Static analysis of functionally graded short beams including warping and shear deformation effects

High-order flexural theories for short functionally graded symmetric beams under three-point bending are presented. The material properties of the plate are assumed to be graded continuously in the direction of thickness. The variation of the material properties follows a simple power-law distribution in terms of the volume fractions of constituents within a symmetric laminated beam to create a functionally graded material (FGM). The formulation allows for warping of the cross-section of the FGM beam and eliminates the need for using arbitrary shear correction coefficients as in other theories. Based on higher-order shear deformation theories, the governing equations are obtained using the principle of virtual work (PVW). The justification for use of higher-order shear deformation theories is established for short and FGM beams where cross-sectional warping is predominant.