The couple stress analysis of Timoshenko micro-beams based on new considerations

In this paper, a new approach is proposed for the couple stress analysis of micro-beams. As the main assumption, power series expansions are assumed for the axial displacement. The lateral and transverse displacements are adopted according to the classical beam theories. It is demonstrated that this consideration imposes a decisive constraint of skew-symmetry on the couple-stress tensor. So, in the case of micro-beams, there is no need for referring to the main arguments in modified couple stress theory (M-CST). This approach also allows for revising the conventional boundary conditions in couple stress analysis of micro-beams. For the special case of Timoshenko micro-beams, the axial displacement is approximated by a first-order polynomial and a new set of boundary conditions similar to the classical model is developed. Benchmark problems are then considered for demonstrating the advantages of the proposed model.