A quadrilateral spline element for couple stress/strain gradient elasticity

Couple stress/strain gradient elasticity has been developed to extend continuum plasticity to the micro- and nano-scale. In order to pass the C0-1 enhanced patch test of a convergence condition, the element need to satisfy C0 and C1 continuity and possess the second-order accuracy simultaneously with nodal parameters including displacement and their first order derivatives. In this paper, a 24-DOF quadrilateral spline element for couple stress/strain gradient elasticity is proposed, which is a single displacement function. Numerical examples presented show that the proposed element is valid for both couple stress and strain gradient theories, and has high accuracy.