A Simple Higher-order Shear Deformation Theory for Static Bending Analysis of Functionally Graded Beams

In this study, a polynomial higher-order shear deformation theory is introduced and developed for static analysis of functionally graded material (FGM) beams. The presented theory has strong similarities with Timoshenko beam theory in some aspects, such as equations of motion, boundary conditions and stress expressions. The developed theory does not require shear correction factor and satisfies the stress-free boundary conditions, such that the transverse shear stress varies parabolically through the beam thickness. The mechanical properties of the FGM beam are assumed to vary continuously in the thickness direction based on power-law distribution in terms of the volume fractions of the constituents. The influences of material distribution, boundary conditions, aspect ratio and neutral axis on the mid-plane deflection, normal stress and shear stress are figured out. The results obtained are compared with the data available in the literature to verify the correctness and the accuracy of the developed theory. The presented theory can provide a reference which other researchers can use for their studies.