Exact elasticity solution of functionally graded beam subjected to transverse loads

The paper presents a two-dimensional exact elasticity solution of a functionally graded material beam with rectangular cross section. The exact solution is based on displacement-based approach under plane stress condition. The beam is subjected to different types of transverse loads, such as uniformly distributed, concentrated, and partial uniform loads. The elastic modulus of the FGM beam varies across its thickness direction according to the exponential law of distribution. Since exact solutions are not available for loading cases other than sinusoidal load, the exact solutions for FG rectangular beam subjected to uniformly distributed load, concentrated load and partial uniform load are obtained and presented for the first time. The influence of aspect ratio and the inhomogeneity of FGM is examined using the present exact solution. The result presented in this study can be served as benchmark solutions to verify the validity of 2D approximate beam theories.