Unified higher order beam theory for behavioral study of FG beams.

The study of behavior of functionally graded structural members is a significant area of research these days. The behavior of such structures is studied in the framework of beam theories proposed for isotropic beams. Usually, three governing equations are derived and solved to arrive at solutions for such beams. However, in literature there is a unique method to unify the three equations to a single governing equation for Timoshenko beams. The theory has been also extended to include correction in shear stresses through Reddy-Bickford (Higher order) beam theory. However, in reported literature, few higher order terms have been ignored for brevity. The authors in this work have formulated a fourth order differential equation following the Higher Order Beam theory and considering more higher order terms unifying all the separate equations representing axial deflection, transverse deflection and rotation with help of a parameter. This formulation has been derived on the basis of Hamilton's principle to obtain a unique equation to study static as well as dynamic behavior of FG beams with various supporting boundary conditions. A comparative study on the effect of higher order term in the formulation for the behavioral study of FGM beams has been reported in this paper. Subsequently comparative studies for deflection and stress behavior of the FG cantilever beams for different cases of aspect ratio and material gradation subjected to uniform loading conditions has been reported. [ABSTRACT FROM AUTHOR]