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In this paper, a new triangular membrane finite element with in-plane drilling rotation has been developed using the strain-based approach for static and free vibration analyses. The proposed element, having three degrees of freedom at each of the three corner nodes, is based on assumed strain functions satisfying both compatibility and equilibrium equations. Numerical investigations have been conducted using several tests, including static and free vibration problems, and the obtained results are compared with analytical and numerical available solutions. It is found that efficient convergence characteristics and accurate results can be achieved using the developed element.

Formulation of a new finite element based on assumed strains for membrane structures