Application of a new improved Airy polynomial function for FGM cantilever beams under concentrated load

This paper addresses the plane stress problem of a cantilever functionally graded beam subjected to concentrated load. The material properties of the beam vary continuously through thickness, according to a powerlaw distribution of volume fraction. The existing solution focuses on resolving differential equations, but a new Airy function proposal is proposed. The paper examines the effect of material graduation on the degree of polynomial degree. A simple formulation developed to predict stress and displacement distributions relative to structural problems. The proposed model validated by comparison with existing literature, ensuring stability and resistance of the materials. A numerical example presented to show the effect of material inhomogeneity on the elastic field in a functionally graded cantilever beam.