A model for functionally graded materials

Modelling the mechanical properties of functionally gradient materials (FGMs) is central for engineers to accurately predict their mechanical behaviors. Beam models for FGMs with regular polygonal cross-sections are developed. It is assumed that material properties of the inner core are constant, and the outer shell gradually change by a power-law throughout the height of the regular polygonal cross-section. The analytical solutions of bending, buckling and free vibration behaviors of proposed FG beams modelled by the Euler‒Bernoulli beam theory and refined Timoshenko beam theory are obtained. In addition, the effects of aspect ratio, Young's modulus ratio, power-law index and topology number on the mechanical behaviors of the FG beams are investigated.