A mixed element based on Lagrange multiplier method for modified couple stress theory

A 2D mixed element is proposed for the modified couple stress theory. The $C^{1}C1 continuity for the displacement field is required because of the second derivatives of displacement in the energy form of the theory. The C^{1}C1 continuity is satisfied in a weak sense with the Lagrange multiplier method. A supplementary rotation is introduced as an independent variable and the kinematic relation between the physical rotation and the...