A New Theoretical Framework for Couple Stress Analysis of Reddy–Levinson Micro-Beams

Abstract

In this paper a new scheme, other than the modified couple stress theory (M-CST) and consistent couple stress theory (C-CST), is proposed for the analysis of micro-beams and based on the main kinematical assumptions in the beam theories, the couple-stress tensor is constrained to be skew-symmetric. This new consideration also makes it possible to revise the governing equations and boundary conditions, derived from Hamilton’s principle into a more convenient form. Then according to the third-order Reddy–Levinson beam theory, a revised couple stress model similar to the classical Timoshenko beam theory is presented in the current study. The validity of the model is demonstrated by static bending and free vibration investigations of isotropic and FG porous micro-beams subjected to a concentrated load at the mid-span.