A 3-node C-0 triangular element for the modified couple stress theory based on the smoothed finite element method

In this paper, a 3-node C-0 triangular element for the modified couple stress theory is proposed. Unlike the classical continuum theory, the second-order derivative of displacement is included in the weak form of the equilibrium equations. Thus, the first-order derivative of displacement, such as the rotation, should be approximated by a continuous function. In the proposed element, the derivative of the displacement is defined at a node using the node-based smoothed finite element method. The derivative fields, continuous between elements and linear in an element, are approximated with the shape functions in element. Both the displacement field and the derivative field of displacement are expressed in terms of the displacement degree of freedom only. The element stiffness matrix is calculated using the newly defined derivative field. The performance of the proposed element is evaluated through various numerical examples.