ABSTRACT

This chapter presents a general third-order beam theory which accounts for the von Karman geometric nonlinearity, thickness stretch, through thickness variation of the material, and modified couple stress effect. It also presents, the kinematics of the third-order theory, governing equations of motion. The chapter develops exact solutions to the linear equations of equilibrium of the Reddy beam theory for functionally graded material beams without the effect of the modified couple stress. It then presents a general third-order beam theory which accounts for the von Karman geometric nonlinearity, thickness stretch, through thickness variation of the material, and modified couple stress effect. The chapter also develops the exact solutions of the Levinson beam theory (LBT), without accounting for the couple stress effect. It aims to establish bending relationships between the bending solutions of the LBT in terms of the corresponding quantities of the Classical Beam Theory.