Bending Analysis of Functionally Graded Beam by Refined Theory

Abstract

A refined theory is applied for the flexural analysis of functionally graded beams. The present study involves four unknown variables which are five in first order shear deformation theory or any other higher order theories. The in-plane displacement field uses sinusoidal function in terms of thickness co-ordinate to include the shear deformation effect. The present study satisfies the zero shear stress condition at top and bottom surfaces of plates without using shear deformation factor. Variationally consistent governing equations and boundary conditions associated with present study are obtained using the virtual work principle. A closed form solution is obtained using double trigonometric series suggested by Navier. The functionally graded beam is analyzed for uniformly distributed load and linearly varying load under simply supported condition. The results are obtained and presented graphically