Large Deflections of a Non-linear Cantilever Functionally Graded Beam

Abstract

The analysis of the large deformation of a non-linear cantilever functionally graded material (FGM) beam is made. When subjected to an end moment, explicit expressions for deflection and rotation are derived for a functionally graded beam with work hardening of power law. The effects of the gradient distribution of Young’s modulus and the material non-linearity parameter on the deflections of the FGM beam are analyzed. Our results show that depth-dependent Young’s modulus and material non-linearity have a significant influence on the deflections of the beam, and a FGM beam can bear larger applied load than a homogeneous beam. Moreover, to determine an optimal gradient distribution, an optimum design of a beam of a lighter weight and larger stiffness is given. The influence of the geometric non-linearity of the beam is also studied. Large and small deformation theories predict nearly the same deflections with 5% error when rotation is less than 45°, and the predictions based on the small deformation theory are overestimated to exceed 10% when rotation is greater than 60°.