Closed form Expressions of Shear Correction Factor for Functionally Graded Beams

Abstract In this work, closed-form expressions of shear correction factor (SCF) have been derived for beams with functionally graded material (FGM), through variational asymptotic method (VAM). An energy equivalence approach has been adopted between VAM and Timoshenko model, for estimating the SCF. A planar FGM beam has been considered and the calculation for SCF has been carried out. The formulation has been derived in a functional form that permits solutions for a large class of gradation models of FGM. In the limiting case when the material becomes homogeneous the estimated SCF matches exactly with that of the literature, thus validating the solution. A detailed discussion has been carried out on the results and conclusions have been drawn.