Abstract: Functionally graded materials (FGM) possess excellent physical properties and have important applications, thus have received increasing attentions in recent years. In this paper, a semi-analytical method for mechanical behavior analysis of the FGM cantilever beam is developed, which has the same accuracy in contrast to the analytical method, and furthermore can be used for cantilever beam with complex material property gradation. The method is applied to the bending stress analysis of FGM cantilever beams with linear gradation, exponential gradation and complex empirical formula gradation. The computed results are compared with those of analytical method, graded finite element method (FEM) and layered FEM. The study shows that the bending stress distribution calculated by semi-analytical method and graded FEM is basically consistent with analytical solution on the condition that the numbers of integration points in height and longitude direction are respectively 11 and 21, whereas the bending stress distribution calculated by layered FEM deviate a lot from analytical solution up to 10%. For the analysis of deflection value, the calculated results of semi-analytical method, gradient FEM and layered FEM are all very close to analytical solution, with the maximum relative error within 1.0%.

Key words: FGM, cantilever beam, semi-analytical method, FEM, composites