Based on hybrid variational principle and analytical solution, a simple and efficient four-node hybrid stress membrane element with drilling degrees of freedom is developed. The stress fields of the element are found from analytical solution of bi-harmonic compatibility equation. The optimal number of analytical Airy stress functions for the proposed element is calculated by numerical experimentation. Allman’s quadratic function is utilized for element’s boundary displacement. In this approach, the drilling degrees of freedom increase the accuracy and robustness of the formulation. Furthermore, numerical results show that the suggested element does not possess any spurious zero energy mode. In addition to these, Poisson’s locking, which may come from Allman’s quadratic displacement, disappears in the new membrane element.

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