Adding bending stiffness to 3-D membrane FEM programs

The Element Bending Group (EBG) method, previously introduced for two-dimensional (2-D) problems, was developed to introduce an approximate bending stiffness in 3-D membrane, static-implicit, rigid-viscoplastic FEM programs. Inter-element stiffness with respect to change in mesh curvature was evaluated by assuming a standard linear variation of engineering strain through the thickness, without adding degrees of freedom to a membrane model. A constant curvature was utilized for the EBG in the plane normal to the edge common to the two elements in order to calculate bending forces and stiffnesses. Patch tests were conducted to evaluate the performance of this new technique when applied to standard problems, and good accuracy was obtained. The technique was then evaluated in three case studies (each with significant bending deformation). The EBG technique was found to approximate the real bending stiffness, thus enhancing the stability of membrane models and allowing simulation of bending-sensitive configurations, at much reduced computation times compared to standard shell approaches. However, well-developed wrinkling and springback cannot be handled adequately by this method because of mesh-orientation dependence and approximate 3-D bending stiffness.