An enhanced rectangular Membrane Finite Element Based on the Strain Approach

Abstract

This study presents the development of a enhanced rectangular membrane finite element using the strain-based approach, designed for both elastic and elastoplastic analyses. Each of the four corner nodes of the element is characterized by three degrees of freedom: two translational degrees and one in-plane rotational degree. The displacement functions of the proposed element accurately capture the rigid body motion modes. For the elastoplastic computations, the material response is evaluated using the Von Mises failure creterion, and the nonlinear solution procedure incorporates viscoplastic-strain approaches. For validation purposes, several selected numerical examples are solved using the developed element in both linear and nonlinear analyses.

The results obtained are compared with analytical solutions and other similar membrane finite elements, demonstrating the strong performance of the proposed element.