Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position

In this project, a novel unified beam formulation and a modified couple stress theory (MCST) that considers a variable length scale parameter in conjunction with the neutral axis concept are proposed to study bending and dynamic behaviors of functionally graded (FG) micro beam. New first and sinusoidal beam theories together with the classical beam theory can easily formulated from this approach. The Mori-Tanaka homogenization technique is used to predict all effective material properties of the FG micro beams - including the length scale parameter - which are assumed to vary in the thickness direction. The constructed models include the physical length scale parameter which can introduce the size effect. Some results are presented to show the effects of the material length scale parameter, the power law index, and shear deformation on the bending and dynamic behaviors of FG micro beams.