Hossein Golbakhshi

In original couple stress theory (CST) the rotation gradient tensor is adopted as an additional measure of deformation, other than the classical strain tensor. As a result, this theory needs at least two extra material length scale parameters corresponding to symmetric and skew-symmetric arts of rotation gradient tensor. However, experimental determination of higher-order constants is very difficult and therefore, the non-classical theories with fewer needed parameters are preferred. In order to reduce the higher-order constants, the modified couple stress theory (M-CST) and consistent couple stress theory (C-CST) are developed based on symmetric and skew-symmetric couple-stress tensors, respectively. Both M-CST and C-CST consider general three dimensional deformation fields. It is noted that in special case of micro-beams, the use of symmetric and skew-symmetric couple-stress tensors leads to a same solution. So in exclusive analysis of micro-beams, the characteristics of couple-stress tensor should be determined more decisively. In this paper a new consideration is proposed for couple stress analysis of micro-beams. Based on main kinematical assumptions in beam theories, the displacements are approximated by power series expansions and used for deriving the variational formulation. This leads to a main conclusion and the couple-stress tensor is found to be skew-symmetric.