A 4-node hybrid stress-function (HS-F) plane element with drilling degrees of freedom less sensitive to severe mesh distortions

A simple but robust 4-node hybrid stress-function (HS-F) membrane element with drilling degrees of freedom is developed based on the principle of minimum complementary energy. Its stress fields are derived from the first seven fundamental analytical solutions of the Airy stress function. The assumed displacements along element boundaries employ compatible mode of Allman for which the nodal drilling degrees of freedom are considered. Numerical results show that the proposed new element, denoted as HSF-Q4θ-7β, exhibits much improved numerical accuracy and robust performance. In particular, the element performs well even when the element shape degenerates into a triangle or concave quadrangle.