Error Estimation on Assuming Neutral Axis at the Middle of the Cross-Section of Functionally Graded Beams

This research aims to estimate error in different stress and strain functions assuming the neutral axis of functionally graded beams (FGBs) at the middle of cross-section. A comparison is made between the stresses, strains, axial forces, axial displacements, and deflections calculated for the two locations of neutral axis (actual and midsection). Different functions for FGBs were used (power and exponential) with different materials combination and different values of the power. Results were obtained for simply supported and cantilever beams. The actual location of the neutral axis was found by defining actual strain function, according to Euler-Bernoulli theory, while satisfying equilibrium and compatibility conditions. It was found that the percentage error is relatively high in axial strain and stress functions and therefore in axial compressive and tensile forces. For many cases of study, error was found to be more than 5%, and most important it increased as the value of the ratio of moduli of component materials, E₁ / E₂, was higher. Therefore, it is important to find and use the actual location of the neutral in the analysis of FGBs.