24-DOF quadrilateral hybrid stress element for couple stress theory

A 24-DOF quadrilateral hybrid stress element for couple stress theory is proposed in this study. In order to satisfy the equilibrium equation in the domain of the element, the $21\beta $ Airy stress functions are chosen a assumed stress interpolation functions, and beam functions are adopted as the displacement interpolation functions on the boundary. This element can satisfy weak C $^{0}$ continuity with second-order accuracy and weak $\hbox {C}^1$ continuity simultaneously. So the element can pass the enhanced patch test of a convergence condition. Moreover, the reduced integration and a stresses smooth technique are introduced to improve the element accuracy. Numerical examples presented show that the proposed model can pass the $\hbox {C}^{0-1}$ enhanced patch test and indeed possesses higher accuracy. Besides, it does not exhibit extra zero energy modes and can capture the scale effects of microstructure.