A new membrane finite element based on the strain approach

Membrane elements with in-plane rotation are applicable for modeling thin planar structures that are only stressed by volume and surface loads acting in their plane. In this paper a new finite element designed for static and free vibration analysis, featuring a four-node configuration is presented. Each node incorporates two engineering displacements and a fictive rotation, aligning with strain approach principles. The displacements field of this element is based on the assumed functions for the various strains satisfying the compatibility equations. This developed element passed all benchmark tests in the case of bending and shear problems. In static analysis, the displacements, strains, and stresses are calculated, while the free vibration analysis aims to determine natural frequencies, including both axial and fundamental frequencies. The proposed membrane element is validate through a series of selected examples, demonstrating its effectiveness and accuracy. The results consistently indicate that the new element exhibits high performance and exactitude in both types of analysis.