported beam under uniformly distributed load. In order to confirm its validity, a third order shear deformation theory is employed. According to this theory, expressions for displacement fields and stresses are expressed and used to perform a comparison with the existing solutions. Therefore, the strength of this method is that no further numerical computing is needed