A new higher-order triangular plane element with drilling degrees of freedom is proposed by assumption of second-order strain field. In addition to inclusion of drilling degrees of freedom and utilization of higher-order assumes strains, satisfaction of equilibrium equations improves performance of the suggested element in comparison with many of the other available elements. After proposition of the new element, a series of benchmark problems are solved to evaluate performance of the suggested element. Accuracy and efficiency of the suggested element is compared with other strain-based plane elements. Detailed discussions are offered after each benchmark problem. Finally, based on the attained results, a final conclusion about characteristics of robust membrane elements is made.

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