Development and evaluation of a Novel strain-based rectangular membrane element for static and free vibration analysis

This study introduces the Strain-based Rectangular Quadrilateral In-plane Element (SBRQIE), a newly developed membrane element designed for structural analysis applications, including static and free vibration scenarios. The SBRQIE incorporates three degrees of freedom per node—two translational and one rotational—enhancing flexibility and accuracy. Comparative analyses with established finite elements demonstrate the superior performance of the SBRQIE across various configurations, including rectangular, parallelogram, and trapezoidal meshes. The results confirm exceptional accuracy in deflection and frequency predictions, robust convergence with mesh refinement, and resilience against mesh distortions. The SBRQIE element’s efficiency in handling complex geometries, irregular meshes, and diverse boundary conditions establishes it as a reliable computational tool for advanced structural analysis.