A new higher-order strain-based plane element

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