A 4-node quasi-conforming quadrilateral element for couple stress theory immune to distorted mesh

• A new formulation of quasi-conforming method is introduced.
• The stress-function matrix is treated as weighted function to weaken the geometric equation.
• A 4-node quasi-conforming quadrilateral element for couple stress theory is formulated.
• The element is immune to the distorted mesh and possesses excellent precision.
• The element does not exhibit extra zero energy modes and can capture the scale effects of microstructure.

In this paper, a 4-node quadrilateral quasi-conforming element for couple stress theory is proposed. The formulation starts from truncated Taylor expansion of stresses, then the stress-function matrix is treated as weighted function to weaken the strain-displacement equations. Finally the string-net functions are introduced to calculate strain integration and the stress smooth technique is adopted to improve the stress accuracy of the element. Numerical results show that the proposed new model can pass the C0-1C0-1 patch test and possesses excellent precision even when the element shape degenerates into triangle or concave quadrangle, which can capture the scale effects of microstructure.