A weak continuity condition of FEM for axisymmetric couple stress theory and an 18-DOF triangular axisymmetric element

The axisymmetric elements of classical continuum mechanics are only required to satisfy C0 continuity. However, the axisymmetric elements based on couple stress theory are required to satisfy C1 continuity. Consequently, traditional axisymmetric elements cannot be adopted directly in the finite element analysis of couple stress theory. In this paper, a weak continuity condition of axisymmetric nonconforming element method based on couple stress theory is proposed. Furthermore, an 18-DOF (degrees of freedom) axisymmetric couple stress triangular element (BCIZ+ART9) is developed by combining the displacement functions of thin plate triangular element BCIZ and refined nonconforming element ART9. The displacement function of BCIZ, which satisfies C0 continuity and quadratic completeness, is used to calculate first derivatives of displacement. The displacement function of ART9, which is constructed by modifying the displacement function of BCIZ based on the proposed C1 weak continuity condition, is used to calculate second derivatives of displacement. Numerical results show that the developed 18-DOF axisymmetric element (BCIZ+ART9) can be used for the analysis of size effect and has desirable convergence characteristic.