A new strain based rectangular finite element with drilling rotation for linear and nonlinear analysis

In this paper a new membrane finite element for linear and materially nonlinear analysis is developed. The displacements field of this element has been developed by the use of the strain based approach, and it is based on the assumed functions for the various components of strain which satisfy the compatibility equation. This rectangular finite element has the three degrees of freedom at each of the four corner nodes (the two translations and the in-plane rotation) and the displacement functions of the developed element satisfy the exact representation of the rigid body modes. For elastoplastic analysis, Von Mises, Tresca and Mohr–Coulomb yield criteria are adopted, and both initial stress and initial strain methods are employed. Numerical experiments in both linear and nonlinear analysis have been conducted to assess accuracy and reliability of the developed element compared to the theoretical results and other membrane finite elements.